Unpowered / passive directional-routing metastructure

Abstract

A metastructure for use in communication systems, such as those operating in the microwave or millimeter wave frequency bands, is physically adapted to passively and simultaneously route, in multiple directions, multiple channels of an incoming signal. The metastructure can be incorporated into communication systems to improve their performance.

Description

Unpowered / Passive Directional-routing MetastructureStatement Regarding Federally Sponsored Research[oooi] This invention was made with Government support under contract FA9550-21-1-0312 awarded by the Air Force Office of Scientific Research. The Government has certain rights in the invention.Statement of Related Cases

[0002] This specification claims priority to U.S. 63 / 537,133 filed September 7, 2023 and incorporated herein by reference.Field of the Invention

[0003] The present invention relates to meta-structures.Background

[0004] Millimeter (mm) wave communication is a key technology for future broadband cellular networks. It allows 5G, and beyond (B5G and 6G) to offer larger bandwidth and hence higher data rates than can be achieved with sub-6GHz frequency communications. This is necessary to satisfy ever increasing demands from a wide range of applications that rely on high-speed, broadband mobile communication networks, such as autonomous vehicles, remote medical care and surgery, augmented and extended reality, wireless control of industrial manufacturing, and the like.

[0005] In contrast to sub-6 GHz technology, which uses omnidirectional antennas to transmit and receive signals, mm-wave technology operates at much higher frequencies, wherein propagation losses are higher. Hence, it relies on beam-forming to overcome these losses, and uses directional beams to communicate between receiver and transmitter. The directionality of the beams means that they are susceptible to being blocked by obstacles (e.g., buildings, walls, etc.) in the propagation environment that are in the path between transmitter and receiver. Such blocking results in loss of communication.

[0006] Since all channels in the beam propagate together in a given direction, they cannot be distributed to other directions. Instead, other directions are covered in a time-multiplexed fashion, which causes communication delays and lower data rates for the users. Moreover, each beam covers the entire spectralbandwidth and, as a result, multi-channel access is impossible. This limits the number of devices that can be connected.Summary

[0007] The present invention provides a way to address some of the problems with millimeter (mm)-wave communications.

[0008] In accordance with an illustrative embodiment, an electromagnetically engineered metastructure —referred to herein as an Unpowered Directional Routing Metastructures ("UDRM")— provides passive, zeropower routing of all frequency components / channels in a multi-channel beam, mm- wave beam. The UDRM is tailored for the specific environment in which the beams propagate, and is capable of routing all channels of a multi-channel beam simultaneously, in a controlled fashion, in different directions. Routing is performed as a function of channel properties, such as, frequency, propagation direction, angle, spatial frequency, amplitude, phase, polarization, spin angular momentum, and orbital angular momentum. And the UDRM is capable of providing such routing without introducing delays, or any additional overhead or power usage. The UDRM thereby enhances or enables communication between transmitter and receiver(s).

[0009] In the illustrative embodiment, The UDRM is a periodic array of repeat units, wherein the routing direction of the various frequency components coincide with the directions of the periodic array's diffraction orders. In a further embodiment, the routing direction of the various spatial frequency components coincide with the directions of the periodic array's diffraction orders. The UDRM may be fabricated with low-cost materials, such as, without limitation, thermoplastic filaments, photopolymer resins, polymer powders, and the like, using low-cost additive manufacturing methods, such as various types of 3D-printing methods. Exemplary materials include, without limitation, polypropylene (PP), polylactic acid (PLA), and polymethylmethacrylate (PMMA), and exemplary 3D- printing processes include, without limitation, stereolithography (SLA), selective laser sintering (SLS), and fused deposition modeling (FDM).[ooio] Because the UDRMs are relatively thin and lightweight, they are readily deployed on existing surfaces (e.g., walls, ceilings, furniture, moving objects, etc.), in both indoor and outdoor environments, and can be placed behind covers / screens. They can be judiciously placed on such surfaces to avoid obstacles,thereby receiving an incoming multi-channel beam, and routing the various channels therein in different directions to various receivers.[ooii] A UDRM in accordance with the present disclosure enables the following: i. Routing of components / channels of a beam incident on the UDRM in different directions based on their channel properties. For a UDRM consisting of a periodic array of repeat units, the directions coincide with the directions of the periodic array's diffraction orders. ii. Completely passive, unpowered directional routing of channels / components ( / .e., the UDRM operates totally unpowered). iii. Flexibility of design; it can be designed for transmission- or reflection-mode operation, including combinations of different incident and outgoing angles on either transmission or reflection sides. iv. High directional-routing efficiency due to the use of low-loss materials, which substantially maximizes the directional-routing efficiency (except for embodiments in which UDRMs are engineered specifically to control the absorption of certain channels). In principle, directional routing with ideal (100%) efficiencies is possible. v. Directional routing of the channels is incoherent. It occurs independently of the number of channels excited simultaneously. vi. Flexibility of design such that simultaneous control of distinct spectral channel responses, such as specular reflection, anomalous reflection, absorption (e.g., to avoid interference) is possible. Individual channels can be routed in individual given directions, an individual channel can be routed in various directions, sets of channels can be routed in given different directions, or combinations of sets and individual channels can be routed in given different directions. vii. The response to the incident beam can be polarization-dependent to enable either additional communication capacity or polarization independent to provide signal robustness. viii. Enables additional degrees of freedom through the control of the wireless environment (e.g., by providing additional routing pathways and / or by routing around obstacles).ix. Useful for both indoor and outdoor communications. Used inside a building ( / .e., surface panels hanging on wall), the UDRM can significantly attenuate interference and enhance signal strength at the receiver side. x. For beam-forming mm-wave technology, UDRM can provide virtual line-of-sight communication to eliminate "dead zones", which are not covered by antenna towers. xi. Communications with users who cannot be reached by direct line-of- sight due to the high sensitivity to blockage that occurs with propagation using beams (e.g., outdoor because of obstacles or indoor due to walls). xii. May be fabricated with low-cost materials (e.g., thermoplastic filaments, photopolymer resins, polymer powders, etc.) using low- cost additive manufacturing fabrication methods (e.g., 3D printing methods, including fused deposition modeling (FDM), stereolithography (SLA), selective laser sintering (SLS), etc.). Moreover, materials used for UDRM fabrication are recyclable. xiii. Results in a relatively thin and light weight structure, which facilitates deployment on existing surfaces / interfaces (e.g., walls, ceilings, furniture, on moving objects, etc.) in indoor and outdoor environments, and can be placed behind covers or screens. xiv. Useful for routing a multichannel signal in the microwave or mm- wave frequency range, including C, X, K, and V bands.

[0012] In some embodiments, the present invention provides a method for communication wherein line-of-sight propagation of electromagnetic radiation between a transmitter and one or more receivers is degraded or blocked by an obstacle, wherein the method comprises: (a) positioning a passive, directional- routing metastructure at a location that has line-of-sight to the transmitter and line-of-sight to the one or more receivers; (b) receiving, at the directional-routing metastructure, a beam comprising multiple communication channels that is transmitted from the transmitter, wherein once received, the directional-routing metastructure passively and simultaneously routes the multiple communication channels based on a characteristic of the communication channels, wherein a first communication channel of the multiple communication channels is routed in a first direction that is different than at least some of the other communication channels; and (c) receiving, at one of the receivers, the first communicationchannel such that propagation of the first communication channel is neither blocked nor substantially degraded.

[0013] Various additional embodiments of the method for communication may further comprise one or more of the following features, in any (nonconflicting) combination, among other features disclosed herein:• Wherein the characteristic of the communication channels is a respective frequency thereof.• Wherein the characteristic of the communication channels is selected from the group consisting of: propagation direction, angle, spatial frequency, amplitude, phase, polarization, spin angular momentum, and orbital angular momentum.• Wherein the passive, directional-routing metastructure routes each of the multiple communications channels in a different direction than each other of the multiple communication channels.• Wherein the passive, directional-routing metastructure absorbs at least one of the multiple communication channels, and therefore does not transmit the at least one absorbed communication channel to a receiver.• Wherein at least two of the multiple communication channels are routed in a second direction that is different than the first direction.• Wherein a single communication channel is routed in multiple directions.• Wherein a backplane that is opaque to the incoming beam is disposed on a rear surface of the passive, directional-routing metastructure.• Wherein a backplane that is transmissive to the incoming beam is disposed on a rear surface of the passive, directional-routing metastructure.• Wherein the passive, directional-routing metastructure and a backplane that is opaque to the incoming beam is disposed on a rear surface of the passive, directional-routing metastructure are attached to a vertical surface.• Wherein the passive, directional-routing metastructure and a backplane that is transmissive to the incoming beam is disposed on a rear surface of the passive, directional-routing metastructure are attached to a vertical surface.• Wherein the passive, directional-routing metastructure is disposed indoors.• Wherein the passive, directional-routing metastructure is disposed outdoor.• Wherein the beam is in the Ka band.• Wherein the beam is in the microwave or mm-wave beam frequency range, including the C, X, K, and V bands.• Wherein the method is used in a 5G or 6G wireless communication network.• Wherein the passive, directional-routing metastructure has dimensions that provide a surface area for the metastructure of at least 1 square meter, and a thickness of at least 2 centimeters.• Wherein the passive, directional-routing metastructure has a periodic structure.• Wherein the passive, directional-routing metastructure does not have a periodic structure.• Wherein the passive, directional-routing metastructure routes less than nine communication channels.• Wherein the passive, directional-routing metastructure routes nine or more communication channels.[ooi4] Some other embodiments of the invention provide a metastructure comprising at least one repeat unit, the at least one repeat unit comprising at least a first material having a relative permittivity ei and a second material having a relative permittivity 62, wherein 62 is greater than 61, and wherein the at least one repeat unit has a length dimension and a width dimension, the metastructure having physical adaptations that enable the metastructure to passively and simultaneously route, in multiple directions, at least some of the multiple channelsof an incoming multi-channel signal, wherein: (a) the length and width dimensions are greater than a wavelength of the incoming signal; and (b) the metastructure routes the at least some multiple channels as a function of a characteristic of the multiple channels.

[0015] Various additional embodiments of the metastructure may further comprise one or more of the following features, in any (non-conflicting) combination, among other features disclosed herein:• Wherein the metastructure comprises a plurality of repeat units.• Wherein the characteristic is a frequency of the respective channels.• Wherein the characteristic is a spatial frequency of the respective channels.• Wherein the characteristic of the communication channels is selected from the group consisting of: propagation direction, angle, spatial frequency, amplitude, phase, polarization, spin angular momentum, and orbital angular momentum.• Wherein the multiple directions correspond to diffraction orders of the metastructure.• Wherein ei = 1.• Wherein £2 = 3.• Wherein £2 = 2.3• Wherein €2 is in a range of 2.3 to 3• Wherein the second material is a lossless material.• Wherein the first material is air.• Wherein the metastructure has dimensions that provide a surface area for the metastructure of at least 1 square meter.• Wherein the metastructure has a thickness greater than a wavelength of the incoming signal.Wherein features of the at least one repeat unit have a size scale smaller than the wavelength of the incoming signal.• Wherein the second material is a polymer.• Wherein the second material is a polymer selected from the group consisting of: polypropylene (PP), polylactic acid (PLA), and polymethylmethacrylate (PMMA).• Wherein the metastructure is physically adapted to absorb at least one of the multiple channels.• Wherein the metastructure is physically adapted to route at least two of the multiple channels in the same direction.• Wherein the metastructure is physically adapted to route at least one channel in more than one direction.• Wherein the metastructure is physically adapted to route a first group of the multiple channels and a second group of the multiple channels, wherein a spacing of the center-channel frequencies of the first group of channels is different from the spacing of the centerchannel frequencies of the second group of channels.• Wherein the metastructure has 2D patterned layers, thereby providing 3D directional routing.• Wherein the metastructure has ID patterned layers, thereby providing 2D directional routing.• Wherein a backplane that is opaque to the mm-wave beam is disposed on a rear surface of the metastructure.

[0016] Some additional embodiments of the invention provide a method for making a metastructure capable of passively routing a signal having multiple channels, the method comprising :(a) selecting structural parameters of the metastructure, wherein the structural parameters are selected as a function of the frequency range of the signal;(b) establishing a candidate design as a starting point for optimization, the candidate design comprising a plurality of design elements, organized in three dimensions, wherein a value is assigned to each design element, the value being a permittivity between two relative permittivity values, wherein one of the values is larger than the other;(c) generating an objective function using performance metrics of the metastructure design, wherein the objective function serves as a basis for optimization;(d) simulating the candidate design;(e) determining the performance of the metastructure, with respect to the performance metrics, based on results of simulating the candidate design;(f) estimating gradients of the objective function, wherein the gradients are used to optimize permittivity values of each design element;(g) updating the metastructure design by altering the permittivity values based on the estimated gradients;(h) estimating and comparing performance of the updated metastructure design, to the performance metrics, wherein:(1) if the performance does not satisfy performance metrics, then continue optimization by repeating operations (f)-(h), and(2) if the performance satisfies the performance metrics, then proceed to operation (i); and(i) fabricating the metastructure design.

[0017] Various additional embodiments of the method for making the metastructure may further comprise one or more of the following features, in any (non-conflicting) combination, among other features disclosed herein:• Wherein in the operation of establishing the candidate design, the two relative permittivity values are 1 and 3.• Wherein in the operation of establishing the candidate design, the two relative permittivity values are 1 and 2.3.• Wherein in the operation of establishing the candidate design, the plurality of design elements have a random organization.• Wherein in the operation of establishing the candidate design, the plurality of design elements have a uniform organization.• Wherein in the operation of establishing the candidate design, the metastructure comprises a periodic array of repeat units, wherein the candidate design of each repeat unit includes the plurality of design elements.• Wherein in the operation of establishing the candidate design, the plurality of design elements collectively represents a totality of the metastructure; that is, there is only one "repeat unit."• Wherein the operation of generating an objective function comprises generating an objective function that maximizes reflectivities of the metastructure for each of the multiple channels to different directions.• Wherein the operation of generating an objective function comprises generating an objective function that maximizes transmissivities of the metastructure for each of the multiple channels to different directions.• Wherein in the operation of generating an objective function, reflectivity is defined as the ratio of outgoing and incoming Poynting flux in the z direction.• Wherein simulating the candidate design comprises using rigorous coupled-wave analysis.• Wherein updating the metastructure design comprises binarizing altered permittivity values, and wherein binarization may be hard or soft.• Wherein determining the performance of the metastructure comprises determining directional routing efficiencies for the multiple channels.• Wherein estimating gradients comprises using a method of moving asymptotes.• Wherein fabricating the metastructure design comprises: (i) converting the metastructure design to a 3D print file; and (ii) printing the metastructure using a 3D printer.Brief Description of the Drawings

[0018] FIG. 1A depicts a UDRM having a first routing capability in accordance with the present teachings.

[0019] FIG. IB depicts a UDRM having a second routing capability in accordance with the present teachings.

[0020] FIG. 1C depicts a UDRM having a third routing capability in accordance with the present teachings.

[0021] FIG. 2 depicts a communication system utilizing a UDRM in accordance with the present teachings.

[0022] FIG. 3 depicts a stylized version of a UDRM in accordance with the present teachings.

[0023] FIG. 4 depicts a method for making a UDRM in accordance with present teachings.

[0024] FIG. 5 depicts sub-operations of a step of the method of FIG. 4.

[0025] FIG. 6A depicts a candidate design with a 2D patterned layer for 3D directional routing, in accordance with the method of FIG. 4.

[0026] FIG. 6B depicts a candidate design with a ID patterned layer for 2D directional routing, in accordance with the method of FIG. 4

[0027] FIG. 7A depicts directional routing performance of a UDRM design with 3D directional routing, showing directional routing efficiencies for nine frequency channels.

[0028] FIG. 7B depicts directional routing performance of a UDRM design with 2D directional routing, showing directional routing efficiencies for six different channels based on two different polarizations and three different spatial frequencies.

[0029] FIG. 8A depicts a UDRM with 3D-directional routing capability.

[0030] FIG. 8B depicts a UDRM with 2D-directional routing capability.

[0031] FIG. 9 depicts a desired response of an embodiment of a 2D- directional routing metastructure.Detailed Description

[0032] The present teachings provide, by way of illustrative embodiments, an electromagnetically engineered metastructure, which is referred to herein as anUnpowered Directional Routing Metastructures ("UDRM"), a communications system utilizing a UDRM, and methods for manufacturing the UDRM.

[0033] A metastructure is a structure that is engineered to have properties that are not normally observed / naturally occurring in the materials that form the structure. Metastructures are formed from existing materials that usually have a high refractive-index contrast, and are patterned at subwavelength scales. Unlike metasurfaces and other types of surfaces that are used to control electromagnetic waves, metastructures are typically 3D structures. They have a thickness that is usually larger than the wavelength of the electromagnetic waves they are intended to manipulate.

[0034] Although the metastructure may include periodic features, this is not a general requirement. In the illustrative embodiments describe herein, the UDRM includes an arrangement of repeating units for convenience. In other embodiments, the URDRM is not a periodic structure ( / .e., it only includes a single "repeat unit").

[0035] In accordance with the present teachings, the repeat unit consists of a large number of design elements to which a material can be assigned and that enable the formation of scattering patterns. The design elements of the repeat unit have a size scale smaller than the wavelength of the phenomena e.g., electromagnetic waves, etc.) they are intended to influence.

[0036] In the illustrative embodiment, the properties of the UDRM, and its ability to influence, for example, electromagnetic waves, derive from the shape, the distribution of material ( / .e., relative permittivities) within the repeat units, and orientation of the repeat units, both on an individual basis and collectively.

[0037] As a function of its design, a metastructure can control a variety of different characteristics of incident electromagnetic waves, such as, without limitation, frequency, propagation direction, angle, spatial frequency, amplitude, phase, polarization, spin angular momentum, orbital angular momentum, and the like.

[0038] Thus, a UDRM in accordance with the present teachings can be tailored to the specific environment in which electromagnetic waves (hereinafter "beams" or "waves" or "signals") propagate, and control the path of the beams for the different channels (e.g., frequency channels, etc.) within a multi-channel signal, thereby enhancing or enabling communication between transmitter andreceiver(s). The present UDRM is a passive structure, and thus provides zero-power routing of all channels in a multi-channel beam. In the illustrative embodiment, the UDRM routes channels simultaneously, in a controlled fashion, in different directions, based on a property / characteristic of the channels, such as frequency, propagation direction, angle, spatial frequency, amplitude, phase, polarization, spin angular momentum, orbital angular momentum, and the like, without any additional delay, overhead, or power usage.

[0039] A UDRM in accordance with the present teachings may provide many different routing schemes, a few of which are shown in FIGs. 1A-1C.

[0040] FIG. 1A depicts a UDRM having a first directional routing capability for several electromagnetic waves having the same frequency but incident at the UDRM at different directions. Appropriately designed, UDRM 1OOA is capable, for example, of specular reflection (EMW-1), anomalous reflection (EMW-3), and absorption (EMW-2). Moreover, this multifunctional operation may be designed to be identical for both s and p polarizations of all three waves. In some other embodiments, a UDRM may be designed to provide a similar routing capability (specular, anomalous, absorption) but for electromagnetic waves having different frequencies.

[0041] FIG. IB depicts a UDRM having a second directional routing capability in conjunction with multichannel beam EMW-4, in accordance with the present teachings. Appropriately designed, UDRM 100B is capable of simultaneously routing different channels CH-1, CH-2, and CH-3 to different directions. And FIG. 1C depicts a UDRM having yet a third directional routing capability in conjunction with multichannel beam EMW-4. In this embodiment, UDRM 100C routes some but not all different channels in the same direction. Specifically, CH-1 is routed in a first direction, and CH-2 and CH-3 are routed in a second direction.

[0042] Channels CH-1, CH-2, and CH-3 may be representative of different frequencies, or may differ based on another characteristic of the beam.

[0043] In addition to the routings depicted in FIGs. 1A-1C, a single channel can be routed in multiple directions, which provides a great deal of additional flexibility. Consider an example in which a first frequency is routed in direction A and direction B, and a second frequency is routed in direction B and direction C.Both frequencies are routed to direction B because there more users there than for directions A and C.

[0044] It is notable that the routings depicted in FIGs. 1A-1C are illustrative of a 2D directional routing metastructure. Embodiments of the invention include both 2D and 3D directional routing metastructure.

[0045] FIG. 2 depicts communications system 250 in accordance with the present teachings, including transmitter 210, UDRM 200, and a plurality of receivers 214-1 through 214-6. The communications system depicted in FIG. 2 is greatly simplified to focus on elements that are germane to an understanding of embodiments of the invention; as will be appreciated to those skilled in the art, such a communications system would typically include various servers, switches, antennas, other hardware and software, etc., as well as many more transmitters and receivers, and UDRMs 200.

[0046] FIG. 2 also depicts the local environment; in particular, the presence of wall 212 between transmitter 210 (e.g., cell tower, etc.) and the various receivers 214-1 through 214-6. In the absence of UDRM 200, wall 212 blocks mm-wave, multichannel signal MCHS from propagating to the receivers. In accordance with the present teachings, UDRM 200 is positioned so that it is capable of receiving multichannel signal MCHS, and is designed to route the (six) individual channels in multichannel signal MCHS in (six) different directions to (six) receivers 214-1 through 214-6. Routing is accomplished passively (unpowered) and simultaneously.

[0047] It is notable that since all channels propagate in the same direction, in the absence of UDRM 200, a communications system would have to time multiplex the beam to direct the beam to multiple receivers. This would cause delays and result in lower data rates. Moreover, since, in the absence of UDRM 200, all channels in the multichannel signal are directed to each receiver, the potential for eavesdropping exists.

[0048] FIG. 3 provides a stylized depiction of a UDRM. UDRM 200 includes both wavelength-size and subwavelength-size features to control its electromagnetic scattering properties. Typically, UDRM 200 has a macroscopic area on the order of square meters, and a thickness that typically ranges from one to multiple wavelengths; that is, millimeters to centimeters for the case of a mm-wave beam. Hence, the UDRM geometry has very different length scales, which presents a challenge for its design.

[0049] In accordance with the illustrative embodiment, UDRM 200 is a periodic structure, which includes a large array of repeat units 302 / that span / cover the large (~m2) transverse area of the UDRM. Each individual repeat unit itself typically includes subwavelength-size features, which enable the entire incident beam to interact with the UDRM. However, each repeat unit 302< has overall dimensions somewhat larger than wavelengths of the signal of interest, so as to enable control over the scattering of the beam components, resulting in the directional-routing functionality of UDRM 200. This is discussed further below.[ooso] For the UDRM repeat unit, a design volume on the order of the wavelength in the frequency band of interest is used. For mm waves in the Ka- band (26.5-40 GHz), for example, the wavelength ranges from approximately 7 to 10 mm. The period is typically chosen to be larger than the wavelengths for the frequencies of interest, to provide a sufficient number of diffraction orders (e.g., to route in n directions, there must be n propagating diffraction orders).

[0051] As noted earlier, the UDRM is not necessarily a periodic structure ( / .e., the UDRM may thus comprise a single repeat unit). In the illustrative embodiments, the UDRM is designed as a periodic structure to reduce computational requirements. That is, with this approach, it is only necessary to optimize the subwavelength patterns in a single repeat unit. Moreover, physical insight and / or physics-informed design (e.g., directions can map into diffraction orders for periodic structures) can be used to facilitate the design.

[0052] FIGs. 4 and 5 depict method 400 for designing and fabricating a UDRM in accordance with the present teachings. Applicant adopts an "inverse" design approach for its UDRM. That is, the target material properties are input, and an optimization strategy is used to predict a material structure that satisfies the target properties.

[0053] Briefly, method 400 includes the following operations:• Operation S401 : selecting structural parameters of the metastructure;• Operation S402: establishing a candidate design of the metastructure;• Operation S403: generating an objective function using performance metrics of the metastructure design;• Operations S404 / S405: Simulating & optimizing the candidate design of the metastructure;• Operation S406: Converting the metastructure design to a 3D print file;• Operation S407: 3D printing the metastructure.Operations S404 / S405 further include the suboperations of:• Suboperation S501 : Performing an electromagnetic simulation of the metastructure;• Suboperation S502: Calculating the performance of the metastructure;• Suboperation S503: Estimating the gradient of the objective function;• Suboperation S504: Updating the metastructure to improve performance based on the gradient; and• Suboperation S505: Optionally binarize the design.

[0054] For pedagogical purposes, the method is described in the context of a specific embodiment of a UDRM; in particular, a UDRM suitable for use in conjunction with the Ka-band, between 26.5 and 40 GHz in the mm-wave spectrum. Such an embodiment is of great relevance for 5G, 6G wireless communication. The UDRM operates in reflection mode, and routes an incoming beam with nine spectral frequency channels to nine different directions depending on the frequency of the channel. It is to be understood, however, that UDRMs in accordance with the present teachings are not limited to the Ka-band; they have utility for processing other signals of other frequencies, such as, generally, those in the microwave or mm-wave frequency range (including C, X, K, and V bands). Nor are the present UDRMs limited to routing based on frequency. As noted above, they can be designed to provide routing for any other channel properties as well, including propagation direction or angle, spatial frequency, amplitude, phase, polarization, spin angular momentum, orbital angular momentum, and the like, or for any combinations thereof, and such design is within the capabilities of those skilled in the art, in conjunction with the present disclosure.

[0055] Example. Directional Routing based on Channel Frequency

[0056] As an example of the flexibility of applicant's UDRM design, the nine frequency channels in this embodiment consist of two groups. A first group of frequency channels is closely spaced with center frequencies separated by 0.7 GHz centered on 26.6, 27.3, 28, 28.7 and 29.4 GHz. The second group of frequency channels is more widely spaced with center frequencies separated by 1GHz centered on 37, 38, 39, and 40 GHz. By way of illustration, not limitation, a normally incident beam is used, which, upon reflection from the UDRM, is separated into the 9 frequency channels with each channel routed in a different direction.

[0057] UDRM Design Approach.

[0058] In accordance with operation S401, structural parameters for the metastructure are selected depending on the frequency range or band of the electromagnetic waves that are to be controlled in the mm-wave communication application.

[0059] For the UDRM repeat unit, a design volume on the order of the wavelength in the frequency band of interest is used. For mm waves in the Ka- band (26.5-40 GHz), the wavelength ranges from approximately 7 to 10 mm. An exemplary structure has a square-lattice periodicity in the transverse (x-y) plane with a lattice constant a=18 mm and includes 20 layers in the longitudinal (z) dimension, with a total thickness of 44.3 mm.

[0060] In this embodiment (although not as a limiting design principle), the period is typically chosen to be larger than the wavelengths for the frequencies of interest, so that there are 9 propagating diffraction orders. The routing directions then correspond to the propagating diffraction order; that is, (- 1,1), (0,1), (-1,0), (-1,-1), (0,0), (1,1), (1,0), (0,-1), and (1,-1) for the respective frequency components in the incident beam.

[0061] The selection of structural parameters (operation S401), and the next operation (S402), may be based on previous (relevant) designs, as a reasonable starting point for the optimization process that follows. In fact, the design provided in this example may suffice as a starting point for the design of a UDRM for use in conjunction with a mm-wave multichannel signal.

[0062] In accordance with operation S402, a candidate design for the metastructure is established. To illustrate the method, the design proceeds for a 3D directional routing metastructure. The same basic steps apply for the design of 2D directional routing metastructure, as described later in conjunction with FIGs. 6B, 7B, 8B, and 9.

[0063] Because the UDRM is to operate in reflection mode, the UDRM structure will be placed on a metallic reflective substrate. For design elements inthe sub-1 mm size range (achievable with 3D-printing technologies), the UDRM design region can contain thousands of elements.

[0064] For this embodiment, the candidate design focuses on the repeat unit. Each repeat unit is patterned into 30 x 30 x 20 design elements in the (x, y, z) direction, respectively. The candidate design, which is a starting point for the optimization, can be random, uniform, a previous design, etc. FIG. 6A depicts candidate design 620A for the UDRM (not including the substrate layer), implemented as a 2D patterned layer (x-y directions), providing 3D directional routing. For a random design, for example, each of the 20 layers (z direction) will have a different random "pattern" of 30 x 30 elements (x-y directions). For a uniform design, each layer will be uniform (the same material), and all layers are identical.

[0065] The "pattern" referenced above is defined by the value assigned to each element, value being a permittivity between two relative permittivity values, wherein one is larger than the other. In this embodiment, the smaller relative permittivity is that of air (ci = 1) and the larger relative permittivity is that of a lossless dielectric, which is assumed to be 62 = 3. In this embodiment, the lossless dielectric is a 3D-printable polymer material.

[0066] To create this design, dielectric materials that are lossless in the range of interest, and compatible with low-cost 3D printing methods are used. The design space becomes exceedingly large when assigning only one of two lossless dielectric materials to each element. To take advantage of the large number of degrees of freedom in the design region, it is preferable to use an efficient computational design approach based on the adjoint variable method and gradient-based optimization.

[0067] In some other embodiments, rather than focusing on the repeat unit as the basis for the candidate design, the complete metastructure is (logically) broken-up into the aforementioned design elements. It will be appreciated that in such embodiments, the metastructure need not have a periodic structure. Currently, it is computationally impractical to take this approach to developing the candidate design. But as processing power increases in the future, such an approach may be practical.

[0068] In operation S403, an objective function is generated using performance metrics of the metastructure design. In the illustrative embodiment, the performance of the UDRM is optimized by minimizing the objective function. This objective function maximizes the reflectivities of the UDRM design, R^'9n, for the different frequency channels f to the different directions of the diffraction orders r by matching them to sets of target reflectivities,As an example, one possibility of choosing the objective function is:

[0069] Various definitions of reflectivity may be used in conjunction with expression (1). For example, in some embodiments, reflectivity is the ratio of outgoing and incoming Poynting flux in the z direction. taycst

[0070] The target reflectivities, Rfr, are nine (r=l, ..., 9) sets of nine reflectivities. In each set, the reflectivity for the direction that a frequency channel (f= 1...9) is to be routed is set to 1, and the reflectivity values for all the other directions are set to 0. The directions can be determined from the transverse wave vector components (kx,n, ky,m), which depend on the periodicity and the propagating diffraction orders (n, m), and making use of the direction cosines (an)m, Pn,m ■where c is the speed of light, f is the frequency, and the symbol signifies a unit vector.

[0071] In operation S404, the candidate design is simulated, and an optimization routine is implemented via suboperations S501 through S505 (and the query at operation S405).

[0072] Per suboperation S501, the UDRM's response to incident light is calculated using a first-principles electromagnetic field approach. In the illustrative embodiment, rigorous coupled-wave analysis (RCWA) is used. Other techniques may suitably be used, such as finite-difference time-domain (FDTD), finite-difference frequency domain (FDFD), etc.

[0073] In suboperation S502, the performance of the design (directional routing efficiencies) is calculated based on EM fields in the simulation domain, as provided by suboperation S501.

[0074] At suboperation S503, the gradient of the objective function with respect to all of the design parameters is estimated, such as by using an adjoint variable method. The gradients are used to optimize the material properties of each design element to improve the performance of the UDRM structure. A gradient-based optimizer using the method of moving asymptotes maximizes power routed to the different directions for the different spectral channels based on the content of incident beam.

[0075] In suboperation S504, the proposed UDRM structure is updated to improve performance based on the estimated gradients. The material properties that are being optimized are the relative permittivity in each design element. As previously noted, during the optimization, each design element is assigned a value between two relative permittivity values, wherein one is large than the other. In the illustrative embodiment, the smaller relative permittivity is that of air (ci = 1) and the larger relative permittivity is that of a lossless dielectric material, which is assumed to be 62 = 3, and represents a 3D-printable polymer material. The gradient-based optimization yields a continuous relative permittivity for each design element. For fabrication, however, it is preferred to have a finite number of materials, e.g., two materials (air and the 3D-printable polymer material), in this UDRM design. As such, in suboperation S505, the continuous permittivity distribution is converted towards a binary permittivity using a projection method; soft binarizing is used. Finally, at the end of the optimization, the remaining permittivity values that have not been binarized in the process are rounded to represent the air and polymer, respectively ( / .e., using hard binarizing). In addition, to facilitate the fabrication of the resulting design structure, the smallest feature size in the structure is regulated by using a blur function.

[0076] At operation S405, the performance of the updated UDRM structure is compared to a set of performance metrics. Such metrics typically include the routing efficiency into the desired channel. If performance does not satisfy the metrics, optimization continues, repeating suboperations S503 through S505.

[0077] If the performance metrics are satisfied, the method continues at operation S406 wherein the metastructure design is converted to a 3D print file in known fashion (e.g., -> CAD file -> STL file -> slicing software to generate G- code).

[0078] The UDRM is then printed using a 3D printer, such as via stereolithography (SLA), selective laser sintering (SLS), fused deposition modeling (FDM), etc.

[0079] Performance of the 3D directional routing UDRM.

[0080] FIG. 7A illustrates the directional routing performance of the UDRM design provided above (3D directional routing), which operates in the reflection mode. It shows the directional routing efficiencies for the frequency channels f=1...9 in the incident beam as they are routed based on their frequency into different reflected directions (diffraction channels) r=1...9.

[0081] The frequency channels f=1...9 have center frequencies of 26.6, 27.3, 28, 28.7, 29.4, 37, 38, 39, and 40 GHz. They are reflected to respective diffraction channels (r=1...9) of the UDRM, which are (-1,1), (0,1), (-1,0), (-1,-1), (0,0), (1,1), (1,0), (0,-1), and (1,-1), respectively. Based on simulation results, the routing efficiency is extremely high, ranging between 0.92 and > 0.99.

[0082] The routing directions here correspond to different diffraction-order directions due to the periodicity the UDRM design. It can be seen that the UDRM achieves directional routing with very high efficiencies.

[0083] FIG. 8A depicts UDRM 800A, which is based on the design for a 3D directional routing metastructure presented above. UDRM 800A was fabricated via stereo-lithography (SLA) 3D printing with a photopolymer resin. It has a periodic structure with eight repeat units in both the x and y directions ( / .e., it is a 3D directional routing structure). As depicted, the structure of UDRM 800A varies in the z- direction.

[0084] 2D directional routing metastructure.

[0085] FIG. 6B depicts candidate design 620B for the UDRM (not including the substrate layer), implemented as a ID patterned layer (x direction), providing 2D directional routing.

[0086] Referring additionally to FIG. 9. in this embodiment, the incident beam is single frequency, but consists of multiple spatial frequency channels; that is, normally incident channel (with spatial frequency kn,i corresponding to an incidence angle of 0 degrees). Metastructure 900 is designed to anomalously reflect it at a large oblique angle. Metastructure 900 is further designed so that a channel impinging on it with spatial frequency (k||,2), corresponding to an angle of 20 degrees, is fully absorbed. Also, metastructure 900 is designed so that an incident channel with spatial frequency (kn,s), corresponding to an angle of 45 degrees, is reflected in the negative direction. Importantly, although metastructure 900 appears fully absorptive for spatial frequency k| 1,2, it can be designed to exhibit nearly zero absorption for kn,i and k||,3. Additionally, in this embodiment, metastructure 900 is designed to provide that same multifunctional operation for both s and p polarizations for all three specified spatial frequencies. This brings the total number of independent channels to six.

[0087] The design proceeds using method 400, which is equally applicable for designing 2D or 3D directional routing metastructures. To obtain the aforementioned angle-selective absorption functionality, layer 920, which is a homogeneous lossy material (E = 4.17±i0.18) having a thickness h = 0.67A is incorporated below metastructure 900. Layer 920 is backed by metal plate 930. As in the previous embodiment, the two materials composing metastructure 920 are lossless, but this time with permittivities EI = 1 and £2 = 2.3. Alternatively, it is also possible to avoid the lossy layer by adding a small imaginary part to E2.

[0088] In this embodiment of a 2D directional routing metastructure, metastructure 900 has continuous translational symmetry along the y-axis and has periodicity along the x-direction with the period D= 4.2A. The period is substantially larger than the wavelength in free space A, and a total thickness of the optimized volume H = 10A is provided to ensure a sufficient number of degrees of freedom to achieve the desired multifunctional response. For the specified period D, there are 9 reflected propagating diffraction orders for each incident spatial frequency kn,i. In this embodiment, metastructure 900 is designed to maximize reflection in the n = +4 order for k||,i and in the n = -1 order for k||,3. For incident spatial frequency k||,2, scattering must be minimized in all diffraction orders simultaneously.

[0089] Metastructure 920 is discretized in the xy plane into rectangular design elements whose height-to-width ratio is chosen as 3. The two-dimensional (xz) simulation domain of a repeat unit includes 120 design elements along the z- direction (excluding lossy layer 920 beneath) and 150 design elements inside one period along the x direction. A binary permittivity distribution for the design elements was developed using a projection method. Additionally, a blur function was used, which enables regulation of the smallest feature size of metastructure 900. The optimizing routine previously described (see FIG. 5) is employed to converge on a design.

[0090] FIG. 7B depicts the directional routing performance of a 2D directional routing metastructure, such as illustrated in FIGs. 6B and 8B, showing directional routing efficiencies for six different channels based on two different polarizations and three different spatial frequencies.

[0091] FIG. 7B illustrates the results of the optimization of the objective function for the six incident channels. The average efficiency is calculated as the arithmetic average of the anomalous reflection efficiency for kn,i, the absorption efficiency for kn,2, and the negative reflection efficiency for kn,3 (all are calculated for the two polarizations). The average efficiency value was 98.6%. As depicted in Fig. 7B, for the incident wave with kn,2, scattering in all 9 diffraction orders (including the fundamental order with n = 0) is very small, yielding nearly complete absorption.

[0092] FIG. 8B depicts UDRM 800B, which is based on the design for a 2D directional routing metastructure presented above. UDRM 800B was fabricated via a fused-deposition modeling (FDM), a filament-based 3D printing method, using polylactic acid as the material. It has eight periods in the x-direction ( / .e., it is a 2D directional routing structure). As depicted, the structure of UDRM 800B varies in the z-direction.

[0093] The exemplary UDRM designs provided herein are merely two embodiments; the present teaching and disclosure contemplates many alternative structures suitable or use as a passive routing structure. For example, in various embodiments, a UDRM in accordance with the present disclosure can: i. function in transmit mode instead of reflect mode; orii. be structured such that it does not consist of a periodic array of repeat units; or iii. be non-periodic, thereby offering additional control over the routing directions; or iv. have fewer than or more than 9 routing directions; or v. have fewer than or more than 20 layers; or vi. have frequency components that are routed differently than in the example shown; or vii. have frequency components that are routed in directions different than those in the example shown; or viii. comprise a material other than a photopolymer resin; or ix. be fabricated using methods other than stereo-lithography (SLA) 3D printing; or x. any combination of i, ii, iii, iv, v, vi, vii, viii, and ix.

[0094] As previously noted, the illustrative method for making a UDRM provides directional routing based on channel frequency. However, in other embodiments, UDRMs may be routed based on other channel properties, including without limitation, propagation direction or angle, spatial frequency, amplitude, phase, polarization, spin angular momentum, orbital angular momentum, and combinations thereof. Designing using such other channel properties is within the capabilities of those skilled in the art, in light of the present disclosure.

Claims

What is Claimed:

1. A metastructure comprising at least one repeat unit, the at least one repeat unit comprising at least a first material having a relative permittivity ei and a second material having a relative permittivity 62, wherein e? is different than 61, the at least one repeat unit having a length dimension and a width dimension, the metastructure having physical adaptations that enable the metastructure to passively and simultaneously route, in multiple directions, at least some of multiple channels of an incoming multi-channel signal, wherein:(a) the length and width dimensions are greater than a wavelength of the incoming multi-channel signal;(b) the metastructure routes said some multiple channels as a function of a characteristic of the multiple channels.

2. The metastructure of claim 1 wherein the characteristic is a frequency of the respective channels.

3. The metastructure of claim 1 wherein the characteristic is a spatial frequency of the respective channels.

4. The metastructure of claim 1 wherein 61 is 1.

5. The metastructure of claim 1 wherein £2 is in a range of 2.3 to 3.

6. The metastructure of claim 1 wherein the multiple directions correspond to diffraction orders of the metastructure.

7. The metastructure of claim 1 wherein the metastructure has dimensions that provide a surface area for the metastructure of at least 1 sq meter.

8. The metastructure of claim 1 wherein the metastructure has a thickness greater than a wavelength of the incoming signal.

9. The metastructure of claim 1 wherein the incoming signal is in a microwave frequency range.

10. The metastructure of claim 1 wherein the incoming signal is in a millimeter-wave frequency range.

11. The metastructure of claim 1 wherein the metastructure absorbs at least one of the multiple channels.

12. The metastructure of claim 1 wherein the metastructure routes at least two of the multiple channels in a same direction, which same direction is different than respective directions to which other of the multiple channels are routed.

13. The metastructure of claim 1 wherein the metastructure routes at least one of the multiple channels in more than one direction.

14. The metastructure of claim 1 wherein the metastructure routes each of multiple channels in a different direction than each other of the multiple channels.

15. The metastructure of claim 1 wherein metastructure comprises a plurality of repeat units.

16. A method for making a metastructure capable of passively routing a signal having multiple channels, the method comprising :(a) selecting structural parameters of the metastructure, wherein the structural parameters are selected as a function of the frequency range of the signal;(b) establishing a candidate design as a starting point for optimization, the candidate design comprising a plurality of design elements, organized in three dimensions, wherein a value is assigned to each design element, the value being a permittivity between two relative permittivity values, wherein one is larger than the other;(c) generating an objective function using performance metrics of the metastructure design, wherein the objective function serves as a basis for optimization;(d) simulating the candidate design;(e) determining the performance of the metastructure, with respect to the performance metrics, based on results of simulating the candidate design;(f) estimating gradients of the objective function, wherein the gradients are used to optimize permittivity values of each design element;(g) updating the metastructure design by altering the permittivity values based on the estimated gradients;(h) estimating and comparing performance of the updated metastructure design, to the performance metrics, wherein:(1) if the performance does not satisfy performance metrics, then continue optimization by repeating operations (f)-(h), and(2) if the performance satisfies the performance metrics, then proceed to operation (i); and(i) fabricating the metastructure design.

17. The method of claim 16 wherein in the operation of establishing the candidate design, the metastructure comprises a periodic array of repeat units, wherein the candidate design of each repeat unit includes the plurality of design elements.

18. The method of claim 16 wherein in the operation of establishing the candidate design, the metastructure is not periodic, and the plurality of design elements collectively represents a totality of the metastructure.

19. The method of claim 16 wherein updating the metastructure design comprises binarizing altered permittivity values.

20. The method of claim 16 wherein in the operation of establishing the candidate design, a smaller of the two relative permittivity values is 1.

21. The method of claim 16 wherein in the operation of establishing the candidate design, the larger of the two relative permittivity values is in a range between 2.3 to 3.

22. The method of claim 16 wherein generating an objective function comprises generating an objective function that maximizes reflectivities of the metastructure for each of the multiple channels to different directions.

23. The method of claim 16 wherein generating an objective function comprises generating an objective function that maximizes transmissivities of the metastructure for each of the multiple channels to different directions.

24. The method of claim 16 wherein simulating the candidate design comprises using rigorous coupled-wave analysis.

25. The method of claim 16 wherein determining the performance of the metastructure comprises determining directional routing efficiencies for the multiple channels.

26. The method of claim 16 wherein estimating gradients comprises using a method of moving asymptotes.

27. The method of claim 16 wherein fabricating the metastructure design comprises: converting the metastructure design to a 3D print file; and printing the metastructure using a 3D printer.

28. A method for communication wherein line-of-sight propagation of electromagnetic radiation between a transmitter and one or more receivers is degraded or blocked by an obstacle, wherein the method comprises:(a) positioning a passive, directional-routing metastructure at a location that has line-of-sight to the transmitter and line-of-sight to the one or more receivers;(b) receiving, at the directional-routing metastructure, a beam comprising multiple communication channels that is transmitted from the transmitter, wherein once received, the directional-routing metastructure passively and simultaneously routes the multiple communication channels based on a characteristic of the communication channels, wherein a first communication channel of themultiple communication channels is routed in a first direction that is different than at least some of the other communication channels; and(c) receiving, at one of the receivers, the first communication channel such that propagation of the first communication channel is neither blocked nor substantially degraded.

29. The method of claim 28 wherein the characteristic of the communication channels is a respective frequency thereof.

30. The method of claim 28 wherein the passive, directional-routing metastructure routes each of the multiple communications channels in a different direction than each other of the multiple communication channels.

31. The method of claim 28 wherein the passive, directional-routing metastructure absorbs at least one of the multiple communication channels, and therefore does not transmit the at least one absorbed communication channel to a receiver.

32. The method of claim 28 wherein at least two of the multiple communication channels are routed in a second direction that is different than the first direction.

33. The method of claim 28 wherein at least one of the multiple communication channels is routed in more than one direction.

34. The method of claim 28 wherein a backplane that is opaque to the beam is disposed on a rear surface of the passive, directional-routing metastructure.

35. The method of claim 28 wherein a backplane that is transparent to the beam is disposed on a rear surface of the passive, directional-routing metastructure36. The method of claim 28 wherein the passive, directional-routing metastructure and backplane are attached to a vertical surface.

37. The method of claim 28 wherein the beam is in a microwave frequency range.

38. The method of claim 28 wherein the beam is in a millimeter-wave frequency range.

39. The method of claim 28 wherein the method is used in a 5G or 6G wireless communication network.

40. The method of claim 28 wherein the passive, directional-routing metastructure has dimensions that provide a surface area for the metastructure of at least 1 square meter, and a thickness of at least 2 centimeters.

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