Nyquist-sampled, high-efficiency metasurface antennas and methods thereof

Abstract

An antenna tile including a printed circuit board (PCB) layer comprising a plurality of radiating elements configured to transmit radio frequency (RF) signals, wherein a spacing between each pair of radiating elements is approximately one-half of a wavelength of the RF signals. A waveguide structure layer is affixed to the PCB layer to form a plurality of waveguide structures. A waveguide feed is coupled to the waveguide structure layer and configured to provide the RF signals to the PCB layer via the plurality of waveguide structures.

Description

Atty Docket No: EXTE-003WONYQUIST-SAMPLED, HIGH-EFFICIENCY METASURFACE ANTENNASAND METHODS THEREOFCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 63 / 700,960, filed on September 30, 2024 and titled “NYQUIST-SAMPLED, HIGH-EFFICIENCY METASURFACE ANTENNAS AND METHODS THEREOF,” the entire contents of which is hereby incorporated by reference herein.GOVERNMENT INTERESTS

[0002] This invention was made with Government support under Federal Grant No. N66001- 21-C-40I6 awarded by the Defense Advanced Research Projects Agency. The Government has certain rights in this invention.TECHNICAL FIELD

[0003] The present disclosure relates to satellite sensing systems, and in particular, to metasurface antennas having phase-diverse feeds and Nyquist sampled elements using grayscale tuning.BACKGROUND

[0004] Metasurface technology has led to a new class of antennas that promises improved hardware characteristics as compared to current microwave sensor technology. Current microwave technology includes phased array architectures that use phase shifters to electronically form and steer a beam. Phased arrays include electronically scanned arrays (ESAs), active electronically scanned arrays (AES As), and other antennas that use phase shifters sampled at or above the Nyquist limit. In addition to phased arrays, metasurface antennas have recently been demonstrated as an alternative technology for microwave beamforming.SUMMARY

[0005] In various examples, the subject matter described herein relates to metasurface antenna devices comprising modular tiles having phase diverse feeds and Nyquist sampled elements using grayscale tuning, antenna systems comprising pluralities of such devices arrayed together to form larger antennas, and methods of forming metasurface antennas by connecting such devices. The disclosed systems and methods enable high-efficiencyI PTS / 200136482.1Atty Docket No: EXTE-003WO operation, large area coverage, and precise beam steering capabilities for synthetic aperture radar and other microwave sensing applications.

[0006] At least one aspect of the present disclosure is directed to an antenna tile including a printed circuit board (PCB) layer comprising a plurality of radiating elements configured to transmit radio frequency (RF) signals, wherein a spacing between each pair of radiating elements is approximately one-half of a wavelength of the RF signals. A waveguide structure layer is affixed to the PCB layer to form a plurality of waveguide structures. A waveguide feed is coupled to the waveguide structure layer and configured to provide the RF signals to the PCB layer via the plurality of waveguide structures.

[0007] The foregoing Summary, including the description of some embodiments, motivations therefor, and / or advantages thereof, is intended to assist the reader in understanding the present disclosure, and does not in any way limit the scope of any of the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] A more complete understanding of the present disclosure, and the attendant advantages and features thereof, will be more readily understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:

[0009] FIG. 1 is a diagram of an example antenna tile, in accordance with some embodiments.

[0010] FIG. 2A is a diagram of an integrated waveguide feed layer, in accordance with some embodiments.

[0011] FIG. 2B is a diagram showing an example configuration of coupling irises of the integrated waveguide feed layer of FIG. 2A, in accordance with some embodiments.

[0012] FIG. 2C is a field pattern for a waveguide feed layer, in accordance with some embodiments.

[0013] FIG. 2D is a graph showing power distribution results corresponding to the integrated waveguide feed layer of FIG. 2A, in accordance with some embodiments.2I PTS / 200136482.1Atty Docket No: EXTE-003WO

[0014] FIG. 3A is diagram of a metamaterial element, in accordance with some embodiments.

[0015] FIG. 3B is a radiation pattern map demonstrating directional gain characteristics of the metamaterial element of FIG. 3 A, in accordance with some embodiments.

[0016] FIG. 3C is a series of graphs showing an S-parameter analysis and efficiency measurements for the metamaterial element of FIG. 3 A, in accordance with some embodiments.

[0017] FIG. 4 is a diagram of an exploded view of an antenna tile, in accordance with some embodiments.

[0018] FIG. 5 is a flowchart of a method for assembling an antenna tile, in accordance with some embodiments.

[0019] FIGS. 6A-6C are photographs of a fabricated antenna tile, in accordance with some embodiments.

[0020] FIG. 7 is a series of graphs showing single-tile simulation results demonstrating beam steering capabilities, frequency response characteristics, and radiation pattern performance across the operational bandwidth, in accordance with some embodiments.

[0021] FIG. 8 is a set of graphs showing azimuth steering results for a single antenna tile, in accordance with some embodiments.

[0022] FIG. 9 is a set of graphs showing elevation steering results for a single antenna tile, in accordance with some embodiments.

[0023] FIG. 10 is a series of graphs showing bandwidth results for a single antenna tile, in accordance with some embodiments.

[0024] FIG. 11 is a set of graphs showing directivity, gain, and efficiency results for a single antenna tile, in accordance with some embodiments.

[0025] FIG. 12 is a diagram of a multi-tile antenna system, in accordance with some embodiments.3I PTS / 200136482.1Atty Docket No: EXTE-003WO

[0026] FIG. 13 is a diagram of a multi-tile antenna system, in accordance with some embodiments.

[0027] FIG. 14 is a series of graphs illustrating broadside and steered beam simulation results for a 4x4 tiled antenna configuration, in accordance with some embodiments.

[0028] FIG. 15 is a series of graphs illustrating bandwidth results for a 4x4 tiled antenna configuration, in accordance with some embodiments.

[0029] FIG. 16 is a set of graphs showing broadside beam results for a 2x4 tiled antenna configuration, in accordance with some embodiments.

[0030] FIG. 17 is a set of graphs showing steered beam results for a 2x4 tiled antenna configuration, in accordance with some embodiments.

[0031] FIG. 18 is a diagram of an example computing device.DETAILED DESCRIPTION

[0032] Early metasurface antenna devices used sub-Nyquist sampled elements and relied on using a dielectric waveguide. However, an improved approach to metasurface construction is provided herein that enables spatial sampling of metasurface antennas at or above the Nyquist limit. The improved architecture includes the use of “grayscale”, or continuous, tuning of the radiating elements and the use of a phase-diverse feed. This allows metasurface antennas to use a sparser spatial sampling near or above the Nyquist limit, while avoiding metasurface grating lobes. Additionally, these improved metasurfaces do not require a dielectric waveguide, allowing them to use hollow or heterogeneous waveguides that can enable higher efficiency. Further, the sparse sampling of these antennas allows easier modeling, since their construction closely aligns with assumptions built into modeling methods, such as discrete dipole approximation. Additionally, the improved Nyquist-sampled metasurface antennas provided herein can be used to create large area antennas.

[0033] In the context of the present disclosure, the following definitions are used:

[0034] “Metasurface antennas” are generally defined as one-dimensional (ID) or two- dimensional (2D) devices that use a guided, or traveling, wave to excite a series of elements etched into a waveguide to couple energy into free space as radiation. The radiators can be metamaterial elements, irises, patches, or other geometries. The elements can be made4I PTS / 200136482.1Atty Docket No: EXTE-003WO tunable through the integration with semiconductors, doping, liquid crystal, or other tuning components. The size of each radiating element is below one-half of the free-space wavelength ( ) in all dimensions. Tuning the elements (e.g., using holographic principles or optimization algorithms) allows for the creation of arbitrary radiation patterns, including one or more steerable, directive beams.

[0035] “Nyquist sampling” refers to spatial sampling corresponding to approximately one- half of the free-space wavelength. The present disclosure applies to metasurface antennas sampled at, near, or above one-half of the free-space wavelength. It is noted that the spatial sampling is distinct from the spatial size of the elements.

[0036] “High efficiency” metasurface antennas are defined as those with total efficiency above approximately 10%.

[0037] “Large area” metasurface antennas are defined as those in which one side of the antenna exceeds approximately ten times the free-space wavelength.

[0038] “Heterogeneous waveguide” refers to a waveguide with multiple materials forming its interior. This may include a metal-backed circuit board, with a portion of the waveguide existing both in the circuit board and in the metal portion.

[0039] One aspect of the present disclosure provides a metasurface antenna device having a phase diverse feed and Nyquist sampled elements with grayscale tuning. In an embodiment, the elements are configured as multiple layers on a single device and function as an independently operating antenna.

[0040] Another aspect of the present disclosure provides an antenna system comprising a plurality of metasurface antenna devices arrayed together to form a larger antenna. The individual antenna devices, which can be referred to as “tiles”, are connected in an adjacent manner (e.g., in a single plane) to cover a larger area while forming a singular, coherent beam or radiation pattern from the overall tiled antenna area. Tiling the antenna thus provides a means of filling a customized and possibly extremely large area by placing the modular tiles in an array.5I PTS / 200136482.1Atty Docket No: EXTE-003WO

[0041] In embodiments, the metasurface antenna device and system comprise hollow or heterogeneous waveguides. These types of waveguides can advantageously lead to higher efficiency than alternative waveguide types.

[0042] FIG. 1 is a schematic illustration of an example antenna tile 100 in accordance with aspects described herein. The antenna tile 100 includes a plurality of waveguides 102, a plurality of metamaterial elements 104, and a plurality of coupling irises 106. The metamaterial elements 104 are alternatively referred to as radiating elements herein. The coupling irises 106 are configured to facilitate an energy transfer between the feed waveguides 102 and radiating metamaterial elements 104. In some examples, the antenna tile 100 has an overall tile size of approximately 25 x 25 cm. In other examples, different tile sizes may be contemplated (e.g., from approximately 10 x 10 cm to 100 x 100 cm or larger). The example layout includes eight parallel rectangular waveguides 102, each containing approximately 30 metamaterial elements 104 spaced at X / 2 intervals to achieve Nyquist sampling. It should be appreciated that different configurations may be used (e.g., between 4 and 16 waveguides, each containing between 10 and 100 metamaterial elements 104). In some examples, the metamaterial elements 104 are complementary electric-inductive- capacitive (cELC) resonators that can be dynamically tuned using varactor diodes to control the phase and amplitude of radiated energy.

[0043] In some examples, each waveguide 102 is a heterogeneous waveguide structure having an air- filled lower section and a dielectric upper section. The heterogeneous waveguide structure provides superior efficiency compared to fully dielectric-filled substrate- integrated waveguide (SIW) approaches while maintaining structural integrity for the printed circuit hoard metasurface layer. For example, by using hollow (air or vacuum filled) waveguides, the aperture avoids propagation losses due to any dielectric filling material, as might be used in a SIW. In some examples, each waveguide 102 has a width of approximately 22.86 mm. In other examples, different waveguide widths may be contemplated (e.g., between approximately 10 mm and 50 mm). In some examples, the airfilled lower section is a 3 mm air-filled lower section. In other examples, the air-filled section may range from approximately 1 mm to 10 mm. In some examples, the dielectric upper section is a 0.5 mm Rogers 4003C dielectric upper section. In other examples, the dielectric section may range from approximately 0.1 mm to 2 mm and may comprise Rogers 4003C, Rogers 4350B, or other suitable low-loss dielectric materials. The metamaterial elements 1046I PTS / 200136482.1Atty Docket No: EXTE-003WO are strategically positioned off a center of the waveguide 102 to optimize coupling strength and achieve target radiation efficiency levels above approximately 70%. In some examples, the metamaterial elements 104 are positioned approximately 6.59 mm off the center axis of each waveguide 102. In other examples, the offset may range between approximately 2 mm and 15 mm.

[0044] In some examples, the antenna tile 100 includes a phase-diverse feed architecture. The phase-diverse feed architecture is configured to suppress grating lobes in Nyquist-sampled metasurface arrays. In some examples, each coupling iris 106 is a rotated iris waveguide feed that utilizes coupling slots oriented at specific angles to achieve equal power distribution across the parallel rectangular waveguides 102, while providing the necessary phase offsets for coherent beam formation. In some examples, the coupling slots are oriented at angles ranging from 12.48° to 52.00°. In other examples, different coupling slot angles may be contemplated (e.g., from approximately 5° to 70°). This approach eliminates the need for separate phase shifters and beamforming networks, reducing system complexity and power consumption while enabling rapid electronic beam steering across ±45° in both azimuth and elevation planes. In some examples, the coupling slot design incorporates optimization algorithms to achieve input return loss below -20 dB and insertion loss of approximately -12 dB across all output ports, ensuring efficient power distribution throughout the operational bandwidth (e.g., 9-10.5 GHz).

[0045] Unlike traditional electronically scanned antennas, metasurface antennas avoid active phase shifters by leveraging the phase advance of the traveling wave feed mode, coupled with dynamically tunable metamaterial radiating elements. In some examples, each metamaterial element 104 comprises an electrical RF circuit, with capacitance and inductance dictated by the element geometry. Because the element is resonant, relatively small changes to the capacitance or inductance leverage a significant shift in the resonance frequency. Thus, passive elements, such as diodes or varactors, can be used to tune the resonance frequency in different ways. For example, a diode can be used to short the capacitive gap between the inner and outer conducting regions of a metamaterial resonator, effectively moving the resonance frequency well away from the operating frequency.

[0046] In some examples, each metamaterial element 104 (e.g., cELC element) incorporates varactor diodes with variable capacitance, enabling continuous grayscale tuning through bias voltages for precise holographic beam formation without the complexity and power7I PTS / 200136482.1Atty Docket No: EXTE-003WO consumption associated with traditional active phase shifters. In some examples, the varactor diodes are MACOM MAVR-011020-1411 varactor diodes with variable capacitance ranging from approximately 0.05 to 0.24 pF. In other examples, equivalent varactor diodes from various manufacturers may be used with variable capacitance ranging from approximately 0.01 pF to 1.0 pF. In some examples, the continuous grayscale tuning is enabled through bias voltages ranging from 0-5 V, though other embodiments may utilize bias voltages ranging from approximately 0V to 10 V.

[0047] In some embodiments, the metasurface antenna device comprises radiating elements that are metamaterial elements, resonant irises, complementary electric-inductive-capacitive (cELC), or other subwavelength geometry elements. In alternative embodiments, the radiating elements may he patches or rectangular irises. The radiating elements can be tuned by changing the input frequency or individually tuned via a control stimulus. In various implementations, the elements are tuned with liquid crystal, diodes (including PIN diodes), transistors, varactor diodes, or other semiconductors.

[0048] The guided or traveling wave in the metasurface antenna device can be supported by various waveguide structures including rectangular waveguides, parallel plate waveguides, substrate integrated waveguides (SIW), or other waveguide configurations. In some embodiments, multiple adjacent waveguides are employed to enhance performance. The waveguide structure may use a homogeneous dielectric fill material, such as a printed circuit board (PCB), or may be implemented with hollow construction (either air- filled or vacuum- filled). In certain implementations, the device utilizes a heterogeneous fill material, such as a metal-backed circuit board.

[0049] The spacing of the radiating elements can be configured in various arrangements relative to the Nyquist sampling criterion. In some embodiments, the elements are separated by one half (1 / 2) of the free space wavelength (X), which is described as "Nyquist sampled." In other embodiments, the elements are nearly Nyquist sampled, defined as separated by less than one half (1 / 2) of the free space wavelength (X), between X / 4 and X / 2. Alternatively, the elements may be nearly Nyquist sampled with separation greater than one half (1 / 2) of the free space wavelength (X), between X / 2 and 2X.

[0050] The metasurface antenna device can achieve various levels of high efficiency operation. In some embodiments, the device achieves radiation and / or total efficiency above8I PTS / 200136482.1Atty Docket No: EXTE-003WO10%. In other embodiments, higher efficiency levels are achieved, including radiation and / or total efficiency above 25%, above 40%, or above 50%. These efficiency levels are accomplished using the various characteristics described herein, including the waveguide configurations, element spacing, and tuning mechanisms.

[0051] The metasurface antenna device can be configured to form specified radiation patterns including one or more steerable directive beams and one or more steerable directive nulls. In some embodiments, the device uses holographic principles to determine the tuning weights, which may be electronic stimulus values or geometric adjustments, needed to set the desired radiation pattern. This capability enables precise beam steering and pattern control for various applications.

[0052] The metasurface antenna device has applications including, but not limited to, remote sensing, radar, synthetic aperture radar (SAR), imaging, radio frequency (RF) sensing, computational imaging, communications, passive radar, and passive sensing. These operational modes may be conducted from airborne, ground, mobile, or spaceborne / satellite platforms. The device can operate in various configurations including monostatic, bistatic, multi-static, multiple input multiple output (MIMO), transmit-only, or receive-only modes.

[0053] In some examples, the antenna tile 100 is manufactured utilizing precision-machined aluminum waveguide structures bonded to printed circuit board layers through conductive prepreg adhesion layers, with via fencing maintaining electrical continuity between upper and lower copper layers. In some examples, RF chokes incorporating 0.1 pF ceramic capacitors can prevent RF leakage along bias lines while maintaining stable holographic tuning algorithm performance, enabling the antenna to achieve target efficiency levels of 40% while supporting advanced synthetic aperture radar (SAR) modes including, for example, spotlight SAR, stripmap SAR, ScanSAR, interferometric SAR, and polarimetric SAR operations.

[0054] Another aspect of the present disclosure provides a method of forming a metasurface antenna by connecting antenna devices (e.g., antenna tiles 100) to form a larger antenna. In some examples, the antenna tiles 100 are individually tuned to form a single beam or radiation pattern. The modular tile architecture enables scalable deployment from single-tile operation through intermediate configurations to large-scale arrays, such as a 4x4 system covering 100 x 100 cm apertures, with each 25 x 25 cm antenna tile functioning as an independently operating antenna module. In some examples, each antenna tile 100 functions9I PTS / 200136482.1Atty Docket No: EXTE-003WO as an independently operating antenna module with integrated digital control boards providing microprocessor-based control and shift register functionality for addressing all metamaterial elements 104.

[0055] The tiled antenna configuration can be implemented in different operational modes depending on the application requirements. In some embodiments, the tiles are used to create one singular, coherent large device where all tiles work together to form a unified antenna system. In alternative embodiments, the tiles are used to create multiple adjacent, but distinct and independent, large devices that can operate separately while sharing the same physical array structure.

[0056] The large overall tiled antenna device can be configured in various physical arrangements. In some embodiments, the device maintains a flat or planar configuration. In other embodiments, the device includes bends, hinges, or rotation joints to create different shaped antenna configurations, providing flexibility for deployment in various environments and applications.

[0057] The tiled antenna system can achieve high efficiency in the antenna control power system through various design optimizations. In some embodiments, high control power efficiency is defined as using less than 1 W per one square meter of antenna / aperture area. In other embodiments, the efficiency targets are less than 10 W per one square meter of antenna / aperture area, or less than 50 W per one square meter of antenna / aperture area. These efficiency levels are realized using the various characteristics described herein, including the heterogeneous waveguide design, varactor tuning mechanisms, and optimized element spacing.

[0058] The modular tile architecture enables coverage of large aperture areas through various scaling configurations. In some embodiments, the tiled antenna system covers an aperture area defined as at least ten (10) times the free space wavelength (X) in one or more dimensions. In other embodiments, larger coverage areas are achieved, including at least twenty-five (25) times the free space wavelength (X) in one or more dimensions, or at least one hundred (100) times the free space wavelength (X) in one or more dimensions.

[0059] Examples of the behavior and performance of the antenna tile 100 and corresponding multi-tile systems are described herein using simulated and experimental depictions and10I PTS / 200136482.1Atty Docket No: EXTE-003WO demonstrations. In such examples, the antenna tile 100 exhibits the following parameters shown in Table 1 :Table 1

[0060] FIGS. 2A-2D illustrate an integrated waveguide feed layer 210 and simulated results demonstrating the phase diverse feed architecture that enables grating lobe suppression in Nyquist-sampled metasurface arrays. FIG. 2A shows the detailed waveguide feed structure 210 with eight parallel rectangular waveguides 102 (e.g., each 22.86 mm wide by 3.5 mm high) featuring the heterogeneous design with air-filled sections and dielectric layers, along with the strategically positioned coupling irises 106 that distribute power from the main feed waveguide 210 to individual branch waveguides 102. The coupling irises 106 (or slots) are precisely oriented at specific angles (e.g., ranging from 12.48° to 52.00°) to provide the necessary phase diversity for grating lobe suppression, while achieving equal power11I PTS / 200136482.1Atty Docket No: EXTE-003WO distribution across all branch waveguides 102. In some examples, the waveguide feed layer 210 provides an insertion loss of approximately -12 dB and input return loss below -20 dB across the 9-10.5 GHz operational bandwidth. The rotated iris waveguide feed design eliminates the need for separate phase shifters and beamforming networks, reducing system complexity and power consumption while enabling rapid electronic beam steering across ±45° in both azimuth and elevation planes.

[0061] FIG. 2B illustrates an example configuration for the waveguide feed layer 210. As shown, each coupling irises 106 is arranged with an specific angle within the dimensions of each waveguide 102. In some examples, the values of the angles increase from approximately 12.48° to 52.00°. However, it should be appreciated that different angles, step sizes, and ranges may be contemplated.

[0062] FIG. 2C illustrates an example field pattern 220 for the waveguide feed layer 210 shown in FIG. 2 A and 2B. The pattern 220 shows the characteristics and electromagnetic field distribution of the waveguide feed, which balance a phase shifting profile and power distribution into the radiation layer.

[0063] FIG. 2D illustrates a graph 230 of the power distribution results across the arms of the branch waveguides 102. The graph 230 demonstrates how the rotated iris waveguide feed 210 achieves uniform power coupling to each of the eight branch waveguides 102 (i.e., 16 arms) while providing the precise phase offsets necessary for coherent beam formation and steering capabilities. The power distribution results confirm equal energy transfer (within ±10% variation) across all waveguide branches, validating the effectiveness of the slot coupling methodology in maintaining phase diversity without requiring complex beamforming networks or active phase shifters.

[0064] FIGS. 3A-3C illustrate a varactor-tuned cELC radiating element and comprehensive modeling results demonstrating the element's performance characteristics. FIG. 3A shows the detailed geometry of the complementary electric-inductive-capacitive (cELC) metamaterial element 102 with integrated varactor capacitors. The element 102 features a square inner conductor footprint of 2.795 mm and an outer boundary of 4.895 mm x 3. 195 mm. In other embodiments, the inner conductor footprint may range from approximately 1-5 mm and the outer boundary may range from approximately 2-8 mm x 1-6 mm. The element incorporates a MACOM MAVR-011020-1411 varactor diode 302 with variable capacitance ranging from12I PTS / 200136482.1Atty Docket No: EXTE-003WO0.05 to 0.24 pF, controlled by bias voltages from 0 to 5V. Alternative embodiments may utilize equivalent varactor diodes with variable capacitance ranging from approximately 0.01 to 1.0 pF, controlled by bias voltages ranging from 0 to 10V. In one example, the element 102 is positioned approximately 6.59 mm off the center longitudinal axis of the 22.86 mm wide rectangular waveguide 102. In other embodiments, the element 102 may be positioned between approximately 2-15 mm off the center axis of waveguides ranging from 10-50 mm in width to optimize coupling and achieve the target radiation efficiency. The figure illustrates capacitive gap widths of 0.2 mm between inner and outer conductors, strategic varactor placement across one of the radiating slots to maximize tuning effectiveness, and the heterogeneous waveguide 102 featuring a 3 mm air-filled lower section and 0.5 mm Rogers 4003C dielectric upper section with via fencing maintaining electrical continuity. The bias line implementation includes a 0.1 mm width bias line with matching gap dimensions, two 0.1 pF ceramic capacitors positioned symmetrically for RF isolation, and a fan-shaped RF choke design to prevent RF signal propagation along bias lines. In some examples, a varactor package size of 0.2 mm x 0.2 mm enables standard pick-and-place assembly with solder reflow process compatibility for mass production. The off-center positioning of the element 102 optimizes coupling strength while reducing scattering, with asymmetric gap design featuring larger spacing on the bias line side to minimize RF current interference and optimized slot dimensions for resonance at a desired design frequency (e.g., 9.75 GHz), enabling the element to function as an effective magnetic dipole radiator while providing continuous phase control necessary for holographic beam formation across the ±45° steering range in both azimuth and elevation planes.

[0065] FIG. 3B illustrates a radiation pattern map 320 showing the directional gain characteristics of the metamaterial element 104. As shown, the element 104 achieves a maximum gain of 2.6 dB in the primary radiation direction and a minimum gain of 0.1 dB at the pattern nulls, providing a gain variation range of 2.5 dB across the radiation pattern. The radiation pattern map 320 validates the element’s ability to radiate as a magnetic dipole, showing typical dipole radiation pattern characteristics with lobes and nulls, directional beam formation consistent with magnetic dipole theory, and azimuthal symmetry expected from the cELC element geometry. The electromagnetic field distribution analysis confirms effective coupling between the waveguide mode and the metamaterial element, optimal radiation efficiency achieved through the off-center positioning (e.g., 6.59 mm from center axis), and clean radiation pattern without spurious lobes or unwanted radiation modes. The radiation13I PTS / 200136482.1Atty Docket No: EXTE-003WO pattern map 320 demonstrates the effectiveness of the design parameters including strategic element positioning within the rectangular waveguide 102, the heterogeneous waveguide structure (e.g., 3 mm air-filled section with 0.5 mm Rogers 4003C dielectric layer), and varactor integration maintaining radiation pattern integrity while enabling tuning. The directional characteristics validate the element's suitability for continuous grayscale tuning through the varactor’s capacitance range, phase control resolution necessary for holographic beam formation, and coherent array operation when integrated into the multi-element tile configuration (e.g., 30 elements per waveguide across 8 parallel rectangular waveguides).

[0066] FIG. 3C is a series of graphs illustrating an S-parameter analysis and efficiency measurements for the metamaterial element 104 across the 9-11 GHz frequency range. The traces in each graph represent the results / measurements for different thicknesses of the dielectric layer (e.g., the Rogers 4003C dielectric layer). As shown, the SI 1 reflection coefficient is below -10 dB, indicating the reduced coupling due to having shifted the element 104 off the longitudinal axis of the waveguide 102. Likewise, the S21 coefficient remains relatively low (e.g., below -4 dB), again indicating the element 104 is not strongly coupled to the waveguide 102. For the single element 104, the total efficiency, defined as the ratio of the radiated power to the incident power, is approximately 38% for all values of the substrate thickness. Even as the substrate thickness is varied, the radiation efficiency remains high, approximately 80% over the X-band frequency span.

[0067] FIG. 4 shows an exploded view of the example antenna tile 100. The exploded view reveals four distinct layers that comprise each 25 x 25 cm tile: the uppermost PCB metasurface layer 402 containing the varactor- tuned cELC radiating elements 104 and bias circuitry, an aluminum waveguide structure layer 404 with eight parallel rectangular waveguides (e.g., each 22.86 mm wide by 3.5 mm high) featuring the coupling irises 106 for power distribution, a digital control board layer 406 providing DC bias control and shift register functionality for element tuning, and a structural support framework layer 408. The metasurface layer 402 utilizes a heterogeneous waveguide design with 0.5 mm Rogers 4003C dielectric material bonded to the 3 mm hollow aluminum waveguide structures 102, enabling high efficiency operation while maintaining the necessary electrical connections through via fencing. The coupling irises 106 in the aluminum layer 404 are precisely oriented at angles ranging from 12.48° to 52.00° to achieve equal power distribution and phase diversity across all eight waveguide branches 102. The digital control board 407 incorporates microprocessors14I PTS / 200136482.1Atty Docket No: EXTE-003WO and control circuitry capable of independently addressing each of the 240 metamaterial elements 104 (i.e., 30 elements per waveguide 102) with bias voltages from 0-5 V for continuous grayscale tuning. This layered architecture enables the tile 100 to function as an independently operating antenna module that can be seamlessly integrated with adjacent tiles to form larger aperture arrays while maintaining mechanical robustness and thermal management capabilities suitable for spacebome applications.

[0068] FIG. 5 is flowchart of a method 500 for assembling an antenna tile, in accordance with aspects described herein. In some examples, the method 500 corresponds to a method for assembling the antenna tile 100 of FIGS. 1 and 4.

[0069] At step 502, a printed circuit board (PCB) layer is received comprising a plurality of radiating elements configured to transmit radio frequency (RF) signals. As described above, the PCB layer 402 comprises a dielectric substrate material, such as Rogers 4003C, with a thickness ranging from approximately 0.1 mm to 2 mm. In some examples, a spacing between each pair of radiating elements 104 is approximately one-half of a wavelength of the RF signals to achieve Nyquist sampling. The plurality of radiating elements 104 may comprise metamaterial elements, resonant irises, or cELC elements, with each element having dimensions below one-half of the free-space wavelength in all dimensions. In embodiments utilizing cELC elements, each element may incorporate varactor diodes with variable capacitance ranging from approximately 0.01 pF to 1.0 pF, such as MACOM MAVR- 011020-1411 varactor diodes, enabling continuous grayscale tuning through bias voltages ranging from 0V to 5 V. In some examples, the PCB layer 402 includes via fencing to maintain electrical continuity between upper and lower copper layers, and bias circuitry incorporating RF chokes with ceramic capacitors to prevent RF leakage along bias lines while maintaining stable tuning algorithm performance.

[0070] At step 504, a waveguide structure layer is affixed to the PCB layer to form a plurality of waveguide structures. In some examples, the waveguide structure layer 404 comprises precision-machined aluminum components that create the lower air- filled sections of the heterogeneous waveguide structures 102, with each waveguide having a width of approximately 22.86 mm and an air-filled height of approximately 3 mm. The affixing process utilizes conductive prepreg adhesion layers to bond the aluminum waveguide structure to the PCB layer, ensuring electrical continuity between the metallic waveguide walls and the copper ground plane of the Rogers 4003C dielectric substrate. In some15I PTS / 200136482.1Atty Docket No: EXTE-003WO examples, the heterogeneous waveguide design combines the 3 mm air-filled lower section formed by the aluminum structure with the 0.5 mm dielectric upper section provided by the PCB layer material, creating an optimized propagation environment that achieves superior efficiency compared to fully dielectric-filled substrate-integrated waveguide approaches while maintaining structural integrity for the metasurface layer 402. Via fencing may be implemented around the perimeter of each waveguide to maintain electrical continuity and prevent RF leakage between adjacent waveguide structures. The affixing process includes precise alignment procedures to ensure that the coupling irises 106 in the aluminum layer are properly positioned relative to the metamaterial elements 104 on the PCB layer 402, with each element positioned approximately 6.59 mm off the center longitudinal axis of its corresponding waveguide to optimize coupling strength and achieve target radiation efficiency levels above 70%.

[0071] At step 506, coupling a waveguide feed to the waveguide structure layer. As described above, the waveguide feed 210 includes a rotated iris waveguide feed system to implement a phase-diverse feed architecture. The waveguide feed 210 utilizes precision-engineered coupling irises 106 oriented at specific angles (e.g., ranging from 12.48° to 52.00°) to achieve equal power distribution across all eight parallel rectangular waveguide structures while providing the necessary phase offsets for coherent beam formation and grating lobe suppression in Nyquist-sampled metasurface arrays. The coupling process involves precise mechanical alignment of the main feed waveguide 210 perpendicular to the branch waveguides 102, with each coupling iris 106 positioned to optimize power transfer efficiency and maintain the target insertion loss (e.g., approximately -12 dB across all output ports).

[0072] In some examples, the main feed waveguide structure 210 utilizes standard WR-90 rectangular waveguide dimensions (22.86 mm x 10.16 mm) to support TE10 mode propagation at the 9.75 GHz design frequency, with the coupling irises 106 machined as rotated rectangular slots with dimensions optimized through electromagnetic simulation to achieve the required coupling coefficients for each branch waveguide 102. In some examples, the feed coupling methodology incorporates impedance matching techniques to ensure input return loss below -20 dB across the 9-10.5 GHz operational bandwidth, with each coupling iris 106 featuring chamfered edges and rounded comers to minimize higher-order mode excitation and reduce insertion loss variations across the frequency band. The rotated iris design provides uniform power coupling (e.g., within ±10% variation) to each of the sixteen16I PTS / 200136482.1Atty Docket No: EXTE-003WO waveguide arms (i.e., 8 waveguides x 2 arms each) while maintaining the precise phase diversity necessary for holographic beam formation when combined with varactor-tuned cELC metamaterial elements 104 positioned 6.59 mm off the center longitudinal axis of each 22.86 mm wide rectangular waveguide structure. The waveguide feed system eliminates the need for separate phase shifters and beamforming networks by leveraging the inherent phase advance of the traveling wave feed mode, reducing system complexity and power consumption while enabling rapid electronic beam steering across ±45° in both azimuth and elevation planes through coordinated tuning of the 240 metamaterial elements (i.e., 30 elements per waveguide x 8 waveguides) using bias voltages ranging from 0-5 V applied to the varactor diodes with variable capacitance ranging from 0.05 to 0.24 pF.

[0073] FIGS. 6A-6C show photographs of an example fabricated antenna tile 100, including the PCB metasurface layer 402, aluminum waveguide structure 404, and the digital control board 407 components.

[0074] FIG. 7 shows various graphs illustrating single-tile simulation results demonstrating the tile’s beam steering capabilities, frequency response characteristics, and radiation pattern performance. The simulation results include azimuth and elevation radiation patterns in graph 702 showing the tile’s ability to steer beams across ±45° in both planes while maintaining directional gain and acceptable sidelobe levels. The frequency response analysis in graph 704 spans the 9.25-10.0 GHz operational bandwidth, demonstrating consistent beam formation and steering performance across the entire X-band range. The radiation patterns in graphs 706, 708 exhibit typical metasurface antenna characteristics with main beam directivity and controlled sidelobe suppression, validating the effectiveness of the phase-diverse feed architecture and Nyquist-sampled element spacing.

[0075] FIG. 8 illustrates azimuth steering results for a single antenna tile 100, demonstrating the tile’s capability to electronically steer beams across a ±45° azimuth range while maintaining directional gain and beam quality. The azimuth steering is achieved through the holographic tuning of the metamaterial elements 104, each biased with voltages ranging from 0-5 V to provide continuous grayscale phase control.

[0076] FIG. 9 illustrates elevation steering results for a single antenna tile 100, demonstrating the tile’s capability to electronically steer beams across a ±45° elevation range while maintaining directional gain and beam quality characteristics comparable to the azimuth17I PTS / 200136482.1Atty Docket No: EXTE-003WO steering performance. The elevation steering is accomplished through the same holographic tuning methodology used for azimuth control, utilizing the metamaterial elements 104 with individual bias voltages ranging from 0-5 V to achieve continuous grayscale phase control.

[0077] FIG. 10 illustrates bandwidth results for a single antenna tile 100, demonstrating the frequency response characteristics and operational performance across the 8.5-11 GHz range. The bandwidth analysis reveals the antenna's ability to maintain consistent beam formation and directional characteristics across the entire X-band operational spectrum.

[0078] FIG. 11 illustrates directivity, gain, and efficiency results for a single antenna tile 100, providing detailed performance analysis across the 8.5-11 GHz frequency range. The directivity measurements demonstrate the antenna's ability to concentrate radiated power in the desired direction, with peak directivity values reaching approximately 20 dB at the 9.75 GHz design frequency. The gain measurements account for both directional focusing and resistive losses within the heterogeneous waveguide structure, showing peak gain values of approximately 18 dB at the center frequency, with the 2 dB difference between directivity and gain attributable to the combined losses in the 3 mm air-filled waveguide sections, 0.5 mm Rogers 4003C dielectric layers, MACOM MAVR-011020-1411 varactor diodes (0.05-0.24 pF capacitance range), and metallic conductor losses in the aluminum waveguide structure. The efficiency analysis reveals that the antenna achieves the target 40% total efficiency specification between 9.5-10 GHz when considering only the main beam, with this efficiency metric calculated as the ratio of useful radiated power to total input power from the rotated iris waveguide feed system. Above approximately 10 GHz, the efficiency measurements indicate that not all energy is concentrated radiated into the energy in the main beam, with some power distributed into higher-order modes and sidelobes due to the frequencydependent behavior of the varactor-tuned cELC metamaterial elements and the phase-diverse feed architecture with coupling angles ranging from 12.48° to 52.00°. The frequencydependent efficiency characteristics show graceful degradation at the band edges, with efficiency dropping to approximately 25-30% at 8.5 GHz and 11 GHz.

[0079] FIG. 12 illustrates an example antenna system 1200 with a 4x4 tile array layout. The 4x4 configuration consists of sixteen individual 25 x 25 cm metasurface antenna tiles 100 arranged in a planar array to create an overall aperture of 100 x 100 cm. In some examples, the antenna system 1200 provides an antenna directivity of approximately 36.8 dB at the 9.75 GHz design frequency. Each tile 100 operates as an independently functioning antenna18I PTS / 200136482.1Atty Docket No: EXTE-003WO module containing eight parallel rectangular waveguides with 240 total metamaterial elements (i.e., 30 elements per waveguide) spaced atintervals for Nyquist sampling. The tiled architecture enables scalable aperture sizes suited for specific mission requirements while providing graceful degradation capability. For example, if an electrical or mechanical failure occurs on one tile, that tile can be removed from the array processing and the remaining tiles continue to perform their tasks. The modular design facilitates cost-effective manufacturing of identical smaller tiles rather than fewer very large structures, while also enabling easier deployment and assembly for spacebome applications. In some examples, the composite antenna system 1200 utilizes a second-level waveguide feed network with coupling points distributed across the array to maintain coherent beam formation and steering capabilities across the entire aperture, making it suitable for high-capacity SAR applications requiring large area coverage and high spatial resolution.

[0080] FIG. 13 illustrates an example antenna system 1300 with a 2x4 tile array layout. The 2x4 configuration consists of eight individual 25 x 25 cm metasurface antenna tiles 100 arranged in a planar array to create an overall aperture of 50 x 100 cm. Each tile 100 operates as an independently functioning antenna module containing eight parallel rectangular waveguides with 240 total metamaterial elements (i.e., 30 elements per waveguide) spaced at k / 2 intervals for Nyquist sampling.

[0081] FIG. 14 is as series of graphs illustrating broadside and steered beam simulation results for a 4x4 tiled antenna configuration. The graph 1402 corresponds to the broadside beam simulation results and graphs 1404, 1406 correspond to the steered beam simulation results, demonstrating the scalable performance characteristics of the modular metasurface antenna architecture. Tn some examples, the 4x4 array consists of sixteen individual 25 x 25 cm tiles (e.g., antenna tile 100) arranged to create a 100 x 100 cm composite aperture, representing an intermediate scaling step between single-tile operation and a full 4x4 configuration. The simulation results show both broadside (i.e., 0° steering) and steered beam patterns across azimuth and elevation planes, with beam steering capabilities extending to ±60° in both dimensions while desired directional gain and acceptable sidelobe suppression

[0082] FIG. 15 is a series of graphs illustrating bandwidth results for a 4x4 tiled antenna configuration. The graphs demonstrate the frequency response characteristics and operational bandwidth performance across the 8-12 GHz range. The bandwidth analysis shows radiation patterns at discrete frequencies including 8 GHz, 9 GHz, 10 GHz, 11 GHz, and 12 GHz,19I PTS / 200136482.1Atty Docket No: EXTE-003WO revealing the antenna's ability to maintain beam formation and directional characteristics across the entire X-band operational spectrum. At the lower frequencies (8 GHz), the antenna exhibits reduced efficiency as indicated by the "low efficiency" annotations, which is consistent with the design optimization for the 9.75 GHz center frequency. The 10 GHz and 11 GHz results show optimal performance with well-formed main beams, narrow beamwidths of approximately 2-3 degrees and sidelobe suppression.

[0083] FIG. 16 shows broadside beam results for a 2x4 tiled antenna configuration, demonstrating the coherent beam formation capabilities and radiation pattern characteristics of the composite metasurface antenna array consisting of eight individual 25 x 25 cm tiles arranged to create a 50 x 100 cm aperture. The broadside beam measurements validate the effectiveness of the modular tiled architecture in maintaining coherent phase relationships across all 1,920 metamaterial elements (240 elements per tile x 8 tiles), with each tile containing 8 parallel rectangular waveguides (22.86 mm width by 3.5 mm height) featuring the heterogeneous design with 3 mm air-filled sections and 0.5 mm Rogers 4003C dielectric layers. The experimental results show a well-formed main beam with peak directivity exceeding 30 dB at the 9.75 GHz design frequency, representing a 10 dB improvement over single-tile operation due to the increased aperture size and coherent power combining from the phase-diverse feed architecture. The broadside radiation pattern exhibits a narrow main lobe in both azimuth and elevation planes, confirming the effectiveness of the Z / 2 Nyquist sampling across the composite aperture and the successful suppression of grating lobes through the rotated iris coupling angles ranging from 12.48° to 52.00° in each tile's waveguide feed network. The sidelobe suppression performance demonstrates levels below - 15 dB across both principal planes, validating the holographic tuning algorithms applied to the 1,920 varactor-controlled cELC metamaterial elements, each biased with voltages ranging from 0-5 V using MACOM MAVR-011020-1411 varactor diodes with 0.05-0.24 pF capacitance range.

[0084] Similarly, FIG. 17 shows steered beam results for a 2x4 tiled antenna configuration, demonstrating the coherent beam steering capabilities and radiation pattern characteristics of the composite metasurface antenna array when directing energy to off-axis target locations.

[0085] FIG. 18 is a block diagram of an example computer system 1800 that may be used in implementing the systems and methods described herein. For example, one or more computer systems, such as the computer system 1800, may be operable to perform the operations of the20I PTS / 200136482.1Atty Docket No: EXTE-003WG engines and models described herein. General-purpose computers, network appliances, mobile devices, or other electronic systems may also include at least portions of the system 1800. The system 1800 includes a processor 1810, a memory 1820, a storage device 1830, and an input / output device 1840. Each of the components 1810, 1820, 1830, and 1840 may be interconnected, for example, using a system bus 1850. The processor 1810 is capable of processing instructions for execution within the system 1800. In some implementations, the processor 1810 is a single-threaded processor. In some implementations, the processor 1810 is a multi-threaded processor. The processor 1810 is capable of processing instructions stored in the memory 1820 or on the storage device 1830.

[0086] The memory 1820 stores information within the system 1800. In some implementations, the memory 1820 is a non-transitory computer-readable medium. In some implementations, the memory 1820 is a volatile memory unit. In some implementations, the memory 1820 is a non-volatile memory unit. In some examples, some or all of the data described above can be stored on a personal computing device, in data storage hosted on one or more centralized computing devices, or via cloud-based storage. In some examples, some data are stored in one location and other data are stored in another location. In some examples, quantum computing can be used. In some examples, functional programming languages can be used. In some examples, electrical memory, such as flash-based memory, can be used.

[0087] The storage device 1830 is capable of providing mass storage for the system 1800. In some implementations, the storage device 1830 is a non-transitory computer-readable medium. In various different implementations, the storage device 1830 may include, for example, a hard disk device, an optical disk device, a solid-date drive, a flash drive, or some other large capacity storage device. For example, the storage device may store long-term data (e.g., database data, file system data, etc.). The input / output device 1840 provides input / output operations for the system 1800. In some implementations, the input / output device 1840 may include one or more of a network interface devices, e.g., an Ethernet card, a serial communication device, e.g., an RS-232 port, and / or a wireless interface device, e.g., an 802.11 card, a 3G wireless modem, or a 4G wireless modem. In some implementations, the input / output device may include driver devices configured to receive input data and send output data to other input / output devices, e.g., keyboard, printer and display devices 1860. In21I PTS / 200136482.1Atty Docket No: EXTE-003WO some examples, mobile computing devices, mobile communication devices, and other devices may be used.

[0088] In some implementations, at least a portion of the approaches described above may be realized by instructions that upon execution cause one or more processing devices to carry out the processes and functions described above. Such instructions may include, for example, interpreted instructions such as script instructions, or executable code, or other instructions stored in a non-transitory computer readable medium. The storage device 1830 may be implemented in a distributed way over a network, such as a server farm or a set of widely distributed servers, or may be implemented in a single computing device.

[0089] Although an example processing system has been described in FIG. 18, embodiments of the subject matter, functional operations and processes described in this specification can be implemented in other types of digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible nonvolatile program carrier for execution by, or to control the operation of, data processing apparatus. Alternatively or in addition, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them.

[0090] The term “system” may encompass all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. A processing system may include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). A processing system may include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.22I PTS / 200136482.1Atty Docket No: EXTE-003WG

[0091] A computer program (which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0092] The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0093] Computers suitable for the execution of a computer program can include, by way of example, general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read-only memory or a random access memory or both. A computer generally includes a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a universal serial bus (USB) flash drive), to name just a few.

[0094] Computer readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of23I PTS / 200136482.1Atty Docket No: EXTE-003WO example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0095] Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), e.g., the Internet.

[0096] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.Some Embodiments

[0097] Some embodiments may include any of the following:

[0098] Al. An apparatus using a guided or traveling wave to couple energy through radiating elements into free space.

[0099] A2. The apparatus of clause Al can include any of the following components or features, in any combination. The radiating elements are metamaterial elements, resonant irises, complementary electric-inductive-capacitive (cELC) elements, or other subwavelength geometry elements. The radiating elements are patches or rectangular irises. The elements are tuned by changing the input frequency. The elements are individually tuned via a control stimulus. The elements are tuned with liquid crystal, diodes (including PIN diodes), transistors, or other semiconductors. The elements are tuned with variable capacitor (i.e. varactor) diodes. The guided or traveling wave is supported by a rectangular waveguide,24I PTS / 200136482.1Atty Docket No: EXTE-003WO parallel plate waveguide, substrate integrated waveguide (SIW), or other waveguide structure. The elements are separated by one half (1 / 2) of the free space wavelength (X), also described as “Nyquist sampled.” The elements are nearly Nyquist sampled, defined as separated by less than one half (1 / 2) of the free space wavelength ( / -), between X / 4 and X / 2. The elements are nearly Nyquist sampled, defined as separated by more than one half (1 / 2) of the free space wavelength (X), between X / 2 and 2X. The apparatus includes multiple adjacent waveguides. The waveguide structure uses a homogeneous dielectric fill material, such as a printed circuit board (PCB). The waveguide structure is implemented with hollow (either air-filled or vacuum- filled) construction. The waveguide structure is implemented with a heterogeneous fill material (e.g. a metal-backed circuit board). The apparatus achieves high efficiency, defined as radiation and / or total efficiency above 10%. The apparatus achieves high efficiency, defined as radiation and / or total efficiency above 25%. The apparatus achieves high efficiency, defined as radiation and / or total efficiency above 40%. The apparatus achieves high efficiency, defined as radiation and / or total efficiency above 50%. The apparatus is used to form specified radiation patterns including one or more steerable directive beams. The apparatus is used to form specified radiation patterns including one or more steerable directive nulls. The apparatus uses holographic principles to determine the tuning weights (either electronic stimulus values or geometric adjustment) needed to set the radiation pattern. The apparatus is used for applications including, but not limited to, remote sensing, radar, synthetic aperture radar (SAR), imaging, radio frequency (RF) sensing, computational imaging, communications, passive radar, passing sensing. Such modes may be conducted from airborne, ground, mobile, or spacebome / satellite platforms. The operational modes may be monostatic, bistatic, multi-static, multiple input, multiple output (MIMO), transmit-only, or receive-only. The apparatus is formed into tiles, placed adjacent to other similar tiles, creating a larger overall device. The apparatus is used to cover a large aperture area, defined as at least ten (10) times the free space wavelength (X) in one or more dimensions. The apparatus is used to cover a large aperture area, defined as at least twenty- five (25) times the free space wavelength (X) in one or more dimensions. The apparatus is used to cover a large aperture area, defined as at least one hundred (100) times the free space wavelength (X) in one or more dimensions. The apparatus is used to create one singular, coherent large device. The apparatus is used to create multiple adjacent, but distinct and independent, large devices. The large overall device is flat / planar or includes bends, hinges, or rotation joints to create different shaped antenna configurations. The apparatus realizes25I PTS / 200136482.1Atty Docket No: EXTE-003WO high efficiency among the antenna control power system. The apparatus realizes high efficiency among the antenna control power system, where high control power efficiency is defined as using less than 1 W per one square meter of antenna / aperture area. The apparatus realizes high efficiency among the antenna control power system, where high control power efficiency is defined as using less than 10W per one square meter of antenna / aperture area. The apparatus realizes high efficiency among the antenna control power system, where high control power efficiency is defined as using less than 50W per one square meter of antenna / aperture area.

[0100] A3. An antenna tile including a printed circuit board (PCB) layer comprising a plurality of radiating elements configured to transmit radio frequency (RF) signals, wherein a spacing between each pair of radiating elements is approximately one-half of a wavelength of the RF signals; a waveguide structure layer affixed to the PCB layer to form a plurality of waveguide structures; and a waveguide feed coupled to the waveguide structure layer, the waveguide feed being configured to provide the RF signals to the PCB layer via the plurality of waveguide structures.

[0101] A4. The antenna tile of clause A3 can include any of the following components or features, in any combination. The plurality of waveguide structures are heterogeneous waveguide structures. Each heterogenous waveguide structure comprises a dielectric section corresponding to a material of the PCB layer and an air- filled section formed by the waveguide structure layer. The waveguide structure layer is fabricated from aluminum. The waveguide feed comprises a plurality of coupling irises configured to provide the RF signals to plurality of waveguide structures. The plurality of coupling irises are oriented at specific angles to provide substantially equal power distribution across the plurality of waveguide structures. Each coupling iris of the plurality of coupling irises is oriented at a different angle between approximately 10-60 degrees. The plurality of radiating elements are one of metamaterial elements, resonant irises, or complementary electric- inductive-capacitive (cELC) elements. The plurality of waveguide structures are arranged to be substantially parallel to one another. The waveguide feed is substantially perpendicular to each of the plurality of waveguide structures. The plurality of radiating elements are positioned on the PCB layer to be offset from a longitudinal center axis of a corresponding waveguide structure of the plurality of waveguide structures. Each radiating element of the plurality of radiating elements is individually tuned to provide continuous grayscale tuning.26I PTS / 200136482.1Atty Docket No: EXTE-003WOThe satellite antenna tile includes a structural support layer affixed to the waveguide structure layer and a digital control board affixed to the structural support layer. The antenna tile is configured for use in a satellite

[0102] A5. An antenna system including a plurality of antenna tiles according to clause A3.

[0103] A6. The antenna system of clause A5 can include any of the following components or features, in any combination. The plurality of antenna tiles are arranged to cover an aperture area having one or more dimensions that are at least ten times the wavelength of the RF signals. The system is configured for applications including at least one of remote sensing, radar, synthetic aperture radar (SAR), imaging, RF sensing, computational imaging, communications, passive radar, and passive sensing. Each of the plurality of antenna tiles is configured to be operated in at least one operational mode. The at least one operational mode comprises at least one of a monostatic, bistatic, multi-static, multiple input multiple output (MIMO), transmit-only, or receive-only operational mode.

[0104] A7. A method of assembling an antenna tile including receiving a printed circuit board (PCB) layer comprising a plurality of radiating elements configured to transmit radio frequency (RF) signals, wherein a spacing between each pair of radiating elements is approximately one-half of a wavelength of the RF signals; affixing a waveguide structure layer to the PCB layer to form a plurality of waveguide structures; and affixing a waveguide feed coupled to the waveguide structure layer, the waveguide feed being configured to provide the RF signals to the PCB layer via the plurality of waveguide structures.

[0105] A8. The method of clause A7 can include any of the following components or features, in any combination. The plurality of waveguide structures are heterogeneous waveguide structures each comprising a dielectric section corresponding to a material of the PCB layer and an air- filled section formed by the waveguide structure layer. The waveguide structure layer is fabricated from aluminum.

[0106] While this specification contains many specific implementation details, these should not be construed as limitations on the scope, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination27I PTS / 200136482.1Atty Docket No: EXTE-003WO in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination.

[0107] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0108] Particular embodiments of the subject matter have been described. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous. Other steps or stages may be provided, or steps or stages may be eliminated from the described processes.

[0109] The phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting.

[0110] The indefinite articles “a’' and “an,” as used in the specification, unless clearly indicated to the contrary, should be understood to mean “at least one.” The phrase “and / or,” as used in the specification, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and / or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and / or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and / or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.28I PTS / 200136482.1Atty Docket No: EXTE-003WO

[0111] As used in the specification, “or” should be understood to have the same meaning as “and / or” as defined above. For example, when separating items in a list, “or” or “and / or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. In general, the term “or” as used shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.”

[0112] As used in the specification, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and / or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

[0113] The use of “including,” “comprising,” “having,” “containing,” “involving,” and variations thereof, is meant to encompass the items listed thereafter and additional items.

[0114] Articles “a” and “an” are used herein to refer to one or to more than one (i.e., at least one) of the grammatical object of the article. By way of example, “an element” means at least one element and can include more than one element.

[0115] “About” is used to provide flexibility to a numerical range endpoint by providing that a given value may be “slightly above” or “slightly below” the endpoint without affecting the desired result.29I PTS / 200136482.1Atty Docket No: EXTE-003WO

[0116] As used herein, the transitional phrase "consisting essentially of" (and grammatical variants) is to be interpreted as encompassing the recited materials or steps "and those that do not materially affect the basic and novel characteristic(s)" of the claimed invention. Thus, the term "consisting essentially of" as used herein should not be interpreted as equivalent to "comprising. "

[0117] Moreover, the present disclosure also contemplates that in some embodiments, any feature or combination of features set forth herein can be excluded or omitted. To illustrate, if the specification states that a complex comprises components A, B and C, it is specifically intended that any of A, B or C, or a combination thereof, can be omitted and disclaimed singularly or in any combination.

[0118] Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. For example, if a concentration range is stated as 1% to 50%, it is intended that values such as 2% to 40%, 10% to 30%, or 1% to 3%, etc., are expressly enumerated in this specification. These are only examples of what is specifically intended, and all possible combinations of numerical values between and including the lowest value and the highest value enumerated are to be considered expressly stated in this disclosure.

[0119] It will be appreciated by persons skilled in the art that the present disclosure is not limited to what has been particularly shown and described herein above. In addition, unless mention was made above to the contrary, it should be noted that all of the accompanying drawings are not to scale. A variety of modifications and variations are possible in light of the above teachings without departing from the scope.30I PTS / 200136482.1

Claims

Atty Docket No: EXTE-003WOCLAIMSWhat is claimed is:

1. An antenna tile, comprising: a printed circuit board (PCB) layer comprising a plurality of radiating elements configured to transmit radio frequency (RF) signals, wherein a spacing between each pair of radiating elements is approximately one-half of a wavelength of the RF signals; a waveguide structure layer affixed to the PCB layer to form a plurality of waveguide structures; and a waveguide feed coupled to the waveguide structure layer, the waveguide feed being configured to provide the RF signals to the PCB layer via the plurality of waveguide structures.

2. The antenna tile of claim 1, wherein the plurality of waveguide structures are heterogeneous waveguide structures.

3. The antenna tile of claim 2, wherein each heterogenous waveguide structure comprises a dielectric section corresponding to a material of the PCB layer and an air-filled section formed by the waveguide structure layer.

4. The antenna tile of claim 1, wherein the waveguide structure layer is fabricated from aluminum.

5. The antenna tile of claim 1 , wherein the waveguide feed comprises a plurality of coupling irises configured to provide the RF signals to plurality of waveguide structures.

6. The antenna tile of claim 5, wherein the plurality of coupling irises are oriented at specific angles to provide substantially equal power distribution across the plurality of waveguide structures.

7. The antenna tile of claim 6, wherein each coupling iris of the plurality of coupling irises is oriented at a different angle between approximately 10-60 degrees.31I PTS / 200136482.1Atty Docket No: EXTE-003WO8. The antenna tile of claim 1, wherein the plurality of radiating elements are one of metamaterial elements, resonant irises, or complementary electric-inductive-capacitive (cELC) elements.

9. The antenna tile of claim 1, wherein the plurality of waveguide structures are arranged to be substantially parallel to one another.

10. The antenna tile of claim 9, wherein the waveguide feed is substantially perpendicular to each of the plurality of waveguide structures.

11. The antenna tile of claim 1, wherein the plurality of radiating elements are positioned on the PCB layer to be offset from a longitudinal center axis of a corresponding waveguide structure of the plurality of waveguide structures.

12. The antenna tile of claim 1, wherein each radiating element of the plurality of radiating elements is individually tuned to provide continuous grayscale tuning.

13. The antenna tile of claim 1, further comprising: a structural support layer affixed to the waveguide structure layer; and a digital control board affixed to the structural support layer.

14. The antenna tile of claim 1, wherein the antenna tile is configured for use in a satellite.

15. An antenna system, comprising: a plurality of antenna tiles according to claim 1.

16. The antenna system of claim 15, wherein the plurality of antenna tiles are arranged to cover an aperture area having one or more dimensions that are at least ten times the wavelength of the RF signals.32I PTS / 200136482.1Atty Docket No: EXTE-003WO17. The antenna system of claim 15, wherein the system is configured for applications including at least one of remote sensing, radar, synthetic aperture radar (SAR), imaging, RF sensing, computational imaging, communications, passive radar, and passive sensing.

18. The antenna system of claim 15, wherein each of the plurality of antenna tiles is configured to be operated in at least one operational mode, the at least one operational mode comprising at least one of a monostatic, bistatic, multi-static, multiple input multiple output (MIMO), transmit-only, or receive-only operational mode.

19. A method of assembling an antenna tile, comprising: receiving a printed circuit board (PCB) layer comprising a plurality of radiating elements configured to transmit radio frequency (RF) signals, wherein a spacing between each pair of radiating elements is approximately one-half of a wavelength of the RF signals; affixing a waveguide structure layer to the PCB layer to form a plurality of waveguide structures; and coupling a waveguide feed to the waveguide structure layer, the waveguide feed being configured to provide the RF signals to the PCB layer via the plurality of waveguide structures.

20. The method of claim 19, wherein the plurality of waveguide structures are heterogeneous waveguide structures each comprising a dielectric section corresponding to a material of the PCB layer and an air- filled section formed by the waveguide structure layer.

21. The method of claim 19, wherein the waveguide structure layer is fabricated from aluminum.33I PTS / 200136482.1

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