System and method for reverse design of optical multi-layer thin film structure by using basic model

Abstract

Systems and methods for reverse design of optical multilayer thin film structures are provided that include receiving optical target parameters based on input cues and applying the received optical target parameters to a base model having a transformer that includes a series of neural network models, the material and thickness of the layers of the optical multi-layer thin film structure are represented using structure serialization using the markers, and the learning of the model on the relationship between the spectrum and the structure is facilitated using spectrum embedding. The application of the optical target parameter based on the base model generates data representing an optical multilayer thin film structure having optical characteristics satisfying the received optical target parameter, and outputs the data.

Description

Government License Rights This invention was made with government support under 2213684 awarded by the National Science Foundation. The government has certain rights in the invention. Cross Reference to Related Applications

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 459,433, filed April 14, 2023. The entire disclosure of the above application is incorporated herein by reference. TECHNICAL FIELD

[0002] The present disclosure relates to inverse design of optical multilayer thin film structures, and more specifically, to systems and methods for inverse design of optical multilayer thin film structures using a base model. BACKGROUND

[0003] This section provides background information relating to the present disclosure and is not necessarily prior art.

[0004] Optical multilayer thin film structures are an important class of photonic structures used in many applications, including spectral filters (e.g., bandpass filters, bandstop filters, etc.), absorbers (e.g., narrow or broadband absorbers), structural colors, distributed Bragg reflectors, and Fabry-Pérot resonators. Multilayer structures can be simulated using the transfer matrix method. However, inverse design is not a simple task because both the arrangement of material choices and the thickness of each layer need to be considered. Existing methods either cannot freely choose materials during the design process or are computationally inefficient.

[0005] Designing a multilayer structure involves determining the material choice for each layer and the corresponding thickness of each layer. The main reason that existing deep learning-based methods cannot adapt to different types of structures is that the output of these neural networks has a fixed size corresponding to a pre-defined structure (e.g., a three-layer structure of Ag / SiO2 / Ag, a six-layer structure of MgF2 / SiO2 / Al2O3 / TiO2 / Si / Ge, and a twenty-layer structure of alternating SiO2 / Si3N4). Therefore, these models can only design the thickness for each layer and do not allow different material choices.

[0006] Reverse design of multilayer structures requires determining the optimal material arrangement and obtaining the thickness combination to achieve the user-desired optical targets. In previous methods, the material arrangement is specified based on domain expertise and the reverse design is simplified as an iterative thickness optimization, where the methods include particle swarm optimization, needle optimization, and genetic algorithm. Optimization-based methods usually rely on numerical simulation and iterative search to minimize the difference between the simulated optical characteristics and the target optical characteristics. However, if the human-specified material arrangement is not optimal, it can not be possible to discover high-performance designs. A global design method that can determine the total number of layers and material arrangement will significantly broaden the design space and bring better performance.

[0007] The main difficulty of global design stems from the fact that materials are usually discrete, which makes the design problem more challenging for broadband applications. Recently, several methods have been proposed to overcome this challenge. For example, the meme algorithm incorporates materials into the design process and designs high-performance radiative cooling devices. Another approach frames the reverse design as sequential generation and develops an algorithm, OML-PPO, based on reinforcement learning to automatically determine the number of layers and material combination. Finally, it has also been suggested to combine GLOnet17 with the reconciled level set method to optimize the material and thickness for the optical transfer function. However, all these methods are inefficient because they require iterative evaluation and time-consuming simulation, which can be problematic when the target changes because a new design process needs to be started from scratch.

[0008] To make the design process more efficient, a number of deep learning-based methods have been proposed and explored, including cascading networks18, generative adversarial networks (GAN)19 and hybrid density networks (MDN)20, 21. Due to the powerful generalization ability of neural networks, these methods can learn a general mapping from the optical target space to the optical multilayer thin film structure space. After training on a dataset, they can generate designs on the fly for different targets without iterative and time-consuming evaluation and simulation. Unfortunately, despite their high efficiency, they cannot adapt to global design. This is because all these neural networks have a fixed output size that does not allow material selection and structures with different numbers of layers.

[0009] Previous algorithms cannot solve the challenges of global and efficient design simultaneously. SUMMARY

[0010] This section provides a general overview of the present disclosure, rather than a comprehensive disclosure of the full scope of the present disclosure or all of the features of the present disclosure.

[0011] In the present disclosure, by treating the inverse design task as a conditional sequence generation problem, structural tokens and structural serialization are used to obtain a collaborative representation of materials and their thicknesses simultaneously.

[0012] In one aspect of the present disclosure, a method of inverse design of an optical multilayer thin film structure includes receiving an optical target to a base model comprising a plurality of sequential decoders, the optical target comprising a target spectrum; receiving a hidden representation of the optical target at the plurality of sequential decoders; receiving a physical embedding and a position embedding at a first decoder of the plurality of sequential decoders; coupling an output of a previous decoder of the plurality of sequential decoders to a subsequent decoder; and generating a token sequence and probabilities representing materials and thicknesses of a plurality of layers of the optical multilayer thin film structure.

[0013] A system is provided that includes a computer readable medium storing code for a base model having a transformer comprising a neural network model and utilizing structural serialization using tokens to represent materials and thicknesses of layers of an optical multilayer thin film structure and utilizing spectral embeddings to facilitate learning by the model of relationships between spectra and structures. The computer readable medium also stores a plurality of computer executable instructions that, when executed by a processor, configure the processor to receive optical target parameters as input cues, generate data representing an optical multilayer thin film structure having optical characteristics satisfying the received optical target parameters based on the base model and the optical target parameters, and output the data representing the optical multilayer thin film structure.

[0014] In other features, the data representing the optical multilayer thin film structure indicates a total number of layers of the optical multilayer thin film structure required to satisfy the optical target parameters and indicates materials and thicknesses of each layer of the optical multilayer thin film structure.

[0015] A method for inverse design of an optical multilayer thin film structure is also provided that includes receiving, with at least one processor, optical target parameters based on input cues, applying, with the at least one processor, the received optical target parameters to a base model having a transformer comprising a neural network model and utilizing structural serialization using tokens to represent materials and layer thicknesses of the optical multilayer thin film structure and utilizing spectral embeddings to facilitate learning by the model of relationships between spectra and structures, generating, with the at least one processor, data representing an optical multilayer thin film structure having optical characteristics satisfying the received optical target parameters based on the application of the optical target parameters to the base model, and outputting, with the at least one processor, the data representing the optical multilayer thin film structure.

[0016] Among the other features, the data representing the optical multilayer thin film structure indicates the total number of layers required to satisfy the optical target parameters, and indicates the material and thickness of each layer of the optical multilayer thin film structure.

[0017] Further applicable aspects will become apparent from the description provided herein. The descriptions and specific examples in this overview are intended for illustrative purposes only and are not intended to limit the scope of this disclosure. Attached Figure Description

[0018] The accompanying drawings described herein are for illustrative purposes only and not for all possible implementations, and are not intended to limit the scope of this disclosure.

[0019] FIG. 1 It is a generative pre-trained transformer based on existing technology.

[0020] FIG. 2A This is a high-level block diagram of an optical generative pre-trained converter system for designing multilayer thin film structures, based on the present disclosure.

[0021] FIG. 2B This is a schematic diagram of an optical generative pre-trained converter system according to the present disclosure.

[0022] FIG. 2C This is a schematic diagram of the system's design goals.

[0023] FIG. 2D It is a representation of the layer structure and tags generated by the system.

[0024] FIG. 3A yes FIG. 2A A high-level block diagram of the converter.

[0025] FIG. 3B This is a block diagram of the publicly disclosed training structure.

[0026] FIG. 3C A schematic diagram illustrating the autoregressive process of this disclosure is shown.

[0027] FIG. 4A A two-dimensional visualization of the hidden space for reducing dimensionality according to this disclosure is shown.

[0028] FIG. 4B An enlarged two-dimensional visualization using the t-SNE process is shown.

[0029] FIG. 5A An example of the mean absolute error (MAE) of a random target using the closest, designed, and fine-tuned results is shown.

[0030] FIG. 5Bis a plot of target layer count versus layer count in a design structure.

[0031] FIG. 5C is a table of simulated time and design time.

[0032] FIG. 5D is an example of inverse design of a verification set according to the present disclosure.

[0033] FIG. 5E is a data table corresponding to FIG. 5D

[0034] FIG. 6A shows a design of a notch filter for artificial light spectrum formed according to the present disclosure.

[0035] FIG. 6B shows a design of a near-infrared high-reflectance filter for artificial light spectrum formed according to the present disclosure.

[0036] FIG. 6C shows a design of an ideal absorber for artificial light spectrum formed according to the present disclosure.

[0037] FIG. 6D shows a design of an arbitrary absorber for artificial light spectrum formed according to the present disclosure.

[0038] FIG. 6E is a table showing the ΔΕ of reflection and transmission chromaticity.

[0039] FIG. 7A is a probability map of a transformer based on applied constraints.

[0040] FIG. 7B to FIG. 7D is a plot of efficiency versus wavelength with different constraints.

[0041] FIG. 8A is a schematic of fine-tuning using different polarizations.

[0042] FIG. 8B to FIG. 8G is a plot of efficiency versus wavelength at different polarizations.

[0043] FIG. 9A is a schematic of a mixed sampling example.

[0044] FIG. 9B to FIG. 9D is a plot of efficiency versus wavelength for different angle-robust spectra.

[0045] FIG. 10A and FIG. 10B show the measured real and imaginary parts of the refractive index of 18 materials according to the present disclosure, respectively.

[0046] FIG. 11A and FIG. 11B ​A histogram showing the number of training data generated according to the present disclosure versus the number of layers is shown.

[0047] FIG. 11B A histogram showing the number of allowable structures according to the present disclosure versus the number of layers is shown.

[0048] FIG. 12A to FIG. 12E A dataset with four examples is shown.

[0049] FIG. 12B A plot of efficiency versus wavelength for four examples in FIG. 12A

[0050] FIG. 13A A table of hyperparameters used in the present disclosure and their values is

[0051] FIG. 13B A plot of training and validation loss curves according to the present disclosure is shown.

[0052] FIG. 14A to FIG. 14C A multi-head attention plot for a structure according to the present disclosure is shown.

[0053] FIG. 15A Details of the thickness fine-tuning process according to the present disclosure are shown.

[0054] FIG. 15B to FIG. 15C A plot of spectrum versus iteration for BFGS and PSO optimization according to the present disclosure is shown.

[0055] FIG. 16A to FIG. 16B A plot of efficiency versus wavelength for a first example of inverse design according to the present disclosure is shown along with a dataset corresponding thereto.

[0056] FIG. 16C to FIG. 16D A plot of efficiency versus wavelength for a second example of inverse design according to the present disclosure is shown along with a dataset corresponding thereto.

[0057] FIG. 17 CIE 1931 2 degree standard observer color matching functions according to the present disclosure are shown.

[0058] FIG. 18 LAB color conversion to spectrum using different alpha factors according to the present disclosure is shown.

[0059] FIG. 19 shows an example of inverse design of reflective and transmissive type structure colors according to the present disclosure.

[0060] FIG. 20A to FIG. 20C A plot of efficiency versus wavelength for two inverse designs of ideal absorbers in 400 nm to 1100 nm and data plots according to the present disclosure are shown.

[0061] ​FIG. 21A to FIG. 21D Efficiency vs. wavelength plots and data tables for two inverse designs of an arbitrary absorber according to the present disclosure in 400 nm to 1100 nm are shown.

[0062] FIG. 22A to FIG. 22D Efficiency vs. wavelength plots and data tables for two inverse designs of a band-stop filter according to the present disclosure in 400 nm to 1100 nm are shown.

[0063] FIG. 23A to FIG. 23D Efficiency vs. wavelength plots and data tables for two inverse designs of a high reflectivity device according to the present disclosure in 400 nm to 1100 nm are shown.

[0064] FIG. 24A to FIG. 24D Efficiency vs. wavelength plots and data tables for two inverse designs of a Fabry-Perot resonator cavity with four different constraints according to the present disclosure in 400 nm to 1100 nm are shown.

[0065] FIG. 25A An example of design flexibility for a transmissive orange structural color according to the present disclosure is shown.

[0066] FIG. 25B Data tables used in the examples of FIG. 25A

[0067] FIG. 26 Comparison table for different design methods.

[0068] Throughout the drawings, like reference numerals will be used to designate like components throughout the several views. DETAILED DESCRIPTION

[0069] Example embodiments are provided so that the present disclosure will be thorough, and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. Those skilled in the art will recognize, however, that the specific details are not to be construed as limiting, but are instead to provide examples of embodiments of the present disclosure. Embodiments of the present disclosure can be embodied in a multitude of different forms and should not be construed as limited to the particular forms set forth herein. In some embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.

[0070] ​The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms "a," "an," and "the" can be intended to mean the singular, including just one, or the plural, including multiple references, unless the context clearly dictates otherwise. The terms "including," "comprising," and "having" are inclusive and therefore specify the presence of stated features, integers, components, steps, operations, and / or components, but do not preclude the presence or addition of one or more other features, integers, components, steps, operations, elements, components, and / or groups thereof. Although the open-ended term "comprising," when used in the description and claims, should be understood to denote various embodiments of the invention, the term, in certain aspects, can also be understood to be a more restrictive term, such as "consisting of or "consisting essentially of. Thus, for any given described embodiment consisting of, including, having, or the like, of a composition, material, component, element, feature, integer, operation, and / or process step, the disclosure also specifically includes embodiments in which that embodiment consists of, or essentially consists of, the stated composition, material, component, element, feature, integer, operation, and / or process step. In the case of "consisting of," alternative embodiments exclude any additional composition, material, component, element, feature, integer, operation, and / or process step, while in the case of "consisting essentially of," any additional composition, material, component, element, feature, integer, operation, and / or process step that does not materially affect the basic and novel characteristic is excluded from the embodiment.

[0071] Any method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order in which they are described, unless explicitly identified as an order of performance. It is also to be understood that additional or alternative steps can be employed.

[0072] When a component, element, or layer is referred to as being "on," "engaged to," "connected to," or "coupled to" another element or layer, it can be directly on, engaged, connected, or coupled to the other component, element, or layer, or intervening elements or layers can be present. In contrast, when an element is referred to as being "directly on," "directly engaged to," "directly connected to," or "directly coupled to" another element or layer, there are no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., "between" versus "directly between," "adjacent" versus "directly adjacent," etc.). As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items.

[0073] Although the terms first, second, third, etc. can be used herein to describe various steps, elements, components, regions, layers and / or sections, these steps, elements, components, regions, layers and / or sections should not be limited by these terms. These terms can be only used to distinguish one step, element, component, region, layer or section from another step, element, component, region, layer or section. Terms such as "first", "second", and other numerical terms as used herein, unless otherwise specified, do not indicate a sequential or chronological order. Thus, as discussed below, a first step, element, component, region, layer or section discussed herein could be termed a second step, element, component, region, layer or section without departing from the teachings of example embodiments.

[0074] For ease of description, spatial or temporal relative terms, such as "front", "back", "inner", "outer", "under", "below", "bottom", "above", and "top", can be used herein to describe a relationship of one element or feature to another element or feature as shown in the figures. The spatial or temporal relative terms can be intended to encompass different orientations of the device or system in use or operation in addition to the orientation depicted in the figures.

[0075] Throughout this disclosure, numerical values represent approximate measurements or range limits to encompass slight deviations from the given values, as well as embodiments having about the stated values as well as embodiments having the exact stated values. Except in the operating examples provided at the end of the DETAILED DESCRIPTION, the numerical values of all parameters (e.g., amounts or conditions) in this specification (including the appended claims) are to be understood as being modified in all instances by the term "about" whether or not "about" is expressly recited in the numerical value. "About" indicates that the value provided can vary from the stated value by a small amount, to the extent that the value is close to the stated value; approximate or reasonably close to the value; nearly. If the inaccuracy provided by "about" is not otherwise understood in the art, then "about" as used herein means at least the variations that can be caused by the ordinary methods of measuring and using the parameters. For example, "about" can include a variation of less than or equal to 5%, optionally less than or equal to 4%, optionally less than or equal to 3%, optionally less than or equal to 2%, optionally less than or equal to 1%, optionally less than or equal to 0.5%, and in certain aspects, optionally less than or equal to 0.1%.

[0076] Furthermore, the disclosure of a range includes disclosure of all values and further divided ranges within the range, including the endpoints given for the range and subranges.

[0077] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0078] For a long time, photonic inverse design has been considered a more difficult problem than simulation, and it presents a high entry barrier for those interested in finding optical designs in specific applications. The system according to the present disclosure makes inverse design based on multilayer thin film structures as easy a task as traditional optical simulation of multilayer thin film structures. By treating inverse design as sequence generation conditioned on an optical target, and training using large-scale datasets, the system set forth in the present disclosure outperforms all existing inverse design methods in four aspects. The system is referred to herein as the OptoGPT system or simply OptoGPT. OptoGPT is a system that serves as a base model (or simply model) for multilayer thin film inverse design, which makes inverse design as simple, fast, and straightforward as running a simulation.

[0079] The discovery of the hidden representation of OptoGPT according to the present disclosure indicates that it has acquired domain-specific knowledge related to optical multilayer structures through the training process. Furthermore, the model of the present disclosure has demonstrated the ability to effectively apply this acquired knowledge in the inverse design process.

[0080] The present disclosure relates to inverse design of optical multilayer thin film structures utilizing a base model. By connecting materials and thicknesses together to form “structure tokens”, materials and thicknesses can be treated equally. By adding tokens one by one, a multilayer structure is converted into a sequence, which will be referred to as “structure tokenization”. Through these two combination techniques, the OptoGPT system automatically determines the total number of layers in the global space and determines the material and thickness of each layer. For example, the model of the present disclosure can consider 18 different types of materials and design structures up to 20 layers, making the total number of possible structures approximately 10 59 However, according to the present disclosure, other numbers of different types of materials and layers can be used, resulting in additional possible structures. A number of design tasks are efficiently completed, including structural color, absorber, filter, distributed Bragg reflector, and Fabry-Perot resonator. On average, each design task can be completed in, for example, 0.1 seconds, close to the time of running a simulation using the transfer matrix method. The present system can output many different designs as needed, which can provide high degrees of freedom for manufacturing. Furthermore, the present system automatically learns the complex relationship between the material space and the response space. Any constraints on material selection and material thickness range can be incorporated into the design process without much effort. For example, when a material arrangement is specified, the model can directly output thicknesses without the need for iterative optimization. Furthermore, by fine-tuning the model on small datasets, the present system is also applicable to oblique incidence, various output angles, and different polarizations.

[0081] The OptoGPT system of the present disclosure eliminates design barriers regarding optical targets, material selection and design constraints, incident angles, and polarizations, thereby making the inverse design task in multilayer structures close to “solved”. The OptoGPT system is analogous to a “foundation model” in computer science, i.e., a large machine learning model that can be adapted to a wide range of downstream tasks after training on large datasets. The results show that the OptoGPT system can serve as a foundation model for the inverse design of multilayer structures, which can simplify the inverse design process and accelerate the development of advanced optical systems. In addition, the model serves as a reliable starting point for researchers and engineers to explore novel designs and optimization of optical performance under the constraints of material properties and manufacturing techniques.

[0082] The OptoGPT system of the present disclosure is the first application of GPT in the specific field of optical science. The two techniques described above, i.e., structure serialization and spectral embedding, make GPT very suitable for the inverse design problem of multilayer structures. In addition, these two techniques are universal and can be used to solve other types of inverse design problems. For example, the fragments of images can be used to serialize metasurfaces and free-form waveguide structures; spectral embedding can be extended to include other design objectives, including angle-resolved spectra, radiation patterns, and phase information, etc. In this way, the OptoGPT system of the present disclosure can perform other types of inverse design problems based on these two implementations. In addition, multimodal GPT can combine different types of photonic structures and design objectives to create a more powerful foundation model to design all photonic structures for general optical targets.

[0083] In addition, the GPT-based method of the present disclosure can solve general inverse tasks beyond photonic inverse design, as long as there is a physical relationship between cause and effect, such as recovering phase facts from intensity images, extracting refractive indices from spectral measurements, or recovering volume information from images. This is because most inverse tasks can be formulated as generation tasks conditioned on input, which can be solved using a similar GPT-based architecture. Therefore, the GPT-based method of the present disclosure can revolutionize the optical community and solve many complex and unsolved problems.

[0084] Reference is now made to FIG. 1A generative pretrained transformer (GPT) 10 is a widely used large language model for natural language processing. Such a system receives input prompts 12 from a user interface. The transformer 10 processes the input to generate a probability output 14 corresponding to a single answer for each input prompt 12. A GPT is an autoregressive language model that produces a text output given an initial text as an input prompt 12. The initial prompt 12 can be a question, a task description, or anything needed for the model to understand the expected output. During training, pairs of text input prompts 12 and expected answers are fed to the GPT 10 together, with the training goal being to recover the expected answer from the model’s probability output. It is well known that a GPT takes only a text prompt and the answer is generated autoregressively.

[0085] Referring now to FIG. 2A The present disclosure provides a system referred to as an OptoGPT system 210. The system 210 has a user interface 212. The user interface 212 can include a keyboard, a mouse, a touchscreen display, another input device, or other combinations thereof. The touchscreen display can be part of a display 214. The display 214 can display a sequence of structures of indicia or other representations of a multilayer optical structure formed in accordance with the present disclosure. The display 214 can display a sequence of structures of one or more layered thin film optical structures including the materials, thicknesses, and relative positions of the layers.

[0086] A computing device 216 is in communication with the user interface 212 and the display 214. The computing device 216 has a microprocessor or processor 218 in communication with a memory 220. The memory 220 is a non-transitory computer readable medium including machine readable instructions executable by the processor 218. The instructions are for performing various functions as described below including determining a sequence of structures of a layered thin film optical structure including the materials, thicknesses, and relative positions of the layers. Although a single processor 218 is shown, multiple processors can be provided. For example, a graphics processor can be used. Likewise, multiple computing devices 216 can work in concert to perform the various functions.

[0087] The computing device 216 includes a transformer 224. The transformer 224 can be referred to as an Opto Generative Pretrained Transformer (OptoGPT). The transformer 224 includes a neural network model 226 stored therein.

[0088] The training device 230 is in communication with the computing device 216. The training device 230 provides training data to the transformer 224 so that determinations of thin-film optical structures can be generated using design goals and constraints provided by the user interface 212. Specifically, the OptoGPT system 210 takes optical target parameters or simple optical targets as input prompts and outputs corresponding multi-layer structure designs. In one example, a training dataset is provided by the training device 230, which dataset consists of 10 million randomly generated samples for training. For example, the model 226 associated with the transformer 224 was trained using an NVIDIA 3090 GPU (processor) for about two weeks. After being trained, the model 226 can be used directly for inverse design without considering the spectral targets and design constraints.

[0089] Referring now to FIG. 2B , the transformer 224 is shown coupled to the optical design targets 240. The probability output 242 is generated by the transformer 224 using the neural network model 226. The probability output 242 is used to provide a probability for determining a multi-layer thin-film structure 244 or data representing the multi-layer thin-film structure.

[0090] Referring now to FIG. 2C , several examples of input prompts are shown. To unify the space of design targets in various applications, all design targets are converted to reflectance and transmittance spectral data 250 at normal incidence. The wavelengths considered cover the visible and near-infrared (NIR) regions, spanning from 400 nm to 1100 nm with 10 nm intervals. The user interface 212 shown in FIG. 2A is used to input design targets to the system 210.

[0091] Different design targets 254 are considered, including structural color 254A, absorber 254B, filter 254C, distributed Bragg reflector (DBR) 254D, Fabry-Pérot (FP) resonator 254E, and other arbitrary spectral targets 254F. All design targets 254 from 400 nm to 1100 nm at normal incidence are converted to reflectance and transmittance spectral data 250 and provided as the optical design targets 240 of FIG. 2B .

[0092] Referring now to FIG. 2D , FIG. 2BAn example of a multilayer thin film structure 244 is shown as a structural sequence in an N-layer structure 260 on a glass substrate 262. In this example, layers 1 to N are shown. The N-layer structure 260 is sequenced by N+1 markers 264. The first N markers 264, formed by concatenating the material and thickness of each layer, are sequenced in an order corresponding to the order in which they are to be formed on the glass substrate 262. As an example, the first marker in the markers 264 shows, for example, titanium dioxide (TiO2_200) with a thickness of 200 nm. The last marker is “EoS”, indicating the end of the sequence. In each layer of this example, there are 18 possible material types 266 and 50 different thicknesses 268 (discrete in 10 nm increments within [10, 500] nm). The refractive index of each material will be discussed in detail below. Therefore, for each layer in the multilayer structure, there are 18 × 50 + 1 = 901 possible markers, corresponding to 900 different combinations of material and thickness plus a special “EoS” marker.

[0093] During reverse engineering, converter 224 is FIG. 2B The probability output at position 242 generates a probability distribution 270 for all 901 labels. Sampling from this distribution gives the design for each layer. If “EoS” is sampled, the OptoGPT system 210 terminates the design process and outputs the existing sequence as the design structure. The design process also terminates when the design structure reaches the maximum number of layers, and the existing sequence is output as the design structure. The maximum number of layers is set to 20, so that the total number of multi-layer structures considered in the design is (901). 20 It is approximately 1.24 × 10⁻⁶. 59 Although 20 is used as the maximum number of layers in the current example, according to this disclosure, the maximum number of layers can be set higher or lower. Using this method, the model of this disclosure can determine the total number of layers required for a given design objective, as well as select appropriate materials and thicknesses for each individual layer.

[0094] The present disclosure utilizes an OptoGPT 224 to resolve the conflict between global design and efficient design. Similar to other GPT models such as GPT-3 and ChatGPT, the OptoGPT system 210 of the present disclosure is a decoder-only transformer that generates a multi-layer structure layer by layer in a self-recursive manner. To incorporate materials into the design process, the systems and methods of the present disclosure utilize structure serialization that uses tokens to represent both the material and thickness of a layer simultaneously. The systems and methods of the present disclosure also apply spectral embedding to facilitate learning of the complex relationship between the spectrum and the structure. In this way, the model of the present disclosure can design in the global space and can simultaneously determine the total number of layers (e.g., up to 20 layers), the material (e.g., up to 18 materials), and the thickness. Furthermore, the systems and methods of the present disclosure utilize a large dataset containing, for example, 10 million designs for training. This large-scale dataset enables the model to capture complex relationships and extend the design capability of the model to different applications, including structural color, filter, absorber, DBR, and Fabry-Perot (FP) resonator. The model of the present disclosure is effective in all of these design applications. For example, the OptoGPT system 210 can complete each design in an average of 0.1 seconds while consistently obtaining better design results than baseline methods. Benefiting from the design efficiency, the model of the present disclosure can also output multiple designs with minimal effort and exhibit high design flexibility under different design constraints, which is beneficial for manufacturing and design considerations. These constraints provide various limitations for various material types, thickness, or material placement. Given the constraints of the material placement of each layer, the OptoGPT system 210 functions as a direct thickness optimizer that bypasses the iterative optimization process.

[0095] Based on the obtained empirical results, the OptoGPT system 210 can serve as a foundational model for optical multilayer thin film design across various applications. By providing high-performance initial optical designs with computational efficiency, the model of the present disclosure can simplify the design process, reduce the need for extensive manual iteration, and accelerate the development of advanced optical systems. Furthermore, by serving as a reliable starting point for researchers and engineers, the model of the present disclosure facilitates the exploration of novel designs and optimization of optical performance under the constraints of material properties and manufacturing techniques. Thus, the OptoGPT system 210 enhances the accessibility and effectiveness of the optical design method.

[0096] Foundation models are large machine learning models that, once trained on diverse and large-scale data, can handle a variety of downstream tasks, leading the research trends in natural language processing, computer vision, and reinforcement learning. However, foundation models have not been previously used for optical multilayer thin film structure inverse design. Current inverse design algorithms either fail to explore the global design space or are computationally inefficient. To fill this gap, the present disclosure utilizes an OptoGPT, which is a decoder-only transformer that autoregressively generates designs based on a specific spectral target. The model according to the present disclosure is trained on a large dataset of 10 million designs and demonstrates extraordinary capabilities, including: 1) autonomous global design exploration by determining, for example, a number of layers up to 20, while simultaneously selecting, for example, up to 18 different types of materials, and thicknesses for each layer; 2) efficient design (comparable to simulation speed) of structural colors, absorbers, filters, distributed Bragg reflectors, and Fabry-Perot resonators in 0.1 seconds; 3) the ability to output diverse designs; and 4) seamless integration of user-defined constraints. By overcoming design barriers regarding optical targets, material selection, and design constraints, the OptoGPT system serves as a foundation model for optical multilayer thin film structure inverse design.

[0097] Reference is now made to FIG. 3A The architecture of the transformer 224 and the neural network model or model 226 for autoregressively forming the sequential layer structure are set forth in greater detail. There are two inputs to the transformer 224 and the model 226. The first input is an optical design target 240 or “spectral target”. From the optical design target 240 a spectral embedding 310 is determined to obtain a high-dimensional hidden representation 312 that is provided to each of N sequential decoders. The second decoder 320B receives the output of the first decoder 320A, and so on, until the output of the last decoder 320N of the N decoders. That is, each subsequent decoder of the plurality of sequential decoders receives the output of the previous decoder. Each decoder 320A-320N includes a multi-head self-attention block 322 that in turn feeds a multi-head cross-attention block 324 that feeds a feed-forward block 326 that provides an output to the next decoder of the model 226 or the final output decoder 320N.

[0098] The structure tokens in the structure token sequence 330 are used to provide constraints to the transformer 224. The structure tokens can take many forms, including specifying or excluding certain materials, limiting the number of layers, providing design goals 254 for the type of optical structure, and certain layer thicknesses, among others. The structure tokens in the structure token sequence 330 will first go through a physical embedding layer 332 to obtain a high-dimensional hidden representation 334. Thereafter, the relative position of each token within the sequence is obtained from the physical embedding layer 332 using a position embedding layer 336.

[0099] The hidden representation 312 of the input spectrum, the physical embedding 332, and the position embedding 336 are processed through the decoder blocks 320A-320N, which contain attention layers as the main working mechanism behind GPTs. The first self-attention layer is a multi-head self-attention layer 322, which is used to learn the relationships between the layers of the structure. The multi-head self-attention layer 322 receives the physical embedding 332 and the position embedding 336. The second attention layer, a multi-head cross-attention layer 324, receives the output of the multi-head self-attention layer 322 and the hidden representation 312. The multi-head cross-attention layer 324 captures the relationships between the input spectrum and the multi-layer structure. A forward layer 326 provides the output of the multi-head cross-attention layer 324 to the next decoder block 320B. The series of decoder blocks ultimately provide the probability output 242 from the last decoder block 320N. The probability output 242 is a probability distribution that covers all tokens. The model 226 is trained for about 200 epochs based on “next word prediction” using this probability output.

[0100] Referring now to FIG. 3B , a large training dataset 340 with 10 million samples and a validation dataset with 1 million samples are used to train the transformer 224. The total number of datasets is only about 1 / 10^52 of the possible structures. Each sample is a pair of a randomly sampled multi-layer thin film structure on a glass substrate and a corresponding spectrum simulated using the Transfer Matrix Method (TMM). The training set has different refractive indices of materials and thicknesses of materials. Details of the training and model architecture are provided below. Once the model 226 is trained, it is used to provide a multi-layer optical structure 344 using an input spectrum target 342.

[0101] Referring now to FIG. 3C , the model 226 and the transformer 224 complete the design layer by layer in a self-recursive approach. That is, the same transformer 224 is shown to perform material and thickness determination for each layer. The target spectrum 240 is provided to each iteration along with the output tokens 350 of the previous layer. In this example, the probability output 242 is shown in graphical form. The probability output 242 and the layer output have structure tokens 352 in a structure sequence that correspond to the materials and thicknesses of the layer.

[0102] In summary, in designing the i-th layer, the model 226 takes the target spectrum 240 together with the sequence of structures of the i-1 markers 350 previously designed and outputs the probability distribution output 242 of all 900+1 markers. Sampling from this distribution gives the design of the i-th layer. In designing the i+1-th layer, the markers 352 of the sequence structure will be used again as input markers 350. The design process will continue until the maximum number of layers, e.g. 20 layers in this example, is reached or the end of sequence (EoS) is sampled.

[0103] There are many advantages of probabilistic sampling. First, due to the randomness in the sampling process, running each individual design process can output different structures. Therefore, this method inherently introduces diversity in the designed structures and is able to output multiple structures that satisfy the design target. In addition, it also enables the model to design structures with different number of layers. For example, when the “EoS” is sampled at the fifth layer, the model 226 terminates the design process and outputs the existing four-layer structure. Probabilistic sampling will also be used to handle the constrained design as described below. FIG. 3C The process in may be performed many times with different results each time, which can be processed as described below.

[0104] FIG. 3C The process of may also be repeated by adding different constraints. That is, a sequence structure can be obtained. The obtained sequence structure and constraints can be provided to the transformer to obtain a modified marker sequence structure. The use of constraints on previously generated sequence structures is described in more detail in FIG. 7A The use of constraints on previously generated sequence structures is described in more detail in

[0105] Reference is now made to FIG. 4A and FIG. 4BIt is beneficial to examine whether the proposed structural labels can capture material and thickness information. t-distributed stochastic neighbor embedding (t-SNE) was used to reduce the dimensionality of the physical embedding to 2D and visualize the results. To further compare the embedding with the spectral input, 1000 spectra were randomly selected from the validation dataset to visualize the dimensionality reduction results of the hidden representation. Several interesting features were immediately observed. First, the physical structure (trajectory 410 consisting of individual points representing structural labels 412) and the spectral response (clusters surrounded by boundary 414) are well separated in this 2D representation, even though they are fed into training with equal importance. This indicates that model 226 has learned to distinguish between material structure and spectral properties while mapping them to the same hidden representation space.

[0106] Secondly, the 900 structural markers are easily distinguishable, either as curves (with start and end points corresponding to thicknesses of 500 nm and 10 nm, respectively) or as clusters of points where there is no overlap between different materials. Upon close examination, it is clear that Model 226 has intelligently separated the low-refractive-index dielectric from the high-refractive-index dielectric (in... FIG. 4B (In magnified views of (i) and (ii)). In both groups, all curves converge to a central region representing the minimum thickness of 10 nm. This is expected in optical physics: when the dielectric layer thickness is reduced to a minimum, all materials will behave similarly because (in the case of high refractive index materials) their contribution to optical phase transitions or optical absorption is negligible. In other words, the model learns that thin dielectric layers of different materials have similar effects on light propagation in multilayer films. Also interesting is that in this 2D plot, all the metals cluster in their respective regions. This is understandable because when the metal layer thickness is greater than the optical penetration depth, its contribution to the optical response (i.e., the spectrum) is almost independent of the thickness. These observations show that even if the model does not directly consider any refractive index or thickness, it can capture this information and learn hidden representations from large datasets, thus validating the use of structure serialization and spectral embedding. This is also consistent with the robust representational capabilities demonstrated in many other fundamental models, such as Galactica27, GaTo28, and PaLM-E29.

[0107] FIG. 4A and FIG. 4B Specifically, a two-dimensional visualization of the hidden space using t-SNE to reduce dimensionality is shown. 900 structure markers and 1000 spectra were randomly selected from the validation dataset. The spectra are labeled, and the structure markers are points corresponding to different materials. Circles indicate the approximate boundary 414 between the spectra and structures. Within this boundary is the spectrum. FIG. 4B(iii) and (iv) give examples of two different spectra. Outside the boundary 414 are structure markers corresponding to different material and thickness combinations. These structure markers with the same material either form lines or are clustered together. For each line, the point size monotonically decreases from one end to the other, corresponding to a monotonically decreasing thickness from 500 nm to 10 nm. Most of the lines converge into two regions, FIG. 4B The zoomed-in details given in (i) and (ii) correspond to low and high refractive index regions, respectively. The model 226 demonstrates the ability to learn materials and thicknesses from large datasets without explicit input of materials and thicknesses.

[0108] Referring now to FIG. 5A to FIG. 5E , the inverse design performance in different application scenarios is described. In use, the model 226 is static after training and all design tasks can be completed almost instantaneously by feeding different inputs of target optical responses into the model. However, in cases where higher accuracy is needed, thickness fine-tuning is needed to improve performance because a thickness discretization of 10 nm can lead to suboptimal performance for certain materials (e.g., metals and absorbing dielectrics). By default, design performance without thickness fine-tuning will be provided unless specified.

[0109] The average inverse design performance is evaluated for 1000 randomly selected spectrum targets from the validation dataset. Based on the multi-layer design outputs from the model 226, TMM is used to simulate the corresponding spectra, and the mean absolute error (MAE) between the input spectrum and the simulated spectrum is calculated to quantify the design accuracy. The closest spectrum in the training dataset with the smallest MAE is considered as the design baseline, i.e., by simply referring to the best spectrum of the training dataset. A good machine learning model should be able to learn from and outperform the training dataset. FIG. 5A A comparison of the MAE of the closest structure, the design structure, and the fine-tuned structure in the training dataset is shown. On average, the MAE of the design structure is 0.0258, which is lower than the MAE of the closest structure in the training dataset (0.0296); fine-tuning the thickness can further reduce the MAE to 0.0192 (about 24% reduction). In FIG. 5B In, the number of layers in the target structure (the structure corresponding to the target spectrum in the validation dataset) is compared to the number of layers in the design structure. The zero upper diagonal matrix means that the model learns to use a simplified structure with fewer layers (about 6 layers on average) to solve the design task, which can facilitate the manufacturing process because structures with fewer layers are easier to manufacture. FIG. 5C The time consumption is listed in. On average, the model completes each design in 0.1 seconds, which is comparable to running a TMM simulation. FIG. 5D and FIG. 5EAn inverse design example is shown. By running the sampling process multiple times, the model 226 outputs multiple different structures with much better approximations to the target spectrum than the training dataset. In FIG. 5D and FIG. 5E the design structures also show diversity.

[0110] Now referring to FIG. 6A to FIG. 6D , the model 226 is evaluated based on real inverse design tasks. One such application is spectral filters that are used to selectively reflect or transmit light of certain wavelength bands. Many deep learning based methods have been proposed to inverse design these filters. Here, several examples are tested: FIG. 6A a band-stop filter at 550 nm, FIG. 6B a band-stop filter at 700 nm, high reflection in NIR, double high reflection in 500-600 nm and 800-1000 nm. The input is set to an ideal rectangular spectrum with 0% transmission in the desired region and 100% transmission in the rest. In all these artificial spectrum design targets, the model can output designs that outperform the training dataset. Thickness fine-tuning can further improve the accuracy. FIG. 6A and FIG. 6B two examples are shown and compared with the respective spectra.

[0111] In FIG. 6C and FIG. 6D , an ideal absorber and an arbitrary absorber are shown, respectively. Ideal absorbers are widely used in the fields of photovoltaics, radiative cooling, detection, solar thermal energy collection, etc. Although the model is trained on reflectance and transmittance spectra, it also demonstrates good performance for ideal absorbers. This can be achieved by simply setting both the reflectance and transmittance input spectra to zero. The model gives multiple designs, one of which is shown in FIG. 6C .

[0112] In addition to ideal absorbers, the model can also be designed for arbitrary absorption. Because energy conservation guarantees that reflectance + transmittance + absorption = 1, the input spectrum can be customized by setting the reflectance to 1 minus the absorption and the transmittance to zero, as shown in FIG. 6D .

[0113] Structural colors have unique advantages in high resolution, stability, and sustainability compared to dyes and chemical pigments, and have been widely applied in color printing, information encryption, sensors, and other fields. Deep learning has been used to solve structural color reverse design. Typically, color can be represented by three-dimensional color coordinates, such as LAB values, RGB values, or xyY values. To make this model well suited for this application, an algorithm that can convert color coordinates to continuous spectra is described in a summarized manner below. The converted spectra can be pre-computed and will not affect the design process. When designing reflective colors, the reflection spectrum is set to the converted spectrum and the transmission spectrum is set to zero. For transmissive colors, the transmission spectrum as this converted spectrum and the reflection spectrum is set to 1 minus transmission. Design performance is evaluated with color difference ΔE (smaller ΔE means smaller color difference). In FIG. 6E a table is given for a variety of colors, evaluating the ΔE of the closest color in the training dataset and the designed color from the model (with thickness tuning). As shown, ΔE is much lower when using the model for each color, and in some cases much lower. The first three colors are reflective, and the last three colors are transmissive.

[0114] Reference is now made to FIG. 7A to FIG. 7E , which gives a visualization of the design process when adding design constraints. The example of "remove Ag from the material selection in the first i layer" is used. The first probability distribution 710 is the initial probability distribution and corresponds to a structure sequence. The second probability distribution 712 is shown, with Ag removed to obtain a second structure sequence. The renormalized probability distribution 714 is shown. When designing the desired first i layer, in this example, the tokens containing "Ag" (e.g., "Ag_10", "Ag_20") that do not satisfy the constraint from the probability distribution are removed, and sampling from the renormalized probability is based only on the remaining tokens.

[0115] As an example, FP resonator design using different constraints is set forth. Here, the target spectrum has a resonant absorption at 610 nm, and corresponds to an initial structure sequence of three layers: 20 nm of Ag; 50 nm of SiO2, and 50 nm of Ag. These layers are used as a resonator on a glass substrate. Different constraints can be used to design the FP resonator. That is, the initial structure sequence can be processed by the transformer 224 and the model 226 with the input as physical and positional embeddings constraints, thereby obtaining a second or subsequent design.

[0116] Constraints can be used for a variety of purposes. Researchers can allow the system to generate initial structure sequences and then limit the design based on the availability of materials and the process limitations they have available. Examples of constraints are constraints 1 through 4, which are “fix the first layer to 100 nm of SiO2,” “remove Ag in the third layer,” “limit the thickness of the first layer to [10, 150] nm and remove Ag / Al in the first layer,” and “specify the material arrangement to a three-layer Ag / Si3N4 / Ag structure and only design the thickness.”

[0117] The first constraint can be used when the dielectric layer at the air interface needs protection. The second constraint is practical when considering that silver is an expensive metal and looking for a replacement for silver. The third constraint is a general example of adding both thickness and material limitations. For the design structure, FIG. 7A to FIG. 7D The design results in Table 1 show that the model can determine a design that satisfies the desired constraints while still providing spectral performance.

[0118] In particular, the fourth constraint specifies the material for each layer and only the thickness needs to be designed. This is the traditional design process that is widely used by human experts and many optimization-based methods. FIG. 7E The design results in Table 1 show that the model can be used for direct thickness design given the spectral target and material arrangement without the need for iterative optimization. Since this feature does not depend on the target optical response, researchers can quickly check whether certain material combinations can achieve the target spectrum and, if so, obtain their corresponding thicknesses.

[0119] Referring now to FIG. 8A to FIG. 8G Although the model is trained on normal incidence spectra, its strong generalization capability enables design for different angles of incidence or output and polarization states, significantly expanding the allowed applications. This is achieved by fine-tuning the model on small datasets. Hybrid sampling can be used to design structures that satisfy multiple requirements simultaneously.

[0120] Starting from the model 226 of the OptoGPT system 210 trained on the 10M dataset, the model 226 can be fine-tuned on smaller datasets to accommodate light incidence with different angles, polarization states, light output directions, or combinations thereof. FIG. 8A A fine-tuning schematic is given. At 812, a particular dataset 810 is used to form an updated model. For example, to design the s-polarization spectrum at 20º angle of incidence, a small 1M dataset containing such spectra is needed, and then the entire model is updated by 10 epochs at 812. This only requires 1% of the computational resources compared to training the entire model from scratch. Similar processes can be done for other angles and polarizations. In FIG. 8B to FIG. 8GThe diagram shows examples of reverse design for fine-tuning of 20º s polarized, 60º s polarized, 10º p polarized, 50º p polarized, 30º unpolarized, and 50º unpolarized light, respectively.

[0121] Now for reference FIG. 9A to FIG. 9D In some cases, the designed structure can achieve multiple spectra simultaneously, rather than being designed for a specific incident angle or output / polarization spectrum. The structure sequence 910 is provided to different trained models 912 to 916, which have been trained with different incident angles, polarizations, or light output directions, or combinations thereof. This can be used... FIG. 3C The system generates the initial sequence structure 910. Target spectra 904, 906, and 908 with different wavelengths can be provided to different trained models 912 to 916. Based on spectra 904 to 908 and the structure sequence 910, the different trained models 912 to 916 generate probability outputs 918 to 922. The probability outputs 918 to 922 are provided by each of the multiple models 912 to 916 and are specific to each particular training iteration. A probability summing block 930 sums the probabilities from each of the individual models 912 to 916. A sampling block 932 samples the probabilities in an autoregressive manner to obtain the layer with the highest probability for the layer material and thickness, such as... FIG. 3C As shown, the output of sampling block 932 is a mixed output. This is called "mixed sampling". Therefore, the mixed sampling output of layer material and thickness can respond to multiple polarizations and incident angles.

[0122] As an example, in FIG. 9B and FIG. 9C This paper proposes a method for designing angle-invariant spectra at 0°, 20°, and 40° for unpolarized light. Solid lines, dashed lines, and square lines correspond to the target spectrum, the spectrum designed by the pre-trained model, and the spectrum designed by the fine-tuned model, respectively.

[0123] By converting multilayer structures into sequences using structural tagging and structural serialization, this system effectively handles the nontrivial reverse design problem in multilayer structures. Combining several proposed techniques, this model can unify the reverse design of different types of input targets under varying incident angles / polarizations / light output directions, is universal for different types of structures, and facilitates the manufacturing process by providing diversity and flexibility. The development of the OptoGPT system 210 makes reverse design based on multilayer thin film structures more methodologically efficient and easier for researchers and engineers to use.

[0124] Interesting findings regarding the hidden representations of the OptoGPT system 210 indicate that it has acquired domain-specific knowledge related to optical multilayer structures through the training process. Furthermore, the model has demonstrated the ability to effectively apply the acquired knowledge during reverse engineering.

[0125] Furthermore, using similar methods, the model can be extended to high-dimensional complex photonic structures, e.g., 2D subsurface or 3D waveguide, using similar tokenization methods in the visual transformer. However, one limitation is that the current model requires a large dataset for training, which is also a common criticism of many GPT models. For example, ChatGPT uses about 10,000 GPUs to train on billions of tokens, with a cost of about $10 million for a single training. In the present disclosure, due to the constraints on computational resources, the design problem can be simplified, including the use of limited types of materials, limited spectral range, thickness discretization, and maximum number of layers that can be designed, all of which can be extended with more computational resources. Despite training with a large-scale dataset of 10 million samples, it is important to recognize that this dataset only covers a small fraction of the vast and complex design space associated with optical multilayer thin-film structures (10 52 ). Due to this limitation of the training dataset, the OptoGPT system 210 can not find designs that lie outside the boundaries of the sampled design space. Close collaboration between multiple research groups is needed to obtain a better model for more general and better photonic inverse design that extends to more complex structures.

[0126] Referring now to FIG. 10A and FIG. 10B , eighteen different materials were chosen that are widely available at many nanofabrication centers. Single layers were experimentally deposited on silicon substrates, and the refractive index of each sample was measured using an ellipsometer. The test data can be stored in a test database or dataset, which is summarized by 340 in FIG. 3B . The refractive index is shown for all 18 materials in FIG. 10A . The measured real part of the refractive index is shown in FIG. 10B . These materials and refractive indices were used during the training process.

[0127] Referring now to FIG. 11A and FIG. 11B , the measured refractive indices were used for simulations during the training dataset generation. The training dataset and validation dataset consist of 10M and 1M (using glass substrates) randomly generated samples, respectively. The randomness here comes from three aspects: materials, thicknesses, and total number of layers. The materials are uniformly sampled from the material database, and the thicknesses are also uniformly sampled from 10 nm to 500 nm with 10 nm discretization. In addition, the two adjacent layers have different materials. When sampling the total number of layers, the number of possible structures increases exponentially with the total number of layers, so the number of layers with increasing ratios is sampled. The histogram of the generated samples is plotted based on the number of layers in FIG. 11A . FIG. 11BA histogram of the total number of possible structures is given. FIG. 11A A histogram showing the number of generated training data versus the number of layers is shown. FIG. 11B A histogram showing the number of allowed structures versus the number of layers is shown, which follows an exponential distribution. The total number of allowed structures reaches 10 59 for structures with twenty layers.

[0128] Now referring to FIG. 12A to FIG. 12E , after sampling the structures, the reflectance and transmittance spectra are simulated using the transfer matrix method (TMM). Simulating all 10M structures takes approximately 1200 hours and can be speeded up by parallel computing. Storing the generated dataset also requires approximately 12 GB of space. FIG. 12A Four examples of generated structures and simulated spectra are given. FIG. 12B to FIG. 12E Four examples in the training dataset are shown. In FIG. 12A , the structures are given, and their transmittance and reflectance spectra are given in FIG. 12B to FIG. 12E .

[0129] Now referring to FIG. 13A and FIG. 13B , the hyperparameters used in the model architecture are summarized in the table in FIG. 13A . The Kullback-Leibler (KL) divergence is used as the training loss, with the goal of recovering the input structure from the probability distribution. During training, the Adam optimizer and a warm-up procedure are used. Residual drop and label smoothing are also used to provide regularization during training. The training and validation loss curves are given in FIG. 13B .

[0130] Now referring to FIG. 14A to FIG. 14B , when reading, one does not usually try to remember all the words in a sentence. Instead, one selectively focuses on the words that are important for forming a basic understanding of the sentence. The self-attention used is a mechanism that links each word to all the other words in the sentence and selectively focuses on a few important words, similar to the way humans read. The multi-head attention mechanism allows the model to be able to focus on different aspects. To better understand, FIG. 14A a visualization of the attention map for the following structure is provided: ['SiO2_240', 'Ta2O5_90', 'SiO2_130', 'TiO2_80', 'MgF2_140', 'HfO2_80','SiO2_130', 'Ta2O5_100', 'SiO2_130', 'Ta2O5_480', 'SiO2_160', 'Ta2O5_490'] FIG. 14A to FIG. 14CA multi-head attention graph with the above structure is provided, exhibiting a high-low exponential distribution. The value at each matrix element represents its attention relative to other labels (normalized to 1).

[0131] The structure described above has twelve alternating high-low refractive index layers, similar to a distributed brag reflector (DBR). The attention map is a matrix where each row corresponds to how much attention a single token should receive from the other tokens in the sequence. The number "000" corresponds to the token "BOS," which stands for "beginning of sentence," a common token placed before the structured token sequence and used in many other transformer models. The number "013" corresponds to the token "EOS" (end of sentence). The other numbers preceding each token specify its relative position within the multi-layered structure. It is often difficult to understand the physical meaning of each attention map because these machine learning models are black boxes. Therefore, only the first 1 of the first decoder block is shown. FIG. 14A ), Head 2 ( FIG. 14B ) and head 4 ( FIG. 14A Attention maps of head 2 and head 4 are more focused on the layers directly below and above, while head 1 is more focused on long-term alternation relationships (corresponding to alternating high-low refractive index distributions).

[0132] Now for reference FIG. 15A to FIG. 15C During training, the thickness is discretized from 10 nm to 500 nm with 10 nm gaps, so the design structure 260 from the model and transformer 224 will also have such discretization. A 10 nm gap may be useful for some fabrication tools that cannot guarantee precise deposition thickness, but may be less useful for other tools with high-precision deposition (e.g., vacuum deposition). Therefore, as... FIG. 15A As shown, the fine-tuning process is performed solely by optimizing the thickness with the objective of minimizing the mean absolute error (MAE) of the spectrum. For structural color applications, visual color difference (denoted as ΔE) is minimized. The thickness is fine-tuned using the finite-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, with the designed thickness from the model serving as the starting point for optimization. FIG. 15A Details of fine-tuning the thickness to achieve the fine-tuned structure in 1510 are shown. Only the thickness is optimized by setting the design structure as the starting point for optimization. FIG. 15B The convergence speed of fine-tuning versus optimization from scratch is shown using the same finite-memory BFGS method. FIG. 15CThe convergence speed of fine-tuning is compared to the convergence speed of optimization from scratch using particle swarm optimization (PSO). Fine-tuning provides better performance and is faster (converges within 20 iterations) compared to designing from scratch.

[0133] In FIG. 15B and FIG. 15C one example of fine-tuning a structure is given. The fine-tuning process has FIG. 15B and FIG. 15C a continuous line 1520 in which the fine-tuned structure quickly converges in less than 20 iterations because the model provides a good starting point for optimization. For comparison, the same optimization algorithm is run from scratch. The optimization task is simplified by using the same materials and optimizing only the thickness. The optimization is run five times starting from five different random points. FIG. 15B The dashed lines in

[0134] Considering the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is a local optimization that depends on the starting point, fine-tuning is compared to an advanced global optimization method, particle swarm optimization (PSO). Five different optimizations are also run starting from random initial points. On average, PSO requires sixty iterations to reach the same performance as the designed structure. None of these optimizations outperform the fine-tuned structure. That is, the designed performance of the model is equivalent to running the optimization algorithm for sixty iterations, saving time and effort.

[0135] FIG. 16A to FIG. 16D Two additional inverse design examples in the validation dataset are provided. In FIG. 16B the target structure corresponding to the design spectrum in the validation dataset, the structure closest to the design spectrum in the training dataset, the structure of the five designs, and the fine-tuned structure are shown. The MAE in the last column represents the spectral performance. FIG. 16A and FIG. 16C show the spectral performance, FIG. 16B and FIG. 16D give the details of the designed structure and the fine-tuned structure.

[0136] Reference is now made to FIG. 17Because the target spectrum covers the visible range and the near-infrared region (400 nm to 1100 nm), the model can be used to design structural colors. Here, LAB is chosen as the color space. There are many other color spaces, including RGB, xyY, XYZ. Those color spaces are not used because the LAB space is uniform, which makes it convenient to define color differences. ΔΕ is used to determine the performance of color accuracy. Lower ΔΕ values indicate higher color accuracy, while higher ΔΕ values indicate significant color mismatch. Typically, when ΔΕ < 2, humans have difficulty distinguishing color differences with the eye. In the reverse design process, the LAB color is first converted to a spectrum from 400 nm to 1100 nm, and then the spectrum is modified to fit the input of the model. This method can be used to design both transmissive and reflective structural colors.

[0137] For a given spectrum S(λ), the CIE 1931 XYZ color is first calculated using the following formula:

[0138] where, is the color matching function, is the relative spectral power distribution of the illuminant light source (using “D65”). is a normalization factor. is the visible spectral range, in this case 400 nm to 800 nm. Then LAB is calculated by conversion from XYZ. FIG. 17 In

[0139] Reference is now made to FIG. 18 , which shows an example of converting a three-dimensional color target LAB target = [a, b, c] 1810 into a 71 -dimensional spectrum , where, This is considered as an optimization task with two different objectives. The first objective is to make the color of the spectrum S as close as possible to the target color. The second objective is to make the spectrum smooth enough because sudden jumps in the spectrum are not physical. Particle swarm optimization (PSO) is used to convert the color to the spectrum S by minimizing the loss:

[0140] where is the color of the converted spectrum. Note that only the visible wavelength part from 400 nm to 800 nm is used when calculating the color. The second term is the second derivative of the spectrum with respect to wavelength from 400 nm to 1100 nm, which quantifies the smoothness of the spectrum. is a factor that balances the color accuracy and the loss of smoothness. In FIG. 18 , it is given that the color accuracy is proportional to the square of the alpha factor, and the loss of smoothness is proportional to the square of the alpha factor. Therefore, the color accuracy and the loss of smoothness are balanced by the alpha factor. An example of converting a yellow color to a spectrum with different alpha factors 50, 100, and 200 is shown in the graphs 1812, 1814, and 1816. In the graph 1812, when the alpha is small, the converted spectrum is not very smooth. An example of converting a yellow color to a spectrum with different alpha factors 50, 100, and 200 is shown in the graphs 1812, 1814, and 1816. In the graph 1812, when the alpha is small, the converted spectrum is not very smooth. FIG. 18 An example of converting a yellow color to a spectrum with different alpha factors 50, 100, and 200 is shown in the graphs 1812, 1814, and 1816. In the graph 1812, when the alpha is small, the converted spectrum is not very smooth.

[0141] Now referring to FIG. 19A to FIG. 19D , two more examples of designing structural colors for the reflective type in FIG. 19A and the transmissive type in FIG. 19C are given. The LAB of the green target is [70, -80, 0]. First, the converted spectrum is obtained from the LAB value using the optimization algorithm described above. Since this model considers both the reflection and transmission spectrum, additional modifications are made to the converted spectrum. Specifically, when designing the reflective type, the reflection spectrum is set to the converted spectrum, and the transmission spectrum is set to 0 (see FIG. 19A ). When designing the transmissive type, the transmission is set to the converted spectrum, and the reflection spectrum is set to one minus the transmission spectrum (see FIG. 19C ). Finally, the modified reflection and transmission spectra are input into the model for inverse design. The spectral performance and color difference are compared in FIG. 19A and FIG. 19C . FIG. 19B and FIG. 19D give the detailed structures of the closest, design structure and fine-tuned structure in the dataset. FIG. 19C and FIG. 19D show more examples of inverse designing reflective and transmissive structural colors.

[0142] Now referring to FIG. 20A to FIG. 20C , more examples of designing perfect absorbers from 400 nm to 1100 nm are presented. To design a perfect absorber, both the transmission and reflection in the target spectrum are set to zero. This is because absorption = 100% - transmission - reflection, and a perfect absorber requires 100% absorption. FIG. 20C Five different designs, FIG. 20A and FIG. 20B are shown. Their spectral performance is shown in FIG. 19Aare given. This is achieved by adding design constraints on material arrangement in the first few layers discussed above. In one case the design structure of the perfect absorber is MgF295.6 nm / SiO214.7 nm / Al2O376.5 nm / TiO248.0 nm / Si 14.2 nm / Ge 12.0 nm / Ti. In another case the design structure of the perfect absorber is MgF2118 nm / TiO256 nm / Si 32 nm / Ge 33 nm / Cr 200 nm / glass. The model can still give similar thickness designs for layers with common materials even if 1) the materials used can have different refractive indices, 2) Ti or Cr is not in the material, and 3) only the spectrum from 400 nm to 1100 nm is used. In FIG. 20B , designs 3 to 5 actually exhibit better absorption performance than designs 1 and 2 (about 98% absorption on average) in the range from 400 nm to 1100 nm. It appears that these structures do not follow the design of graded refractive index thin dielectric layers on a metallic mirror. FIG. 20A to FIG. 20C Examples of reverse design of perfect absorbers in the range from 400 nm to 1100 nm are shown. Five more designs are given, whose spectral comparison is shown in FIG. 20A and FIG. 20B , and the structures are shown in FIG. 20C .

[0143] Now referring to FIG. 21A to FIG. 21D , the model 226 can be used to design arbitrary absorbers. By calculating the absorption = 100% - transmission - reflection, an arbitrary target absorption spectrum is randomly selected from the validation dataset. When converting this arbitrary absorption spectrum to a model input, the target transmission spectrum is set to zero and the target reflectance = 100% - target absorption. Two examples of arbitrary absorbers are given. Their spectra are shown in FIG. 21A and FIG. 21B , and the design structures and fine-tuning structures are given in FIG. 21C and FIG. 21D . FIG. 21A to FIG. 21D Two examples of designing arbitrary absorbers in the range from 400 nm to 1100 nm are shown. The spectral performance is given in FIG. 21A and FIG. 21B , and the structures are given in FIG. 21C and FIG. 21D , respectively.

[0144] More examples of reverse design of band-stop filters at 700 nm ( FIG. 22A ) and 900 nm ( FIG. 22B ) and the corresponding structures are given in FIG. 22A to FIG. 22D , FIG. 22C and FIG. 19D , respectively.

[0145] Reference is now made to FIG. 23A to FIG. 23D , showing more details of the inverse design of DBRs. Three inverse design tasks of DBRs are compared, but only one spectral performance is shown. FIG. 23A “High reflection within 600 nm to 900 nm” in FIG. 23B “Double high reflection within 500 nm to 600 nm, 800 nm to 1000 nm” task in FIG. 23C and FIG. 23D , respectively.

[0146] Reference is now made to FIG. 24A to FIG. 24D , showing detailed results of the fine-tuned structures with four constraints discussed above in FIG. 7A to FIG. 7E . Constraints 1 to 4 are “fix the first layer to 100 nm of SiO2”, “remove Ag in the third layer”, “restrict the thickness of the first layer to [10, 150] nm and remove Ag / Al in the first layer”, “specify the material arrangement to a three-layer Ag / Si3N4 / Ag structure and design only the thickness.” Only the best structure (highlighted in FIG. 7B ) is fine-tuned. FIG. 24A to FIG. 24D Spectra of the fine-tuned structures with constraints 1 to 4 are shown, respectively. FIG. 24E Detailed structures and spectral performances are shown.

[0147] Reference is now made to FIG. 25A to FIG. 25B , setting forth another example of the design flexibility of a transmissive orange structural color LAB [70.0, 40.0, 80.0]. Four different constraints are considered here: “1: fix the first layer to 70 nm of ZnO”, “2: restrict the first layer to [10, 200] nm”, “3: use only SiO2 and TiO2”, “4: specify the material of each layer to TiO2 / MgF2 / ZnSe / SiO2 / ZnSe and design only the thickness”. FIG. 25A Results of the color impression ΔE are given in FIG. 25B Design structures are given.

[0148] Reference is now made to FIG. 26The table compares the model with existing methods in the following four aspects: (1) global design: the method should be able to design the total number of layers, material arrangement, and thickness simultaneously. (2) efficient design: the method should quickly adapt to different design objectives without restarting the design process. (3) multiple design: the method should output multiple designs. In principle, different designs can be obtained when the optimization process is restarted or the model is retrained from different random points, so we do not consider this case. (4) flexible design: the method should be able to incorporate different design constraints without restarting the optimization process or retraining the model.

[0149] FIG. 26 The existing methods are shown to fail to resolve the conflict between global design and efficient design. The method of the present disclosure fills this gap and shows good performance over existing methods.

[0150] The foregoing description is merely illustrative in nature and is in no way intended to limit the disclosure, its application, or uses. The broad teachings of the disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be limited to such examples. The methods of the present disclosure can be performed by any operation, including human operators, without departing from the scope of the present disclosure. One or more steps in the methods can be performed in different orders (or concurrently) without departing from the principles of the present disclosure. Additionally, although various embodiments have been described above, it should be understood that many variations and modifications of the embodiments described above can become apparent to those skilled in the art once informed of the general nature of the embodiments where the principles of the present disclosure can be applied. Accordingly, the true scope of the present disclosure is not limited to the embodiments described above, but by the claims and their equivalents.

[0151] Various terminology is used to describe the spatial and functional relationships between elements (for example, modules) in the above disclosure, including “connected,” “engaged,” “interfaced,” and “coupled.” Unless explicitly described as being “direct,” a relationship between or among two elements described in the above disclosure using the above terminology includes a direct relationship and also an indirect relationship where one or more other elements can be present (spatially or functionally) between the two elements.

[0152] As used herein, the phrase “at least one of A, B, and C” shall be interpreted to mean the logical (A or B or C) using non-exclusive logical “or.” For example, a phrase “at least one of A, B, and C” should be interpreted to mean any of: (i) A alone; (ii) B alone; (iii) C alone; (iv) A and B together; (v) A and C together; (vi) B and C together; (vii) A, B, and C together. The phrase “at least one of A, B, and C” should not be interpreted to mean “at least one of A, at least one of B, and at least one of C.”

[0153] In the diagrams, the direction of an arrow generally indicates the flow of information (e.g., data or instructions) that is of interest at the diagrammed point. For example, if elements A and B exchange a variety of information, but the diagram only concerns the flow of information from A to B, the arrow can point from A to B. This does not mean that there is no other information flowing from B to A. This does not mean that there is no other information flowing from B to A. Further, for information sent from A to B, B can send requests for the information or receive acknowledgements of receipt of the information from A. The term subset does not necessarily require a proper subset. In other words, a first subset of a first set can be identical to the first set.

[0154] The term “module” or the term “controller” can refer to, be part of, or include: an electrical circuit and / or processor hardware (shared, dedicated, or group) that executes code; and a memory hardware (shared, dedicated, or group) that stores code executed by the processor hardware.

[0155] The module or controller can include one or more interface circuits. In some examples, the one or more interface circuits can implement wired or wireless interfaces to connect to a local area network (LAN) or a wireless personal area network (WPAN). Examples of LANs include Institute of Electrical and Electronics Engineers (IEEE) Standard 802.11-2016 (also known as the WIFI wireless networking standard) and IEEE Standard 802.3-2015 (also known as the ETHERNET wired networking standard). Examples of WPANs are IEEE Standard 802.15.4 (including the ZIGBEE standard from the ZigBee Alliance) and the BLUETOOTH wireless networking standard from the BLUETOOTH Special Interest Group (SIG) (including the core specification versions 3.0, 4.0, 4.1, 4.2, 5.0, and 5.1 from the BLUETOOTH SIG).

[0156] The module or controller can communicate with other modules or controllers using one or more interface circuits. Although a module or controller can be described herein as being in electrical communication with another module or controller, in various implementations the module or controller can actually communicate over a communication system. The communication system includes physical and / or virtual networking equipment, such as hubs, switches, routers, and gateways. In some embodiments, the communication system connects or traverses a wide area network (WAN), such as the Internet. For example, the communication system can include multiple LANs that are connected to each other over the Internet or point-to-point leased lines using technologies including Multiprotocol Label Switching (MPLS) and virtual private networks (VPNs).

[0157] In various implementations, the functionality of a module or controller can be distributed among multiple modules that are connected through a communication system. For example, multiple modules can implement the same functionality that is distributed by a load balancing system. In another example, the functionality of a module or controller can be divided between a server (also referred to as a remote or cloud) module and a client (or user) module. For example, the client module can include a local or web application that executes on a client device and that network communicates with the server module.

[0158] As described above, the term code can include software, firmware, and / or microcode, and can refer to programs, routines, functions, classes, data structures, and / or objects. Shared processor hardware encompasses a single microprocessor that executes portions of code from multiple modules or controllers. Grouped processor hardware encompasses a microprocessor that executes portions of code from one or more modules in conjunction with additional microprocessors. References to multiple microprocessors include multiple microprocessors on discrete dies, multiple microprocessors on a single die, multiple cores of a single microprocessor, multiple threads of a single microprocessor, or a combination thereof.

[0159] Shared memory hardware encompasses a single memory device that stores portions or all of the code from multiple modules. Grouped memory hardware encompasses a memory device that stores portions or all of the code from one or more modules in conjunction with other memory devices. The term "memory hardware" is a subset of the term "computer-readable medium." The term "computer-readable medium" as used herein does not encompass transitory propagating signals or electromagnetic waves through a medium (e.g., on a carrier or the atmosphere). Thus, the term "computer-readable medium," as used herein, is considered tangible and non-transitory. Non-limiting examples of non-transitory computer-readable media are nonvolatile memory devices (e.g., flash memory devices, erasable programmable read only memory devices, or mask programmable read only memory devices), volatile memory devices (e.g., static random access memory devices or dynamic random access memory devices), magnetic storage media (e.g., analog or digital tapes or hard disk drives), and optical storage media (e.g., CDs, DVDs, or Blu-ray discs).

[0160] The apparatus and methods described in this application can be partially or entirely implemented by a special purpose computer created by configuring a general purpose computer to execute one or more particular functions embodied in the computer program. The foregoing described hardware elements and in-flow chart elements can be considered in a computer program product archi tectur al context, including a computer-readable medium. The computer program product can include a computer-readable medium having stored thereon computer program code means comprising computer program code means designed to carry out the functions of the program code means described above.

[0161] These computer program instructions can also be stored in a computer- readable medium that can be a non-transitory computer-readable medium that can contain the instructions for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor- containing system, or a system that can fetch the instructions from the instruc tion execution system, apparatus, or device and execute the instructions. The computer program instructions can also be loaded onto a computer, other programmable instruction execution system, or device to cause a series of operati on steps to be performed on the computer, other programmable instruction execution system, or other device to produce a computer implemented process such that the instructions that execute on or in connection with the instruc tion execution system, apparatus, or device that produce the computer implemented process.

[0162] A computer program can include: (i) a descriptive text to be interpreted by an interpreter, e.g., hypertext markup language (HTML), extensible markup language (XML), or JSON (JavaScript Object Notation), (ii) an assembly of instructions, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. As examples only, source code can be written using syntax from a language including: C, C++, C#, Objective-C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl, Pascal, Curl, OCaml, JavaScript, Hypertext Markup Language 5th revision (HTML5), Ada®, Active Server Pages (ASP), ASP.NET, PHP (PHP: Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, MATLAB, SIMULINK, and Python®. (vi) optical simulations, e.g., TMT.

[0163] Example embodiments are provided so as to be thorough, and to convey the scope to those skilled in the art. Numerous specific details are set forth such as examples of specific components, devices, and methods, in order to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art, however, that at least some embodiments of the present disclosure can be practiced without employing these specific details, and that within the scope of the claims, the present disclosure can be implemented in many different ways, utilizing

[0164] The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms "a," "an," and "the" can be intended to mean the singular, including just one, or the plural, including multiple references, unless the context clearly dictates otherwise. The terms "including," "comprising," and "having" are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and / or components but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order in which they are discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps can be employed.

Claims

1. A method of performing inverse design of an optical multilayer thin film structure, comprising: receiving an optical target to a base model comprising a plurality of sequential decoders, the optical target comprising a target spectrum; receiving a hidden representation of the optical target at the plurality of sequential decoders; receiving a physical embedding and a position embedding at a first decoder of the plurality of sequential decoders; coupling an output of a previous decoder of the plurality of sequential decoders to a subsequent decoder; and generating a sequence of tokens and probabilities representing materials and thicknesses of a plurality of layers of the optical multilayer thin film structure. Receiving an optical target comprises receiving at least one of: a structural color; an absorber; a filter; a distributed Bragg reflector; and a Fabry-Perot (FP) resonator.

2. The method of claim 1, wherein, Receiving an optical target comprises receiving reflection and transmission spectral data.

3. The method of claim 1, wherein, Receiving an optical target comprises receiving polarization and direction of light output.

4. The method of claim 1, wherein, Receiving a hidden representation comprises receiving a hidden representation to a multi-head cross-attention layer of the first decoder.

5. The method of claim 1, wherein, Receiving the physical embedding and the position embedding to a decoder comprises receiving the physical embedding and the position embedding to a multi-head self-attention layer and providing an output of the multi-head self-attention layer to the multi-head cross-attention layer.

6. The method of claim 5, wherein, Generating a sequence of tokens and probabilities comprises receiving constraints and generating a sequence and tokens with the constraints.

7. The method of claim 1, wherein, Providing constraints comprises providing single or multi-layer material limits.

8. The method of claim 1, wherein, Providing constraints comprises providing single or multi-layer thickness limits.

9. The method of claim 1, wherein, Outputting data representing a plurality of optical multilayer thin film structures with at least one processor.

10. The method of claim 1, further comprising: Determining a mean absolute error (MAE) of data representing each of the plurality of optical multilayer thin film structures and selecting one of the plurality of optical multilayer thin film structures having a lowest mean absolute error.

11. The method of claim 10, further comprising: Selecting a combination of materials and thicknesses based on a lowest mean absolute error between target spectra.

12. The method of claim 11, further comprising: Generating a sequence of tokens comprises generating a sequence of tokens by forming a sequence layer autoregressively.

13. The method of claim 1, wherein, 14. A system for inverse design of an optical multilayer thin film structure, comprising: a computer readable medium storing code for a base model having a transformer comprising a neural network model and utilizing a structural sequence of tokens to represent materials and thicknesses of layers of an optical multilayer thin film structure and utilizing spectral embeddings to facilitate learning by the model of relationships between spectra and structures, the computer readable medium further storing computer executable instructions that, when executed by a processor, configure the processor to: receive optical target parameters as input cues; generate data representing the optical multilayer thin film structure based on the base model and the optical target parameters, the optical multilayer thin film structure having optical characteristics that satisfy the received optical target parameters; and output data representing the optical multilayer thin film structure. The data representing the optical multilayer thin film structure indicates a total number of layers of the optical multilayer thin film structure required to satisfy the optical target parameters and indicates materials and thicknesses of each layer of the optical multilayer thin film structure.

15. The system of claim 14, wherein, ​ 16. The system of claim 14, wherein, The optical target parameters include at least one of: structural color; absorber; filter; distributed Bragg reflector; and Fabry-Perot (FP) resonator.

17. The system of claim 14, wherein, The optical target parameters include reflectance and transmittance spectral data.

18. A method of inverse design of an optical multilayer thin film structure, comprising: receiving, with at least one processor, optical target parameters based on input prompts; applying, with the at least one processor, the received optical target parameters to a base model, the base model having a transformer, the transformer including a neural network model and utilizing structure serialization with labeled sequences to represent materials and thicknesses of layers of the optical multilayer thin film structure and utilizing spectral embedding to facilitate learning by the model of relationships between spectra and structures; generating, with the at least one processor, data representing an optical multilayer thin film structure having optical characteristics that satisfy the received optical target parameters based on the application of the base model to the optical target parameters; and outputting, with the at least one processor, the data representing the optical multilayer thin film structure. The data representing the optical multilayer thin film structure indicates a total number of layers of the optical multilayer thin film structure required to satisfy the optical target parameters and indicates materials and thicknesses of each layer of the optical multilayer thin film structure.

19. The method of claim 18, wherein, Receiving optical target parameters includes receiving at least one of: structural color; absorber; filter; distributed Bragg reflector; and Fabry-Perot (FP) resonator.

20. The method of claim 18, wherein, Receiving optical target parameters includes receiving reflectance and transmittance spectral data.

21. The method of claim 18, wherein, ​

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