Tamm polariton emitter, and method for producing and using the same

Abstract

Tamm polariton emitters, as well as methods of making and using them, are disclosed herein. The Tamm polariton emitters disclosed herein comprise a distributed Bragg reflector and a layer comprising a conductive material and / or a polariton material, the distributed Bragg reflector being disposed on the layer of the conductive material and / or the polariton material. The Tamm polariton emitter may further comprise a layer of a polar material. Also disclosed herein is a non-dispersive infrared sensor comprising any of the Tamm polariton emitters disclosed herein, wherein the Tamm polariton emitter is configured to selectively emit radiation at a frequency corresponding to the rotational speed or vibrational resonance frequency of a target analyte, and a detector configured to receive an electromagnetic signal from the Tamm polariton emitter and / or the target analyte. Also disclosed herein is a method for designing a Tamm polariton emitter. The method may include, for example, an inverse design protocol and / or machine learning.

Description

Technical Field

[0001] Cross - reference to Related Applications This application claims the benefit of priority of U.S. Provisional Patent Application No. 63 / 327,982, filed on April 6, 2022, which is hereby incorporated by reference in its entirety.

[0002] Description of Government Support The present invention was made with government support under Award No. N00014 - 18 - 1 - 2107 awarded by the Office of Naval Research. The government has certain rights in the invention.

Background Art

[0003] Wavelength - selective thermal emitters (WS - EM) are interesting due to the lack of high - cost - effective narrow - band sources in the mid - to long - wave infrared. Most proposed wavelength - selective thermal emitters use patterned nanostructures, which thereby require high - cost, low - throughput lithography methods and are thus unsuitable for many applications. An alternative solution is the Tamm polariton heterostructure. Despite the broad potential of Tamm polariton emitters, the design of such structures is difficult.

[0004] There is still a need for wavelength - selective thermal emitters and methods of making the same. The compositions, devices, methods, and systems discussed herein address these and other needs.

Summary of the Invention

[0005] In accordance with the objectives of the disclosed compositions, devices, methods, and systems embodied and broadly described herein, the disclosed subject matter relates to Tamm polariton emitters, as well as methods of making and using the same.

[0006] For example, a Tamm polariton emitter is disclosed herein that includes a distributed Bragg reflector and a layer comprising a conductive material and / or a polaritonic material, with the distributed Bragg reflector disposed on the layer of the conductive material and / or the polaritonic material.

[0007] In some examples, the Tamm polariton emitter further includes a layer of a polar material disposed on top of the distributed Bragg reflector, such that the distributed Bragg reflector is sandwiched between the layer of the conductive material and / or the polaritonic material and the polar material.

[0008] Also disclosed herein is a Tamm polariton emitter that includes a layer of a polar material, a distributed Bragg reflector, and a layer comprising a conductive material and / or a polaritonic material, with the distributed Bragg reflector disposed on the layer of the conductive material and / or the polaritonic material and the layer of the polar material disposed on top of the distributed Bragg reflector, such that the distributed Bragg reflector is sandwiched between the layer of the conductive material and / or the polaritonic material and the polar material, or the layer of the polar material is disposed under the layer of the conductive material and / or the polaritonic material, such that the layer of the conductive material and / or the polaritonic material is sandwiched between the layer of the polar material and the distributed Bragg reflector.

[0009] In some examples, the polar material layer has an average thickness of from 1 nanometer (nm) to 100 millimeters (mm). In some examples, the polar material includes hexagonal boron nitride, silicon carbide, aluminum nitride, gallium nitride, or a combination thereof. In some examples, the polar material includes hexagonal boron nitride.

[0010] In some examples, the Tamm polariton emitter further comprises a substrate, and the layer of conductive material and / or polariton material is disposed on the substrate, and the layer of conductive material and / or polariton material is sandwiched between the substrate and the distributed Bragg reflector, and the distributed Bragg reflector is disposed on the substrate, and the distributed Bragg reflector is sandwiched between the substrate and the layer of conductive material and / or polariton material, and the layer of polar material is present and disposed on the substrate, and the layer of polar material is sandwiched between the substrate and the distributed Bragg reflector, or the layer of polar material is present and disposed on the substrate, and the layer of polar material is sandwiched between the substrate and the layer of conductive material and / or polariton material.

[0011] In some examples, the layer of conductive material and / or polariton material comprises a polariton material. In some examples, the polariton material comprises a phonon polariton material. In some examples, the polariton material has an adjustable carrier density. In some examples, the polariton material comprises a transparent conductive oxide, a III-V semiconductor, or a combination thereof. In some examples, the polariton material comprises a transparent conductive oxide. In some examples, the polariton material comprises cadmium oxide. In some examples, the polariton material further comprises a dopant. In some examples, the presence and / or concentration of the dopant adjusts the carrier density of the polariton material. In some examples, the polariton material comprises a doped cadmium oxide such as n-doped cadmium oxide. In some examples, the polariton material comprises n-type In-doped CdO.

[0012] In some examples, the layer of conductive material and / or polariton material has an average thickness of 1 nanometer (nm) to 100 millimeters (mm). In some examples, the layer of conductive material and / or polariton material has a carrier density of 1×10 10 cm -3 ~1×10 25 cm -3 .

[0013] In some examples, the distributed Bragg reflector includes an aperiodic distributed Bragg reflector. In some examples, the distributed Bragg reflector comprises a plurality of layers of a plurality of materials having different refractive indices. In some examples, the distributed Bragg reflector comprises a plurality of alternating layers of a first material having a first refractive index and a second material having a second refractive index, the first refractive index and the second refractive index being different. In some examples, the first material includes Ge. In some examples, the second material includes aluminum oxide or ZnSe. In some examples, the total number of layers is from 1 to 10,000. In some examples, each of the plurality of layers independently has an average thickness from 1 nanometer (nm) to 100 millimeters (mm).

[0014] In some examples, the Tamm polariton emitter emits radiation at a certain frequency, which is the emission frequency. In some examples, the Tamm polariton emitter has a single emission frequency. In some examples, the Tamm polariton emitter has a plurality of emission frequencies. In some examples, the Tamm polariton emitter has an emission frequency within the visible spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the ultraviolet spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the terahertz spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the infrared spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the short-wave to long-wave infrared spectral region, the mid-wave to long-wave infrared region, the long-wave infrared region to the telecommunications band region, or a combination thereof.

[0015] In some examples, the Tamm polariton emitter includes a Tamm plasmon polariton emitter, a Tamm phonon polariton emitter, or a Tamm hybrid polariton emitter.

[0016] Also disclosed herein is a method of fabricating any of the Tamm polariton emitters disclosed herein. In some examples, the method includes disposing a distributed Bragg reflector on a layer of a conductive material and / or a polariton material. In some examples, the method includes complementary metal oxide semiconductor (CMOS) processing.

[0017] Also disclosed herein is a method of using any of the Tamm polariton emitters disclosed herein, for example, in free space communication applications, as beacons, in barcode applications, in encryption applications, in sensing applications, or combinations thereof.

[0018] Also disclosed herein is an infrared beacon comprising any of the Tamm polariton emitters disclosed herein. Also disclosed herein is a method of using the infrared beacon, for example, in search and rescue, police, and / or military applications.

[0019] Also disclosed herein is a sensor comprising any of the Tamm polariton emitters disclosed herein.

[0020] Also disclosed herein is a non-dispersive infrared sensor comprising any one of the Tamm polariton emitters disclosed herein, wherein the Tamm polariton emitter is configured to selectively emit radiation at a frequency corresponding to the rotational or vibrational resonance frequency of the analyte of interest, and a detector configured to receive an electromagnetic signal from the Tamm polariton emitter and / or the analyte of interest. In some examples, the sensor further comprises a fluid cell extending from a proximal end to a distal end and having an inlet and an outlet, the Tamm polariton emitter is disposed towards the proximal end of the fluid cell, and the detector is disposed towards the distal end of the fluid cell, such that when the sensor is assembled with a fluid sample, the fluid cell is configured to contain the fluid sample and the detector is configured to receive an electromagnetic signal from the Tamm polariton emitter and / or the fluid sample. In some examples, the detector is configured to selectively receive an electromagnetic signal from the Tamm polariton emitter and / or the analyte of interest. In some examples, the detector includes a Tamm polariton detector, and the Tamm polariton detector includes the Tamm polariton emitter according to any one of claims 1 to 35. In some examples, the Tamm polariton emitter and / or the Tamm polariton detector (if present) independently includes a Tamm plasmon polariton emitter, a Tamm phonon polariton emitter, or a Tamm hybrid polariton emitter. In some examples, the sensor further comprises a computing device configured to receive a signal from the detector and process it to determine the characteristics of the fluid sample. In some examples, the sensor is further configured to output the characteristics of the fluid sample and / or a feedback signal based on the characteristics of the fluid sample. In some examples, the feedback signal includes tactile feedback, auditory feedback, visual feedback, or a combination thereof. In some examples, the characteristics of the fluid sample include the presence of the analyte of interest in the fluid sample, the concentration of the analyte of interest in the fluid sample, the identity of the analyte of interest, or a combination thereof.In some examples, the fluid sample includes a gaseous sample. In some examples, the analyte of interest includes a gas. In some examples, the analyte of interest includes a plurality of analytes.

[0021] In some examples, the analyte of interest includes a plurality of analytes, and the Tamm polariton emitter is configured to selectively emit radiation at a plurality of frequencies, or the sensor includes a plurality of Tamm polariton emitters, each of the plurality of Tamm polariton emitters is configured to selectively emit radiation at a certain frequency, and thus, the plurality of Tamm polariton emitters are selectively configured to emit radiation at a plurality of frequencies, and at least a portion of each of the plurality of frequencies corresponds to the rotational speed or vibration resonance frequency of each of the plurality of analytes of interest, and thus, the sensor can simultaneously detect a plurality of analytes.

[0022] In some examples, the detector includes a Tamm polariton detector, and the Tamm polariton detector is configured to selectively receive radiation at a plurality of frequencies, or the detector includes a plurality of Tamm polariton detectors, each of the plurality of Tamm polariton detectors is configured to selectively receive radiation at a certain frequency, and thus, the plurality of Tamm polariton detectors are selectively configured to receive radiation at a plurality of frequencies.

[0023] In some examples, the analyte of interest includes a single analyte, and the Tamm polariton emitter is configured to selectively emit radiation at a plurality of frequencies, or the sensor includes a plurality of Tamm polariton emitters, each of the plurality of Tamm polariton emitters is configured to selectively emit radiation at a certain frequency, and thus, the plurality of Tamm polariton emitters are selectively configured to emit radiation at a plurality of frequencies, and at least a portion of each of the plurality of frequencies corresponds to the plurality of rotational speeds or vibration resonance frequencies of the analyte of interest, and thus, the sensor can detect the analyte of interest with high sensitivity.

[0024]

[0024] In some examples, the detector includes a Tamm polariton detector configured to selectively receive radiation at a plurality of frequencies, or the detector includes a plurality of Tamm polariton detectors, each configured to selectively receive radiation at a particular frequency, such that the plurality of Tamm polariton detectors are selectively configured to receive radiation at a plurality of frequencies.

[0025]

[0024] In some examples, the analyte of interest includes toxins, contaminants, pollutants, warfare agents, or combinations thereof. In some examples, the analyte of interest includes greenhouse gases. In some examples, the analyte of interest includes gases used as, produced in, and / or produced by by-products of semiconductor manufacturing, industrial production, chemical synthesis, or combinations thereof. In some examples, the analyte of interest is a gas or chemical that needs to be maintained at a particular concentration. In some examples, the analyte of interest includes CO2, SO2, formaldehyde, CO, NH3, N2O, O3, CH4, NO, dimethyl methylphosphonate (DMMP), or combinations thereof.

[0026]

[0024] In some examples, the sensor is filterless.

[0027]

[0024] Also disclosed herein is a method of using any of the sensors disclosed herein, for example, for gas sensing. Also disclosed herein is a method of using any of the sensors disclosed herein, for example, for environmental sensing, atmospheric sensing, chemical sensing, or combinations thereof.

[0028]

[0024] Also disclosed herein is a method for designing any of the Tamm polariton emitters disclosed herein. In some examples, the method includes an inverse design protocol. In some examples, the method includes machine learning.

[0029] Also, a method for designing a Tamm polariton emitter, wherein the Tamm polariton emitter is a distributed Bragg reflector, the distributed Bragg reflector comprising a stack of a plurality of layers of a plurality of materials having various refractive indices, each layer comprising a material having a certain refractive index, each layer having a certain average thickness, and the refractive index of each layer being different from that of the preceding and / or succeeding layers, a distributed Bragg reflector, and a layer comprising a conductive material and / or a polariton material, the distributed Bragg reflector being disposed on the layer of the conductive material and / or the polariton material, the Tamm polariton emitter emitting radiation at a certain frequency, the method comprising: a) defining a target spectrum of the radiation emitted by the Tamm polariton emitter; b) defining an initial set of values for a set of parameters of the designed Tamm polariton emitter, the set of parameters including the total number of layers of the distributed Bragg reflector, the composition of each of the plurality of layers, the thickness of each of the plurality of layers, the composition of the layer of the conductive material and / or the polariton material, the carrier density of the layer of the conductive material and / or the polariton material, and the thickness of the layer of the conductive material and / or the polariton material, for the initial set of values, the initial total number of layers being user-defined and the remaining parameters being randomly initialized; c) modeling the emission spectrum of the designed Tamm polariton emitter having the initial set of parameters written as a vector (t), the modeled emission spectrum being the designed emission spectrum; d) determining an error by comparing the designed emission spectrum with the target emission spectrum, the designed emission spectrum being modeled and compared with the target emission spectrum using the transfer matrix method, the error being a scalar error that is a combination of the mean squared error and the mean absolute error, and if the error is greater than a pre-defined threshold, the error is backpropagated to find the gradient over t by the stochastic gradient descent method, and the gradient is used to update t in the next iteration of steps c and d.

Number

[0030] Also, a method for designing a Tamm polariton emitter, wherein the Tamm polariton emitter comprises a layer of a polar material and a distributed Bragg reflector, the distributed Bragg reflector comprising a stack of a plurality of layers of a plurality of materials having different refractive indices, each layer comprising a material having a certain refractive index, each layer having a certain average thickness, and the refractive index of each layer being different from that of the preceding and / or succeeding layers, a distributed Bragg reflector, and a layer comprising a conductive material and / or a polariton material, the distributed Bragg reflector being disposed on the layer of the conductive material and / or the polariton material, the layer of the polar material being disposed on top of the distributed Bragg reflector, so that the distributed Bragg reflector is sandwiched between the layer of the conductive material and / or the polariton material and the layer of the polar material, the Tamm polariton emitter emits radiation at a certain frequency, and the method comprises: a) defining a target spectrum of the radiation emitted by the Tamm polariton emitter; b) defining an initial set of values for a set of parameters of the designed Tamm polariton emitter, the set of parameters including the total number of layers of the distributed Bragg reflector, the composition of each of the plurality of layers, the thickness of each of the plurality of layers, the composition of the layer of the conductive material and / or the polariton material, the carrier density of the layer of the conductive material and / or the polariton material, the thickness of the layer of the conductive material and / or the polariton material, the composition of the layer of the polar material, the carrier density of the layer of the polar material, and the thickness of the layer of the polar material, for the initial set of values, the initial total number of layers is user-defined and the remaining parameters are randomly initialized; c) modeling the emission spectrum of the designed Tamm polariton emitter having the initial set of parameters written as a vector (t), the modeled emission spectrum being the designed emission spectrum; d) determining an error by comparing the designed emission spectrum with the target emission spectrum, the designed emission spectrum being modeled and compared with the target emission spectrum using the transfer matrix method, the error being a scalar error that is a combination of the mean squared error and the mean absolute error, and if the error is greater than a pre-defined threshold, the error is backpropagated to find the gradient over t by the stochastic gradient descent method,The gradient is used to update t in the next iteration of steps c and d,

Number

[0031] In some examples, the error is given by the following formula: Error = average(ratio1(DS - TS) 2 + ratio2|DS - TS|) where ratio1 and ratio2 are hyperparameters customized for different purposes, and DS and TS are vectors each having elements representing the absorption rates at corresponding wavelengths.

[0032] In some examples, steps c and / or d of the method include a weighted sampling technique. In some examples, the weighted sample technique is based on a desired application, a target frequency region, a target analyte, or a combination thereof. In some examples, the parameters further include the frequency, amplitude, and / or linewidth of the emitted radiation.

[0033] In some examples, the parameters further include a quality factor (e.g., Q factor). In some examples, the Q factor is between 1 and 1,000,000.

[0034] In some examples, the Tamm polariton emitter includes any of the Tamm polariton emitters disclosed herein.

[0035] In some examples, the method includes machine learning.

[0036] In some examples, the Tamm polariton emitter includes a plurality of Tamm polariton emitters, and the parameter further includes the number of Tamm polariton emitters in the plurality of Tamm polariton emitters.

[0037] In some examples, the method includes designing a first Tamm polariton emitter and a second Tamm polariton emitter, the second Tamm polariton emitter comprising a Tamm polariton detector. In some examples, the first Tamm polariton emitter is configured to selectively emit radiation at one or more frequencies, and the second Tamm polariton emitter is configured to selectively receive at least a portion of the radiation emitted by the first Tamm polariton emitter (e.g., the first Tamm polariton emitter and the Tamm polariton detector are matched). In some examples, the method further includes maximizing an overlap between the radiation emitted by the Tamm polariton emitter and the radiation received by the detector. In some examples, the first Tamm polariton emitter includes a first plurality of Tamm polariton emitters, the second Tamm polariton emitter includes a second plurality of Tamm polariton emitters, or a combination thereof. In some examples, the first Tamm polariton emitter includes a first plurality of Tamm polariton emitters, the parameter includes the number of the first plurality of first Tamm polariton emitters, the second Tamm polariton emitter includes a second plurality of Tamm polariton emitters, the parameter includes the number of the plurality of second Tamm polariton emitters, or a combination thereof.

[0038] Further advantages of the disclosed compositions, devices, systems, and methods will be apparent in part from the following description and in part will become apparent from the description. The advantages of the disclosed compositions, devices, systems, and methods will be realized and achieved by the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed compositions, devices, systems, and methods as claimed.

[0039] Details of one or more embodiments of the invention are set forth in the accompanying drawings and the following description. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

[0040] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate some aspects of the present disclosure and, together with the description, serve to explain the principles of the present disclosure.

Brief Description of the Drawings

[0041]

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DETAILED DESCRIPTION OF THE INVENTION

[0042] The compositions, devices, methods, and systems described herein can be more readily understood by reference to the following detailed description of the disclosed subject matter and specific aspects of the examples included herein.

[0043] Before the compositions, devices, methods, and systems are disclosed and described, it should be understood that the aspects described below are not limited to a particular synthesis method or a particular reagent and can of course be various in themselves. Also, it should be understood that the terms used herein are for the purpose of describing particular aspects only and are not intended to be limiting.

[0044] Throughout this specification, various publications are referenced. The disclosures of these publications are hereby incorporated by reference into this application in their entirety to more fully describe the state of the art to which the disclosed matters pertain. The disclosed references are also discussed in the context of the references and are hereby specifically incorporated by reference herein, individually and specifically, for the materials contained therein.

[0045] In this specification and the following claims, several terms are referenced that are to be defined to have the following meanings.

[0046] Throughout the description of this specification and the claims, the word "comprise", and other forms of the words "comprising" and "comprises", mean, for example, including but not limited to other additives, components, integers, or steps, and are not intended to exclude these.

[0047] As used in this specification and the appended claims, the singular forms "a", "an", and "the" include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to "a composition" includes a mixture of two or more such compositions, reference to "a medicament" includes a mixture of two or more such medicaments, and reference to "a component" includes a mixture of two or more such components.

[0048] "Optional" or "optionally" means that the event or circumstance described later may or may not occur, and that this description includes examples where this event or circumstance occurs and examples where it does not occur.

[0049] In this specification, a range can be expressed as "about" a particular value and / or "about" another particular value. "About" means within 5% of the value, for example, within 4, 3, 2, or 1% of the value. When such a range is expressed, another aspect includes from one particular value and / or to another particular value. Similarly, when a value is expressed as an approximation by use of the antecedent "about", it will be understood that the particular value forms another aspect. Further, it will be understood that each endpoint of a range is important both in relation to the other endpoint and independently of the other endpoint.

[0050] "Exemplary" means "an example of" and is not intended to convey an indication of a preferred or ideal embodiment. "Such as" is used for illustrative purposes and not in a limiting sense.

[0051] Throughout this specification, it is understood that the identifiers "first" and "second" are used only to assist in distinguishing various components and steps of the disclosed subject matter. The identifiers "first" and "second" are not intended to imply any particular order, quantity, priority, or importance to the components or steps modified by these terms.

[0052] As used herein, the term "plurality" means two or more (e.g., three or more, four or more, five or more, ten or more, fifteen or more, twenty or more, twenty-five or more, thirty or more, forty or more, fifty or more, seventy-five or more, one hundred or more, one hundred and fifty or more, two hundred or more, two hundred and fifty or more, three hundred or more, four hundred or more, five hundred or more, seven hundred and fifty or more, one thousand or more, one thousand five hundred or more, two thousand or more, two thousand five hundred or more, three thousand or more, four thousand or more, or five thousand or more).

[0053] As used herein, the term "artificial intelligence" is defined to include any technology that enables one or more computing devices or computing systems (i.e., machines) to mimic human intelligence. Artificial intelligence (AI) includes, but is not limited to, knowledge-based, backpropagation-based, machine learning, representational learning, and deep learning.

[0054] As used herein, the term "machine learning" is defined as a subset of AI that enables a machine to acquire knowledge by extracting patterns from raw data. Machine learning techniques include, but are not limited to, logistic regression, support vector machines (SVMs), decision trees, Naive Bayes classifiers, and artificial neural networks. As used herein, the term "representation learning" is defined as a subset of machine learning that enables a machine to automatically discover representations necessary for feature detection, prediction, or classification from raw data. Representation learning techniques include, but are not limited to, autoencoders. As used herein, the term "deep learning" is defined as a subset of machine learning that enables a machine to automatically detect representations necessary for feature detection, prediction, classification, etc. using layers of processing. Deep learning techniques include, but are not limited to, artificial neural networks or multi-layer perceptrons (MLPs).

[0055] Machine learning models include supervised, semi-supervised, and unsupervised learning models. In a supervised learning model, the model learns a function that maps inputs (also known as features or a set of features) to outputs (also known as targets or a target) during training using a labeled dataset (or datasets). In an unsupervised learning model, the model learns a function that maps inputs (also known as features or a set of features) to outputs (also known as targets or a target) during training using an unlabeled dataset. In a semi-supervised learning model, the model learns a function that maps inputs (also known as features or a set of features) to outputs (also known as targets or a target) during training using both labeled data and unlabeled data.

[0056] Tamm polariton emitter A distributed Bragg reflector (e.g., one or more distributed Bragg reflectors) and a layer (e.g., one or more layers) comprising a conductive material and / or a polaritonic material, wherein the distributed Bragg reflector is disposed (e.g., fabricated or grown) on the layer of the conductive material and / or the polaritonic material, and a Tamm polariton emitter is disclosed herein.

[0057] In some examples, the Tamm polariton emitter further includes a layer (e.g., one or more layers) of a polar material. The layer of the polar material may be disposed, for example, on top of the distributed Bragg reflector, such that the distributed Bragg reflector is sandwiched between the polaritonic material and the polar material, or is disposed under the layer of the conductive material and / or the polaritonic material, such that the layer of the conductive material and / or the polaritonic material is sandwiched between the layer of the polar material and the distributed Bragg reflector. In some examples, the layer of the polar material is disposed on top of the distributed Bragg reflector, such that the distributed Bragg reflector is sandwiched between the polaritonic material and the polar material. The polar material may include any suitable material. In some examples, the polar material includes hexagonal boron nitride, silicon carbide, silicon dioxide, aluminum nitride, gallium nitride, etc., or combinations thereof. In some examples, the polar material includes hexagonal boron nitride, silicon carbide, aluminum nitride, gallium nitride, etc., or combinations thereof. In some examples, the polar material includes hexagonal boron nitride.

[0058] The polar material layer may have an average thickness, for example, several times or less of the free-space wavelength of operation, for example, an average thickness on the order of the thickness of a single layer to approximately the free-space wavelength scale.

[0059] In some examples, the polar material layer can have an average thickness of 1 nanometer (nm) or more (e.g., 2 nm or more, 3 nm or more, 4 nm or more, 5 nm or more, 10 nm or more, 15 nm or more, 20 nm or more, 30 nm or more, 40 nm or more, 50 nm or more, 75 nm or more, 100 nm or more, 125 nm or more, 150 nm or more, 200 nm or more, 250 nm or more, 300 nm or more, 400 nm or more, 500 nm or more, 750 nm or more, 1 micrometer (micron, μm) or more, 1.25 μm or more, 1.5 μm or more, 1.75 μm or more, 2 μm or more, 2.5 μm or more, 3 μm or more, 3.5 μm or more, 4 μm or more, 4.5 μm or more, 5 μm or more, 6 μm or more, 7 μm or more, 8 μm or more, 9 μm or more, 10 μm or more, 15 μm or more, 20 μm, 30 μm or more, 40 μm or more, 50 μm or more, 75 μm or more, 100 μm or more, 125 μm or more, 150 μm or more, 200 μm or more, 250 μm or more, 300 μm or more, 400 μm or more, 500 μm or more, 750 μm or more, 1 millimeter (mm) or more, 1.25 mm or more, 1.5 mm or more, 1.75 mm or more, 2 mm or more, 2.5 mm or more, 3 mm or more, 3.5 mm or more, 4 mm or more, 4.5 mm or more, 5 mm or more, 6 mm or more, 7 mm or more, 8 mm or more, 9 mm or more, 10 mm or more, 15 mm or more, 20 mm or more, 25 mm or more, 30 mm or more, 35 mm or more, 40 mm or more, 45 mm or more, 50 mm or more, 60 mm or more, 70 mm or more, 80 mm or more, or 90 mm or more).In some examples, the polar material layer may have an average thickness of 100 millimeters (mm) or less (e.g., 90 mm or less, 80 mm or less, 70 mm or less, 60 mm or less, 50 mm or less, 45 mm or less, 40 mm or less, 35 mm or less, 30 mm or less, 25 mm or less, 20 mm or less, 15 mm or less, 10 mm or less, 9 mm or less, 8 mm or less, 7 mm or less, 6 mm or less, 5 mm or less, 4.5 mm or less, 4 mm or less, 3.5 mm or less, 3 mm or less, 2.5 mm or less, 2 mm or less, 1.75 mm or less, 1.5 mm or less, 1.25 mm or less, 1 mm or less, 750 micrometers (μm) or less, 500 μm or less, 400 μm or less, 300 μm or less, 250 μm or less, 200 μm or less, 150 μm or less, 125 μm or less, 100 μm or less, 75 μm or less, 50 μm or less, 40 μm or less, 30 μm or less, 20 μm or less, 15 μm or less, 10 μm or less, 9 μm or less, 8 μm or less, 7 μm or less, 6 μm or less, 5 μm or less, 4.5 μm or less, 4 μm or less, 3.5 μm or less, 3 μm or less, 2.5 μm or less, 2 μm or less, 1.75 μm or less, 1.5 μm or less, 1.25 μm or less, 1 μm or less, 750 nanometers (nm) or less, 500 nm or less, 400 nm or less, 300 nm or less, 250 nm or less, 200 nm or less, 150 nm or less, 125 nm or less, 100 nm or less, 75 nm or less, 50 nm or less, 40 nm or less, 30 nm or less, 20 nm or less, 15 nm or less, 10 nm or less, or 5 nm or less). The average thickness of the polar material layer can be in the range from any of the above minimum values to any of the above maximum values. For example, the polar material layer may have an average thickness of 1 nanometer (nm) to 100 millimeters (mm) (e.g., 1 nm to 10 microns, 10 microns to 100 millimeters, 1 nm to 100 nm, 100 nm to 10 microns, 10 microns to 1 millimeter, 1 millimeter to 100 millimeters, 5 nm to 100 mm, 1 nm to 90 mm, 5 nm to 90 mm, 1 nm to 1 mm, 1 nm to 500 microns, or 1 nm to 1 μm).

[0060] In some examples, the Tamm polariton emitter may further comprise a substrate. In some examples, the polaritonic material is disposed on the substrate, and the layer of conductive material and / or polaritonic material is sandwiched between the substrate and the distributed Bragg reflector. In some examples, the distributed Bragg reflector is disposed on the substrate, and the distributed Bragg reflector is sandwiched between the substrate and the layer of conductive material and / or polaritonic material. In some examples, the layer of polar material is present and disposed on the substrate, and the layer of polar material is sandwiched between the substrate and the distributed Bragg reflector. In some examples, the layer of polar material is present and disposed on the substrate, and the layer of polar material is sandwiched between the substrate and the layer of conductive material and / or polaritonic material.

[0061] The substrate can include any suitable material. For example, the substrate can include a dielectric, semiconductor, ceramic, transparent conductive oxide, polymer, metal, or combinations thereof. In some examples, the substrate can be transparent. As used herein, "transparent substrate" means any substrate that is transparent at the wavelength or wavelength region of interest. Examples of substrates include, but are not limited to, silicon, III-V semiconductors, glass, quartz, parylene, silicon dioxide, sapphire, mica, poly(methyl methacrylate), polyamide, polycarbonate, polyester, polypropylene, polytetrafluoroethylene, polydimethylsiloxane (PDMS), hafnium oxide, hafnium silicate, tantalum pentoxide, zirconium dioxide, zirconium silicate, and combinations thereof. The substrate can include, for example, glass, quartz, silicon dioxide, silicon nitride, polymer, or combinations thereof. In some examples, the substrate includes sapphire.

[0062] The layer of conductive material and / or polariton material can include any suitable material such as those known in the art. In some examples, the layer includes a plurality of layers, and each layer can independently include any suitable material. In some examples, the layer includes a polariton material. The polariton material can include any suitable material that supports polaritons such as those known in the art. In some examples, the polariton material includes a phonon polariton material. Examples of polariton materials include, but are not limited to, metals, transparent conductive oxides, III-V semiconductors, and combinations thereof. In some examples, the polariton material has an adjustable carrier density.

[0063] In some examples, the polariton material includes a III-V semiconductor. For example, the polariton material can include a Group III element selected from the group consisting of B, Al, Ga, In, Tl, and combinations thereof, and a Group V element selected from the group consisting of N, P, As, Sb, Bi, and combinations thereof. In some examples, the polariton material can include a Group III nitride semiconductor such as, for example, InAs, InP, InN, GaN, AlN, BN, and alloys thereof.

[0064] In some examples, the polariton material includes a transparent conductive oxide. Transparent conductive oxides (TCOs) can include metal oxide A x O z wherein A is one or more metals. Oxygen combined with different metals or metal combinations results in compound semiconductors A x O z with different optoelectronic properties. These optoelectronic properties are doped with metals, metalloids, or non-metals (A x O z: It can be changed by doping (D = dopant). Thus, the metal can be part A of the compound semiconductor itself or the dopant D. Examples of transparent conductive oxides include, but are not limited to, indium-doped tin oxide (ITO), fluorine-doped tin oxide (FTO), aluminum zinc oxide (AZO), tin-doped indium oxide, and combinations thereof.

[0065] In some examples, the polariton material includes a transparent conductive oxide containing a metal oxide. Examples of metal oxides include simple metal oxides (e.g., having a single metal element) and mixed metal oxides (e.g., having different metal elements). The metal oxide can include a metal selected from the group consisting of, for example, Cd, Cr, Cu, Ga, In, Ni, Sn, Ti, W, Zn, and combinations thereof. In some examples, the polariton material can include CdO, CdIn2O4, Cd2SnO4, Cr2O3, CuCrO2, CuO2, Ga2O3, In2O3, NiO, SnO2, TiO2, ZnGa2O4, ZnO, InZnO, InGaZnO, InGaO, ZnSnO, Zn2SnO4, CdSnO, WO3, or combinations thereof. In some examples, the polariton material includes cadmium oxide.

[0066] In some examples, the polariton material further includes a dopant. The dopant can include any suitable dopant for the polariton material. The dopant can be selected, for example, to adjust the optical and / or electronic properties of the polariton material. In some examples, the presence and / or concentration of the dopant can adjust the carrier density of the polariton material. In some examples, the concentration and / or identity of the dopant within the polariton material can vary, for example, by thickness and / or lateral dimensions (e.g., concentration gradient with thickness).

[0067] In some examples, the dopant may include an n-type dopant. The dopant may include, for example, Al, B, Ce, Cl, Cs, Dy, Er, Eu, F, Ga, Gd, Ho, In, La, Mg, Mo, N, Nb, Nd, Sb, Sn, Sm, Tb, or combinations thereof.

[0068] In some examples, the polariton material includes doped cadmium oxide such as n-doped cadmium oxide. In some examples, the polariton material includes n-type In-doped CdO.

[0069] The layer of the conductive material and / or the polariton material may have an average thickness of, for example, 1 nanometer (nm) or more (e.g., 2 nm or more, 3 nm or more, 4 nm or more, 5 nm or more, 10 nm or more, 15 nm or more, 20 nm or more, 30 nm or more, 40 nm or more, 50 nm or more, 75 nm or more, 100 nm or more, 125 nm or more, 150 nm or more, 200 nm or more, 250 nm or more, 300 nm or more, 400 nm or more, 500 nm or more, 750 nm or more, 1 micrometer (micron, μm) or more, 1.25 μm or more, 1.5 μm or more, 1.75 μm or more, 2 μm or more, 2.5 μm or more, 3 μm or more, 3.5 μm or more, 4 μm or more, 4.5 μm or more, 5 μm or more, 6 μm or more, 7 μm or more, 8 μm or more, 9 μm or more, 10 μm or more, 15 μm or more, 20 μm or more, 30 μm or more, 40 μm or more, 50 μm or more, 75 μm or more, 100 μm or more, 125 μm or more, 150 μm or more, 200 μm or more, 250 μm or more, 300 μm or more, 400 μm or more, 500 μm or more, 750 μm or more, 1 millimeter (mm) or more, 1.25 mm or more, 1.5 mm or more, 1.75 mm or more, 2 mm or more, 2.5 mm or more, 3 mm or more, 3.5 mm or more, 4 mm or more, 4.5 mm or more, 5 mm or more, 6 mm or more, 7 mm or more, 8 mm or more, 9 mm or more, 10 mm or more, 15 mm or more, 20 mm or more, 25 mm or more, 30 mm or more, 35 mm or more, 40 mm or more, 45 mm or more, 50 mm or more, 60 mm or more, 70 mm or more, 80 mm or more, or 90 mm or more).In some examples, the layer of conductive material and / or polariton material can have an average thickness of, for example, 100 millimeters (mm) or less (e.g., 90 mm or less, 80 mm or less, 70 mm or less, 60 mm or less, 50 mm or less, 45 mm or less, 40 mm or less, 35 mm or less, 30 mm or less, 25 mm or less, 20 mm or less, 15 mm or less, 10 mm or less, 9 mm or less, 8 mm or less, 7 mm or less, 6 mm or less, 5 mm or less, 4.5 mm or less, 4 mm or less, 3.5 mm or less, 3 mm or less, 2.5 mm or less, 2 mm or less, 1.75 mm or less, 1.5 mm or less, 1.25 mm or less, 1 mm or less, 750 micrometers (μm) or less, 500 μm or less, 400 μm or less, 300 μm or less, 250 μm or less, 200 μm or less, 150 μm or less, 125 μm or less, 100 μm or less, 75 μm or less, 50 μm or less, 40 μm or less, 30 μm or less, 20 μm or less, 15 μm or less, 10 μm or less, 9 μm or less, 8 μm or less, 7 μm or less, 6 μm or less, 5 μm or less, 4.5 μm or less, 4 μm or less, 3.5 μm or less, 3 μm or less, 2.5 μm or less, 2 μm or less, 1.75 μm or less, 1.5 μm or less, 1.25 μm or less, 1 μm or less, 750 nanometers (nm) or less, 500 nm or less, 400 nm or less, 300 nm or less, 250 nm or less, 200 nm or less, 150 nm or less, 125 nm or less, 100 nm or less, 75 nm or less, 50 nm or less, 40 nm or less, 30 nm or less, 20 nm or less, 15 nm or less, 10 nm or less, 5 nm or less). The average thickness of the layer of conductive material and / or polariton material can be in the range from any of the above minimum values to any of the above maximum values. For example, the layer of conductive material and / or polariton material can have an average thickness of 1 nanometer (nm) to 100 millimeters (mm) (e.g., 1 nm to 10 microns, 10 microns to 100 millimeters, 1 nm to 100 nm, 100 nm to 10 microns, 10 microns to 1 millimeter, 1 millimeter to 100 millimeters, 5 nm to 100 mm, 1 nm to 90 mm, 5 nm to 90 mm, 1 nm to 1 mm, 1 nm to 500 microns, or 1 nm to 1 μm).

[0070] The layer of conductive material and / or polariton material has a carrier density that can be fixed or adjustable. For example, the layer of conductive material and / or polariton material can have a carrier density of 1×10 10 cm -3 or more (e.g., 1×10 11 cm -3 or more, 1×10 12 cm -3 or more, 1×10 13 cm -3 or more, 1×10 14 cm -3 or more, 1×10 15 cm -3 or more, 1×10 16 cm -3 or more, 1×10 17 cm -3 or more, 1×10 18 cm -3 or more, 1×10 19 cm -3 or more, 1×10 20 cm -3 or more, 1×10 21 cm -3 or more, 1×10 22 cm -3 or more, 1×10 23 cm -3 or more, or 1×10 24 cm -3 or more). In some examples, the layer of conductive material and / or polariton material has a carrier density of 1×10 25 cm -3 or less (e.g., 1×10 24 cm -3 or less, 1×10 23 cm -3 or less, 1×10 22 cm -3 or less, 1×10 21 cm -3 or less, 1×10 20 cm -3 or less, 1×10 19 cm -3 or less, 1×10 18 cm -3 or less, 1×10 17 cm -3 or less, 1×10 16 cm -3The following, 1×10 15 cm -3 The following, 1×10 14 cm -3 The following, 1×10 13 cm -3 The following, 1×10 12 cm -3 The following, or 1×10 11 cm -3 The following) may have a carrier density. The carrier density of the layer of the conductive material and / or the polariton material can be in the range from any of the above minimum values to any of the above maximum values. For example, the layer of the conductive material and / or the polariton material is 1×10 10 cm -3 ~1×10 25 cm -3 (For example, 1×10 10 cm -3 ~5×10 17 cm -3 5×10 17 cm -3 ~1×10 25 cm -3 1×10 10 cm -3 ~1×10 15 cm -3 1×10 15 cm -3 ~1×10 20 cm -3 1×10 20 cm -3 ~1×10 25 cm -3 5×10 10 cm -3 ~1×10 25 cm -3 1×10 10 cm -3 ~5×10 24 cm -3 or 5×10 10 cm -3 ~5×10 24 cm -3 ) may have a carrier density.

[0071] In some examples, the layer of the conductive material and / or the polariton material is 0.2×10 20 cm-3 above (e.g., 0.5×10 20 cm -3 above, 1×10 20 cm -3 above, 1.5×10 20 cm -3 above, 2×10 20 cm -3 above, 2.5×10 20 cm -3 above, 3×10 20 cm -3 above, 4×10 20 cm -3 above, 5×10 20 cm -3 above, 10×10 20 cm -3 above, 15×10 20 cm -3 above, 20×10 20 cm -3 above, 25×10 20 cm -3 above, 30×10 20 cm -3 above, 35×10 20 cm -3 above, 40×10 20 cm -3 above, 45×10 20 cm -3 above, 50×10 20 cm -3 above, 60×10 20 cm -3 above, 70×10 20 cm -3 above, 80×10 20 cm -3 above, 90×10 20 cm -3 above, or 100×10 20 cm -3 above) may have a carrier density. In some examples, the layer of the conductive material and / or the polariton material is 120×10 20 cm -3 below (e.g., 110×10 20 cm -3 below, 100×10 20 cm -3 below, 90×10 20 cm -3Hereinafter, 80×10 20 cm -3 Hereinafter, 70×10 20 cm -3 Hereinafter, 60×10 20 cm -3 Hereinafter, 50×10 20 cm -3 Hereinafter, 45×10 20 cm -3 Hereinafter, 40×10 20 cm -3 Hereinafter, 35×10 20 cm -3 Hereinafter, 30×10 20 cm -3 Hereinafter, 25×10 20 cm -3 Hereinafter, 20×10 20 cm -3 Hereinafter, 15×10 20 cm -3 Hereinafter, 10×10 20 cm -3 Hereinafter, 5×10 20 cm -3 Hereinafter, 4×10 20 cm -3 Hereinafter, 3×10 20 cm -3 Hereinafter, 2.5×10 20 cm -3 Hereinafter, 2×10 20 cm -3 Hereinafter, 1.5×10 20 cm -3 Hereinafter, or 1×10 20 cm -3 Hereinafter) may have a carrier density. The carrier density of the layer of the conductive material and / or the polariton material can be in the range from any of the above minimum values to any of the above maximum values. For example, the layer of the conductive material and / or the polariton material is 0.2×10 20 cm -3 ~120×10 20 cm -3 (For example, 0.2×10 20 cm -3 ~60×10 20 cm -3 、60×10 20 cm -3 ~120×10 20 cm-3 , 0.2 × 10 20 cm -3 ~ 40 × 10 20 cm -3 , 40 × 10 20 cm -3 ~ 80 × 10 20 cm -3 , 80 × 10 20 cm -3 ~ 120 × 10 20 cm -3 , 0.5 × 10 20 cm -3 ~ 120 × 10 20 cm -3 , 0.2 × 10 20 cm -3 ~ 110 × 10 20 cm -3 , 0.5 × 10 20 cm -3 ~ 110 × 10 20 cm -3 , 0.2 × 10 20 cm -3 ~ 12 × 10 20 cm -3 , 1 × 10 20 cm -3 ~ 12 × 10 20 cm -3 , or 1 × 10 20 cm -3 ~ 4 × 10 20 cm -3 ) may have a carrier density of.

[0072] The distributed Bragg reflector may include any suitable distributed Bragg reflector. In some examples, the distributed Bragg reflector includes aperiodic distributed Bragg reflectors.

[0073] In some examples, a distributed Bragg reflector comprises a plurality of layers (e.g., a stack) of a plurality of materials having different refractive indices. For example, a distributed Bragg reflector comprises a plurality of layers, each layer including a material having a refractive index, and the refractive index of a given layer is different from the refractive index of the preceding and / or succeeding layer(s). In some examples, a distributed Bragg reflector comprises a plurality of alternating layers of a first material having a first refractive index and a second material having a second refractive index, the first refractive index and the second refractive index being different. The materials can include, but are not limited to, any suitable materials such as dielectric materials, semiconductors, ceramics, transparent conductive oxides, phase change materials, polymers, and combinations thereof.

[0074] In some examples, a distributed Bragg reflector comprises a plurality of alternating layers of a first material having a first refractive index and a second material having a second refractive index, the first refractive index and the second refractive index being different. The first and second materials can include, but are not limited to, any suitable materials such as dielectric materials, semiconductors, ceramics, transparent conductive oxides, phase change materials, polymers, and combinations thereof. In some examples, the first material includes Ge, Si, or a combination thereof. In some examples, the second material includes an oxide (e.g., AlO x , SiO2), ZnSe, or a combination thereof.

[0075] In some examples, the total number of layers of the distributed Bragg reflector can be 1 or more (e.g., 2 or more, 3 or more, 4 or more, 5 or more, 10 or more, 15 or more, 20 or more, 30 or more, 40 or more, 50 or more, 75 or more, 100 or more, 125 or more, 150 or more, 175 or more, 200 or more, 250 or more, 300 or more, 350 or more, 400 or more, 450 or more, 500 or more, 600 or more, 700 or more, 800 or more, 900 or more, 1,000 or more, 1,250 or more, 1,500 or more, 1,750 or more, 2,000 or more, 2,250 or more, 2,500 or more, 3,000 or more, 3,500 or more, 4,000 or more, 4,500 or more, 5,000 or more, 6,000 or more, 7,000 or more, or 8,000 or more). In some examples, the total number of layers of the distributed Bragg reflector can be 10,000 or less (e.g., 9,000 or less, 8,000 or less, 7,000 or less, 6,000 or less, 5,000 or less, 4,500 or less, 4,000 or less, 3,500 or less, 3,000 or less, 2,500 or less, 2,250 or less, 2,000 or less, 1,750 or less, 1,500 or less, 1,250 or less, 1,000 or less, 900 or less, 800 or less, 700 or less, 600 or less, 500 or less, 450 or less, 400 or less, 350 or less, 300 or less, 250 or less, 200 or less, 175 or less, 150 or less, 125 or less, 100 or less, 75 or less, 50 or less, 40 or less, 30 or less, 25 or less, 15 or less, 10 or less, 5 or less, 4 or less, or 3 or less). The total number of layers of the distributed Bragg reflector can be in the range from any of the above minimum values to any of the above maximum values. For example, the total number of layers of the distributed Bragg reflector can be 1 to 10,000 (e.g., 1 to 5,000, 5,000 to 10,000, 1 to 100, 100 to 1,000, 1,000 to 10,000, 2 to 10,000, 1 to 9,000, 2 to 9,000, 2 to 8,000, 2 to 5,000, 2 to 1,000, or 2 to 100).

[0076] Each of the plurality of layers of the distributed Bragg reflector can independently have an average thickness, e.g., several times or less the operating free space wavelength, e.g., an average thickness on the order of the free space wavelength scale from a single layer to approximately that thickness.

[0077] For example, each of the plurality of layers of the distributed Bragg reflector can independently have an average thickness of 1 nanometer (nm) or more (e.g., 2 nm or more, 3 nm or more, 4 nm or more, 5 nm or more, 10 nm or more, 15 nm or more, 20 nm or more, 30 nm or more, 40 nm or more, 50 nm or more, 75 nm or more, 100 nm or more, 125 nm or more, 150 nm or more, 200 nm or more, 250 nm or more, 300 nm or more, 400 nm or more, 500 nm or more, 750 nm or more, 1 micrometer (micron, μm) or more, 1.25 μm or more, 1.5 μm or more, 1.75 μm or more, 2 μm or more, 2.5 μm or more, 3 μm or more, 3.5 μm or more, 4 μm or more, 4.5 μm or more, 5 μm or more, 6 μm or more, 7 μm or more, 8 μm or more, 9 μm or more, 10 μm or more, 15 μm or more, 20 μm or more, 30 μm or more, 40 μm or more, 50 μm or more, 75 μm or more, 100 μm or more, 125 μm or more, 150 μm or more, 200 μm or more, 250 μm or more, 300 μm or more, 400 μm or more, 500 μm or more, 750 μm or more, 1 millimeter (mm) or more, 1.25 mm or more, 1.5 mm or more, 1.75 mm or more, 2 mm or more, 2.5 mm or more, 3 mm or more, 3.5 mm or more, 4 mm or more, 4.5 mm or more, 5 mm or more, 6 mm or more, 7 mm or more, 8 mm or more, 9 mm or more, 10 mm or more, 15 mm or more, 20 mm or more, 25 mm or more, 30 mm or more, 35 mm or more, 40 mm or more, 45 mm or more, 50 mm or more, 60 mm or more, 70 mm or more, 80 mm or more, or 90 mm or more).In some examples, each of the plurality of layers in the distributed Bragg reflector can independently have an average thickness of 100 millimeters (mm) or less (e.g., 90 mm or less, 80 mm or less, 70 mm or less, 60 mm or less, 50 mm or less, 45 mm or less, 40 mm or less, 35 mm or less, 30 mm or less, 25 mm or less, 20 mm or less, 15 mm or less, 10 mm or less, 9 mm or less, 8 mm or less, 7 mm or less, 6 mm or less, 5 mm or less, 4.5 mm or less, 4 mm or less, 3.5 mm or less, 3 mm or less, 2.5 mm or less, 2 mm or less, 1.75 mm or less, 1.5 mm or less, 1.25 mm or less, 1 mm or less, 750 micrometers (μm) or less, 500 μm or less, 400 μm or less, 300 μm or less, 250 μm or less, 200 μm or less, 150 μm or less, 125 μm or less, 100 μm or less, 75 μm or less, 50 μm or less, 40 μm or less, 30 μm or less, 20 μm or less, 15 μm or less, 10 μm or less, 9 μm or less, 8 μm or less, 7 μm or less, 6 μm or less, 5 μm or less, 4.5 μm or less, 4 μm or less, 3.5 μm or less, 3 μm or less, 2.5 μm or less, 2 μm or less, 1.75 μm or less, 1.5 μm or less, 1.25 μm or less, 1 μm or less, 750 nanometers (nm) or less, 500 nm or less, 400 nm or less, 300 nm or less, 250 nm or less, 200 nm or less, 150 nm or less, 125 nm or less, 100 nm or less, 75 nm or less, 50 nm or less, 40 nm or less, 30 nm or less, 20 nm or less, 15 nm or less, 10 nm or less, 5 nm or less). The average thickness of each of the plurality of layers of the distributed Bragg reflector can independently be in the range from any of the above minimum values to any of the above maximum values. For example, each of the plurality of layers in the distributed Bragg reflector can independently have an average thickness in the range of 1 nanometer (nm) to 100 millimeters (mm) (e.g., 1 nm to 10 microns, 10 microns to 100 millimeters, 1 nm to 100 nm, 100 nm to 10 microns, 10 microns to 1 millimeter, 1 millimeter to 100 millimeters, 5 nm to 100 mm, 1 nm to 90 mm, 5 nm to 90 mm, 1 nm to 1 mm, 1 nm to 500 microns, or 1 nm to 1 μm).

[0078] In some examples, the Tamm polariton emitter emits radiation at a certain frequency (e.g., one or more frequencies), and the frequency is the emission frequency. In some examples, the Tamm polariton emitter has a single emission frequency. In some examples, the Tamm polariton emitter has multiple emission frequencies.

[0079] In some examples, the Tamm polariton emitter has an emission frequency within the visible spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the ultraviolet spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the terahertz spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the infrared spectral region. In some examples, the Tamm polariton emitter has an emission frequency within the short-wave infrared spectral region, mid-wave infrared spectral region (e.g., 2600~2800 cm -1 )), long-wave infrared spectral region (e.g., 1100~1300 cm -1 ), telecommunications band region (e.g., 1.5~1.6 μm), or a combination thereof. In some examples, the Tamm polariton emitter has an emission frequency within the short-wave to long-wave infrared spectral region, mid-wave to long-wave infrared region, long-wave infrared region to the telecommunications band region, or a combination thereof.

[0080] The Tamm polariton emitter may include, for example, a Tamm plasmon polariton emitter, a Tamm phonon polariton emitter, or a Tamm hybrid polariton emitter.

[0081] Fabrication method Also disclosed herein is a method of fabricating any of the Tamm polariton emitters disclosed herein. The method can include, for example, disposing a distributed Bragg reflector on a layer of a conductive material and / or a polariton material. In some examples, the method can further include disposing the distributed Bragg reflector or the layer of the conductive material and / or the polariton material on a substrate before disposing the distributed Bragg reflector on the layer of the conductive material and / or the polariton material. In some examples, the method can further include disposing a layer of a polar material on the distributed Bragg reflector.

[0082] In some examples, the method can include using techniques such as, for example, electroplating, lithographic deposition, electron beam deposition, thermal deposition, spin coating, drop casting, zone casting, dip coating, blade coating, spraying, vacuum filtration, chemical vapor deposition (CVD), atomic layer deposition (ALD), physical vapor deposition (PVD), sputtering, pulsed layer deposition, molecular beam epitaxy, evaporation, or combinations thereof. In some examples, the method includes complementary metal oxide semiconductor (CMOS) processing.

[0083] Method of Use Also disclosed herein is a method of using any of the Tamm polariton emitters disclosed herein. The method can include, for example, using the Tamm polariton emitter in free space communication applications, as a beacon, in barcode applications, in encryption applications, in sensing applications, or combinations thereof.

[0084] For example, also disclosed herein is an infrared beacon comprising any of the Tamm polariton emitters disclosed herein. The infrared beacon can be used, for example, in search and rescue, police, and / or military applications.

[0085] Devices and Sensors Also disclosed herein is a device comprising any of the Tamm polariton emitters disclosed herein. For example, also disclosed herein is a sensor comprising any of the Tamm polariton emitters disclosed herein.

[0086] In some examples, also disclosed herein is a non-dispersive infrared sensor (NDIR) comprising any of the Tamm polariton emitters disclosed herein, wherein the Tamm polariton emitter is configured to selectively emit radiation at a frequency (e.g., one or more frequencies) corresponding to the rotational speed or vibrational resonance frequency (e.g., one or more rotational speeds or vibrational resonance frequencies) of a target analyte (e.g., one or more analytes), and a detector configured to receive an electromagnetic signal from the Tamm polariton emitter and / or the target analyte.

[0087] In some examples, the non-dispersive infrared sensor further comprises a fluid cell extending from a proximal end to a distal end and having an inlet and an outlet, the Tamm polariton emitter is disposed toward the proximal end of the fluid cell, and the detector is disposed toward the distal end of the fluid cell, such that when the sensor is assembled with a fluid sample, the fluid cell is configured to contain the fluid sample and the detector is configured to receive an electromagnetic signal from the Tamm polariton emitter and / or the fluid sample. As used herein, "fluid" includes liquids, gases, supercritical fluids, or combinations thereof. In some examples, the fluid sample includes a gaseous sample. In some examples, the target analyte includes a gas.

[0088] In some examples, the detector is configured to selectively receive an electromagnetic signal from the Tamm polariton emitter and / or the target analyte (e.g., the detector is not a broadband detector).

[0089] In some examples, the detector includes a Tamm polariton detector, and the Tamm polariton detector includes any of the Tamm polariton emitters disclosed herein.

[0090] In some examples, the Tamm polariton emitter and / or the Tamm polariton detector (if present) independently includes a Tamm plasmon polariton emitter, a Tamm phonon polariton emitter, or a Tamm hybrid polariton emitter.

[0091] In some examples, the non-dispersive infrared sensor further includes a computing device configured to receive a signal from the detector and process it to determine a characteristic of the fluid sample.

[0092] In some examples, the sensor is further configured to output a characteristic of the fluid sample and / or a feedback signal based on the characteristic of the fluid sample. The feedback signal can include, for example, tactile feedback, auditory feedback, visual feedback, or a combination thereof.

[0093] The characteristics of the fluid sample can include, for example, the presence of a target analyte in the fluid sample, the concentration of the target analyte in the fluid sample (e.g., the concentration of the target gas in the gas sample), the identity of the target analyte, or a combination thereof.

[0094] In some examples, the analyte of interest includes multiple analytes. In some examples, the analyte of interest includes multiple analytes, and the Tamm polariton emitter is configured to selectively emit radiation at multiple frequencies, and at least a portion of each of the multiple frequencies corresponds to the rotational or vibrational resonance frequency (e.g., one or more rotational or vibrational frequencies) of each of the multiple analytes of interest, such that the sensor can simultaneously detect multiple analytes. In some examples, the sensor includes multiple Tamm polariton emitters, and each of the multiple Tamm polariton emitters is configured to selectively emit radiation at a certain frequency, such that the multiple Tamm polariton emitters are selectively configured to emit radiation at multiple frequencies, and at least a portion of each of the multiple frequencies corresponds to the rotational or vibrational resonance frequency of each of the multiple analytes of interest, such that the sensor can simultaneously detect multiple analytes. In some examples, the detector includes a Tamm polariton detector, and the Tamm polariton detector is configured to selectively receive radiation at multiple frequencies, or the detector includes multiple Tamm polariton detectors, and each of the multiple Tamm polariton detectors is configured to selectively receive radiation at a certain frequency, such that the multiple Tamm polariton detectors are selectively configured to receive radiation at multiple frequencies.

[0095] In some examples, the analyte of interest comprises a single analyte, and the Tamm polariton emitter is configured to selectively emit radiation at a plurality of frequencies corresponding to a plurality of rotational or vibrational resonance frequencies of the analyte of interest, such that the sensor can detect the analyte of interest with high sensitivity. In some examples, the analyte of interest comprises a single analyte, and the sensor comprises a plurality of Tamm polariton emitters, each of the plurality of Tamm polariton emitters being configured to selectively emit radiation at a certain frequency, such that the plurality of Tamm polariton emitters are selectively configured to emit radiation at a plurality of frequencies, at least a portion of each of the plurality of frequencies corresponding to a plurality of rotational or vibrational resonance frequencies of the analyte of interest, such that the sensor can detect the analyte of interest with high sensitivity. In some examples, the detector comprises a Tamm polariton detector, the Tamm polariton detector being configured to selectively receive radiation at a plurality of frequencies, or the detector comprises a plurality of Tamm polariton detectors, each of the plurality of Tamm polariton detectors being configured to selectively receive radiation at a certain frequency, such that the plurality of Tamm polariton detectors are selectively configured to receive radiation at a plurality of frequencies.

[0096] In some examples, the analyte of interest comprises a toxin, an adulterant, a contaminant, a weapon agent (e.g., a chemical or biological weapon agent), or a combination thereof.

[0097] In some examples, the analyte of interest comprises an organic molecule, a biological agent (e.g., a bacterium, a virus, a protozoan, a parasite, a fungus, a biological weapon agent, or a combination thereof), or a combination thereof. In some examples, the analyte of interest comprises a pathogen such as an infectious microorganism (e.g., a bacterium, a virus, a fungus, a protozoan, etc.).

[0098] In some examples, the analyte of interest may include chemical or biological warfare agents. Examples of chemical warfare agents include nerve agents (e.g., sarin, soman, cyclosarin, tabun, ethyl {2-[bis(propan-2-yl)amino]ethyl}sulfanyl)(methyl)phosphinate (VX), O-pinacolyl methylphosphonofluoridate), vesicants or blister agents (e.g., mustard, lewisite), respiratory agents (e.g., chlorine, phosgene, diphosgene), cyanides, antimuscarinic agents (e.g., anticholinergic compounds), opioid agents, lacrimators (e.g., a-chlorotoluene, benzyl bromide, bromoacetone (BA), bromobenzyl cyanide (CA), capsaicin (OC), chloroacetophenone (MACE), chloromethyl chloroformate, dibenzoxazepine (CR), ethyl iodoacetate, ortho-chlorobenzylidene malononitrile (CS), trichloromethyl chloroformate, xylyl bromide), and vomiting agents (e.g., adamsite (DM), diphenylchloroarsine (DA), diphenylcanoarsine (DC)), but are not limited thereto.Biological warfare agents include, but are not limited to, bacteria (e.g., Bacillus anthracis, Bacillus abortus, Brucella suis, Vibrio cholerae, Corynebacterium diptheriae, Shigella dysenteriae, Escherichia coli, burkholderia mallei, listeria monocytogenes, Burkholderia pseudomallei, yersinia pestis, Francisella tularensis, Chlamydophila psittaci, Coxiella burnetii, rickettsia, rickettsia prowazekii, rickettsia typhi), viruses (e.g., Eastern equine encephalitis virus, Venezuelan equine encephalitis virus, Western equine encephalitis virus, Japanese encephalitis virus, Rift Valley fever virus, Variola virus, Yellow Fever virus, Ebola virus, Marburg virus, coronaviruses), protozoa, parasites, fungi (coccidioides immitis), pathogens, toxins, and biotoxins (Abrin, Botulinum toxin, Ricin, Saxitoxin, Staphylococcal enterotoxin B, tetrodotoxin, trichothecene mycotoxins).

[0099] In some examples, the analyte of interest includes greenhouse gases. Examples of greenhouse gases include, but are not limited to, water vapor, CO2, CH4, N2O, O3, and combinations thereof.

[0100] In some examples, the analyte of interest includes gases that were used as, produced in, and / or generated as by-products of semiconductor manufacturing, industrial production, chemical synthesis, or combinations thereof. In some examples, the analyte of interest includes gases or chemicals used in semiconductor manufacturing, examples of which include, but are not limited to, C4F8, SF6, and CF4. In some examples, the analyte of interest includes by-product gases or chemicals in semiconductor manufacturing, an example of which includes, but is not limited to, HCl. In some examples, the analyte of interest includes gases or chemicals used in industrial production, an example of which includes, but is not limited to, NO2. In some examples, the analyte of interest includes products or by-product gases or chemicals in industrial production, examples of which include, but are not limited to, NO2 and NO. In some examples, the analyte of interest includes gases or chemicals used in chemical synthesis, an example of which includes, but is not limited to, acetone. In some examples, the analyte of interest includes products or by-product gases or chemicals in chemical synthesis, an example of which includes, but is not limited to, HNO3.

[0101] In some examples, the analyte of interest includes gases or chemicals that need to be maintained at a certain concentration, examples of which include, but are not limited to, chemicals used in pest control such as SO2F2.

[0102] In some examples, the analyte of interest includes CO2, SO2, formaldehyde, CO, NH3, N2O, O3, CH4, NO, dimethyl methylphosphonate (DMMP), or combinations thereof.

[0103] In some examples, the sensor is filterless (e.g., the sensor comprises a filterless NDIR sensor).

[0104] Also disclosed herein is a method of using any of the devices or sensors disclosed herein. For example, also disclosed herein is a method of using any of the sensors disclosed herein for gas sensing. Also, for example, disclosed herein is a method of using any of the sensors disclosed herein for environmental sensing, atmospheric sensing, chemical sensing, or combinations thereof.

[0105] Design method Also disclosed herein is a method for designing a Tamm polariton emitter. For example, also disclosed herein is a method for designing any of the Tamm polariton emitters disclosed herein. The method can include, for example, an inverse design protocol. In some examples, the method can include machine learning.

[0106] For example, also, a method for designing a Tamm polariton emitter, wherein the Tamm polariton emitter is: A distributed Bragg reflector comprising a stack of a plurality of layers of a plurality of materials having different refractive indices, each layer comprising a material having a certain refractive index, each layer having a certain average thickness, and the refractive index of each layer being different from that of the preceding and / or subsequent layers; a distributed Bragg reflector, A layer comprising a conductive material and / or a polariton material, Comprising, wherein the distributed Bragg reflector is disposed on the layer of the conductive material and / or the polariton material, The Tamm polariton emitter emits radiation (e.g., electromagnetic radiation) at a certain frequency (e.g., one or more frequencies): The method is, a. Defining a target spectrum of the radiation emitted by the Tamm polariton emitter, b. Defining an initial set of values for a set of parameters of the designed Tamm polariton emitter, The set of parameters includes the total number of layers of the distributed Bragg reflector, the composition of each of the plurality of layers, the thickness of each of the plurality of layers, the composition of the layer of the conductive material and / or the polariton material, the carrier density of the layer of the conductive material and / or the polariton material, and the thickness of the layer of the conductive material and / or the polariton material, Defining, for an initial set of values, that the initial total number of layers is user-defined and the remaining parameters are initialized randomly, c. Modeling the emission spectrum of a designed Tamm polariton emitter having an initial set of parameters written as a vector (t), wherein the modeled emission spectrum is the designed emission spectrum, d. Determining an error by comparing the designed emission spectrum with a target emission spectrum, Modeling the designed emission spectrum and comparing it with the target emission spectrum using the transfer matrix method, The error is a scalar error that is a combination of the mean squared error and the mean absolute error, If the error is greater than a pre-defined threshold, the error is backpropagated to find the gradient over t by stochastic gradient descent, and the gradient is used to update t in the next iteration of steps c and d: [Number] The iteration continues until a pre-defined maximum number of iterations is reached or the error is minimized, If the number of iterations reaches the pre-defined maximum without reaching the error threshold, the number of layers is increased and the method is repeated, If the error is below the defined threshold, the method includes outputting the set of parameters, the designed emission spectrum, the target emission spectrum, or a combination thereof. A method is disclosed herein.

[0107] Also, for example, a method for designing a Tamm polariton emitter, wherein the Tamm polariton emitter is: A layer of polar material, A distributed Bragg reflector comprising a stack of a plurality of layers of a plurality of materials having various refractive indices, each layer comprising a material having a certain refractive index, each layer having a certain average thickness, and the refractive index of each layer being different from that of the preceding and / or succeeding layers; A layer comprising a conductive material and / or a polariton material, The distributed Bragg reflector is disposed on the layer of the conductive material and / or the polariton material, The layer of polar material is disposed on top of the distributed Bragg reflector, so that the distributed Bragg reflector is sandwiched between the layer of the conductive material and / or the polariton material and the polar material, A Tamm polariton emitter emits radiation at a certain frequency, The method is: a. Defining a target spectrum of the radiation emitted by the Tamm polariton emitter, b. Defining an initial set of values for a set of parameters of the designed Tamm polariton emitter, The set of parameters includes the total number of layers of the distributed Bragg reflector, the composition of each of the plurality of layers, the thickness of each of the plurality of layers, the composition of the layer of the conductive material and / or the polariton material, the carrier density of the layer of the conductive material and / or the polariton material, the thickness of the layer of the conductive material and / or the polariton material, the composition of the layer of the polar material, the carrier density of the layer of the polar material, and the thickness of the layer of the polar material, For the initial set of values, defining that the initial total number of layers is user-defined and the remaining parameters are initialized randomly, c. Modeling the emission spectrum of the designed Tamm polariton emitter having the initial set of parameters written as a vector (t), the modeled emission spectrum being the designed emission spectrum, d. Determining the error by comparing the designed emission spectrum with the target emission spectrum, The designed emission spectrum is modeled and compared with the target emission spectrum using the transfer matrix method, the error being a scalar error that is a combination of the mean squared error and the mean absolute error, if the error is greater than a pre-defined threshold, the error is backpropagated to find the gradient over t by stochastic gradient descent, and the gradient is used to update t in the next iteration of steps c and d:

Number

[0108] In some examples, the error is given by the following formula: error = mean(ratio1(DS - TS) 2 + ratio2|DS - TS|) where ratio1 and ratio2 are hyperparameters customized for different purposes, and DS and TS are vectors with respective elements representing absorbance at corresponding wavelengths.

[0109] In some examples, steps c and / or d of the method include a weighted sampling technique. In some examples, the weighted sampling technique is based on the desired application, the frequency region of interest, the analyte of interest, or a combination thereof.

[0110] In some examples, the parameter may further include the frequency, amplitude, and / or linewidth (e.g., FWHM) of the emitted radiation. In some examples, the parameter may further include a quality factor (e.g., Q factor). In some examples, the Q factor may be 1 or more (e.g., 2 or more, 3 or more, 4 or more, 5 or more, 10 or more, 15 or more, 20 or more, 30 or more, 40 or more, 50 or more, 75 or more, 100 or more, 125 or more, 150 or more, 175 or more, 200 or more, 250 or more, 300 or more, 350 or more, 400 or more, 450 or more, 500 or more, 600 or more, 700 or more, 800 or more, 900 or more, 1,000 or more, 1,250 or more, 1,500 or more, 1,750 or more, 2,000 or more, 2,250 or more, 2,500 or more, 3,000 or more, 3,500 or more, 4,000 or more, 4,500 or more, 5,000 or more, 6,000 or more, 7,000 or more, 8,000 or more, 9,000 or more, 10,000 or more, 12,500 or more, 15,000 or more, 17,500 or more, 20,000 or more, 22,500 or more, 25,000 or more, 30,000 or more, 35,000 or more, 40,000 or more, 45,000 or more, 50,000 or more, 60,000 or more, 70,000 or more, 80,000 or more, 90,000 or more, 100,000 or more, 125,000 or more, 150,000 or more, 175,000 or more, 200,000 or more, 250,000 or more, 300,000 or more, 350,000 or more, 400,000 or more, 450,000 or more, 500,000 or more, 600,000 or more, 700,000 or more, or 800,000 or more).In some examples, the Q factor can be 1,000,000 or less (e.g., 900,000 or less, 800,000 or less, 700,000 or less, 600,000 or less, 500,000 or less, 450,000 or less, 400,000 or less, 350,000 or less, 300,000 or less, 250,000 or less, 200,000 or less, 175,000 or less, 150,000 or less, 125,000 or less, 100,000 or less, 90,000 or less, 80,000 or less, 70,000 or less, 60,000 or less, 50,000 or less, 45,000 or less, 40,000 or less, 35,000 or less, 30,000 or less, 25,000 or less, 20,000 or less, 17,500 or less, 15,000 or less, 12,500 or less, 10,000 or less, 9,000 or less, 8,000 or less, 7,000 or less, 6,000 or less, 5,000 or less, 4,500 or less, 4,000 or less, 3,500 or less, 3,000 or less, 2,500 or less, 2,250 or less, 2,000 or less, 1,750 or less, 1,500 or less, 1,250 or less, 1,000 or less, 900 or less, 800 or less, 700 or less, 600 or less, 500 or less, 450 or less, 400 or less, 350 or less, 300 or less, 250 or less, 200 or less, 175 or less, 150 or less, 125 or less, 100 or less, 75 or less, 50 or less, 40 or less, 30 or less, 25 or less, 15 or less, 10 or less, 5 or less, 4 or less, or 3 or less). The Q factor can be in the range from any of the above minimum values to any of the above maximum values. For example, the Q factor can be 1 to 1,000,000 (e.g., 1 to 1,000, 1,000 to 1,000,000, 1 to 100, 100 to 10,000, 10,000 to 100,000, 10 to 1,000,000, 1 to 900,000, 10 to 900,000, 1 to 900,000, 1 to 500,000, 1 to 100,000, 5 to 1,000,000, 50 to 1,000,000, 100 to 100,000, or 500 to 1,000,000).

[0111] In some examples, the method includes machine learning.

[0112] In some examples, the Tamm polariton emitter includes a plurality of Tamm polariton emitters, and the parameter further includes the number of Tamm polariton emitters in the plurality of Tamm polariton emitters.

[0113] In some examples, the method includes designing a first Tamm polariton emitter and a second Tamm polariton emitter, the second Tamm polariton emitter comprising a Tamm polariton detector. In some examples, the first Tamm polariton emitter is configured to selectively emit radiation at one or more frequencies, and the second Tamm polariton emitter is configured to selectively receive at least a portion of the radiation emitted by the first Tamm polariton emitter (e.g., the first Tamm polariton emitter and the Tamm polariton detector are matched). In some examples, the method further includes maximizing an overlap between the radiation emitted by the Tamm polariton emitter and the radiation received by the detector.

[0114] In some examples, the first Tamm polariton emitter includes a first plurality of Tamm polariton emitters, the second Tamm polariton emitter includes a second plurality of Tamm polariton emitters, or a combination thereof. In some examples, the first Tamm polariton emitter includes a first plurality of Tamm polariton emitters, and the parameter includes the number of the first plurality of first Tamm polariton emitters, the second Tamm polariton emitter includes a second plurality of Tamm polariton emitters, and the parameter includes the number of the plurality of second Tamm polariton emitters, or a combination thereof.

[0115] Computing device The device (e.g., a sensor) may include, in some examples, a computing device. Any of the methods disclosed herein may be executed in whole or in part on one or more computing devices or processing devices.

[0116] Figure 71 shows an exemplary computing device 1000 in which examples disclosed herein may be implemented. The computing device 1000 may include a bus or other communication mechanism for communicating information among various components of the computing device 1000. In its most basic configuration, the computing device 1000 typically includes at least one processing unit 1002 (processor) and a system memory 1004. Depending on the exact configuration and type of the computing device, the system memory 1004 can be volatile (such as random access memory (RAM)), non-volatile (such as read-only memory (ROM), flash memory, etc.), or some combination of the two. This most basic configuration is shown in Figure 71 by dashed line 1006. The processing unit 1002 can be a standard programmable processor that performs the arithmetic and logical operations necessary for the operation of the computing device 1000.

[0117] The computing device 1000 may have additional features / functions. For example, the computing device 1000 may include additional storage such as removable storage 1008 and non-removable storage 1010, including but not limited to magnetic or optical disks or tapes. The computing device 1000 may also include network connection(s) 1016 that enable the device to communicate with other devices. The computing device 1000 may also have input device(s) 1014 such as a keyboard, mouse, touch screen, antenna, or other system configured to communicate with a camera within the above system. Output device(s) 1012 such as a display, speaker, printer, etc. may also be included. Additional devices may be connected to the bus to facilitate communication of data among the components of the computing device 1000.

[0118] The processing unit 1002 may be configured to execute program code encoded in a tangible computer-readable medium. A computer-readable medium refers to any medium that can provide data for operating a computing device 1000 (i.e., a machine) in a specific manner. Various computer-readable media can be utilized to send instructions to the processing unit 1002 for execution. General forms of computer-readable media include, for example, magnetic media, optical media, physical media, memory chips or cartridges, carrier waves, or any other media readable by a computer. Exemplary computer-readable media can include, but are not limited to, volatile media, non-volatile media, and transmission media. Volatile and non-volatile media can be implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data, and their general forms will be discussed in detail below. Transmission media can include acoustic or light waves such as coaxial cables, copper wire and / or fiber optic cables, and those generated during radio and infrared data communications. Examples of tangible computer-readable recording media include, but are not limited to, integrated circuits (e.g., field programmable gate arrays or application specific ICs), hard disks, optical disks, magneto-optical disks, floppy disks, magnetic tapes, holographic storage media, solid state devices, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices.

[0119] In an exemplary implementation, the processing unit 1002 can execute program code stored in the system memory 1004. For example, the bus can carry data to the system memory 1004, and the processing unit 1002 receives instructions therefrom and executes them. The data received by the system memory 1004 can optionally be stored in the removable storage 1008 or the non-removable storage 1010 before or after execution by the processing unit 1002.

[0120] The computing device 1000 typically includes various computer-readable media. The computer-readable media can be any available media accessible by the device 1000 and includes both volatile and non-volatile media, removable and non-removable media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules, or other data. System memory 1004, removable storage 1008, and non-removable storage 1010 are all examples of computer storage media. Computer storage media includes, but is not limited to, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disk (DVD) or other optical storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage, or any other medium that can be used to store the desired information and is accessible by the computing device 1000. Any such computer storage media can be part of the computing device 1000.

[0121] It should be understood that the various techniques described herein can be implemented in relation to hardware or software, or, where appropriate, in combination thereof. Accordingly, the methods, systems, and associated signal processing of the subject matter of the present disclosure, or certain aspects or portions thereof, can take the form of program code (i.e., instructions) embodied in a tangible medium such as a floppy disk, a CD-ROM, a hard drive, or any other machine-readable storage medium, and when the program code is loaded and executed by a machine such as a computing device, the machine becomes an apparatus for practicing the subject matter of the present disclosure. In the case of program code execution on a programmable computer, the computing device generally includes a processor, a storage medium readable by the processor (including volatile and non-volatile memory, and / or storage elements), at least one input device, and at least one output device. One or more programs can implement or utilize the processes described in connection with the subject matter of the present disclosure, for example, through the use of an application programming interface (API), reusable controls, etc. Such programs can be implemented in a high-level procedural or object-oriented programming language for communicating with a computer system. However, if desired, the program(s) can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language, which can be combined with hardware implementations.

[0122] In a particular example, the method can be executed, in whole or in part, on a computing device 1000 that includes a processor 1002 and a memory 1004 operatively coupled to the processor 1002, and the memory 1004 further has computer-executable instructions stored therein that, when executed by the processor 1002, cause the processor 1002 to execute one or more of the above method steps.

[0123] Some embodiments of the present invention have been described. Nevertheless, it should be understood that various modifications can be made without departing from the spirit and scope of the present invention. Accordingly, other embodiments are within the scope of the following claims.

[0124] The following examples are intended to further illustrate certain aspects of the systems and methods described herein and are not intended to limit the scope of the claims.

Example

[0125] The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to cover all aspects of the disclosed subject matter, but rather are representative methods and results. These examples are not intended to exclude equivalents and variations of the present invention that are apparent to those skilled in the art.

[0126] Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperatures, etc.), but some errors and deviations need to be taken into account. Unless otherwise specified, parts are parts by weight, temperature is in °C, or ambient temperature, and pressure is at or near atmospheric pressure. There are many variations and combinations of measurement conditions, such as component concentrations, temperatures, pressures, and other measurement ranges and conditions, that can be used to optimize the described processes.

[0127] Example 1 - Deterministic inverse design of a Tamm plasmon thermal emitter with multi-resonance control. Abstract. In this specification, a Tamm plasmon polariton emitter (TPP-EM) composed of an aperiodically distributed Bragg reflector deposited on a doped cadmium oxide (CdO) film is optimized using stochastic gradient descent, where the layer thickness and carrier density are inversely designed. The combination of the aperiodically distributed Bragg reflector and the designable plasma frequency of CdO enables the simultaneous design of multiple Tamm plasmon polariton emitter modes with any spectral control that is not achievable with metal-based Tamm plasmons. Using this approach, a Tamm plasmon polariton emitter exhibiting single or multiple emission bands with designable frequencies, linewidths, and amplitudes is experimentally demonstrated and numerically proposed. This enables a lithography-free wafer-scale wavelength-selective thermal emitter, a complementary metal-oxide semiconductor suitable for applications such as free-space communication and gas sensing.

[0128] Introduction. The development of inexpensive and effective light sources in the infrared is highly desirable for many applications. These range from free-space communication and infrared beacons to barcodes, and could improve the ability to monitor environmental pollutants and toxins through molecular sensing measurements such as non-dispersive infrared (NDIR) sensing. Therefore, wavelength-selective thermal emitters are of particular interest due to the lack of cost-effective light sources in the mid- and long-wave infrared (MWIR, LWIR) (Baranov DG et al. Nat. Mater. 2019, 18, 920-930). Most proposed wavelength-selective thermal emitters use patterned nanostructures, which thereby require high-cost, low-throughput lithography methods and are thus unsuitable for many applications. An alternative solution is the Tamm plasmon polariton heterostructure (Kaliteevski M et al. Phys. Rev. B 2007, 76, 165415). Such Tamm plasmon polariton structures typically consist of a distributed Bragg reflector (DBR) on a conductor, which is typically a noble metal (Figure 1), and the distributed Bragg reflector provides an optical phase that matches the metal surface and results in an absorption resonance with a high quality factor (Q-factor; narrow linewidth) at near-normal angles of incidence (Kaliteevski M et al. Phys. Rev. B 2007, 76, 165415; Sasin ME et al. Appl. Phys. Lett. 2008, 92, 251112; Sakurai A et al. ACS Cent. Sci. 2019, 5, 319-326; Wang Z et al. ACS Photon. 2020, 7, 1569-1576; Wang Z et al. ACS Photon. 2018, 5, 2446-2452). Since only thin-film deposition is required for fabrication, Tamm plasmon polariton emitters can be grown on wafer scale at relatively low cost and with minimal fabrication steps, presenting a promising candidate for wavelength-selective thermal emitters (Sakurai A et al. ACS Cent. Sci. 2019, 5, 319-326; Wang Z et al. ACS Photon. 2020, 7, 1569-1576; Wang Z et al. ACS Photon. 2018, 5, 2446-2452).

[0129] Despite the broad potential of Tamm plasmon polariton emitters, in most applications, it is necessary to simultaneously control both the emission frequency and the corresponding Q factor and suppress emission at other frequencies, so the design of such structures is difficult. Compared with conventional Tamm plasmon polariton emitters based on periodic distributed Bragg reflectors (Yang ZY et al. ACS Photon. 2017, 4, 2212 - 2219), aperiodic structures provide additional spectral control and enable suppression of spurious emission peaks (Botros J et al. J. Appl. Phys. 2020, 127, 114502), while at the same time achieving ultra-high Q factors (Sakurai A et al. ACS Cent. Sci. 2019, 5, 319 - 326; Wang Z et al. ACS Photon. 2020, 7, 1569 - 1576). However, due to the large parameter space associated with the design of aperiodic distributed Bragg reflectors, forward design methodologies are not efficient, and thus, an inverse design protocol is needed using high-Q-factor Tamm plasmon polariton emitters demonstrated at a single desired wavelength by high-precision Bayesian optimization and genetic algorithms (Botros J et al. J. Appl. Phys. 2020, 127, 114502). However, such initial studies exhibited low optimization efficiency and required simulations of over 24 days for each optimized structure (Sakurai A et al. ACS Cent. Sci. 2019, 5, 319 - 326). More importantly, the design of multiple emission peaks where the frequency, amplitude, and linewidth of each resonance can be independently controlled has not been realized. The use of such multiple-peak Tamm plasmon polariton emitters may enable both the sensing of multiple target gases and, simultaneously, highly sensitive gas detection when the resonances of the Tamm plasmon polariton emitter are matched to some vibrational modes of one or more chemical substances. Furthermore, experimental reports have so far only used noble metals, which severely limit spectral control due to the plasma frequency being in the visible range and, on the other hand, are incompatible with complementary metal-oxide-semiconductor (CMOS) processing.

[0130] In this specification, an inverse design algorithm is presented to efficiently optimize a Tamm plasmon polariton emitter composed of an aperiodic distributed Bragg reflector grown on an n-type In-doped cadmium oxide (CdO) film, and to exhibit individual control of a multi-peak wavelength-selective thermal emitter. The inverse design protocol is based on a stochastic gradient descent (SGD) method (Nolen JR et al. Phys. Rev. Mater. 2020, 4, 025202) that enables efficient (within minutes on a consumer-grade desktop) optimization of the individual layer thicknesses, as well as the carrier density (and thus the dielectric function) of CdO. The design approach is experimentally verified, realizing single, double, and triple-band Tamm plasmon polariton emitters over a wide spectral range, and all structures exhibit excellent agreement between experiment and simulation. Importantly, the advantages of multi-peak Tamm plasmon polariton emitters for non-dispersive infrared applications, such as enabling highly sensitive simultaneous detection of multiple gases, are numerically verified. Furthermore, the design capabilities of CdO-based Tamm plasmon polariton emitters include the ability to define the Q factor over a wide range of values at any given frequency (e.g., 27 to 10,117 for 2,360 cm -1It is shown by demonstrating the ability to match the resonance frequencies, linearities, and amplitudes of arbitrarily shaped spectra extending from long-wavelength infrared to the communication band (demonstrated in [reference]). Finally, it is emphasized that such functionality is not possible in noble-metal-based Tamm plasmon polariton emitters, but instead is enabled by the widely tunable plasma frequency of CdO (Nolen JR et al. Phys. Rev. Mater. 2020, 4, 025202; Liu CP et al. Phys. Rev. Appl. 2016, 6, 064018; Runnerstrom EL et al. ACS Photonics, 2017, 4, 1885 - 1892; Sachet E et al. Nat. Mater. 2015, 14, 414 - 420; Cleri A et al. Phys. Rev. Mater. 2021, 5, 035202). The combination of efficient inverse design algorithms and advances in these materials facilitates the realization of high-cost-effective, wafer-scale, CMOS-compatible, and lithography-free Tamm plasmon polariton emitters for many applications, including multi-gas non-dispersive infrared, environmental, atmospheric, and chemical sensing, free-space communication, and infrared beacons.

[0131] An inverse design protocol based on stochastic gradient descent. The Tamm plasmon polariton emitters discussed herein are grown on a thin (∼500 nm) CdO film on a sapphire substrate with Ge and AlO xIt is composed of an aperiodic distributed Bragg reflector with an interaction layer (Figure 1). All individual layer thicknesses and CdO carrier densities (and thus the dielectric function (Nolen JR et al. Phys. Rev. Mater. 2020, 4, 025202)) are included as design parameters written as a vector (t). Using an inverse design technique based on stochastic gradient descent, t is determined such that the difference between the absorption spectrum of the designed structure (designed spectrum, DS) and the target spectrum (TS) is minimized. The design process is initiated by assigning the maximum number of layers of the distributed Bragg reflector preferred by the user, and t is initialized randomly. Through the transfer matrix method (TMM), the designed spectrum of the corresponding structure t is calculated, compared with the target spectrum, and a scalar error is obtained. The error is written as a combination of the mean squared error (the first term) and the mean absolute error (the second term): Error = mean(ratio1(DS - TS) 2 + ratio2|DS - TS|)(1) where ratio1 and ratio2 are hyperparameters customized for different purposes, and DS and TS are vectors with respective elements representing the absorption rates at the corresponding wavelengths. This combination of errors is generally used in the field of deep learning, and it should be noted that related techniques are powerful for optimizing Tamm plasmon polariton emitter designs such as weighted sampling approaches (Section S1). Then, this error is backpropagated to find the gradient over t by stochastic gradient descent. For each iteration, the gradient is used to update t:

Equation

[0132] After each successive iteration, the error decreases, and the iteration continues until a predefined maximum number. Thus, the structure of the Tamm plasmon polariton emitter is optimized to the point where the error between the target spectrum and the designed spectrum is minimized.

[0133] The optimization process takes different forms for each execution, and one example is shown in Fig. 2. First, the absorption spectrum of the randomly initialized structure (red solid line) is significantly different from the target spectrum. After several iterations, the designed spectrum converges towards the target spectrum (see the red → blue → green → purple solid lines in Fig. 2). Different from the normal gradient descent calculations used in commercial software and previous publications (Xue W et al. Arxiv, 2021, https: / / arxiv.org / abs / 2101.03160; Jiang J et al. Nanophotonics 2021, 10, 361 - 369), the stochastic gradient descent approach used herein reduces the possibility of falling into low local minima and improves the optimization performance (Section S2) (Bordes A et al. J. Mach. Learn. Res. 2009, 10, 1737 - 1754; Sohl - Dickstein J et al. Proc. Mach. Learn. Res. 2014, 32, 604 - 612; Kingma D P et al. Arxiv, 2015, https: / / arxiv.org / abs / 1412.6980; Robbins H et al. Ann. Math. Stat. 1951, 22, 400 - 407). The method is still a local optimization, but the stochastic gradient descent methodology approaches that of global optimization and exhibits high accuracy and efficiency compared to other methods (Table 1). The code is downloadable online (https: / / my.vanderbilt.edu / caldwellgroup / ).

[0134] Experimental demonstration of an inverse-designed Tamm plasmon polariton emitter. Based on an inverse design algorithm, several Tamm plasmon polariton emitter structures were designed and fabricated, exhibiting a wide range of unique spectral features. The carrier density of CdO in these structures, as well as the designed and as-grown layer thicknesses, are described in Section S4 below, and the growth process is discussed in the methods. Note that when a distributed Bragg reflector with more layers is utilized, more complex spectra (higher Q factors, more peaks, etc.) can be realized; however, adding additional layers does not provide any additional benefits if the target is achievable with a certain number of layers (Section S6). Therefore, in the experimental demonstration, to simplify the fabrication, the fewest possible number of layers were used to match the target spectrum. To demonstrate the power of the inverse-designed Tamm plasmon polariton emitter, an experimental device featuring a single emission peak in the long-wavelength infrared (800 - 1250 cm -1 ) for free-space communication was first provided. The target spectrum was modeled as a flat line with a single sharp absorption peak centered at 1,250 cm -1 , and the designed spectrum was matched to the narrowest possible target spectral linewidth using the stochastic gradient descent method (Figure 3). Following this optimization, the spectrum of the designed structure exhibits a single peak centered at 1,250 cm -1 with a Q factor of 13, while the experimentally obtained Q factor is approximately 9. All experimentally measured and calculated spectra based on the designed and as-grown thicknesses show excellent agreement, with all four exhibiting nearly overlapping resonance lines (Figure 3).

[0135] In addition to emitters for communication, long-wave infrared and mid-wave infrared contain molecular absorption features, and thus one use of wavelength-selective thermal emitters is filterless non-dispersive infrared gas sensing. A filterless non-dispersive infrared sensor comprises a wavelength-selective thermal emitter, a gas cell, and a broadband detector (Section S7). The emission frequency of the wavelength-selective thermal emitter is centered on the absorption frequency of the target gas having a high enough Q factor to eliminate false positives arising from absorption by other gases present. For such applications, we first demonstrated a heterostructure supporting a single emissivity peak in one absorption band of CO2 (2,349 cm -1 ). Again, as shown in Fig. 4, an excellent match is observed with the measured (target) emission peak centered at 2,360 cm -1 (2,350 cm -1 ) with a Q factor of 21(40). However, while these single-peak emitters can be efficiently designed using the protocol described herein, they can also be realized by other approaches such as intuitive inductive forward design (Yang ZY et al. ACS Photon. 2017, 4, 2212-2219), Bayesian optimization (Sakurai A et al. ACS Cent. Sci. 2019, 5, 319-326; Zhang W et al. ACS Appl. Energy Mater. 2021, 4, 2004-2013), and genetic algorithms (Botros J et al. J. Appl. Phys. 2020, 127, 114502), although these require substantially more effort.

[0136] So far, Tamm plasmon polariton emitter designs have been demonstrated with isolated adjustable emission rate peaks that make these devices suitable for single, simple applications such as gas detection. In addition to the applications enabled by such single-peak Tamm plasmon polariton emitters, more advanced functions such as infrared signature management and multi-channel non-dispersive infrared can be realized via multi-frequency Tamm plasmon polariton emitters. In the case of non-dispersive infrared, additional emission channels can be used to detect more of the target gases or enhance the sensitivity to specific gases by aligning the emission to multiple vibrational modes. However, wavelength-selective thermal emitters with independent design control for multiple distinct emission peaks have not been previously demonstrated. First, the functionality of the Tamm plasmon polariton emitter is illustrated by demonstrating a device suitable for simultaneous dual-gas sensing of SO2 and CO2, and the theoretical basis for the target spectrum is described in Section S8 below. In addition, the SO2 and CO2 concentrations can be independently evaluated using this Tamm plasmon polariton emitter operating at different temperatures (Section S9). Here, five dielectric layers are used to obtain a designed spectrum with two absorption peaks centered at 1,367 and 2,339 cm -1 (Fig. 5), a designed spectrum with two absorption peaks centered at (Fig. 5) was obtained. The experimental data also agree well, with some minor exceptions. While the central frequencies are in close agreement (1,358 and 2,360 cm -1 ), some degradation in the Q factor and emissivity amplitude is observed. Despite the difference between the grown and designed thicknesses, the spectral mismatch is minimal, indicating robustness to manufacturing errors (Section S10). In particular, at the foundry level of manufacturing, limited thickness errors are expected.

[0137] The function of the Tamm plasmon polariton emitter is not limited to dual-band emission, and more bands at user-designed frequencies can be realized. To illustrate this ability, a target spectrum characterized by three emission peaks centered at the absorption bands of CO and formaldehyde (1,750 cm -1 , 2,150 cm -1 , and 2,800 cm -1 ) was also modeled, and the FWHM was increased to compensate for the blackbody emission shapes (20, 30, and 40 cm -1 , respectively) imposed on the resulting Tamm plasmon polariton emission spectrum. Again, the excellent agreement between the target spectrum, the designed spectrum, and the experimental structure for the designed Tamm plasmon polariton emitter is realized for each curve (Figure 6) by the peak analysis described in Table 3. The difference in thickness from manufacturing shifts one resonance by 70 cm -1 , which remains within the formaldehyde absorption band and thereby still enhances the sensitivity for non-dispersive infrared applications.

[0138] Previously demonstrated multi-resonance control is crucial for many applications such as multi-frequency infrared beacons for encryption purposes and advanced non-dispersive infrared applications. Here, the implications of experimental devices in filterless non-dispersive infrared applications are theoretically shown and compared with conventional non-dispersive infrared devices enabled by blackbody emitters and filters (Tables 4 and 5). The advantages of the multi-peak Tamm plasmon polariton emitter are (1) improved sensitivity when multiple absorption bands are aligned, (2) the potential for multi-gas sensing within a single compact package, and (3) reduced power consumption. Note that the single-peak Tamm plasmon polariton emitter provides the same sensitivity with approximately 5 - 10 times lower power consumption (Figs. 37 and 6). Importantly, the angular dispersion of the Tamm plasmon polariton emitter is inherently low (Figs. 38 - 41), eliminating problems from the field of view angle as well. Thus, the experimentally demonstrated ability to control the emission frequency with a desired Q factor provides substantial advantages for such applications, including a low false positive rate and the ability to highly sensitively sense multiple gases simultaneously within a single compact non-dispersive infrared package.

[0139] Potential of the inverse-designed Tamm plasmon polariton emitter. For advanced wavelength-selective thermal emitter applications such as spectral barcoding and multi-gas sensing, it is necessary to realize user-defined FWHM and amplitude at single or multiple frequencies. However, no design approach has been previously proposed to achieve these tasks with the required accuracy. To address these challenges and further demonstrate the potential of the inverse-designed Tamm plasmon polariton emitter, the design capabilities were explored by utilizing a Ge / ZnSe distributed Bragg reflector with 29 layers on a bilayer of CdO (all designed structures are included in Section S14).

[0140] First, excellent control over the linewidth at a fixed frequency was demonstrated by showing structures with Q - factors in the range of 26 to 10,117 while maintaining nearly single emission for all designs (Figs. 7 and 42). Thus, not only was it possible to achieve an ultra - high Q - factor for the Tamm - based structure (fitting in Fig. 43), but also the potential to match the required Q - factor for a given frequency was shown. Since different applications have various requirements regarding the signal - to - noise ratio, such an ability is essential. Based on this, the potential for such a multi - peak design was expanded by providing a target spectrum presenting three emission peaks with different linewidths (Q - factors = 25, 37, and 145). Such a Tamm plasmon polariton emitter design is suitable for spectral barcoding and sensing, but has not been demonstrated or proposed, probably due to extensive design challenges in matching such complex spectra. Despite this difficulty, the designed spectrum has only minor mismatches and can match the target spectrum very well (Fig. 8).

[0141] CdO's widely adjustable plasma frequency (about 1,200 cm -1 ~7,800 cm -1 ) can also be used to realize a Tamm plasmon polariton emitter with absorption peaks ranging from short - wave infrared to long - wave infrared. To demonstrate such an ability, another Tamm plasmon polariton emitter structure was optimized, which features three spectrally distinct emission peaks located simultaneously at long - wave infrared (1,200 cm -1 ), mid - wave infrared (2,700 cm -1 ), and short - wave infrared (1.55 μm) (Fig. 9). Again, the resulting designed spectrum matches the target spectrum very well. Additional modes exist in the spectral regions between these desired emission resonances (Fig. 13), which is a fundamental limitation of the multimodal nature of distributed Bragg reflectors. However, the influence of these additional peaks can be mitigated by weighted sampling techniques (Sections S1 and S15).

[0142] Finally, the potential of Tamm plasmon polariton emitters in advanced non-dispersive infrared applications is emphasized. Here, for two reasons, it is desirable to match the emitted power to the chemical absorption spectrum: (1) the amount of power emitted should be absorbed as much as possible, i.e., this should emit energy in all chemical absorption bands; (2) the emitted power should be absorbed only by the gas of interest to avoid false positives, i.e., the FWHM of the target spectrum cannot be made substantially wider than the gas spectrum. Since the emitted power depends on temperature, this concept is generalized by matching the Tamm plasmon polariton emitter to the chemical absorption spectrum. An example for nitric oxide non-dispersive infrared gas sensing is described in FIG. 10. This molecule has various FWHMs and 800 - 2,400 cm -1Characterized by a plurality of arbitrarily distributed absorption bands having an amplitude therebetween, making forward design approaches unrealistic. However, the inverse design algorithm herein provides an optimized Tamm plasmon polariton emitter structure having a designed spectrum that closely matches the spectral position, amplitude, and FWHM of the target spectral peak, and unwanted additional modes are significantly suppressed (FIG. 10). The same approach is applied to non-dispersive infrared sensing of greenhouse gases such as CO, O3, NH3, and CH4, as shown in FIGS. 48-51. Additionally, the shape of the blackbody emission can be inverse convolved in the design process so as to match an arbitrarily shaped target spectrum with the emitted power rather than the emissivity, which is illustrated for N2O non-dispersive infrared sensing at an operating temperature of 250° C. (FIGS. 52-53). None of the designs in FIGS. 7-10 have been previously proposed because user-defined control of FWHM and amplitude at single / multiple frequencies is not realistic within conventional forward design approaches. Thus, the design capabilities highlighted herein facilitate applications based on free space communication, spectral barcoding, multi-band chemical sensing at high signal-to-noise ratios for highly selective non-dispersive infrared, or wavelength-selective thermal emitters for alternative gas sensing measurements.

[0143] CdO as a component enabling the inventors' Tamm plasmon polariton emitter. To date, exceptional design freedoms presented by an inverse design approach for prescribing the emission rate and / or spectral emitted power of Tamm plasmon polariton emitter devices have been demonstrated. The deterministic design capabilities benefit from two aspects: the use of an aperiodic distributed Bragg reflector optimized by a stochastic gradient descent method and In-doped CdO with a designable dielectric function. This is an aperiodic distributed Bragg reflector that utilizes control over the photonic band structure, and the designable dielectric function of CdO improves this spectral control to an unprecedented level, enabling more advanced designs. To illustrate this point, an algorithm based on the stochastic gradient descent method was used to design CdO-based and gold-based Tamm plasmon polariton emitters to match the absorption spectrum of dimethyl methylphosphonate, a nerve agent mimic for highly sensitive gas detection. The relevant detailed optimization is discussed in Section S18. Here, an exceptional match is achieved between the target spectrum, including spectral position, line shape, and even amplitude, and the CdO-based Tamm plasmon polariton emitter design spectrum (Figure 11). However, in the case of the gold-based structure, the absorption spectra cannot be well matched (Figure 11, blue line). This increased spectral control is due to the designable plasma frequency of CdO.

[0144] To develop the underlying advantages presented by CdO, different plasma frequencies, namely, 2,700 cm -1 (red dashed curve; Figure 12) and 4,300 cm -1A plurality of Tamm plasmon polariton emitters composed of the same distributed Bragg reflector grown simultaneously on a plurality of CdO layers, characterized by (a red solid curve; FIG. 12), were fabricated. Both samples feature the same distributed Bragg reflector structure, but different dielectric functions (carrier concentrations) of CdO result in a distinction between the impedance models of the two systems (Section S19). This leads to significant differences in the emission spectra, e.g., in frequency and amplitude. Thus, an adjustable carrier concentration can regulate the Tamm plasmon polariton mode and the non-Tamm plasmon polariton mode, and thus can match a more arbitrarily shaped spectrum than can be achieved with a fixed carrier density. A series of comparisons were further carried out between inversely designed Tamm plasmon polariton emitters with CdO characterized by a fixed carrier concentration and / or mobility (Section S20), verifying that an adjustable dielectric function provides the spectral control necessary for complete user design of the emission spectrum amplitude, linewidth, and resonance frequency. The loss of CdO (mobility) affects the Tamm plasmon polariton emitter (Brand S et al. Phys. Rev. B 2009, 79, 085416; Morozov KM et al. Sci. Rep. 2019, 9, 9604; Kaliteevski MA et al. Plasmonics 2015, 10, 281 - 284), but the codes and platforms herein can mitigate the effect of this loss by correcting the corresponding carrier density (Section S20). Thus, the wide tunability of the CdO plasma frequency increases the design capabilities of Tamm plasmon polariton emitters to a level unprecedented compared to conventional noble-metal-based Tamm plasmon polariton emitters. In addition to spectral control, replacing noble metals with n-type In-doped CdO makes the manufacturing process CMOS-compatible and potentially enables integrated applications. In particular, this approach can also be applied to other doped materials such as III-V semiconductors and other transparent conductive oxides (Bikbaev RG et al. J. Opt. Soc. Am. B 2019, 36, 2817 - 2823).

[0145] Conclusion. As a conclusion, the combination of the widely tunable plasma frequency of CdO and the efficient gradient descent-based inverse design enables the deterministic design of numerically and experimentally verified Tamm plasmon polariton emitters. Using the gradient descent method, the structure of the Tamm plasmon polariton emitter can be efficiently optimized for any target spectrum (in a few minutes on a consumer-grade desktop). With this method, single- and multi-band Tamm plasmon polariton emitters suitable for a wide range of applications (including free-space communication, infrared beacons, and single and multiple gas filterless non-dispersive infrared sensing) were experimentally demonstrated, all showing a great agreement between experiment and simulation. Importantly, the demonstration of multiple peaks opens up the possibility of sensing multiple gases and single gases with multiple vibrational bands that cannot be achieved with single filters, compact non-dispersive infrared blackbody-based devices. Furthermore, the unprecedented ability to match the target spectrum, i.e., frequency, FWHM, and even amplitude (emissivity or spectral irradiance), is shown by exemplifying several designs in the range from long-wave infrared to the telecommunication band (1.55 μm), including isolated emissions at desired frequencies with user-defined Q factors (28 - 10,117), multiple-peak emissions for spectral barcodes, and non-dispersive infrared for matching complex gas absorption spectra. Such a wide range of functionality is not inherent to the Tamm plasmon polariton emitter; instead, this is made possible by the wide tunability of the CdO plasma frequency. Enhanced by the gradient descent algorithm and this tunability, the demonstrated spectral control of the Tamm plasmon polariton emitter promises a high-cost-effective, wafer-scale, CMOS-compatible, and lithography-free solution for many applications across the infrared.

[0146] Method Manufacture of the device. In-doped CdO (n-type) was deposited on a 2-inch r-plane (012) sapphire single crystal substrate at 400 °C by a reactive co-sputtering process using high-power impulse magnetron sputtering and radio frequency sputtering from metal cadmium and indium targets with a diameter of 2 inches each. The high-power impulse magnetron sputtering driving conditions were a frequency of 800 Hz and a pulse time of 80 μs, resulting in a period of 1,250 μs and a duty cycle of 6.4%. Film growth occurred at a total pressure of 10 mtorr in an environment of mixed argon (20 sccm) and oxygen (14.4 sccm). After deposition, the sample was annealed in a static oxygen atmosphere at 635 °C for 30 minutes.

[0147] The dielectric stack (Ge and AlO x ) was deposited at ambient temperature from Ge (99.999%) and a sapphire source using electron beam evaporation in a vacuum. The thickness was monitored throughout the deposition using a quartz crystal microbalance. After deposition, the sample was cut and the layer thickness was measured using a cross-sectional scanning electron microscope.

[0148] Thermal emission measurement. All thermal emissions were measured at a normal incidence angle. Thermal emissions were measured using a Bruker VERTEX 70v Fourier transform infrared (FTIR) spectrometer by placing the device on a vertical temperature controller located at the back port of the Fourier transform infrared spectrometer. The emission from the sample was then induced and collected through a KBr window into the internal beam path of the Fourier transform infrared spectrometer. In this configuration, the emitted signal passes through the interferometer block instead of the internal broadband source of the off spectrometer. An aperture was placed in the sample compartment to limit the solid angle detected from the device and reduce the emission detected from within the Fourier transform infrared spectrometer. The signal was measured using an IR Labs cadmium telluride mercury detector. To calculate the emissivity, thermal emission measurements were collected from the inventors' device at 150 °C. These measurements were then compared to the thermal emissions measured from an emissivity standard at the same temperature and emission angle. Emissivity standard

Number

[0149] M(T サンプル 、T 周囲 、λ、θ)=R(T 周囲 、λ)(S(T サンプル 、λ、θ)+G(T 周囲 、λ))(3) Here, M is the total measurement signal, R is the response function of the internal and external optics, S is the signal from the sample, G is the "background" emission from the internal optics, θ is the measured emission angle, λ is the corresponding wavelength, T 周囲 is the ambient temperature, and T サンプル is the sample temperature. Therefore, to separate the signal from the sample, background measurements were taken by replacing the sample with a gold mirror. The resulting spectrum is the product of the response function R with the background emission G. Once the sample, emissivity standard, and background emission have been measured, Equation (3) can be rearranged: R(T 周囲 、λ)S サンプル (T サンプル、 λ、θ)=M サンプル (T サンプル 、T 周囲 、λ、θ)-R(T 周囲 、λ)G(T 周囲 、λ)(4) R(T 周囲 、λ)S 標準 (T サンプル 、λ、θ)=M 標準(T サンプル 、T 周囲 、λ, θ)-R(T 周囲 、λ)G(T 周囲 、λ)(5) wherein, M 標準 and S 標準 are, respectively, the total measurement signal and the signal derived from the standard blackbody (VACNT). By taking the ratio of equations (4) and (5), the response function can be normalized and the emissivity with respect to the standard can be determined.

Equation

[0150] It should be noted that this technique is much faster than the conventional approach of measuring emissivity using Fourier transform infrared spectroscopy and enables multiple background measurements throughout the day. Therefore, fluctuations in the ambient temperature can be easily taken into account.

[0151] Numerical calculation of the Tamm plasmon polariton emitter. The calculation of the transfer matrix method used in the inverse design is from a textbook. Since the materials are absorptive and dispersive, the calculation of the transfer matrix method implemented in this specification is from the literature for cross-validation purposes (Passler NC et al. J. Opt. Soc. Am. B 2017, 34, 2128 - 2139; Passler NC et al. Phys. Rev. B 2020, 101, 165425). Ge and AlO xThe dielectric function is fitted by ellipsometry measurements with the WVase software from J.A. Woollam (Li HH. J. Phys. Chem. Ref. Data 1980, 9, 561 - 658), and the temperature - dependent values are adjusted with reflectivity data (Section S5). Dielectric function models of CdO with various carrier concentrations are from the literature (Nolen JR et al. Phys. Rev. Mater. 2020, 4, 025202), and the corresponding MATLAB (registered trademark) code for generating the CdO dielectric function in the mid - to long - wave infrared is posted on the website (https: / / my.vanderbilt.edu / caldwellgroup / ). The Outlook section treats the dielectric functions of Ge (Burnett JH et al. SPIE 2016, 9974, 99740X) and ZnSe (Gao W. SPIE 2009, 7283, 72832L) as constants over the entire frequency range: 16 + 0i and 5.0625 + 0i, respectively.

[0152] The computational resources used in the algorithm. All optimizations were performed on a consumer - grade desktop with an Intel I7 - 8700K CPU (which cost approximately $400 US dollars when first released in 2017) and 16GB of memory, and no GPU units were used. The algorithm is written in Python 3.6 using TensorFlow 2.3.0. The specific version of the stochastic gradient descent method used is the Adaptive Moment Estimation (Adam) provided by TensorFlow, and the optimization step is 0.005. All optimizations performed in this paper took approximately 1 - 10 minutes. The code is open - sourced online (https: / / my.vanderbilt.edu / caldwellgroup / ) and can be freely used for non - profit purposes.

[0153] Absorption data for various chemical substances. All chemical absorption spectra are obtained from the website of the National Institute of Standards and Technology.

[0154] Section S1. Highly customized errors for special designs. In the above description, it was mentioned that the error is written as a combination of terms: mean squared error (MSE, the first term) and mean absolute error (MAE, the second term):

Number

[0155] In the case shown in Figure 9, long-wave infrared (1100~1300 cm -1 ), mid-wave infrared (2600~2800 cm -1) and only three discrete frequency ranges in the telecommunications (1.5 - 1.6 μm) band are optimized, so that a single Tamm plasmon polariton emitter operating in such a dramatically wide frequency range can be realized. The spectrum of this device over the entire range is shown in FIG. 13. In a commercially designed scenario, such a technique can be used to specifically optimize frequency ranges where bandpass filters are not available or are prohibitively costly.

[0156] Still, in the case shown in FIG. 9, since performance in the telecommunications band was assumed to be more important than long-wave infrared, the former was sampled at a higher density: in the telecommunications band, there was one frequency point every 0.5 cm -1 whereas, in the long-wave infrared and mid-wave infrared, there was only one every 2 cm. -1 This is extremely important because trade-offs are inevitable in product design, and the algorithm quantifies this trade-off and "prioritizes" a certain range as defined by human intervention.

[0157] Section S2. Advantage of the Stochastic Gradient Descent method in the Tamm plasmon polariton emitter design. In the optimization process, each frequency (wavelength) point is considered as an individual sample, and the absorption rate at that frequency is compared with the target value. In the normal Gradient Descent (GD) method, the differences across the entire data distribution are calculated, summed together to obtain the gradient, and all parameters are evaluated with the same computational complexity. In the Stochastic Gradient Descent (SGD) method, in each iteration, only a subsample of the data points is used to obtain the gradient and update the vectors representing thickness and carrier concentration. The selected portion is randomly chosen from the entire collection of data points, and thus the algorithm is known as the "stochastic" gradient descent method (SGD) (Robbins H et al. The Annals Of Mathematical Statistics, 1951, 400 - 407; Bordes A et al. Journal of Machine Learning Research, 2009, 10, 1737 - 1754; Sohl-Dickstein J et al. PMLR, 2014, 32(2), 604 - 612; Kingma DP et al. arXiv, 2014, arXiv:1412.6980). The specific version used in this specification is the Adaptive Moment Estimation (Adam) optimization (Kingma DP et al. arXiv, 2014, arXiv:1412.6980). Exemplary code is publicly available online (Xiong Y et al. Applied Physics Letters 2009, 94, 203108). In deep learning, the Stochastic Gradient Descent method is considered to outperform the normal Gradient Descent method and avoid low local minima (Robbins H et al. The Annals Of Mathematical Statistics, 1951, 400 - 407; Bordes A et al. Journal of Machine Learning Research, 2009, 10, 1737 - 1754; Sohl-Dickstein J et al. PMLR, 2014, 32(2), 604 - 612; Kingma DP et al. arXiv, 2014, arXiv:1412.6980).

[0158] Here, to demonstrate that stochastic gradient descent provides better optimization than normal gradient descent, a series of optimizations were performed on the same target: matching the DMMP neuroagent and evaluating performance based on the mean squared difference error (MSE). With stochastic gradient descent, the overall error is significantly lower than the optimization performed with normal gradient descent. Within 20 optimization runs, the minimum error with stochastic gradient descent is approximately 40, while for normal gradient descent this value is approximately 70 (Figure 14). To visualize any unit of "error", design spectra with different errors were plotted against the target spectrum (Figures 15 - 17). The main feature is that they match for errors less than 100 (Figure 15), but designs with higher errors lose one or more of the main absorption peaks.

[0159] Section S3. Comparison between different design strategies. There are several strategies proposed and applied in the literature for designing Tamm plasmon polariton emitters. Here, their advantages and limitations are summarized in Table 1. The algorithms disclosed herein provide balanced optimization performance, i.e., high efficiency and high precision. The code has been open-sourced and can be downloaded online (https: / / my.vanderbilt.edu / caldwellgroup / ).

[0160] Section S4. Thickness and photographs of samples. The layer thickness of the grown samples was characterized by cross-sectional SEM (XSEM). The designed and as-grown layer thicknesses are listed in Table 2, and the carrier density (N d ) of CdO is also listed. One exemplary XSEM (Figure 6) of a 7-layer sample designed to emit at three specific different resonance frequencies is described in Figure 18. One wafer-scale Tamm plasmon polariton emitter device is shown in Figure 19.

Table 1

Table 2

[0161] Section S5. Dielectric function fitting of the materials used: CdO, Ge, and AlO x The fitting of the dielectric function of CdO has been studied previously (Nolen JR et al. Physical Review Materials 2020, 4, 025202). In this study, the dielectric function and carrier concentration of CdO were determined following the same process. Both the exemplary listed dielectric function and the MATLAB® script for generating the dielectric function of CdO with a user - defined carrier concentration from 1000 to 5000 cm -1 are downloadable online (https: / / my.vanderbilt.edu / caldwellgroup / ). This MATLAB® script is also integrated into the inverse design code (which is open - sourced and downloadable from https: / / my.vanderbilt.edu / caldwellgroup / ).

[0162] As-grown Ge and AlO x The dielectric functions of x were extracted using IR-VASE ellipsometry measurements as shown in FIGS. 20-23. The fitting was performed with WVase software from J.A.Woolam, Inc (Li HH. Journal of Physical and Chemical Reference Data, 1980, 9, 561-658).

[0163] Based on the literature, it was assumed that the thermal expansion of each component could be ignored (<0.1%) at operating temperatures below 300 °C (Kagaya HM et al. Physica Status Solidi (B), 1985, 129, K5-K8). Based on the results of the literature (De Silans TP et al. Journal of Physics: Condensed Matter 2009, 21, 255902), the dielectric function of AlO x was assumed to remain constant over temperature. The dielectric constant of Ge at 150 °C was modeled based on measurements at high temperature by varying the high-frequency dielectric constant. At 150 °C, the high-frequency dielectric constant was determined to be 0.5 higher than at room temperature (FIGS. 24-25), which was consistent with the results of the literature (Li HH. Journal of Physical and Chemical Reference Data, 1980, 9, 561-658).

[0164] Section S6. Achievable complexity of spectra with different numbers of layers. In this document, the achievable complexity of Tamm plasmon polariton emitters with a defined number of dielectric layers is discussed. The complexity of the spectra is not fully quantifiable and is application-specific, and three cases are used: (1) Given frequencies (2350 cm in this document) using dielectric stacks of 3, 5, 7, 9, and 11 layers -1Determining the achievable Q factor in (1), calculating the most closely matched spectrum achievable for the tasks shown in FIG. 6 (triple peak design), limited to dielectric stacks of 3, 5, 7, 9, and 11 layers in (2), and repeating this process to match a complex spectrum, i.e., DMMP, but using 7, 11, 19, and 29 dielectric layers in (3). In this section, the dielectric materials used are Ge and ZnSe, and the permittivity values are 16 + 0i and 5.25 + 0i.

[0165] From this set of comparisons, it was concluded that references to more complex spectra, i.e., Q factor and number of peaks, can be achieved by increasing the number of dielectric layers in the stack (FIGS. 26, 28). Note that for a given application, i.e., a multi-peak design with a required Q factor, more dielectric stacks do not guarantee better results. For the task in FIG. 27, using more than 9 dielectric layers does not result in significantly better results even if it is found that the "error" is reduced, and the difference in spectrum matching is negligible.

[0166] In summary, with more layers, more complex spectra can be matched, and if the target spectrum can be achieved with a given number of dielectric stack layers, increasing this does not provide further significant additional benefits. For experimentally verified structures, the design is initiated by determining whether optimization is achievable with three dielectric layers, and if so, this is the case in FIGS. 3 and 4 and is used to minimize potential errors in layer thickness. If the function is not achievable through three dielectric stacks, an attempt is made by increasing the number of layers until a suitable match is found.

[0167] Section S7. Non-dispersive infrared operating principle. Conventional non-dispersive infrared sensors comprise a gas cell including a broadband emitter and a broadband detector integrated with a narrow bandpass filter that is transmissive at the vibration frequency of the analyte of interest (FIG. 29). The presence of the gas of interest within the cell results in a detected reduction in transmission, and the difference in amplitude is related to the molecular concentration according to Beer's law. Due to their simple design and small footprint, these sensors are generally implemented in industrial scenarios, but they suffer from inherent inefficiencies as off-resonance emissions from the broadband emitter are not utilized and filtering is required. Thus, there has been great interest in improving the design of non-dispersive infrared sensors and expanding their functionality by combining the functions of the emitter and the bandpass filter into a single device. The approach to filterless non-dispersive infrared devices consists of several iterations, as shown in FIG. 30, of (1) a wavelength-selective thermal emitter, (2) a gas cell, and (3) a broadband detector such as a thermopile. The emission frequency of the wavelength-selective thermal emitter is typically centered around the absorption frequency of the gas of interest having a sufficiently high Q factor so as to eliminate false negatives that would result from non-negligible absorption from other gases that may be present. Usually, there are two detectors, one as shown in FIGS. 29-30 and the other for measuring the power with a reference gas, such as nitrogen, so as to obtain a power difference.

[0168] Section S8. Theoretical basis for the target spectra in FIGS. 5 and 6. In FIG. 5, a Tamm plasmon polariton emitter for dual gas sensing was also demonstrated. The target is to simultaneously match the absorption characteristics of SO2 and CO2 absorption. To determine the target spectrum for designing this device, absorption spectra of SO2 and CO2 were taken from the National Institute of Standards and Technology (NIST) and the two main absorption peaks of SO2 and CO2 were covered using the envelope spectrum (FIG. 31). A number of gases, such as CH4, are in the range of 1000-1500 cm -1has an absorption band in the spectral range, and heat release brings more energy in a lower frequency range, 1380 cm -1 The target spectrum at -1 is set sharper (20 cm -1 FWHM) to reduce the energy released for compensation. The FWHM at 2360 cm -1 , which is the absorption peak of CO2, is set larger (50 cm -1 ) to compensate for the low emission power defined by Planck's law. The frequency range is set between 1000 cm -1 and 2500 cm -1 . Since the loss of AlO x is difficult to predict, especially at high temperatures, the spectrum below 1000 cm -1 was not attempted to match, but it is important to note that emissions at lower energies can be removed very efficiently through a long-pass filter. Since the emitted power drops significantly below this value for the proposed operating temperature as defined by Planck's law, and thus higher frequencies can be considered negligible, the high frequency is set at 2500 cm -1 .

[0169] Also, using the same theoretical basis, the target spectra for dual-gas sensing of CO and formaldehyde were created (Figure 32). The target spectra have an increasing FWHM with increasing frequency: for the peaks at 1750, 2150, and 2800 cm -1 , 20, 30, and 40 cm -1 .

[0170] Section S9. Discrimination of CO2 and SO2 with a single Tamm plasmon polariton emitter by linear regression. Since the emitted power is affected by the operating temperature, such differences can be used to find the concentrations of CO2 and SO2 by linear regression. The absorbed power of one gas can be described as follows:

Equation

[0171] When there are multiple gas types (in this specification, for example, CO2 and SO2), the absorption spectrum is extended to a matrix, and different rows represent different gas types. Therefore, there are two unknown variables [1×2], that is, [Number] which represent the concentrations of CO2 and SO2 respectively. Then, the power change read by the detector is as follows: [Number] In the formula, [Absorption spectra of CO2 and SO2] are [2×N] matrices representing the absorption rates of CO2 and SO2 respectively, and × represents matrix multiplication. In formula (S4), [Absorption spectra of CO2 and SO2] are pre-calibrated, and [Power emitted by EM] is the measured power of the wavelength-selective thermal emitter before being assembled with non-dispersive infrared rays.

Number

Number

[0172] Example of distinguishing CO2 and SO2 with the Tamm plasmon polariton emitter in Fig. 5. In the case of distinguishing CO2 and SO2 with the emitter in Fig. 5, the system has two separated frequency points 1380 and 2360 cm -1 which are the only two emission peaks of the Tamm plasmon polariton emitter, so it can be simplified by considering only these. Therefore, the emissivity vector is [0.6 1.0]. At 100, 150, 200, 250 °C, the power (W / m 2 / sr / cm -1 ) emitted by the blackbody is as follows:

Number

Number

[0173] Why a wavelength - selective thermal emitter instead of a black - body emitter? In the above discussion, it seems that any emitter type, even a black - body, can perform the above calculations, which is true when there is no noise and only CO2 and SO2 are present. However, other gases such as water vapor are present in the environment, and thus, in the case of a black - body emitter, changes in moisture and / or other atmospheric gases result in corresponding power changes and false positives. However, since the Tamm plasmon polariton emitter does not emit power within the water absorption band, the selectivity is significantly improved.

[0174] Section S10. Dielectric material thickness error analysis. In this specification, we discuss the influence of thickness error, i.e., how the results are affected when the thickness cannot be accurately controlled experimentally. Generally, different combinations of layer - thickness mismatches can lead to different results: as shown in FIGS. 33 - 36, (1) shifting the resonance frequency (cases 2, 3); (2) broadening / sharpening the resonance linewidth (cases 1, 4); (3) affecting the resonance amplitude(s) (cases 1, 2, 3, 4); and (4) removing the resonance (case 1). Here, the designed layer thickness for the device shown in FIG. 5 varied with some results.

[0175] The original design is [389 797 494 310 494] (layer thickness from top to bottom, starting with Ge and ending with Ge), and the CdO carrier concentration is 3.6e+20 cm -3 The following bold and italicized numbers indicate that the corresponding layer thickness is different from the original design.

[0176] In Case 1, the calculation is

Number

Number

Number

Number

[0177] Section S11. Peak analysis of the device in Figure 6. Table 3 provides a peak analysis of the target spectrum, the designed spectrum, and the experimental structure for the designed Tamm plasmon polariton emitter from Figure 6.

Table 3

[0178] Note that the Q factor of these peaks is about 100, equivalent to the highest reported values for isolated nanophotonic resonators using lower-loss surface phonon polariton resonators (about 100 - 400) (Wang T et al. ACS Photonics, 2017, 4, 1753 - 1760; Caldwell JD et al. Nature Communications 2014, 5, 5221; Caldwell JD et al. Nano Letters, 2013, 13, 3690 - 3697; Tamagnone M et al. arXiv, 2019, arXiv:1905.02177; Autore M et al. Light: Science & Applications, 2018, 7, 17172) and plasmonic Fano structures (about 100 - 400) (Wang B et al. Advanced Optical Materials, 2021, 2001520). The possible Q factor of the Tamm plasmon polariton emitter is related to the number of dielectric layers used (Section S6).

[0179] Section S12. Evaluation of the theoretical detection limit in a non-dispersive infrared scheme. In a non-dispersive infrared device, the power emitted from the emitter (EM) propagates through the gas cell and reaches the detector. When the gas cell is filled with a reference gas, e.g., nitrogen, the power reading at the detector is as follows: Reference signal = Emissivity of EM × Blackbody emissivity × Area of EM × Solid angle (S5)

[0180] Generally, the performance and power of the sensor strongly depend on the collection optics, but some approximations can be made based on the geometry of commercial sensors. Here, it is assumed that the emitter is a circle with a diameter of 2 cm and the detector is also 2 cm in diameter. The optical path length of the gas cell is 10 cm, which is a typical design (https: / / www.edmundoptics.com / f / infrared-ir-bandpass-filters / 14290 / ) and 2.2×10 -4results in a solid angle of sr. The gas absorption rate is determined by the Beer-Lambert law: Transmittance in CO2 = exp(-kcL) (S6) where k is the absorption coefficient, c is the gas concentration, and L is the optical path length of the sample. The absorption spectra of CO2, CO, SO2, and formaldehyde at a given concentration and a specific length of the gas cell were obtained or estimated from the literature and NIST (Naganathappa M et al. Astrophysics and Space Science, 2011, 332, 249-256; Dong M et al. Infrared Physics & Technology 2017, 85, 450-456; Livingood A et al. ACS Photonics. 2021, 8(2), 472-480). Therefore, the transmittance (equivalent to the absorption rate) of CO2 at any concentration could be calculated. The reference power, for example, the power received by the detector when the gas cell is filled with nitrogen, can be calculated by Equation (S6). When the reference power and the CO2 transmittance for a given concentration are known, the power collected by the detector when CO2 is present is as follows: Power detected in chemical substance = Reference signal × Transmittance in CO2 (S7)

[0181] To determine the detection limit of a virtual filterless non-dispersive infrared device equipped with one of the Tamm plasmon polariton emitters, a commercial coin-sized pyroelectric detector with a responsivity of 150,000 V / W and an estimated noise of 180 μV at 10 Hz (Asano T et al. Science Advances 2016, 2, e1600499) was assumed. For the device in Fig. 4, the operating temperature was first set to 600 °C, which is a typical design setting. At such an operating temperature, when the difference between the reference signal and the detection power with the chemical substance is 3σ (a signal-to-noise ratio of 3:1), i.e., when the voltage difference is 540 μV, the CO2 concentration is 0.5 ppm. Therefore, the detection limit is determined to be 0.5 ppm. Next, this calculation was repeated for the device in Fig. 5, resulting in a CO2 (SO2) concentration detection limit of 0.5 (3.3) ppm. For comparison, this calculation was also performed for a conventional non-dispersive infrared design, i.e., assuming the same detector and gas cell, but using a blackbody emitter of the same size combined with a band-pass filter designed for CO2 gas sensing (Granier CH et al. JOSA B 2014, 31, 1316-1321). Here, the obtained CO2 concentration detection limit is also 0.5 ppm. For comparison, a commercial CO2 non-dispersive infrared detector has a detection limit of 8 ppm (Howes A et al. Advanced Optical Materials 2020, 8, 1901470). Despite the imperfect distributed Bragg reflector growth technology, the Tamm plasmon polariton emitter enabled a filterless non-dispersive infrared sensor that still has the same performance for single-gas sensing as the conventional blackbody / filter design while allowing for multi-gas sensing.

[0182] Based on the same assumptions, the performance of the triple-peak design is evaluated and the benefits of such a multi-peak emitter are discussed. One obvious point that has been discussed is the ability to sense multiple gases simultaneously. Another advantage is the improved sensitivity, i.e., the reduced detection limit. In the device of Figure 6, the detection limit of formaldehyde is 1.4 ppm. However, for a blackbody emitter with a band-pass filter centered at 2750 cm -1 having a Q factor of 90, the detection limit is 3.1 ppm.

[0183] The power consumption of these light sources based on the emitted power was also estimated. The power consumption of a non-dispersive infrared light source is due to heat conduction, heat convection, and the emitted power (the emissivity multiplied by the blackbody emissivity). Conduction and convection can be reduced by using thermally insulating materials and evacuating the emitter environment, but the emitted power is basically defined by the emissivity and the temperature. Therefore, the power consumption was estimated based on the emitted power to be as low as possible, and the value for a blackbody at 600 °C is 1.03 W, while the power consumption of the wavelength-selective Tamm plasmon polariton emitter is only about 0.1 W. The comparison is summarized in Table 4.

Table 4

[0184] In summary, the multi-peak design offers several advantages compared to conventional non-dispersive infrared with a single-band filter: (1) enabling multi-gas sensing, (2) improving sensitivity when multiple absorption bands of one chemical substance coincide, and (3) reducing power consumption. The single-peak Tamm plasmon polariton emitter provides approximately the same sensitivity as conventional non-dispersive infrared, but the power consumption and potential design complexity will be significantly reduced. In particular, with current commercial filters, dual-peak and multi-peak designs cannot be achieved with a single filter (Table 5).

Table 5

[0185] Since CO, SO2, and formaldehyde are all highly toxic gases, gas sensing measurements could not be experimentally performed using a multi-band emitter, but it was verified that a single-peak Tamm plasmon polariton emitter provides nearly the same sensitivity as the conventional non-dispersive infrared approach using a conventional blackbody emitter. In this benchmark experiment, first, the non-dispersive infrared response as a function of CO2 concentration was experimentally measured using a blackbody emitter (vertically aligned carbon nanotubes herein, ε ≈ 0.97) and a commercial CO2 filter (central wavelength of 4.26 um, bandwidth of 105 nm) as shown in FIG. 37. A broadband pyroelectric detector (RM9 with chopper) having a 10 Hz chopper wheel was used. The gas cell was first purged with dry nitrogen gas and then purged with 5% and 1% CO2, respectively. Before and after the gas cell was filled with a specific concentration of CO2, it was purged with dry nitrogen. This measurement was repeated using the Tamm plasmon polariton emitter device shown in FIG. 4 and then again using the device of FIG. 5. These results are listed in Table 6. The Tamm plasmon polariton emitter was found to result in greater power fluctuations than a combination of a CO2 filter (Q = 42) and a blackbody emitter, arising from a broader linewidth (Q = 20 and 36) of the Tamm plasmon polariton emitter peak and a nearly single emissivity at the resonance frequency. Thus, the proposed Tamm plasmon polariton emitter functions similarly to a blackbody emitter combined with a narrowband pass filter when only one absorption peak of a certain type of gas coincides. When more bands are integrated, it is possible to enable either multi-gas sensing (device of FIG. 5) or enhanced sensitivity (device of FIG. 6) by matching the absorption rates of multiple vibrational or rotational modes of the target molecule using additional emission frequencies. Unfortunately, this concept could not be experimentally demonstrated because the gases for which multiple Tamm plasmon polariton emissions were designed are highly toxic.

Table 6

[0186] Section S13. Measurement of heat release at various angles. The angular spread of the Tamm plasmon polariton emitter is limited to a small range, and the TM (transverse magnetic) polarization is typically slightly more dispersive than the TE (transverse electric) polarization (Liu X et al. Nanoscale 2019, 11, 19742 - 19750; Kaliteevski M et al. Physical Review B 2007, 76, 165415). Here, the emissivities of the samples in FIGS. 5 and 6 at different angles and polarizations are shown in FIGS. 38 - 41.

[0187] Section S14. Designed structures for the inverse - designed Tamm plasmon polariton emitter. Here, the parameters of the designed structures in FIGS. 7 - 10, FIG. 11, FIGS. 48 - 51, and FIG. 53 are provided. All designs had a 29 - layer distributed Bragg reflector on top of a CdO double - layer with Ge as the first and last layers of the distributed Bragg reflector. The CdO carrier concentration was constrained between 0.2 and 12.0e+20 cm -3 as demonstrated in the literature (Nolen JR et al. Physical Review Materials 2020, 4, 025202; Liu CP et al. Physical Review Applied 2016, 6, 064018). Using the published model, the dielectric function of CdO as a function of carrier density was calculated (Nolen JR et al. Physical Review Materials 2020, 4, 025202), and the corresponding MATLAB® code is publicly available online (https: / / my.vanderbilt.edu / caldwellgroup / ). The dielectric functions of Ge (Burnett JH et al. SPIE 2016, 9974, 99740X) and ZnSe (Gao W. SPIE 2009, 7283, 72832L) were considered as constants over the entire frequency range: 16 + 0i and 5.0625 + 0i, respectively. The substrate was 12.0×10 20 cm -3(Plasma frequency = 7800 cm -1 ) is fixed to CdO at the carrier concentration, so that transmission is surely eliminated. All units are in nanometers.

Table 7

Table 8

Table 9

Table 10

Table 11

Table 12

Table 13

Table 14

Table 15

Table 16

Table 17

[0188] Section S15. Optimized Tamm plasmon polariton emitters within different frequency ranges. Here, we discuss how the "optimization frequency range" affects the results. Since the frequency range to be optimized is wider, the design becomes more difficult due to the multi-mode characteristics of the distributed Bragg reflector (Figure 13). Here, one case is exemplified: the design for the same task shown in Figure 6, having 11 dielectric layers with different frequency ranges integrated for the optimization routine. The three peaks remain the same, and the aim is to maintain the absorption (emissivity) as zero outside these three main peaks. From Figures 44 to 47, the optimization frequency range is gradually increasing. The algorithm can sufficiently suppress the side peaks, but at the expense of the performance for the main peaks. Depending on the application, a specific frequency range of interest can be optimized. For example, in free-space communication, since the energy is attenuated through spatial propagation, the performance of the wavelength-selective thermal emitter within the water absorption band can be ignored. The frequency points can also be sampled more densely so that the algorithm focuses on the frequency of interest (Section S1), and a similar balance can be achieved through a weighted error function.

[0189] Section S16. Further demonstration of the inverse-designed Tamm plasmon polariton emitter. Several additional Tamm plasmon polariton emitter designs have been demonstrated, such as those that match the infrared active vibration spectra of nitric oxide (NO) and dimethyl methylphosphonate (DMMP), a nerve agent simulant. Here, additional examples are described in Figures 48 to 51. Note that the absorption spectra of O3, CH4, and NH3 are characterized by slopes or many sharp peaks, so an exact match to the spectra cannot be achieved. Instead, the envelope spectra were used to cover their chemical spectra, and then these envelope spectra were used as the target spectra (TS). All the chemical absorption spectra are from the website of the National Institute of Standards and Technology (NIST).

[0190] Section S17. Emitted power matching the N2O absorption spectrum. Since the emitted power is determined by both the emissivity and temperature of the object, a Tamm plasmon polariton emitter operating at 250 °C used for N2O non-dispersive infrared sensing was designed. First, the operating temperature was determined to be 250 °C, and this value can be adjusted according to commercial product design based on signal intensity and power consumption. Next, the target emissivity spectrum is as follows: [Number] Here, the normalization is performed to ensure that the maximum emissivity is single. The background absorption of N2O was also removed. Therefore, the emissivity was adjusted to a specific operating temperature as shown in FIGS. 52 to 53.

[0191] Section S18. Optimization of Tamm plasmon polariton emitter with gold and CdO. Also, the inverse design based on the stochastic gradient descent method was performed using the same constraints for the total number of dielectric layers (29 layers) in both cases of CdO and gold as the bottom conductive layer. Each optimization was performed 20 times to ensure that no local minimum values were reported. These errors are shown in FIG. 54, and these structures exhibit the lowest error values reported in FIG. 11.

[0192] Section S19. Mechanism of Tamm plasmon polariton emitter. Generally speaking, the absorption resonances supported by the Tamm plasmon polariton emitter structure are classified into two categories: Tamm mode (cavity mode between a distributed Bragg reflector mirror and a conductive substrate) and non-Tamm mode (light transmitted from a distributed Bragg reflector absorbed by a conductor). In the case of the Tamm plasmon polariton mode existing within the photonic bandgap of the distributed Bragg reflector, the reflection phases of the two mirrors (along opposite directions) must be equivalent but have different signs (φ1 + φ2 = 0). In this specification, AlOx A metal-on-bottom distributed Bragg reflector - metal geometry in which alternating layers of Ge and CdO are grown on top of a doped CdO film was utilized. Since the Tamm plasmon polariton mode is supported by the phase matching condition between the conductor and the distributed Bragg reflector, by calculating the Fresnel reflection coefficients directed towards the distributed Bragg reflector and the conductor, it is possible to determine whether the Tamm plasmon polariton mode is supported at the conductor-distributed Bragg reflector interface. There are several techniques for calculating the reflection coefficients of multilayer structures, such as the transfer matrix method used in inverse design calculations. However, for this simple model, an impedance model is used because this method is conceptually intuitive due to its connection to circuit theory. Furthermore, through a lumped element model approach, this analysis can be extended to Tamm plasmon polariton supporting films characterized by metasurfaces instead of unstructured conductive films.

[0193] Complex dielectric function ε n The characteristic p-polarized impedance in a material having it is given as follows

Number

Number

[0194] Here, using the calculated characteristic impedance of each material, the total lumped impedance of the distributed Bragg reflector and the conductive film can be calculated. FIG. 57 shows an equivalent circuit model representation of the Tamm plasmon polariton film in a conductor-on-bottom geometry. To calculate the lumped impedance of the distributed Bragg reflector, starting from the dielectric layer farthest from the CdO distributed Bragg reflector interface, the impedance of each layer can be calculated using a recursive method. The impedance of an individual layer with a finite thickness is given as follows: [Equation] where d n is the thickness of the layer and n is an index indicating the layer number in the stack. Z n+1 is the total impedance behind the layer. Thus, when calculating the impedance of the first layer of the distributed Bragg reflector in a CdO-on-bottom geometry, Z n+1 = Z 空気 . Then, the total impedance (Z DBR ) of the distributed Bragg reflector is solved by proceeding through the remaining layers in the stack. The impedance of the CdO layer (Z CdO ) is calculated using the same method, which is thus limited to only a single layer.

[0195] When the calculated lumped impedances Z DBR and Z CdO seen from the distributed Bragg reflector-CdO interface are looking in the opposite directions (see the arrows in FIG. 57), the TP film can be modeled as a simple AC equivalent circuit (FIG. 57) with source and load impedances. From circuit theory, the maximum available power is dissipated by the load under the conjugate impedance matching condition. [Equation] In the Tamm plasmon polariton film, this is Im[Z DBR = -Im[ZCdO is converted to the Tamm plasmon polariton mode supported at that time, and the absorption rate is Re[Z DBR =Re[Z CdO is also maximized at that time.

[0196] To explain this further, the reflectance (black line) of an aperiodic distributed Bragg reflector (on Si) and the emission (red line) from a Tamm plasmon polariton emitter having the same distributed Bragg reflector (on CdO, N d =3.5×10 20 cm -3 ) are shown in Fig. 55. In Fig. 58, the imaginary parts of the impedances of the distributed Bragg reflector (Im[Z DBR ) and the CdO layer (-Im[Z CdO ) are provided to this Tamm plasmon polariton emitter. From Figs. 55 and 58, the peak of the emissivity from the Tamm plasmon polariton emitter corresponds to the intersection of Im[Z DBR and -Im[Z CdO . The dip in the reflectance of the distributed Bragg reflector corresponds to the resonance feature in Im[Z DBR . The large peak in the emissivity is the result of the high carrier density of the CdO film, and thus the result of the low Re[Z CdO of CdO within this spectral range. Beyond the plasma frequency of CdO, Re[Z CdO increases substantially, and thus the impedance matching between the distributed Bragg reflector and CdO becomes insufficient. Fig. 56 shows the emissivities of two Tamm plasmon polariton emitters having the same distributed Bragg reflector, one deposited on a low-doped (N d =7×10 19 cm -3 ) and the other deposited on a highly doped (N d =4.3×10 20 cm -3 ) CdO film. For both carrier densities of CdO, Im[Z DBR and -Im[Z CdOintersects at the same frequency (see Fig. 59), but the increased Re[Z of the Tamm plasmon polariton emitter film with low carrier density CdO (see Fig. 60) results in a Tamm plasmon polariton mode that is not supported beyond the plasma frequency of CdO (the dashed vertical black line in Fig. 56).

[0197] Section S20. Role of CdO in the inverse-designed Tamm plasmon polariton emitter: Carrier concentration (real part of the dielectric function) and mobility (imaginary part of the dielectric function). Here, a discussion is developed on how the adjustable dielectric function (both real and imaginary parts) of CdO leads to enhanced spectral control. The dielectric function of CdO is mainly defined by two components, the carrier concentration (N d ) and the mobility. N d mainly determines the real part, while the mobility mainly determines the ratio of the imaginary part to the real part. Here, except for this section, since the manufacturing process does not dramatically change the mobility, the mobility is treated as a constant of 200 cm -2 / V / s. N d is designable as shown by the experimental data.

[0198] Influence of carrier concentration. As previously discussed with respect to Fig. 11, it was observed that CdO-based Tamm plasmon polariton emitters exhibit better performance, i.e., a closer match to the target spectrum, but the inverse design algorithm does not provide physical intuition. Here, an attempt was made to clarify the origin of how the adjustable carrier concentration brings such a substantial improvement in the performance of the Tamm plasmon polariton emitter. For this purpose, as shown in Figs. 61 - 62, the same optimization was performed at exponentially spaced different fixed N 20 cm -3 in the range of 0.2 - 120.0×10 d s to match the absorption spectrum of DMMP. The maximum possible carrier concentration of CdO is 12.0×10 20 cm -3(Nolen JR et al., Physical Review Materials 2020, 4, 025202; Liu CP et al., Physical Review Applied 2016, 6, 064018), and in this specification, this is purely extended to 120.0×10 20 cm -3 for the purpose of exploring the mechanism. It should be noted that the number of dielectric layers in the distributed Bragg reflector stack is fixed at 29 to match that in FIG. 11. The performance of the CdO-based Tamm plasmon polariton emitter has been found to be strongly defined by the carrier concentration: when the carrier concentration is less than 1.0×10 20 cm -3 , the optimized structure has similar performance. However, when the carrier concentration is fixed at a value exceeding 4.0×10 20 cm -3 , the performance deteriorates. Therefore, the dielectric function of CdO (equivalent to the carrier concentration in our case) can be considered as a parameter, and the algorithm can optimize this value for a given task. From a physics perspective, the dielectric function of CdO (FIG. 63) can be adjusted through doping to tune the impedance model (FIG. 64), so that the spectrum of the Tamm plasmon polariton emitter (Section S19), which is determined by the impedance of the conductive layer and the distributed Bragg reflector together, can be matched to any spectrum.

[0199] Mobility of influence. The CdO mobility determines the imaginary part of the dielectric function at a given carrier concentration (Figure 66), which, according to the reference, should affect the performance of the Tamm plasmon polariton emitter (Brand S et al. Physical Review B 2009, 79, 085416; Morozov KM et al. Scientific Reports 2019, 9, 1-9; Kaliteevski MA et al. Plasmonics 2015, 10, 281-284). Here, we discuss what happens when the mobility is increased (decreased) due to improved manufacturing techniques (restricted manufacturing processes due to cost, compatibility issues, etc.). The calculations reported herein use a mobility of 200 cm -2 / V / s, which is approximately consistent with the lower limit of the experimentally measured observations for this material (Nolen JR et al. Physical Review Materials 2020, 4, 025202). However, here, in this thought experiment, equivalent designs with artificially reduced and increased values of 50 and 800 cm -2 / V / s are implemented.

[0200] First, the maximum achievable Q factor with a given number of dielectric stacks (11 in this document) is compared, and it is found that a higher Q factor can be achieved with a higher mobility film, i.e., a lower imaginary part of the CdO dielectric function, as expected (Figures 65, 66). Then, with the carrier concentration (N d ) of CdO fixed, the performance of the inverse-designed Tamm plasmon polariton emitter with different mobilities is compared for the same task with 11 and 29 dielectric layers, respectively. It is found that both of the two tasks can be realized with the best performance at a specific mobility value of 50 cm -2 / V / s. For comparison, the carrier concentration is 4.0×10 20 cm -3Although fixed to [a certain value], at different fixed carrier concentrations, since the mobility and carrier concentration together determine the complex dielectric function of CdO (and thus the optical properties), the optimal mobility can be 200 or 800 cm -2 / V / s. It should be noted that finally, the mobility of CdO was fixed at 50, 200, and 800 cm -2 / V / s, and N d was allowed to vary freely. When the carrier density can vary considering different mobility values, as shown in FIGS. 69-70, even with dramatically different mobilities, equivalent performance was observed from all three. Therefore, the use of CdO, whose carrier density can be controlled over a wide range, implies that an increase / decrease in mobility (loss of CdO) does not affect the performance of the inverse-designed Tamm plasmon polariton emitter for many tasks, and provides unprecedented spectral control for such CdO-based designs.

[0201] Example 2 - Designer Tamm Plasmon Thermal Emitter Using Gradient Descent Regression Optimization The mid-infrared (MIR) spectral range is often called the molecular fingerprint region because of the many molecular vibration signatures it contains. Therefore, research focused on the development of mid-infrared light sources with a sufficiently narrow bandwidth, minimum power requirements, and small form factor is very interesting for potential spectroscopic and sensing applications such as bio and chemical sensing, as well as the detection of harmful gases. One approach for such applications that has recently received significant attention is the frequency-selective thermal emitter. Here, by wisely selecting and / or structuring semiconductor materials, the thermal photonic density of states can be tailored to achieve frequency-dependent far-field impedance matching and thus absorptivity. Conversely, by Kirchhoff's law, this results in an emissivity of equivalent direction and magnitude. In this specification, there is a report on a powerful approach for realizing a narrowband thermal emitter with a high degree of frequency selectivity without sacrificing the narrow emission linewidth typically problematic for plasmon-based emitters through the inverse design of aperiodic Tamm plasmon (TP) devices.

[0202] The Tamm plasmon is an optical interface state formed between a distributed Bragg reflector (DBR) and a metal or between two different distributed Bragg reflectors. These excitations exhibit a parabolic dispersion within the photonic bandgaps of the distributed Bragg reflector and the air cone, and are thus available from free space without the need for expensive and time-consuming lithography and etching steps. Here, a gradient descent regression (GDR) algorithm is used to design a Tamm plasmon-supporting film with a metal distributed Bragg reflector geometry and to grow a film that reproduces the predicted spectral features of the design with great success. n-CdO deposited by high-power impulse magnetron sputtering is used as the metal layer. This highly promising transparent conductive oxide (TCO) has been demonstrated to exhibit a wide spectral tunability of the plasma frequency while maintaining exceptionally low optical losses. This is due to CdO having both a carrier density in the range of 10 19 ~10 20 cm -3 (in the range of 0.12 to 0.26 in epitaxial growth films) and an electron mobility reaching up to 500 cm 2 / V-s. Since the Tamm plasmon mode corresponds to an impedance matching state of the distributed Bragg reflector and the metal film, such control over the impedance of both the distributed Bragg reflector (by changes in the individual layer thickness and dielectric index) and the CdO layer (by changes in the carrier density and layer thickness) gives the design a great deal of flexibility.

[0203] Inverse design has been used in the past to design Tamm plasmon supported films, but these efforts rely on computationally expensive techniques such as genetic algorithms, Bayesian optimization, or deep learning and often require hours or days to reach a final solution for a single peak emission spectrum. In contrast, the gradient descent regression approach can reach a solution on the time scale of seconds or minutes while running on all consumer grade CPUs. As demonstrated herein, this opens the door to realizing thermal emitters with various levels of spectral complexity. For example, realizing arbitrarily placed single and multiple peak thermal emission spectra that can exactly match the IR absorption spectra of greenhouse gases such as CO2 and N2O. The method herein also achieves a quality factor far exceeding that of conventional plasmonic devices (Q > 300 for designed films), controls the complete Tamm plasmon dispersion while maintaining a simple planar structure, and thus can control the spatial coherence of thermal emission. Therefore, the design principles used herein outline a highly tunable and potentially scalable platform for applications such as filterless non-dispersive infrared gas sensing and free space communication.

[0204] Example 3 - Designer emission spectra from an infrared thermal emitter as a light source It has been previously described that using a thin film of a polaritonic material (a material or medium that exhibits a negative real part of the permittivity tensor along one or more Cartesian or crystal axes) above / below / within one or more dielectric Bragg reflectors (multilayer dielectric photonic crystals) results in a structure suitable for supporting one or more dielectric plasmon polariton (TPP) resonances. Tamm plasmon polaritons can result in single and / or multiple resonances and thus enable thermal emission lines at single / multiple wavelengths.

[0205] This specification describes new wavelength-selective emitters that can be used in non-dispersive infrared (NDIR) or other chemical sensors. This can be used to sense chemical substances in the gas, liquid, or solid phase in reflection, transmission, absorption, or emission modes. In a non-dispersive infrared sensor, the use of a wavelength-selective emitter eliminates the need for conventional bandpass filters within the non-dispersive infrared device, while the emitter itself also serves to replace the conventional broadband blackbody emitter used. The emission frequency (frequencies) of the device can be designed by physical intuition and / or algorithms. When the emission frequency of the device is aligned with the absorption frequency of one or more vibrational or rotational modes for the chemical substance of interest, the chemical substance concentration can be sensed in a non-dispersive infrared setup. Tamm plasmon polaritons, since they naturally support multiple emission frequencies, could use these frequencies to enhance the sensitivity to one gas / chemical substance or enable the sensing of multiple chemical substances of interest. For example, if multiple emission wavelengths are aligned with some of the absorption wavelengths of one particular chemical substance, the sensitivity for sensing that chemical substance can be improved. Alternatively, if the absorption frequencies of several gases match from the emitter, each of those gases can be sensed simultaneously. More details and demonstrations can be found in the previous examples. The two functions are not mutually exclusive and can be achieved simultaneously as demonstrated previously. Furthermore, the Tamm approach can also be modified to create frequency-specific absorption bands for other broadband detectors (e.g., cadmium mercury telluride, deuterated lanthanum α-alanine-doped triglycine sulfate detector). Thus, this technology presents an opportunity to use wavelength-selective thermal emitters or detectors in advanced chemical, environmental, or remote sensing applications (high sensitivity, high signal-to-noise, and multiplexed chemical sensing).

[0206] The implementation of an unpatterned multilayer planar film as a means of achieving narrowband heat emission is newly described herein. Also, multiple emission frequencies from this structure can be designed and / or dynamically modulated, thereby enabling high sensitivity and / or multiple chemical sensing. In the latter case, active modulation can be achieved through several means, such as carrier injection into one or more of the Tamm structure layers, incorporation of a ferroelectric or piezoelectric material into the Tamm structure, or incorporation of a phase change material.

[0207] Practical applications include gas, liquid, or solid material / chemical sensing via a non-dispersive infrared sensor, or alternative approaches in the infrared. This overcomes the need for the incorporation of band-pass filters, or for bulky and expensive rotating band-pass filter wheels. By including multiple Tamm-based detectors and / or emitters within the same design that can operate, for example, simultaneously or sequentially using multiple emission frequencies, sensitivity can be enhanced and / or more chemical substances of interest can be sensed within the same device.

[0208] Compared to current non-dispersive infrared or similar IR gas or liquid sensors, the approach herein enables multiple frequency and multiple chemical substance detection within a compact single package without the need for a band-pass filter. Further, variable temperature and computational algorithms can be included to differentiate multiple gas concentrations.

[0209] Example 4 DBR growth is already cheaper than nanopatterning, but the cost can still increase linearly with the number of DBR layers required. To further reduce costs, it has been demonstrated that Tamm hybrid polaritons (THPs) can be used to achieve multiple emissions with fewer DBR layers than TPPs (three times as exemplified below). One representative schematic of a THP support structure is shown in FIG. 72: a polar material, such as hexagonal boron nitride, and a plasmonic material, such as a metal or doped semiconductor, and one or more DBRs. The positions of the three components are not limited to the schematic and can be in any order. The TPP support structure is a DBR-plasmonic material heterostructure (FIG. 73), as discussed in detail in Example 1.

[0210] Here, an example is given of how much cheaper it is to fabricate a THP support structure than a TPP support structure. To achieve high-sensitivity sulfuryl fluoride gas sensing, two emission peaks (equivalent to absorption peaks) are required. When using a TPP support structure, the number of DBR layers (N d ) is determined to be 9. However, as shown in FIG. 74, three N d s are sufficient for the THP to achieve this function. Such a difference implies that the manufacturing cost can be reduced by at least a factor of two when using a THP support structure. Since THP support structures do not require any nanopatterning, they are even lower cost than TPPs and can be mass-produced on a wafer scale by thin-film deposition, and they can still be used for applications such as chemical sensing and infrared beacons.

[0211] Example 5 - Coupled Tamm phonons and plasmon polaritons for a designer's planar multi-resonant absorber Abstract. Wavelength selective absorbers (WS absorbers) are of interest for various applications including chemical sensing and light sources. Lithography-free fabrication of wavelength selective absorbers can be achieved by Tamm plasmon polaritons (TPPs) supported by distributed Bragg reflectors (DBRs) on plasmonic materials. Multi-frequency and almost arbitrary spectra can be realized with Tamm plasmon polaritons by inverse design algorithms, but thick distributed Bragg reflectors with stringent requirements are necessary for high quality factor (Q-factor) and / or multi-band Tamm plasmon polariton absorbers, increasing cost and reducing manufacturing error tolerance. Here, high-Q multi-band absorption is experimentally demonstrated with a limited distributed Bragg reflector layer (three layers) by Tamm hybrid polaritons (THPs) formed by coupling Tamm plasmon polaritons and Tamm phonon polaritons (TPhPs) when modal frequencies overlap. Compared with the Tamm plasmon polariton component, the Q-factor of the Tamm hybrid polariton is improved by a factor of two, and the angular spread is also reduced by a factor of two, facilitating applications that require narrowband and non-dispersive wavelength selective absorbers. Furthermore, an open-source algorithm for inverse designing Tamm hybrid polariton absorbers made of anisotropic media is developed, exemplifying that modal frequencies can be assigned to desired positions. Furthermore, it is demonstrated that the inverse-designed Tamm hybrid polariton absorber can achieve the same spectral resonance with fewer distributed Bragg reflector layers than a Tamm plasmon polariton absorber, thus reducing manufacturing complexity and enabling a higher cost-effective, lithography-free wafer-scale wavelength selective emitter for applications such as free-space communication and gas sensing.

[0212] Results and Discussion. The development of wavelength-selective absorbers (WS absorbers) in the infrared has been highly desirable for many applications ranging from optical sensing, imaging, and photothermovoltaic devices to narrowband and / or multi-frequency thermal emitters, and their rapid design and fabrication have been long-standing scientific and technological goals. However, most wavelength-selective absorbers use patterned nanostructures and require lithography and other costly manufacturing steps, especially for small-scale production for each design, making such an approach potentially inaccessible for many applications. Recently, it has been demonstrated that Tamm plasmon polaritons (TPPs) can be supported by planar films consisting of distributed Bragg reflectors (DBRs) and plasmonic materials (Kaliteevski M et al. Physical Review B 2007, 76, 165415). The distributed Bragg reflector brings optical phase matching to the plasmonic surface, resulting in absorption resonances with high quality (Q) factors available in free space (Kaliteevski M et al. Physical Review B 2007, 76, 165415; Sasin ME et al. Applied physics letters 2008, 92, 251112; Sakurai A et al. ACS central science 2019, 5, 319-326; Wang Z et al. ACS Photonics 2020, 7(6), 1569-1576; Wang Z et al. ACS photonics 2018, 5, 2446-2452). Since only thin-film deposition is required to fabricate these structures, Tamm plasmon polariton absorbers present a promising simplified platform that can be grown on a wafer scale and thus function as strong candidates for wavelength-selective absorbers for various applications (Sakurai A et al. ACS central science 2019, 5, 319-326; Wang Z et al. ACS Photonics 2020, 7(6), 1569-1576; Wang Z et al. ACS photonics 2018, 5, 2446-2452).

[0213] Despite the high promise of Tamm plasmon polariton absorbers, the distributed Bragg reflectors required for wavelength-selective absorbers are sophisticated and can be difficult to fabricate. As previously discussed in the literature, high-Q factors (Wang Z et al. ACS Photonics 2020, 7(6), 1569-1576; He M et al. Nature Materials 2021, 20, 1663-1669; Wang Z et al. Advanced Functional Materials 2021, 31(26), 2102183; Yang ZY et al. ACS Photonics 2017, 4, 2212-2219) and multi-resonant (He M et al. Nature Materials 2021, 20, 1663-1669) wavelength-selective absorbers are only possible with a sufficient number of distributed Bragg reflector layers, and the specific requirements vary from 5 to dozens of dielectric layers. Thus, in some applications of wavelength-selective absorbers, such as high-sensitivity non-dispersive infrared sensing (NDIR), it is desirable to further optimize the structure, i.e., reduce the number and total thickness of the distributed Bragg reflector layers necessary to reduce cost. One solution is to introduce polaritonic strong coupling (Yoo D et al. Nature Photonics 2021, 15, 125-130; Runnerstrom EL et al. Nano letters 2018, 19, 948-957; Passler NC et al. Nano letters 2018, 18, 4285-4292) and / or hybridize these herein with Tamm plasmon polaritons, thereby inducing additional resonances without modifying the distributed Bragg reflector.Previous studies have demonstrated the manipulation of spectral (Hu J et al. Optics express 2019, 27, 18642-18652; Hu J et al. Optics letters 2019, 44, 5642-5645) and spatial (Balevicius Z. Coatings 2020, 10, 1187; Buzavaite-Verteliene E et al. Optics express 2020, 28, 10308-10319; Kaliteevski M et al. Applied Physics Letters 2009, 95, 251108) properties in hybrid Tamm plasmon polariton-polariton systems (as well as other coupled systems). However, the coupling of low-loss phonon polaritons has not yet been explored. In addition, the resonance changes resulting from such hybridization make the design more difficult than that of pure Tamm plasmon polariton resonances, and anisotropic phonon materials (He M et al. ACS Photonics 2022, 9(4), 1078-1095) further complicate the system in the angular regime.

[0214] In this specification, an approach is demonstrated to realize a high-Q multiple resonance wavelength selector by inducing Tamm hybrid polaritons (THPs), and an open-source inverse design algorithm for structure optimization compatible even with anisotropic materials is provided. The Tamm hybrid polariton absorber is realized by coupling Tamm plasmon polaritons and Tamm phonon polaritons (TPhPs), which are supported by a doped semiconductor (cadmium oxide, CdO) and a phonon polariton material, in this case hexagonal boron nitride (hBN) in a distributed Bragg reflector. Experimentally, the Tamm phonon polariton absorber (hBN on a distributed Bragg reflector) is shown to have a linewidth approximately 10 times narrower than its Tamm plasmon polariton counterpart (distributed Bragg reflector on CdO) resulting from the lower optical loss of the phonon polariton mode. In the hBN distributed Bragg reflector-CdO structure, the Tamm hybrid polariton is formed by spectrally overlapping the two modes, and the Tamm hybrid polariton exhibits a linewidth twice as narrow as the uncoupled Tamm plasmon polariton component. In addition to the modified spectral behavior, it is also shown that the spatial dispersion of the planar Tamm polariton within the light cone can be manipulated by the Tamm plasmon polariton-Tamm phonon polariton coupling. In particular, the spectral detuning due to the angular dispersion of the Tamm hybrid polariton mode is reduced by half compared to the uncoupled Tamm plasmon polariton mode which is a result of the non-dispersive Tamm phonon polariton. Furthermore, a stochastic gradient descent (SGD)-based inverse design algorithm is developed for designing Tamm hybrid polaritons supported by anisotropic materials. The design of Tamm hybrid polaritons by matching frequencies and linearities is shown, and it is shown that these tasks can be achieved with a Tamm hybrid polariton with significantly fewer and thinner (by about 2 - 5 times) distributed Bragg reflector layers compared to the Tamm plasmon polariton.In this specification, exfoliated hBN was used for this proof-of-concept demonstration, but high-quality polar materials that support Tamm hybrid polaritons (e.g., hBN (Wang G et al. Fundamental Research 2021, 1(6), 677-683), SiO2 (Chen DZA et al. Applied Physics Letters 2007, 91, 121906)) can be grown on wafer scale (Lattemann M et al. Surface and Coatings Technology 2003, 174, 365-369; Ma KY et al. Nature 2022, 606, 88-93; Li Q et al. Advanced Functional Materials 2022, 32(38), 2206094). Thus, the combination of an efficient inverse design algorithm and modal operation enables the realization of high-cost-effective, wafer-scale, and lithography-free Tamm hybrid polariton absorbers for many applications, including non-dispersive infrared, environmental, atmospheric, and chemical sensing, free-space communication, and infrared beacons.

[0215] The discussed Tamm polariton absorber consists of an aperiodic distributed Bragg reflector with alternating layers of Ge and AlO above / below the polariton supporting material. To support the Tamm plasmon polariton resonance, the geometry of the distributed Bragg reflector on a doped semiconductor (n-type CdO in this specification (Nolen JR et al. Physical Review Materials 2020, 4, 025202)) is used, whereby any resonance spectrum can be matched by an inverse design algorithm (He M et al. Nature Materials 2021, 20, 1663-1669), and the resulting Tamm plasmon polariton magnetic field profile is shown in FIG. 75. To support the Tamm phonon polariton, as shown in FIG. 76, a van der Waals material that supports the phonon polariton x 10We used B-enriched hBN (Giles AJ et al. Nature Materials 2018, 17, 134; Liu S et al. Chemistry of Materials 2018, 30, 6222 - 6225) and transferred it onto the top of the distributed Bragg reflector. Thus, the two modes can be simultaneously supported in the hBN distributed Bragg reflector-CdO structure, resulting in modal coupling when the frequencies overlap. The Tamm phonon polariton frequency is inherently restricted to a small frequency range (within the Reststrahlen band (RB)), while the Tamm plasmon polariton mode can be designed to occur at any frequency below the plasma frequency of the material. Therefore, to achieve the essential spectral overlap of the Tamm plasmon polariton and Tamm phonon polariton modes, we used an inverse design algorithm (He M et al. Nature Materials 2021, 20, 1663 - 1669) to design a Tamm plasmon polariton absorber with resonances aligned within the Reststrahlen band of hBN (1400 cm -1 ). The three stacks simulated in Figures 75 - 77 were fabricated by a combination of sputtering, evaporation, and layer transfer using the corresponding IR spectra shown in Figure 79.

[0216] In the inversely designed and fabricated Tamm plasmon polariton absorber, a resonance was observed at approximately 1400 cm -1 with a FWHM of 204 cm -1 . The relatively low Q factor is caused by the intrinsic losses associated with the AlO x layer. During the manufacturing process, the same distributed Bragg reflector stack was also deposited on a sapphire substrate, so we were able to transfer hBN onto the same distributed Bragg reflector to study the corresponding Tamm phonon polariton mode. In contrast to the Tamm plasmon polariton mode, the linewidth of the Tamm phonon polariton supported by the same distributed Bragg reflector is significantly narrower, with a FWHM of only 16 cm -1 , and the central frequency is 1400 cm-1 This is the case. The improved Q factor results from the lower losses of polar dielectric materials compared to plasmonic materials, similar to the results reported in the literature (He M et al. ACS Photonics 2022, 9(4), 1078 - 1095; Lee IH et al. Nature communications 2020, 11, 1 - 8; He M et al. Nano Letters 2021, 21, 7921 - 7928; Caldwell JD et al. Nano letters 2013, 13, 3690 - 3697). As described above, due to the intentional use of different stacking orders (hBN - dispersed Bragg reflector vs. dispersed Bragg reflector - CdO), two modes can be simultaneously supported in the hBN - dispersed Bragg reflector - CdO geometry. In fact, the Tamm plasmon polariton and Tamm phonon polariton modes couple to form two hybridized modes (Tamm hybrid polariton), one below and one above the transverse optical (TO) phonon frequency of hBN (Figure 79). The Tamm hybrid polariton resonance is denoted as the upper and lower polariton branches (UPB and LPB) based on the resonance frequency. Importantly, the Tamm hybrid polariton results in a Q factor that is nearly twice that of the Tamm plasmon polariton component, due to the contribution of the inherently high - Q Tamm phonon polariton; thus, this hybridization was used to manipulate the spectral properties of Tamm polaritons. Evidence of modal coupling can also be inferred from the Tamm hybrid polariton magnetic - field profile. For uncoupled resonances, the magnetic field is confined to the bottom and top Ge layers for the Tamm plasmon polariton absorber and Tamm phonon polariton absorber, respectively, which are Ge layers adjacent to the polariton - supporting material. In the Tamm hybrid polariton absorber, the magnetic field is confined to both the top and bottom Ge layers, presenting the profiles of the Tamm plasmon polariton and Tamm phonon polariton simultaneously, thereby verifying modal hybridization again.

[0217] Before discussing the modal coupling that gives rise to the Tamm hybrid polariton mode further, we first investigate the uncoupled Tamm phonon polariton modes, which have not been fully explored compared to their Tamm plasmon polariton counterparts. For this purpose, we used a conceptually intuitive model (circuit impedance model) to understand how Tamm phonon polaritons arise at the distributed Bragg reflector-hBN interface and how these modes can be manipulated. Through the circuit impedance model, the effective impedance for the distributed Bragg reflector can be derived for any multilayer dielectric stack Z DBR Similarly, the optical impedance (Z hBN ) of the hBN layer can be defined from the dielectric function and thickness. Then, the Tamm phonon polariton mode is supported when the impedance matching condition between hBN and the distributed Bragg reflector:

Equation

[0218] Since the Tamm phonon polariton mode depends on the hBN thickness, this inherently affects the properties of the Tamm hybrid polariton. To study the thickness dependence of the Tamm hybrid polariton in hBN, a series of hBN flakes were transferred onto the Tamm plasmon polariton absorber. In thicker hBN, due to the greater spatial overlap with the electric field distributions of the Tamm plasmon polariton and the Tamm phonon polariton modes (Figure 75 and SI, Section 7), the splitting between the two hybridized modes increases (Figure 82, Figure 83). To further understand the hybridization phenomenon, a harmonic oscillator model was used. The Hamiltonian matrix (H) of this coupled system can be written as follows:

Equation

Number

Number

[0219] In addition to the spectral properties, modal dispersion is engineered in momentum space through modal coupling. First, the reflectivities of Tamm plasmon polariton absorbers at different angles of incidence are calculated, and then this is measured with three different objective lenses, enabling the acquisition of the spectral response at different angles of incidence (details of the measurements are given in the Methods section). The accuracy of the numerical calculations is then verified by overlapping with the experimentally extracted resonance frequencies, and the fitting details are included in SI, Section 2. The dispersion of the Tamm plasmon polariton mode is approximated through a second-order Taylor expansion (Kaliteevski M et al. Physical Review B 2007, 76, 165415; Overvig AC et al. Physical Review X 2021, 11, 021050): [Number] where b is the phenomenologically determined band curvature and θ is the angle of incidence in degrees. The band curvature is 0.08 cm -1 / degree 2 for the Tamm plasmon polariton absorber, but as shown in FIGS. 86, 87, and 89, this value is much smaller (0.016 cm -1 / degree 2 ) for the Tamm phonon polariton mode. Rabi splitting is observed in the Tamm hybrid polariton dispersion at the intersection between the Tamm plasmon polariton and the "slower" Tamm phonon polariton dispersion, which is an indicator of modal coupling (FIG. 88) (Lu G et al. Nano Letters 2021, 21, 1831-1838; Dovzhenko DS et al. Nanoscale 2018, 10, 3589-3605). Quantitatively, the band curvatures of the upper and lower polariton branches of the Tamm hybrid polariton are 0.04 cm -1 / degree 2 and 0.02 cm -1 / degree 2and both are in between the Tamm plasmon polariton and the Tamm phonon polariton mode curvatures, as shown in Fig. 89. Therefore, Tamm plasmon polariton-Tamm phonon polariton hybridization also provides a means to manipulate modes in momentum space: hybridization with more (less) dispersive modes can increase (decrease) the spatial coherence of heat emission (Lu G et al. Nano Letters 2021, 21, 1831-1838).

[0220] Benefiting from modal coupling, Tamm hybrid polariton absorbers exhibit a moderate dispersion and multiple resonances that can be more advantageous than pure Tamm plasmon polariton absorbers in many applications. First, the implications of the dispersion characteristics of Tamm hybrid polariton absorbers are discussed. In applications where the spectral characteristics should be independent of the angle, a small modal dispersion across the entire momentum space is desired. For example, a wavelength-selective absorber can be used as a wavelength-selective thermal emitter for filterless chemical sensing and infrared beacons, and the light emitted within a range of incident or exit angles can be collected by a parabolic mirror to increase the signal intensity. Therefore, the device response is a convolution between different angles, resulting in a spectral broadening. However, it has been found that the Tamm plasmon polariton dispersion is inherently limited within a certain range by attempting to match different band curvatures with an inverse design protocol. For example, in the case of a Tamm plasmon polariton absorber composed of Ge, AlO x , and CdO, the band curvature is limited between approximately 0.06 and 0.1 cm -1 / degree 2 (raw data are described in SI, Section 3). Therefore, for a typical Tamm plasmon polariton absorber, when the incident light (collected by a parabolic mirror with NA +0.7) extends to ±45°, the minimum spectral broadening obtained is approximately 60 cm -1is. In contrast, as shown in Fig. 86, by adding hBN with a thickness of 100 nm to the same design, the spectral broadening is reduced. Quantitatively, the FWHM of the Tamm plasmon polariton absorber is 38 cm -1 ~100 cm -1 is broadened, while on the other hand, the FWHM of the corresponding Tamm hybrid polariton is increased from 24 cm -1 to only 44 cm -1 . For the FWHM of the high-Q Tamm plasmon polariton absorber (5.8 cm -1 ), the angular spread (60 cm -1 ) is significantly larger than the resonance FWHM, and numerically, it was found that the resonance is suppressed when considering the range of incident angles simultaneously. In contrast, the Tamm hybrid polariton absorber response persists with angular convolution. Detailed calculations and discussions can be found in SI, Section 4. In summary, the angular dispersion of the Tamm plasmon polariton absorber basically limits the spectral coherence when considering a certain angle range, and an important finding of this report is the observation that the Tamm hybrid polariton absorber significantly overcomes this limitation.

[0221] In addition to finer control of the dispersion, the Tamm hybrid polariton absorber design potentially reduces manufacturing costs. As discussed in previous research (He M et al. Nature Materials 2021, 20, 1663 - 1669), the multi - resonance features can be deterministically achieved by the inverse - designed Tamm plasmon polariton absorber (He M et al. Nature Materials 2021, 20, 1663 - 1669), but these advanced designs are only feasible with multi - layer distributed Bragg reflector stacks. Here, it is shown that the spectral features realized with a three - layer distributed Bragg reflector Tamm hybrid polariton absorber can be highly sophisticated and may require more complex Tamm plasmon polariton absorber stacks. Using the normalized experimental Tamm hybrid polariton reflectivity (Figure 82) as the target spectrum, an attempt was made to optimize the Tamm plasmon polariton absorber to mimic it. Figure 91 shows the measured Tamm hybrid polariton reflection spectrum and the numerically simulated Tamm plasmon polariton spectrum when the distributed Bragg reflector stack contains 13, 17, and 21 layers and more than 17 layers are required to fully replicate the infrared response. This comparison shows that the Tamm hybrid polariton spectral characteristics can be matched to the Tamm plasmon polariton absorber, but the associated distributed Bragg reflector must also be more complex, thus demonstrating that non - uniformities, defects, and thickness errors that can potentially degrade performance are more likely to occur.

[0222] Since hBN exhibits strong anisotropy, i.e., the dielectric constant in the x - y plane is negative, while it is positive along the z - axis between about 1390 cm -1 ~1650 cm -1 it is important to discuss how this anisotropy affects the hybridized system. For that purpose, hBN is assigned an ε xy (negative dielectric constant along all axes) equal to the ε zArtificially modeled as an isotropic medium (Chatzakis I et al. Optics Letters 2018, 43, 2177-2180; He M et al. Journal of Materials Research 2021, 36, 4394-4403). In particular, the Berreman modes near the longitudinal optical (LO) phonons of hBN (1650 cm -1 ) are excited in this artificially isotropic hBN, but since these can only be excited along the out-of-plane axis, they do not exist in the actual material (Zhu H et al. Advanced Optical Materials 2021, 9(21), 2100645). Thus, by using hyperbolic media, it becomes possible to selectively turn off those modes that may be desired in many applications (SI, Sections 5 and 8). In addition, the responses of isotropic hBN and anisotropic hBN are different at high angles of incidence, e.g., 60°, while they are nearly identical at low angles. Thus, the Tamm hybrid polaritons highlighted herein can be supported by other isotropic polar materials, while anisotropy further modifies the behavior of Tamm hybrid polaritons by restricting which modes can participate in the coupled system. Similar coupled phenomena are exemplified by other phonon polariton supporting materials (SiO2 and SiC) with realizable designs in SI, Section 8.

[0223] Despite the advantages, it is difficult to design a Tamm hybrid polariton absorber that exhibits multiple resonances at arbitrary frequencies. This challenge partially stems from the fact that all resonances within the stack are interdependent, the distributed Bragg reflectors are aperiodic, and the polar dielectrics are potentially anisotropic. Therefore, designing Tamm hybrid polaritons with conventional intuitive models is impractical. To address this challenge, a previous stochastic gradient descent-based inverse design algorithm was modified to enable the integration of anisotropy in materials such as hBN. The operating principle of the algorithm has been discussed in detail in a previous publication (He M et al. Nature Materials 2021, 20, 1663 - 1669), and this version is freely available online. In the following discussion demonstrating this latest version, all parameters such as the thickness of individual distributed Bragg reflector layers, the thickness of polariton materials (hBN and CdO), and the carrier concentration of CdO are designable parameters, and thus, the design freedom of Tamm hybrid polariton absorbers can be exploited.

[0224] First, it is shown that the two resonance frequencies of the Tamm hybrid polariton absorber can be assigned independently, which is very difficult based on physical intuition as described above. In the first case, the frequency of the lower polariton branch was fixed, and an attempt was made to vary the frequency of the upper polariton branch in 50 cm -1 steps. The inverse design algorithm achieved this task while all lower polariton branch frequencies were locked at 1350 cm -1 as the upper polariton branch changed from 1450 to 1950 cm -1 , as shown in Fig. 92. Subsequently, the algorithm was tested with a symmetric task: moving the lower polariton branch frequency while the upper polariton branch frequency was fixed at 1450 cm -1 , and the target was still achieved by the inverse design algorithm (Fig. 93).

[0225] The hybridized mode exhibits multiple resonances naturally in a narrow frequency range. Utilizing this property, a multi-frequency wavelength selective absorber can be designed. It has been demonstrated that the Tamm plasmon polariton resonance itself can be matched to an arbitrary spectrum using an inverse design algorithm (He M et al. Nature Materials 2021, 20, 1663 - 1669), but this can only be achieved with a sufficient number of distributed Bragg reflector layers (denoted as n DBR ), where n DBR depends on specific design requirements. For the spectral barcoding application shown in Fig. 94 where three resonance peaks are desired, the task can be achieved with n = 5 for the Tamm hybrid polariton absorber. In contrast, the optimized Tamm plasmon polariton with n = 5 can only provide two peaks, and the peak at 1500 cm DBR cannot be matched. With more dielectric layers, the inverse designed Tamm plasmon polariton resonance can ultimately match any of these shapes, but the n DBR required for this barcoding task is 9, as shown by the yellow curve in Fig. 94. It should be noted that the resonance at approximately 1400 cm -1 for the Tamm hybrid polariton absorber cannot be avoided because they are due to the high positive dielectric constant of hBN near the transverse optical phonon absorption and transverse optical phonons (Howes A et al. Advanced Optical Materials 2020, 8, 1901470; Zhu H et al. Advanced Optical Materials 2021, 9(21), 2100645). However, considering the very narrow linewidth (about 5 cm DBR ), the influence of that mode can be safely ignored in most cases. For example, in a thermal emitter application, assuming an operating temperature of 600 °C, the power emitted at approximately 1400 cm -1 is for these designs in the range of 1000 - 2000 cm -1 ) is considered, the influence of that mode can be safely ignored in most cases. For example, in a thermal emitter application, assuming an operating temperature of 600 °C, the power emitted at approximately 1400 cm -1 is for these designs in the range of 1000 - 2000 cm -1Only count 4% of the total emission power within the range (SI, section 6).

[0226] Further demonstrate the advantages of the Tamm hybrid polariton absorber over the Tamm plasmon polariton absorber for filterless non-dispersive infrared applications. As detailed previously, the wavelength-selective absorber can be used as a wavelength-selective thermal emitter for filterless non-dispersive infrared applications. Additionally, when multiple absorption (equivalent to emission) frequencies of the wavelength-selective absorber are aligned with the chemical absorption spectrum, high-sensitivity chemical sensing can be achieved, and thus the signal intensity can be optimized. Here, sulfuryl fluoride non-dispersive infrared gas sensing is used as an example, where sulfuryl fluoride is a widely used pest control chemical and the target spectrum is an envelope for covering an irregularly shaped absorption spectrum. Similar to the spectral barcoding application, it is shown again that the Tamm hybrid polariton absorber can achieve the same task with fewer dielectric layers (5 layers vs. 9 layers) than the Tamm plasmon polariton absorber (Figure 95). Therefore, by reducing the requirements for the distributed Bragg reflector for the Tamm hybrid polariton, low-cost, wafer-scale, and lithography-free manufacturing for many applications becomes possible.

[0227] Conclusion. In summary, the combination of the coupling phenomenon and an efficient inverse design algorithm enables a designer's multi-band wavelength selective absorber with a limited distributed Bragg reflector layer that has been numerically and experimentally verified. By aligning the modal frequencies of Tamm plasmon polaritons and Tamm phonon polaritons, two modes can be coupled and both spectral and spatial characteristics can be manipulated. The hybridized Tamm hybrid polariton modes exhibit improved Q factors and slower spatial dispersion compared to their Tamm plasmon polariton components. Furthermore, as more and more phonon polariton supporting materials are being discovered and / or utilized, an algorithm for inverse designing Tamm hybrid polaritons including anisotropic materials has been developed (Ma W et al. Nature 2018, 562, 557; Taboada-Gutierrez J et al. Nature materials 2020, 19, 964 - 968; Passler NC et al. Nature 2022, 602, 595 - 600; Caldwell JD et al. Nanophotonics 2015, 4, 44 - 68). It has been demonstrated that this algorithm can individually determine the two branches of the Tamm hybrid polariton. Subsequently, the Tamm hybrid polariton absorber can be used as a multi-band wavelength selective absorber with significantly fewer (2 - 5 times) distributed Bragg reflector layers than a Tamm plasmon polariton absorber, and it has been demonstrated that the manufacturing complexity can be significantly reduced. It is emphasized that similar couplings can be induced using other polar materials, and the material selection plays a crucial role in the resulting Tamm hybrid polariton response. Reinforced by the stochastic gradient descent algorithm and this tunability, the demonstrated spectral control of Tamm plasmon polariton absorbers promises a high cost-effective, wafer-scale, and lithography-free solution for many applications across the infrared.

[0228] Method Manufacture of the device. In-doped CdO (n-type) was deposited on a 2-inch r-plane (012) sapphire single crystal substrate at 400 °C by a reactive co-sputtering process using high-power impulse magnetron sputtering (HiPIMS) and radio frequency (RF) sputtering from metal cadmium and indium targets with a diameter of 2 inches each. The HiPIMS driving conditions were a frequency of 800 Hz and a pulse time of 80 μs, resulting in a period of 1250 μs and a duty cycle of 6.4%. Film growth occurred at a total pressure of 10 mTorr in an environment of mixed argon (20 sccm) and oxygen (14.4 sccm). After deposition, the samples were annealed in a static oxygen atmosphere at 635 °C for 30 minutes.

[0229] The dielectric stack (Ge and AlOx) was deposited at ambient temperature from Ge (99.999%) and sapphire sources using electron beam evaporation in a vacuum. The thickness was monitored throughout the deposition using a quartz crystal microbalance (QCM). After deposition, the samples were cut and the layer thickness was measured using cross-sectional SEM.

[0230] 10 B-enriched hBN (approximately 99% enrichment (Giles AJ et al. Nature Materials 2018, 17, 134; Vuong T et al. Nature materials 2018, 17, 152)) flakes were exfoliated and transferred onto Tamm plasmon polariton absorber and distributed Bragg reflector samples using a low-contamination transfer technique. The hBN crystals were grown from a boron source that is almost 100% 10 B isotope (Liu S et al. Chemistry of Materials 2018, 30, 6222-6225).

[0231] Infrared reflection measurement. All infrared reflection measurements were carried out using a Bruker Vertex 70v FTIR with a Hyperion II microscope, and the detector was a liquid nitrogen-cooled mercury cadmium telluride (MCT) detector. To obtain spectra at different incident angles, 15×, 36×, and grazing angle objective lenses were used, and the incident angles were estimated to be 20, 25, and 55 degrees. The measurements using the grazing angle objective lens were p-polarized, while the other measurements were unpolarized. The spectral resolution was 2 cm -1 and the spectra were referenced to a gold mirror.

[0232] Computing resources used in the algorithm. All optimizations were carried out on a consumer-grade desktop equipped with an Intel I7-8700K CPU (initially released in 2017 at approximately $400) and 16 Gb of memory, and no GPU unit was used. The algorithm was written in Python 3.6 using TensorFlow 2.3.0. The specific version of the stochastic gradient descent method used was the adaptive moment estimation (Adam) provided by TensorFlow, and the optimization step was 0.005. All optimizations performed in this paper took approximately 1 - 10 minutes.

[0233] Supporting Information (SI) Section 1. Mechanisms of Tamm polaritons explained by impedance models. The mechanisms of Tamm phonons or plasmon polaritons have been discussed in a series of papers (Tsurimaki Y et al. Acs Photonics 2018, 5, 929 - 938; Wang Z et al. Acs Photonics 2018, 5, 2446 - 2452; He M et al. Nature Materials 2021, 20, 1663 - 1669; Kaliteevski M et al. Physical Review B 2007, 76, 165415; Brand S et al. Physical Review B 2009, 79, 085416). In this specification, Tamm plasmons and phonon polaritons (TPP and TPhP) are explained by an impedance model (Tsurimaki Y et al. Acs Photonics 2018, 5, 929 - 938). For the case of Tamm modes existing within the photonic bandgap of a distributed Bragg reflector, the reflection phases of the two mirrors (along opposite directions) should have equal amplitudes but opposite signs (φ1 + φ2 = 0). Here, this method is conceptually intuitive due to its connection to circuit theory and thus depends on the impedance model. Furthermore, through a lumped - element model approach, this analysis can also be extended to Tamm plasmon polariton - supporting films characterized by metasurfaces instead of unstructured conductive films.

[0234] The normalized complex optical impedance of the surface is given by Z / Z0=(1 + r) / (1 - r) in terms of the complex surface reflection coefficient r = |r|e iδis directly related to (Tsurimaki Y et al. Acs Photonics 2018, 5, 929 - 938) and can be calculated from the transfer matrix model (Passler NC et al. Physical Review B 2020, 101, 165425; Passler NC et al. JOSA B 2017, 34, 2128 - 2139) (Figure 96). When the imaginary parts of the impedances of the two components (distributed Bragg reflector and polariton supporting material) match (the amplitudes are equal but the signs are opposite), a Tamm resonance can be supported. -Imag(Z DBR ) and Imag(Z ポラリトン支持材料 ), as shown in Figure 97, determines the Tamm resonance. The thickness of CdO is about 500 nm, which can be considered optically bulk, while the thickness of hBN is relatively thin (10 - 200 nm). The impedance of hBN, as shown in Figure 98, changes rapidly with thickness when the thickness is less than 100 nm.

[0235] The Tamm resonance only exists when Imag(Z hBN ) - Imag(Z DBR ) = 0. Therefore, the faster the two components branch away from each other, the narrower the Tamm resonance becomes because the condition is no longer satisfied. In fact, the dispersion of Imag(Z hBN ) is significantly faster than that of Imag(Z CdO ), and the dispersion is slower for thicker hBN, which is consistent with the following observation: The Q factor of the Tamm phonon polariton is larger than that of the Tamm plasmon polariton, and this decreases with increasing thickness of hBN.

[0236] To further understand the improved Q factor of Tamm phonon polaritons compared to Tamm plasmon polaritons, the quality factors of the two systems induced by impedance dispersion (radiative loss) and material loss (non-radiative loss) were analyzed. To find the radiative loss of the Tamm mode(s), both CdO and hBN were modeled in a lossless manner by artificially setting the mobility and phonon lifetime to infinity, respectively, following the methodology of Yoon et al. (Yoon J et al. Optics Express 2008, 16, 1269 - 1279) (Figs. 99 - 100). The radiative loss of the Tamm phonon polariton is significantly lower than that of the Tamm plasmon polariton (Q factor of about 33 vs. 7.6) caused by the high-speed dispersion of the hBN impedance mirror and is further discussed in the following paragraphs. The non-radiative loss can be derived from the radiative loss and the total loss of the two systems (Yoon J et al. Optics Express 2008, 16, 1269 - 1279), and the non-radiative loss of the Tamm phonon polariton is negligible while still playing an indispensable role that the Tamm plasmon polariton lacks. Assuming a phonon polariton material with the same dispersion of hBN but with the material quality of a plasmonic material (phonon lifetime of 0.145 ps), the obtained Q factor of the Tamm phonon polariton was found to decrease from about 33 to about 25, indicating that the low loss of the phonon polariton material remains important.

[0237] The Q factor of Tamm polaritons remains lower than that of Tamm phonon polaritons even when both are lossless, which is to be noted as being caused by different impedance dispersions. The radiative loss is determined by the relative dispersions of the two mirrors in the system: the distributed Bragg reflector and the polariton mirror. As mentioned elsewhere (Tsurimaki Y et al. Acs Photonics 2018, 5, 929 - 938; Wang Z et al. Acs Photonics 2018, 5, 2446 - 2452; He M et al. Nature Materials 2021, 20, 1663 - 1669; Kaliteevski M et al. Physical Review B 2007, 76, 165415; Brand S et al. Physical Review B 2009, 79, 085416), the Tamm mode is supported when the imaginary parts of the impedances of the two components match. In other words, for a system where the two impedances deviate from each other more rapidly within the spectral domain, the mode is supported over a smaller frequency range, thus a narrower linewidth, and thus a higher Q factor. Since the impedance of hBN is much more dispersive than that of CdO (Figs. 96 - 98), the corresponding Tamm mode is supported only within a narrower frequency range, and thus the modal linewidth is reduced even when the scattering lifetimes of the phonon and plasmon polariton materials are equivalent. To further confirm this, systems featuring hBN with different artificial longitudinal optical phonon frequencies were also modeled to correct the spectral dispersion at a fixed scattering lifetime, and it was found that the quality factor increases with faster material dispersion (Fig. 101). Thus, the improved Q factor of Tamm phonon polaritons can be attributed to both material dispersion (radiative loss) and material quality (non - radiative loss).

[0238] Section 2. Peak fitting. Samples of Tamm phonon polaritons, Tamm plasmon polaritons, and Tamm hybrids were measured with three different objective lenses while varying the angle of incidence. The FWHM and central maximum of those peaks were determined using an asymmetric peak fitting function provided by Origin Lab.

[0239] Section 3. Band curvature of Tamm plasmon polariton absorbers and Tamm hybrid polariton absorbers. The spectral characteristics can be matched by having more distributed Bragg reflector layers in the Tamm plasmon polariton absorber, but the angular dispersion of the Tamm plasmon polariton is basically limited to a narrow range in a distributed Bragg reflector composed of Ge and AlOx. Here, different band curvatures are targeted, and the resulting band curvatures are always between 0.058 and 0.094 cm -1 / degree 2 as shown in FIGS. 102 to 107. Thus, hybridization provides a unique way to flatten the dispersion for applications where non-dispersive characteristics are ideal.

[0240] Next, the band curvature was analyzed from the perspective of material dispersion. For that purpose, a structure of hBN with a thickness of 100 nm in the design of the Tamm plasmon polariton absorber was used, and the longitudinal optical phonon frequency of hBN was artificially modified to study how the band curvature of the Tamm hybrid polariton absorber changes. As shown in FIGS. 108 to 111, high-speed dispersive materials, namely, closely spaced transverse optical (TO) and longitudinal optical (LO) phonon frequencies, are found to further reduce the band curvature of the Tamm hybrid polariton absorber. In particular, the dispersion of the system is mainly determined by the Tamm plasmon polariton component (band curvature of 0.058 cm -1 / degree 2 ), which is much more dispersive than the Tamm phonon polariton component (about 0.01 cm -1 / degree 2 ).

[0241] Section 4. Band curvature of Tamm plasmon polariton absorbers and Tamm hybrid polariton absorbers. Herein, the implications of band curvature in applications where a range of incident angles are simultaneously considered are discussed. For any metamaterial with angular dispersion, such as continua (Yang S et al. Nano Letters, 2022, 22(20), 8060 - 8067; Leitis A et al. Science Advances 2019, 5, eaaw2871), the quasi - bound states in directive thermal emitters, the spectra collected are combinations of different incident angles. For example, a wavelength - selective absorber can be used as a filterless chemical sensor and a wavelength - selective thermal emitter for infrared beacons, and the emitted light at different incident angles can be collected by a parabolic mirror to increase the signal intensity. A typical parabolic mirror has a numerical aperture of 0.5 - 0.7, showing collection angles of ±30° and ±45°.

[0242] First, as shown in FIG. 112, consider a Tamm plasmon polariton absorber with a FWHM of 38 cm at normal incidence. The convolution spectra at collection angles of ±30° and ±45° are significantly broadened, and the FWHMs increase to 61 cm -1 and 100 cm -1 respectively (FIG. 114). However, for the same structure, by adding 100 - nm - thick hBN to form a Tamm hybrid polariton, the band curvature is significantly reduced (FIG. 113). Quantitatively, the FWHMs of the lower polariton branch (upper polariton branch) at normal incidence, collection angles of ±30°, and ±45° are 24, 31, 43 cm -1 (12, 29, 54 cm -1 ) respectively. -1

[0243] Next, only 5.8 cm -1A Tamm plasmon polariton absorber with a high Q factor and having an FWHM was considered (Figure 115). The spectrum is suppressed and the resonances are nearly indistinguishable for collection angles of ±30° and ±45°, as shown in Figure 117. However, for the corresponding Tamm hybrid polaritons (Figure 116), the lower polariton branch, which is less dispersive, remains transparent even at a collection angle of ±45°.

[0244] Section 5. Influence of the anisotropy of hBN on the system. Hexagonal boron nitride (hBN) is a hyperbolic material in the upper and lower reststrahlen bands, and volume-confined hyperbolic modes can be supported by hBN. However, all the properties discussed herein are not related to the hyperbolicity of hBN. To discuss the role of anisotropy in the system, Tamm phonon polaritons and Tamm hybrids were modeled with two types of hBN: the actual hBN with the dielectric function from the reference (Giles AJ et al. Nature materials 2018, 17, 134), and artificially isotropic hBN by assigning ε z = ε xy The dispersive Bragg reflector structures used herein are from Figures 75 - 85.

[0245] First, the influence at an incident angle of 30° for p-polarized light is discussed. For the Tamm phonon polariton resonance, the responses of hBN and artificial hBN are nearly the same, as shown in Figures 118, 119, and 120. Since the Berreman mode is excited only when the permittivity along the z-axis approaches zero (near the longitudinal optical phonon) (Zhu H et al. Advanced Optical Materials, 2021, 9(21), 2100645), the isotropic model cannot predict the true response. For the Tamm hybrid polariton, as shown in Figures 121 - 123, the difference between the isotropic model and the anisotropic model is the same as in the Tamm phonon polariton case.

[0246] The responses of hBN and artificial isotropic hBN in the Tamm polariton structure are almost the same at low incident angles (30°), but not the same at high incident angles (60° in this specification). Here, the Tamm hybrid polaritons and Tamm phonon polaritons with different modeled hBNs were calculated at different incident angles (Figs. 124 - 129). Not only the Berehman mode, which is axis - selective, but also the spectrum of artificially isotropic hBN deviates from the true model as it approaches the longitudinal optical phonon frequency, and this deviation appears in both Tamm phonon polaritons and Tamm hybrid polaritons. Therefore, the fact that hBN is an anisotropic material cannot be ignored, and thus the response cannot be simply approximated by a simple isotropic material, and the complex anisotropic response further poses challenges to the structural design.

[0247] Section 6. Inevitable transverse optical phonons in the Tamm phonon polariton structure and their influence. About 1400 cm -1 The transverse optical phonons of hBN at are along the x - y plane, so as long as hBN is included in the structure, such phonon absorption modes exist. Therefore, the influence of such inevitable modes on the application is evaluated. The multi - band absorber is used as a thermal emitter light source for spectral barcoding applications (Fig. 88), and the operating temperature is assumed to be 600 °C. Therefore, the power emitted in the spectrum can be calculated by multiplying the power emitted by the blackbody by the absorption rate, resulting in Fig. 131. By integrating over the entire frequency range, the power emitted between 1000 cm -1 ~2000 cm -1 was found to be 917 W / m 2 / sr. Then, integrating only the range between 1380 - 1410 cm -1 , where the Fabry - Perot and transverse optical phonon absorption (emission) lines exist, a power emission of 37 W / m 2 / sr is obtained, which accounts for only about 4% of the total emission power. Therefore, these additional but unavoidable absorption lines can be ignored in most applications.

[0248] Section 7. Magnetic field distribution with different hBN thicknesses. Here, the magnetic field distribution of the Tamm polariton absorber is discussed. For thicker hBN, as shown in FIGS. 132 - 133 and FIGS. 134 - 135, the magnetic field strength becomes stronger. Therefore, the magnetic field distribution overlapping with the Tamm plasmon polariton mode (FIGS. 134 - 135) increases as the hBN thickness increases, thus inducing stronger light - matter interaction and more significant resonance splitting (FIG. 141).

[0249] Section 8. Tamm hybrid polariton absorbers with different polar materials. Here, it is shown that Tamm hybrid polariton absorbers can be realized with other polar materials such as silicon dioxide and silicon carbide. In the case of SiO2, the same geometry as in the text was used: since high - quality SiO2 can be deposited by atomic layer deposition (ALD) on many substrates, SiO2 - dispersed Bragg reflector - CdO substrates (Yoo D et al. Nature Photonics 2021, 15, 125 - 130). The Tamm hybrid polariton spectrum is clearly different from the Tamm plasmon polariton or Tamm phonon polariton and shows modal hybridization (FIG. 136). Since SiO2 is an isotropic medium, it is remarkable that the Berreman mode (about 1240 cm -1 ) is excited.

[0250] In the case of SiC, due to the ability to deposit 3C - SiC on a silicon substrate by CVD, a different geometry, namely, a dispersed Bragg reflector - CdO - SiC - silicon, was used. Still, Tamm hybrid polaritons and coupled resonances are observed (FIG. 137). Therefore, Tamm hybrid polaritons can be formed by various phonon - polariton - supporting materials for applications in different frequency ranges.

[0251] Section 9. Comparison between different modes supported by a planar structure. The comparison is summarized in Table 7.

Table 18

[0252] Section 10. Performance of Tamm polaritons for gas sensing. The performance of Tamm hybrid polaritons for non - dispersive infrared applications was theoretically evaluated according to previous procedures. Principle of this calculation: Assume a specific operating temperature (600 °C) of the Tamm absorber and function it as a thermal emitter (Baranov D.G. et al. Nature materials, 2019, 18, 920 - 930). Then, calculate the transmitted power through SO2F2 with different concentrations, which is detected by a dual - channel pyroelectric detector with a responsivity of 150,000 V / W (https: / / www.boselec.com / wp - content / uploads / Linear / Heimann / HeimannLiterature / Heimann - Pyros - 11 - 27 - 19.pdf.). Generally, the power change in a non - dispersive infrared device can be calculated by integrating the absorption rate in the spectral domain, and the gas absorption rate is determined by the Beer - Lambert law: Transmittance in SO2F2 = exp(−kcL) Equation (S1) where k is the absorption coefficient (estimated from data of the National Institute of Standards and Technology) (https: / / webbook.nist.gov / chemistry / #;https: / / webbook.nist.gov / cgi / cbook.cgi?ID=C2699798&Units=SI&Type=IR-SPEC&Index=0#IR-SPEC), c is the gas concentration, and L is the optical path length of the sample (assumed to be 10 cm in this specification). Based on this principle, the detector readings of different devices were calculated: from the text, the 5-layer Tamm plasmon polariton (TPP-5), the 9-layer Tamm plasmon polariton (TPP-9), and the 5-layer Tamm hybrid polariton (THP-5). In addition, the performance was benchmarked against that of a standard non-dispersive infrared device characterized by a band-pass filter (BP) in mid-infrared centered on only one of the vibrational modes (1504 cm -1 ) having bandwidths of 100 nm and 500 nm as shown in FIG. 138.

[0253] The performance is determined by the following two performance indices: (1) sensitivity (detection limit), i.e., the point at which the minimum amount of sulfuryl fluoride can be detected; and (2) selectivity, i.e., the relative power change when 1% of sulfuryl fluoride is present. Since the narrow-band filter passes only a small frequency range, a significant amount of energy used to indicate the presence of the gas is wasted, leading to the lowest detection limit (89 ppm) (FIG. 139). On the other hand, the bandwidth results in the best selectivity (90%, FIG. 140) because it is almost completely within the chemical absorption band. To enhance the detection limit, a band-pass filter with a wider bandwidth that includes more energy in the absorption band actually improves the detection limit to 47 ppm. However, the wide-bandwidth band-pass filter results in the worst selectivity (45%) for the wide bandwidth. The trade-off between sensitivity and selectivity can be avoided if the band-pass filter is characterized by only one transmission band.

[0254] To improve the detection limit while maintaining the selectivity, a Tamm emitter with three simultaneous vibration modes and overlapping emission frequencies is used. The detection limit obtained from all cases is improved from a single-band bandpass filter, and the selectivity is improved from a 500 nm bandpass filter. THP-5 provides nearly the same performance as the TPP-9 design, and both were found to be approximately 25 ppm. From the perspective of selectivity, for TPP-9 and THP-5, the relative power change per 1% gas is 62% and 60%, respectively. In particular, the infrared bandpass filter is mainly based on a thin film structure, and the manufacture of the bandpass filter can involve material deposition with a thickness exceeding 8 μm (more than 20 layers), which is significantly higher than that of the Tamm hybrid polariton device (Zhou S et al. Coatings 2021, 11, 803). In summary, the THP-5 design provides an equivalent detection limit compared to TPP-9, which is the best in this comparison set. It is important to note that these multi-frequency emitters enhance both selectivity and detection limit simultaneously compared to a wide bandpass filter that cannot be achieved with a single-band bandpass filter.

[0255] The designed structural parameters are listed below. Note that all structures use alternating Ge and ZnSe layers, assuming constant refractive indices of 4.0 and 2.25, respectively. TPP5 layers: 572 (Ge) 732 (ZnSe) 190 (Ge) 391 (ZnSe) 356 (Ge) 400 (CdO of 1.07×1020 cm-3). Total thickness of 2375 nm TPP9 layers: 516 (Ge) 741 (ZnSe) 119 (Ge) 530 (ZnSe) 545 (Ge) 621 (ZnSe) 244 (Ge) 559 (ZnSe) 429 (Ge) 400 (CdO of 6.9×1020 cm-3). Total thickness of 4700 nm THP5 layers: 320 (hBN) 656 (Ge) 370 (ZnSe) 843 (Ge) 950 (ZnSe) 545 (Ge) 400 (CdO of 0.26×1020 cm-3). Total thickness of 4084 nm

[0256] Example 6 Describe the observable matrix for a multilayer planar semiconductor heterostructure using the anisotropic scattering matrix method. This avoids the singularities associated with the transfer matrix method in a lossy medium and allows the optimization algorithm to robustly explore the parameter space. This approach also allows both isotropic and uniaxial materials to be investigated.

[0257] The loss matrix was developed to optimize the design of mid-infrared emitters in the presence of target gases (e.g., those desired to be detected) and non-target gases (e.g., those desired to avoid detection). The optimization procedure aims to minimize the numerical value of the loss having two components. The first, which is positive, measures the degree of overlap between the emissivity and the non-target gases. This is defined as the sum of the convolution of the emissivity and each of the non-target gas spectra weighted by the relative concentration of each gas at the operating point. The second contribution measures the overlap between the emissivity and the target gas spectrum and is the negation of the convolution of the two spectra. To compensate for the smaller emissivity in the non-target region as the optimization proceeds, the positive component is weighted by an adjustable hyperparameter ε that ensures both goals are achieved. The total loss is the sum of these quantities.

[0258] The excellent data processing libraries in the TensorFlow ecosystem are utilized to stream molecular spectra from a local database constructed using the HITEMP and HITRAN open-source libraries. Using TensorFlow Transform and Apache Beam, it is possible to stream with latency in multiple highly spectral density molecular absorption curves while minimizing overhead.

[0259] Using TensorFlow's automatic differentiation tool, the loss matrix using Newton's method was optimized quickly. As a result, the developed complex loss matrix and the individual convolution matrices for each gas can be easily tracked.

[0260] Example 7 In the case of emitter / detector pairings, in some examples, since the same design approach can be used for both, there is no difference between the results of the emitter and detector given the same initial conditions.

[0261] In some examples, in the case of emitter / detector pairings, the optimization approach for the detector can be different from that of the emitter. For example, instead of using the spectrum to optimize the detector, the emitter emission profile can be used. Taking the same approach maximizes the overlap with the matching emitter and minimizes the overlap with other emitters. The optimization procedure again minimizes the numerical values of the two component losses. The positive contribution now measures the overlap between the detector and emitters that do not match (the sum of the convolution of the detector's emissivity and the emissivity of each non-matching emitter). The negative contribution is the cancellation of the convolution of the emissivities of the matching detector and emitter. As before, hyperparameters are introduced to weight the positive contribution. Compared to reusing the detector design, this means less signal waste because the detector peak is wider than the emitter peak.

[0262] Other advantages that are obvious and unique to the present invention will be apparent to those skilled in the art. It will be understood that certain features and subcombinations are useful and can be used without reference to other features and subcombinations. This is contemplated by the claims and is within the scope of the claims. Since many possible embodiments can be made from the present invention without departing from the scope of the present invention, all matters shown or indicated in the accompanying drawings should be construed as illustrative and not in a limiting sense.

[0263] The method of the appended claims is not limited in scope by the specific methods described herein, which are intended as examples of some aspects of the claims, and any method that is functionally equivalent is intended to fall within the scope of the claims. In addition to what is shown and described herein, various modifications of the method are intended to fall within the scope of the appended claims. Further, although only certain representative method steps disclosed herein are specifically recited, other combinations of method steps are also intended to fall within the scope of the appended claims even if not specifically enumerated. Accordingly, steps, elements, components, or combinations of components may be explicitly recited herein or below, but other combinations of steps, elements, components, and components are included even if not explicitly described.

Claims

1. Dispersive Bragg reflectors, A layer comprising a conductive material and / or a polaritonic material, A Tamm polariton emitter comprising the dispersed Bragg reflector, wherein the dispersed Bragg reflector is disposed on the layer of the conductive material and / or polaritonic material.

2. The Tamm polariton emitter according to claim 1, further comprising a layer of polar material disposed on top of the dispersed Bragg reflector, wherein the dispersed Bragg reflector is sandwiched between the layer of conductive material and / or polaritonic material and the polar material.

3. A layer of polar material, Dispersive Bragg reflectors, A layer comprising a conductive material and / or a polaritonic material, The dispersed Bragg reflector is disposed on the layer of the conductive material and / or polaritonic material, The layer of the polar material is positioned above the dispersed Bragg reflector, so that the dispersed Bragg reflector is sandwiched between the layer of the conductive material and / or polaritonic material and the polar material, or A Tamm polariton emitter, wherein the layer of the polar material is located beneath the layer of the conductive material and / or polariton material, so that the layer of the conductive material and / or polariton material is sandwiched between the layer of the polar material and the dispersed Bragg reflector.

4. The Tamm polariton emitter according to claim 2, wherein the polar material layer has an average thickness of 1 nanometer (nm) to 100 millimeters (mm).

5. The Tamm polariton emitter according to claim 2, wherein the polar material includes hexagonal boron nitride, silicon carbide, aluminum nitride, gallium nitride, or a combination thereof.

6. The Tamm polariton emitter according to claim 2, wherein the polar material comprises hexagonal boron nitride.

7. The circuit board is further equipped, The layer of the conductive material and / or polaritonic material is disposed on the substrate, and the layer of the conductive material and / or polaritonic material is sandwiched between the substrate and the dispersed Bragg reflector. The dispersed Bragg reflector is arranged on the substrate, and the dispersed Bragg reflector is sandwiched between the substrate and the layer of the conductive material and / or polaritonic material. The layer of the polar material is present and arranged on the substrate, and the layer of the polar material is sandwiched between the substrate and the dispersed Bragg reflector, or The Tamm polariton emitter according to claim 1, wherein the layer of the polar material is present and arranged on the substrate, and the layer of the polar material is sandwiched between the substrate and the layer of the conductive material and / or polaritonic material.

8. The Tamm polariton emitter according to claim 1, wherein the layer of conductive material and / or polariton material comprises a polariton material.

9. The Tamm polariton emitter according to claim 8, wherein the polaritonic material includes a phonon polariton material.

10. The Tamm polariton emitter according to claim 8, wherein the polaritonic material has an adjustable carrier density.

11. The Tamm polariton emitter according to claim 8, wherein the polaritonic material includes a transparent conductive oxide, a III-V semiconductor, or a combination thereof.

12. The Tamm polariton emitter according to claim 8, wherein the polaritonic material includes a transparent conductive oxide.

13. The Tamm polariton emitter according to claim 8, wherein the polaritonic material contains cadmium oxide.

14. The Tamm polariton emitter according to claim 8, wherein the polaritonic material further comprises a dopant.

15. The Tamm polariton emitter according to claim 14, wherein the presence and / or concentration of the dopant adjusts the carrier density of the polaritonic material.

16. The Tamm polariton emitter according to claim 8, wherein the polaritonic material includes doped cadmium oxide such as n-doped cadmium oxide.

17. The Tamm polariton emitter according to claim 8, wherein the polaritonic material includes n-type In-doped CdO.

18. The Tamm polariton emitter according to claim 1, wherein the layer of the conductive material and / or polariton material has an average thickness of 1 nanometer (nm) to 100 millimeters (mm).

19. The layer of the conductive material and / or polaritonic material is 1 × 10 １０ cm －３ ~1 x 10 ２５ cm －３ A Tammm polariton emitter according to claim 1, having a carrier density of the specified value.

20. The Tamm polariton emitter according to claim 1, wherein the dispersed Bragg reflector includes an aperiodic dispersed Bragg reflector.

21. The Tamm polariton emitter according to claim 1, wherein the dispersed Bragg reflector comprises multiple layers of multiple materials having various refractive indices.

22. The Tamm polariton emitter according to claim 1, wherein the dispersed Bragg reflector comprises a plurality of alternating layers of a first material having a first refractive index and a second material having a second refractive index, wherein the first refractive index and the second refractive index are different.

23. The Tamm polariton emitter according to claim 22, wherein the first material comprises Ge.

24. The Tamm polariton emitter according to claim 22, wherein the second material comprises aluminum oxide or ZnSe.

25. The Tamm polariton emitter according to claim 21, wherein the total number of layers is 1 to 10,000.

26. The Tamm polariton emitter according to claim 21, wherein each of the plurality of layers independently has an average thickness of 1 nanometer (nm) to 100 millimeters (mm).

27. The Tamm polariton emitter according to claim 1, wherein the Tamm polariton emitter emits radiation at a certain frequency, and the frequency is the emission frequency.

28. The Tamm polariton emitter according to claim 27, wherein the Tamm polariton emitter has a single emission frequency.

29. The Tamm polariton emitter according to claim 27, wherein the Tamm polariton emitter has a plurality of emission frequencies.

30. The Tamm polariton emitter according to claim 27, wherein the Tamm polariton emitter has an emission frequency in the visible spectral region.

31. The Tamm polariton emitter according to claim 27, wherein the Tamm polariton emitter has an emission frequency in the ultraviolet spectral region.

32. The Tamm polariton emitter according to claim 27, wherein the Tamm polariton emitter has an emission frequency in the terahertz spectral region.

33. The Tamm polariton emitter according to claim 27, wherein the Tamm polariton emitter has an emission frequency in the infrared spectral region.

34. The Tamm polariton emitter according to claim 27, wherein the Tamm polariton emitter has an emission frequency in the short-wave to long-wave infrared spectral region, the medium-wave to long-wave infrared region, the long-wave infrared region to the telecommunications band region, or a combination thereof.

35. The Tamm polariton emitter according to claim 1, wherein the Tamm polariton emitter includes a Tamm plasmon polariton emitter, a Tamm phonon polariton emitter, or a Tamm hybrid polariton emitter.

36. A method for producing a Tamm polariton emitter according to any one of claims 1 to 35.

37. The method according to claim 36, wherein the method comprises arranging the dispersed Bragg reflector on the layer of the conductive material and / or polaritonic material.

38. The method according to claim 37, wherein the method includes complementary metal oxide semiconductor (CMOS) processing.

39. A method of using a Tamm polariton emitter according to any one of claims 1 to 35 in free-space communication applications, as a beacon, in barcode applications, in encryption applications, in sensing applications, or in a combination thereof.

40. An infrared beacon comprising a Tamm polariton emitter according to any one of claims 1 to 35.

41. A method of using the infrared beacon according to claim 40 for search and rescue, police, and / or military purposes.

42. A sensor comprising a Tmm polariton emitter according to any one of claims 1 to 35.

43. The Tamm polariton emitter according to any one of claims 1 to 35, wherein the Tamm polariton emitter is configured to selectively emit radiation at a frequency corresponding to the rotational speed or vibrational resonance frequency of the analyte to be analyzed, A non-dispersive infrared sensor comprising a Tamm polariton emitter and / or a detector configured to receive an electromagnetic signal from the analyte being analyzed.

44. The sensor according to claim 43, further comprising a fluid cell extending from a proximal end to a distal end and having an inlet and an outlet, wherein the Tamm polariton emitter is positioned toward the proximal end of the fluid cell, and the detector is positioned toward the distal end of the fluid cell, so that when the sensor is assembled together with a fluid sample, the fluid cell is configured to contain the fluid sample, and the detector is configured to receive an electromagnetic signal from the Tamm polariton emitter and / or the fluid sample.

45. The sensor according to claim 43, wherein the detector is configured to selectively receive the electromagnetic signal from the Tamm polariton emitter and / or the analyte being analyzed.

46. The sensor according to claim 43, wherein the detector includes a Tamm polariton detector, and the Tamm polariton detector includes a Tamm polariton emitter according to any one of claims 1 to 35.

47. The sensor according to claim 43, wherein the Tamm polariton emitter and / or the Tamm polariton detector (if present) independently include a Tamm plasmon polariton emitter, a Tamm phonon polariton emitter, or a Tamm hybrid polariton emitter.

48. The sensor according to claim 44, further comprising a computing device configured to receive and process signals from the detector to determine the characteristics of the fluid sample.

49. The sensor according to claim 48, further configured to output the characteristics of the fluid sample and / or a feedback signal based on the characteristics of the fluid sample.

50. The sensor according to claim 49, wherein the feedback signal includes tactile feedback, auditory feedback, visual feedback, or a combination thereof.

51. The sensor according to claim 48, wherein the characteristics of the fluid sample include the presence of the target analyte in the fluid sample, the concentration of the target analyte in the fluid sample, the identity of the target analyte, or a combination thereof.

52. The sensor according to claim 44, wherein the fluid sample includes a gaseous sample.

53. The sensor according to claim 43, wherein the target analyte includes a gas.

54. The sensor according to claim 43, wherein the target analyte includes a plurality of analytes.

55. The aforementioned target analytes include multiple analytes, The Tamm polariton emitter is configured to selectively emit radiation at multiple frequencies, or the sensor comprises multiple Tamm polariton emitters, each of which is configured to selectively emit radiation at a certain frequency, and so on, the multiple Tamm polariton emitters are selectively configured to emit radiation at multiple frequencies. The sensor according to claim 43, wherein at least a portion of each of the plurality of frequencies corresponds to the rotational speed or vibration resonance frequency of each of the plurality of target analytes, and so that the sensor can detect the plurality of analytes simultaneously.

56. The detector includes a Tamm polariton detector, and the Tamm polariton detector is configured to selectively receive radiation at the plurality of frequencies, or The sensor according to claim 55, wherein the detector includes a plurality of Tamm polariton detectors, each of the plurality of Tamm polariton detectors is configured to selectively receive radiation at a certain frequency, and so the plurality of Tamm polariton detectors are selectively configured to receive radiation at a plurality of frequencies.

57. The aforementioned analyte includes a single analyte, The Tamm polariton emitter is configured to selectively emit radiation at multiple frequencies, or the sensor comprises multiple Tamm polariton emitters, each of which is configured to selectively emit radiation at a certain frequency, and so on, the multiple Tamm polariton emitters are selectively configured to emit radiation at multiple frequencies. The sensor according to claim 43, wherein at least a portion of each of the plurality of frequencies corresponds to a plurality of rotational speeds or vibrational resonance frequencies of the target analyte, and so the sensor can detect the target analyte with high sensitivity.

58. The detector includes a Tamm polariton detector, and the Tamm polariton detector is configured to selectively receive radiation at the plurality of frequencies, or The sensor according to claim 57, wherein the detector includes a plurality of Tamm polariton detectors, each of the plurality of Tamm polariton detectors is configured to selectively receive radiation at a certain frequency, and so the plurality of Tamm polariton detectors are selectively configured to receive radiation at the plurality of frequencies.

59. The sensor according to claim 43, wherein the analyte subject to analysis includes toxins, contaminants, pollutants, warfare agents, or combinations thereof.

60. The sensor according to claim 43, wherein the analyte to be analyzed includes greenhouse gases.

61. The sensor according to claim 43, wherein the analyte subject to analysis includes gases produced in and / or generated as by-products of semiconductor manufacturing, industrial production, chemical synthesis, or a combination thereof.

62. The sensor according to claim 43, wherein the analyte to be analyzed is a gas or chemical substance that needs to be maintained at a specific concentration.

63. where the analyte of interest is CO ２ , SO ２ , formaldehyde, CO, NH ３ , N ２ O, O ３ , CH ４ , NO, dimethyl methylphosphonate (DMMP), or a combination thereof, the sensor according to claim 43.

64. The sensor according to claim 43, wherein the sensor is filterless.

65. A method of using the sensor according to claim 43 for gas sensing.

66. A method of using the sensor according to claim 43 for environmental sensing, atmospheric sensing, chemical sensing, or a combination thereof.

67. A method for designing a Tamm polariton emitter according to any one of claims 1 to 35.

68. The method according to claim 67, wherein the method includes a reverse design protocol.

69. The method according to claim 67, wherein the method includes machine learning.

70. A method for designing a Tamm polariton emitter, wherein the Tamm polariton emitter is A dispersed Bragg reflector comprising a stack of multiple layers of multiple materials having various refractive indices, each layer containing a material having a certain refractive index, each layer having a certain average thickness, and the refractive index of each layer being different from that of preceding and / or succeeding layers, A layer comprising a conductive material and / or a polaritonic material, The dispersed Bragg reflector is disposed on the layer of the conductive material and / or polaritonic material, The Tamm polariton emitter emits radiation at a certain frequency, The method described above is a. Define the target spectrum of the radiation emitted by the Tamm polariton emitter. b. Defining an initial set of values ​​for the set of parameters of the designed Tamm polariton emitter, The set of parameters includes the total number of layers of the dispersed Bragg reflector, the composition of each of the plurality of layers, the thickness of each of the plurality of layers, the composition of the conductive material and / or polaritonic material of the layer, the carrier density of the conductive material and / or polaritonic material of the layer, and the thickness of the conductive material and / or polaritonic material of the layer, For the aforementioned initial set of values, the initial total number of layers is user-defined, and the remaining parameters are initialized randomly. c. Modeling the emission spectrum of the designed Tamm polariton emitter having the initial set of parameters written as vector(t), wherein the modeled emission spectrum is the designed emission spectrum. d. Comparing the designed emission spectrum with the target emission spectrum to determine the error, The designed emission spectrum is modeled and compared with the target emission spectrum using the transfer matrix method. The aforementioned error is a scalar error which is a combination of the mean squared error and the mean absolute error. If the error is greater than a predefined threshold, the error is backpropagated to find the gradient over t by stochastic gradient descent, and the gradient is used to update t in the next iteration of steps c and d. [Math 1] The iteration continues until the predetermined maximum number of iterations is reached or the error is minimized. If the number of iterations reaches the predefined maximum number without reaching the error threshold, the number of layers increases, and the method is repeated. If the error is less than or equal to a defined threshold, the method comprises outputting the set of parameters, the designed emission spectrum, the target emission spectrum, or a combination thereof.

71. A method for designing a Tamm polariton emitter, wherein the Tamm polariton emitter is A layer of polar material, A dispersed Bragg reflector comprising a stack of multiple layers of multiple materials having various refractive indices, each layer containing a material having a certain refractive index, each layer having a certain average thickness, and the refractive index of each layer being different from that of preceding and / or succeeding layers, A layer comprising a conductive material and / or a polaritonic material, The dispersed Bragg reflector is disposed on the layer of the conductive material and / or polaritonic material, The layer of the polar material is positioned on top of the dispersed Bragg reflector, and so the dispersed Bragg reflector is sandwiched between the layer of the conductive material and / or polaritonic material and the polar material. The Tamm polariton emitter emits radiation at a certain frequency, The method described above is a. Define the target spectrum of the radiation emitted by the Tamm polariton emitter. b. Defining an initial set of values ​​for the set of parameters of the designed Tamm polariton emitter, The set of parameters includes the total number of layers of the dispersed Bragg reflector, the composition of each of the plurality of layers, the thickness of each of the plurality of layers, the composition of the conductive material and / or polaritonic material layer, the carrier density of the conductive material and / or polaritonic material layer, the thickness of the conductive material and / or polaritonic material layer, the composition of the polar material layer, the carrier density of the polar material layer, and the thickness of the polar material layer. For the aforementioned initial set of values, the initial total number of layers is user-defined, and the remaining parameters are initialized randomly. c. Modeling the emission spectrum of the designed Tamm polariton emitter having the initial set of parameters written as vector(t), wherein the modeled emission spectrum is the designed emission spectrum. d. Comparing the designed emission spectrum with the target emission spectrum to determine the error, The designed emission spectrum is modeled and compared with the target emission spectrum using the transfer matrix method. The aforementioned error is a scalar error which is a combination of the mean squared error and the mean absolute error. If the error is greater than a predefined threshold, the error is backpropagated to find the gradient over t by stochastic gradient descent, and the gradient is used to update t in the next iteration of steps c and d. [Math 2] The iteration continues until the predetermined maximum number of iterations is reached or the error is minimized. If the number of iterations reaches a predefined maximum number without reaching an error threshold, the number of layers increases, and the method is repeated. If the error is less than or equal to a defined threshold, the method comprises outputting the set of parameters, the designed emission spectrum, the target emission spectrum, or a combination thereof.

72. The aforementioned error is given by the following formula: Error = Average (Ratio 1 (DS - TS)) ２ +Ratio 2 |DS-TS|) The method according to claim 70 or 71, defined by the formula, wherein ratio 1 and ratio 2 are hyperparameters customized for different purposes, and DS and TS are vectors having elements that represent the absorption rate at the corresponding wavelength.

73. The method according to claim 70 or 71, wherein step c and / or d of the method includes a weighted sampling technique.

74. The method according to claim 73, wherein the weighted sample technique is based on a desired application, a target frequency range, a target analyte, or a combination thereof.

75. The method according to claim 70 or 71, wherein the parameters further include the frequency, amplitude, and / or linewidth of the emitted radiation.

76. The method according to claim 70 or 71, wherein the parameter further includes a quality factor (e.g., Q factor).

77. The method according to claim 76, wherein the Q coefficient is 1 to 1,000,000.

78. The method according to claim 70 or 71, wherein the Tammm polariton emitter includes the Tammm polariton emitter described in any one of claims 1 to 35.

79. The method according to claim 70 or 71, wherein the method includes machine learning.

80. The method according to claim 70 or 71, wherein the Tamm polariton emitter comprises a plurality of Tamm polariton emitters, and the parameter further comprises the number of Tamm polariton emitters in the plurality of Tamm polariton emitters.

81. The method according to claim 70 or 71, wherein the method comprises designing a first Tamm polariton emitter and a second Tamm polariton emitter, the second Tamm polariton emitter comprising a Tamm polariton detector.

82. The method according to claim 81, wherein the first Tamm polariton emitter is configured to selectively emit radiation at one or more frequencies, and the second Tamm polariton emitter is configured to selectively receive at least a portion of the radiation emitted by the first Tamm polariton emitter (for example, the first Tamm polariton emitter and the Tamm polariton detector are identical).

83. The method according to claim 82, further comprising maximizing the overlap between the radiation emitted by the Tamm polariton emitter and the radiation received by the detector.

84. The method according to claim 81, wherein the first Tamm polariton emitter comprises a first plurality of Tamm polariton emitters, or the second Tamm polariton emitter comprises a second plurality of Tamm polariton emitters, or a combination thereof.

85. The method according to claim 81, wherein the first Tamm polariton emitter includes a first plurality of Tamm polariton emitters, and the parameter includes the number of the first plurality of first Tamm polariton emitters, or the second Tamm polariton emitter includes a second plurality of Tamm polariton emitters, and the parameter includes the number of the plurality of second Tamm polariton emitters, or a combination thereof.

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