RELATED APPLICATIONS

[0001] This application claims priority to U.S. Patent Application No. 18/459,310, titled “Two-Dimensional Metasurface Beam Forming Systems and Methods,” filed on August 31 , 2023, which application claims priority to and benefits under 35 U.S.C. § 119 to U.S. Provisional Patent Application No. 63/376,129, filed on September 19, 2022, titled “Two- Dimensional Metasurface Beam Forming Systems and Methods,” which applications are both hereby incorporated by reference in their entireties.

TECHNICAL FIELD

[0002] This disclosure relates to optical metasurfaces, including tunable resonant optical metasurfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

[0003] FIG. 1 A illustrates a perspective view of a simplified block diagram of reflective and resonator layers of a two-dimensional optical metasurface, according to one embodiment.

[0004] FIG. 1 B illustrates an exploded perspective view of the simplified block diagram of the reflective and resonator layers of the two-dimensional optical metasurface, according to one embodiment.

[0005] FIG. 1 C illustrates a top perspective view of the simplified block diagram of the reflective and resonator layers of the two-dimensional optical metasurface, according to one embodiment.

[0006] FIG. 1 D illustrates a side perspective view of the simplified block diagram of the reflective and resonator layers of the two-dimensional optical metasurface, according to one embodiment.

[0007] FIG. 2 illustrates an example diagram of a control layer of a two-dimensional optical metasurface with passive matrix addressing, according to one embodiment.

[0008] FIG. 3 illustrates an example diagram of a control layer of a two-dimensional optical metasurface with active matrix addressing, according to one embodiment. [0009] FIG. 4 illustrates a side-view diagram of the layers of a portion of a tunable optical metasurface, according to one embodiment.

[0010] FIG. 5A illustrates an example diagram of optical fields in an optical resonator of a resonator layer of a tunable optical metasurface, according to one embodiment.

[0011] FIG. 5B illustrates the tunable dielectric material between two pillars aligned in a first direction to provide a first refractive index without any applied voltage, according to one embodiment.

[0012] FIG. 50 illustrates the tunable dielectric material between the pillars aligned in a second direction to provide a second refractive index with an applied voltage of 5 volts, according to one embodiment.

[0013] FIG. 5D illustrates a graph of a phase response of the resonant unit cell with respect to applied voltage values, according to one embodiment.

[0014] FIG. 6A illustrates a top-view diagram of a portion of a tunable optical metasurface with offset rows of pillars, according to one embodiment.

[0015] FIG. 6B illustrates an example diagram of an offset off-resonance gap in a reflector layer of the tunable optical metasurface to reduce or eliminate coupling between unit cells, according to one embodiment.

[0016] FIG. 6C illustrates an example diagram of an aligned off-resonance gap in a reflector layer of the tunable optical metasurface, according to one embodiment.

[0017] FIG. 6D illustrates an example diagram of optical fields in a resonator layer of the tunable optical metasurface with offset rows of pillars, according to one embodiment. [0018] FIG. 7A illustrates a top-view diagram of a portion of a tunable optical metasurface with row-aligned pillars, according to one embodiment.

[0019] FIG. 7B illustrates an example diagram of an off-resonance gap in a reflector layer of the tunable optical metasurface to reduce or eliminate coupling between unit cells, according to one embodiment.

[0020] FIG. 70 illustrates an example diagram of optical fields in row-aligned pillars in a resonator layer of the tunable optical metasurface, according to one embodiment.

[0021] FIG. 8 illustrates an example diagram of another example of a metasurface, according to one embodiment. [0022] FIG. 9 illustrates an example of an active-matrix driver architecture with a tiled aperture with each tile representing a diffraction-limited building block of individually addressable elements, according to one embodiment.

[0023] FIG. 10A illustrates an example diagram of a top view of an XY plane of a tunable optical metasurface, according to one embodiment.

[0024] FIG. 10B illustrates an example diagram of a first cut-away side view of an XZ plane of the tunable optical metasurface of FIG. 10A, according to one embodiment.

[0025] FIG. 10C illustrates an example diagram of a second cut-away side view of the XZ plane of the tunable optical metasurface of FIG. 10A, according to one embodiment.

[0026] FIG. 10D illustrates optical fields in the resonator layer from the perspective of the top view of the XY plane of the tunable optical metasurface of FIG. 10A, according to one embodiment.

DETAILED DESCRIPTION

[0027] Tunable optical metasurfaces can be dynamically tuned to spatially modulate incident optical radiation. Modulating the phase and/or amplitude of incident optical radiation can be used to generate output optical radiation with a target profile. Spatial light modulation may be used for beam shaping, beam forming, beam steering, etc. The presently described systems and methods can be applied to tunable metasurfaces utilizing various architectures and designs to deflect optical radiation within an operational bandwidth. In various embodiments, a controller or metasurface driver selectively applies a pattern of voltages to a two-dimensional array of optical structures positioned on a reflective layer. Voltage differentials across adjacent optical structures modify the refractive indices of dielectric material therebetween. A combination of phase delays created by the pattern of applied voltages can be used to create constructive interference. [0028] Various examples of tunable optical metasurfaces are described herein and depicted in the figures. For example, a tunable optical metasurface can include a two- dimensional array of metallic optical pillars (e.g., antenna elements, elongated pillar elements, metal pillar pairs, etc.). Liquid crystal, or another refractive index tunable dielectric material, is positioned in the gaps or channels between adjacent metallic optical pillars. Liquid crystal is used in many of the examples provided in this disclosure. However, it is appreciated that alternative dielectric materials with tunable refractive indices and/or combinations of different dielectric materials with tunable refractive indices may be utilized instead of liquid crystal in many instances. Examples of suitable tunable dielectric materials that have tunable refractive indices include liquid crystals, electrooptic polymer, electro-optical crystal, chalcogenide glasses, and/or various semiconductor materials.

[0029] In various embodiments, biasing the liquid crystal in a metasurface with a pattern of voltage biases changes the reflection phase of the optical radiation. For example, each different voltage pattern applied across the metasurface corresponds to a different reflection phase pattern. Each different reflection phase corresponds to a unique spatial modulation, steering, beamforming, or other controlled optical transmission. A digital or analog controller (controlling current and/or voltage), such as a passive or switch-matrix active driver, may apply a differential voltage bias pattern to achieve a target phase modulation pattern across the two-dimensional array. The metasurface may be controlled for optical spatial modulation to accomplish a target beam shaping, onedimensional beam steering (i.e., steering in one direction), two-dimensional beam steering (i.e., steering in two directions), wavelength filtering, beam divergence, beam convergence, beam focusing, and/or controlled deflection, refraction, and/or reflection of incident optical radiation.

[0030] Additional descriptions, variations, functionalities, and usages for optical metasurfaces are described in U.S. Patent No. 10,451 ,800 granted on October 22, 2019, entitled “Plasmonic Surface-Scattering Elements and Metasurfaces for Optical Beam Steering;” U.S. Patent No. 10,665,953 granted on May 26, 2020, entitled “Tunable Liquid Crystal Metasurfaces;” U.S. Patent No. 11 ,092,675 granted on August 17, 2021 , entitled “Lidar Systems based on Tunable Optical Metasurfaces;” and U.S. Patent No. 11 ,429,008 granted on August 20, 2022, entitled “Liquid Crystal Metasurfaces with Cross-Backplane Optical Reflectors,” each of which is hereby incorporated by reference in its entirety.

[0031] This disclosure includes various embodiments and variations of tunable optical metasurface devices and methods for manufacturing the same. It is appreciated that the metasurface technologies described herein may incorporate or otherwise leverage prior advancements in surface scattering antennas, such as those described in U.S. Patent Publication No. 2012/0194399, published on August 2, 2012, entitled “Surface Scattering Antennas;” U.S. Patent Publication No. 2019/0285798 published on September 19, 2019, entitled “Plasmonic Surface-Scattering Elements and Metasurfaces for Optical Beam Steering;” and U.S. Patent Publication No. 2018/0241131 published on August 23, 2018, entitled “Optical Surface-Scattering Elements and Metasurfaces;” each of which is hereby incorporated by reference in its entirety. Additional elements, applications, and features of surface scattering antennas are described in U.S. Patent Publication No. 2014/0266946, published September 18, 2014, entitled “Surface Scattering Antenna Improvements;” U.S. Patent Publication No. 2015/0318618, published November 5, 2015, entitled “Surface Scattering Antennas with Lumped Elements;” U.S. Patent Publication No. 2015/0318620 published November 5, 2015, entitled “Curved Surface Scattering Antennas;” U.S. Patent Publication No. 2015/0380828 published on December 31 , 2015, entitled “Slotted Surface Scattering Antennas;” U.S. Patent Publication No. 2015/0162658 published June 11 , 2015, entitled “Surface Scattering Reflector Antenna;” U.S. Patent Publication No. 2015/0372389 published December 24, 2015, entitled “Modulation Patterns for Surface Scattering Antennas;” PCT Application No. PCT/US18/19269 filed on February 22, 2018, entitled “Control Circuitry and Fabrication Techniques for Optical Metasurfaces,” U.S. Patent Publication No. 2019/0301025 published on October 3, 2019, entitled “Fabrication of Metallic Optical Metasurfaces;” and U.S. Publication No. 2018/0248267 published on August 30, 2018, entitled “Optical Beam-Steering Devices and Methods Utilizing Surface Scattering Metasurfaces,” each of which is hereby incorporated by reference in its entirety.

[0032] In some examples, a tunable optical device includes a substrate layer, a reflective layer, and a two-dimensional array of metallic optical pillars. The two- dimensional array of metallic optical pillars may be arranged in parallel rows extending vertically relative to the substrate layer. Gaps between row-adjacent pillars form optical resonators, such that each row of pillars includes a plurality of optical resonator gaps or cavities. In various embodiments, the pillars in each row are spaced from one another by less than a smallest wavelength in an operational bandwidth (referred to as subwavelength spacing). In other embodiments, the pillars in each row may be spaced from one another by more than a largest wavelength or many wavelengths of an operational bandwidth. A tunable dielectric material that has a tunable refractive index (e.g., liquid crystal) is positioned between the pillars, including within the optical resonators formed by the gaps between row-adjacent pillars. The reflective layer is positioned between the substrate layer and the two-dimensional array of pillars to reflect optical radiation.

[0033] In some examples, the width of each pillar along each row is less than one-half of the smallest wavelength of the operational bandwidth and the length of each pillar in a direction perpendicular to each row is less than the smallest wavelength of the operational bandwidth.

[0034] The reflective layer includes a two-dimensional array of elongated rectangular reflector patches arranged in parallel rows. An electrical isolation gap separates reflector patches in adjacent rows, while an off-resonance gap separates reflector patches that are in the same row. The reflector patches are arranged lengthwise in the row (perpendicular to the length of the corresponding pillars). In some embodiments, the parallel rows of reflector patches are offset with respect to one another, such that the off-resonance gaps between adjacent reflector patches in one row are not aligned with the off-resonance gaps between adjacent reflector patches in an adjacent row (e.g., misaligned or staggered). In other embodiments, the reflector patches may be aligned with respect to one another, such that the off-resonance gaps between adjacent reflector patches are aligned with one another in the column direction.

[0035] In some examples, the width of each reflector patch combined with the electrical isolation gap between adjacent rows of reflector patches is less than the length of each pillar, such that each pillar spatially overlaps reflector patches in at least two adjacent rows of reflector patches. In some examples, the electrical isolation gap between adjacent rows of reflector patches and/or the off-resonance gap between adjacent reflector patches in the same row may be filled with a dielectric material. The metasurface may be controlled by a controller. For example, a controller may comprise a passive or active switch-matrix of control lines to selectively apply a voltage differential bias pattern to the tunable dielectric material between adjacent metallic optical pillars.

[0036] The metasurface may also be described in the context of a resonant unit cell. A two-dimensional optical metasurface may include a two-dimensional array of dynamically tunable resonant unit cells arranged in rows and columns. Each resonant unit cell may comprise first and second elongated optical pillars extending vertically relative to a substrate. The pillars in each resonant unit cell may be positioned with sides parallel to one another and spaced apart by less than the smallest wavelength in an operational bandwidth to form a gap therebetween. The pillars of the resonant unit cell extend lengthwise in a first direction with a tunable dielectric material positioned to fill (at least partially) the gap.

[0037] In addition to the pillars extending lengthwise in a first direction, the resonant unit cell includes reflector patches that extend lengthwise in a second direction that are perpendicular to the first direction. The reflector patches are part of the reflective layer positioned between the first and second elongated optical pillars and the substrate. The reflector patches in each resonant unit cell are electrically isolated from one another (e.g., via an electrical isolation gap). Off-resonance gaps (for wavelengths within the operational bandwidth) separate reflector patches of each resonant unit cell from adjacent reflector patches of adjacent resonant unit cells. The off-resonance gaps of each resonant unit cell may be offset with respect to one another, such that the off-resonance gaps between reflector patches of adjacent resonant unit cells are staggered.

[0038] Examples of metasurfaces are described herein that can be used for transmitting or receiving. Systems incorporating the metasurfaces described herein may be operated as only a transmitter, as only a receiver, simultaneously as a transmitter and receiver, as a time-multiplexed transmitter/receiver, as a frequency-multiplexed transmitter/receiver, with the first metasurface acting as a transmitter and a second metasurface acting as a receiver, or in another transmit/receive configuration or operation technique. The metasurfaces described herein may be used to control, tune, or modify reflection phase patterns. For example, one or more metasurfaces may be used to control (i) the reflection phase, (ii) the reflection amplitude, or (iii) the reflection phase and the reflection/transmission amplitude of an optical signal. Accordingly, a metasurface may be utilized in any of the embodiments described herein to control the complex phase and/or complex amplitude of reflected optical radiation.

[0039] Any of the variously described embodiments herein may be manufactured with dimensions suitable for optical bandwidths for optical sensing systems such as LiDAR, optical communications systems, optical computing systems, and displays. For example, the systems and methods described herein can be configured with metasurfaces that operate with optical radiation, including without limitation optical wavelengths in the nearinfrared, mid-infrared, long wave-infrared, and/or visible-wavelength ranges (. Given the feature sizes needed for sub-wavelength optical antennas and antenna spacings, the described metasurfaces may be manufactured using micro-lithographic and/or nano-lithographic processes, such as fabrication methods commonly used to manufacture complementary metal-oxide-sem iconductor (CMOS) integrated circuits.

[0040] Some of the infrastructure that can be used with embodiments disclosed herein is already available, such as general-purpose computers, computer programming tools and techniques, digital storage media, and communication links. Many of the systems, subsystems, modules, components, and the like that are described herein may be implemented as hardware, firmware, and/or software. Various systems, subsystems, modules, and components are described in terms of the function(s) they perform because such a wide variety of possible implementations exist. For example, it is appreciated that many existing programming languages, hardware devices, frequency bands, circuits, software platforms, networking infrastructures, and/or data stores may be utilized alone or in combination to implement a specific control function.

[0041] It is also appreciated that two or more of the elements, devices, systems, subsystems, components, modules, etc. that are described herein may be combined as a single element, device, system, subsystem, module, or component. Moreover, many of the elements, devices, systems, subsystems, components, and modules may be duplicated or further divided into discrete elements, devices, systems, subsystems, components, or modules to perform subtasks of those described herein. Any aspect of any embodiment described herein may be combined with any other aspect of any other embodiment described herein or in the other disclosures incorporated by reference, including all permutations and combinations thereof, consistent with the understanding of one of skill in the art reading this disclosure in the context of such other disclosures.

[0042] To the extent used herein, a computing device, system, subsystem, module, driver, or controller may include a processor, such as a microprocessor, a microcontroller, logic circuitry, or the like. A processor may include one or more special-purpose processing devices, such as application-specific integrated circuits (ASICs), programmable array logic (PAL), programmable logic array (PLA), a programmable logic device (PLD), field-programmable gate array (FPGA), or another customizable and/or programmable device. The computing device may also include a machine-readable storage device, such as non-volatile memory, optical memory, flash memory, or another transitory or non-transitory machine-readable storage media. Various aspects of some embodiments may be implemented or enhanced using hardware, software, firmware, or a combination thereof.

[0043] The components of some of the disclosed embodiments are described and illustrated in the figures herein to provide specific examples. Many portions thereof could be arranged and designed in a wide variety of different configurations. Furthermore, the features, structures, and operations associated with one embodiment may be applied to or combined with the features, structures, or operations described in conjunction with another embodiment. In many instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of this disclosure.

[0044] FIG. 1 A illustrates a perspective view of a simplified block diagram of a reflective layer 110 and resonator layer 120 of a two-dimensional optical metasurface 100, according to one embodiment. As illustrated, the resonator layer 120 includes a two- dimensional array of metallic optical pillars 125 arranged in parallel rows. Each pillar 125 in the resonator layer 120 extends vertically relative to an underlying substrate layer (not shown). The pillars 125 in each row may be spaced from one another by less than a smallest wavelength in an operational bandwidth. The width (W) of each pillar 125 along each row may be less than one-half of the smallest wavelength of the operational bandwidth. The length (L) of each pillar 125 in a direction perpendicular to each row (e.g., along the columns) may be less than the smallest wavelength of the operational bandwidth.

[0045] The gaps between adjacent pillars 125 in each row of pillars form optical resonators. A tunable dielectric material may be deposited within the resonator layer to fill the space between the pillars 125 in all direction, such that tunable dielectric material is positioned within the optical resonators formed by the gaps between row-adjacent pillars 125. Examples of suitable tunable dielectric materials that have tunable refractive indices include liquid crystals, electro-optic polymer, electro-optic crystals, chalcogenide glasses, and/or various semiconductor materials.

[0046] In alternative embodiments, the pillars 125 in each row may be spaced from one another by more than a wavelength in an operational bandwidth (e.g., ten times the largest wavelength in the operational bandwidth. Similarly, in some embodiments, the width (W) of each pillar 125 along each row may be more than one-half of the smallest wavelength and the length (L) of each pillar 125 in a direction perpendicular to each row (e.g., along the columns) may be many times larger than the largest wavelength of the operational bandwidth.

[0047] The reflective layer 110 includes a two-dimensional array of elongated rectangular reflector patches 115 extending lengthwise along parallel rows. That is, as illustrated, the reflector patches 115 extend lengthwise in a direction that is perpendicular with respect to the lengthwise direction of the pillars 125. An electrical isolation gap 130 separates reflector patches 115 in adjacent rows. An off-resonance gap 140 separates adjacent reflector patches 115 in the same row. The direction of the electrical isolation gap 130 is off-resonance with the incident electric field so there is no resonant coupling. The off-resonance gap 140 between adjacent reflector patches 115 is perpendicular to the incident electrical field. Accordingly, the dimension of the off-resonance gap 140 is selected to minimize or avoid any possible resonance between reflector patches 115 in the same row, for a range of optical radiation wavelengths. The off-resonance gap 140 may be a different size than the electrical isolation gap 130.

[0048] A dielectric via layer 150 may be positioned between the reflective layer 110 and the resonator layer 120. Each pillar 125 may be electrically connected to one underlying reflector patch 115 by a conductor via 155 within the dielectric via layer 150. The dielectric of the dielectric via layer 150 has been removed from the figure for clarity to show the positioning of the conductor vias 155.

[0049] FIG. 1 B illustrates an exploded perspective view of the simplified block diagram of the reflective layer 110 and the resonant layer 120 of the two-dimensional optical metasurface 100. As illustrated, the parallel rows of reflector patches 115 are offset with respect to one another, such that the off-resonance gaps 140 between adjacent reflector patches 115 in one row are not aligned (e.g., staggered or misaligned) with the off- resonance gaps 140 between adjacent reflector patches 115 in an adjacent row. Each conductor via 155 of the dielectric via layer 150 (shown with the dielectric material removed from around the conductor vias 155 removed) connects one pillar 125 to one of the underlying reflector patches 115. Notably, since the pillars 125 extend lengthwise in a direction perpendicular to the direction in which the underlying reflector patches 115 extend, half of the pillars 125 (alternating every other one) in the first row of pillars 125 are connected to reflector patches 115 in the first row of reflector patches 115, while the other half (alternating) are connected to reflector patches 115 in the second row of reflector patches 115.

[0050] FIG. 1 C illustrates a top perspective view of the simplified block diagram of the reflective layer 110 and the resonant layer 120 of the two-dimensional optical metasurface 100. The top perspective view illustrates that the pillars 125 are aligned in rows and columns, with the pillars extending lengthwise in a first direction (e.g., perpendicular to the angle of the incident optical radiation). In the illustrated example, the length of each pillar 125 is less than the smallest wavelength of an operational bandwidth, and the width of each pillar 125 is less than one-half of the smallest. The gap between adjacent pillars 125 in the same row also has subwavelength dimensions. As described herein, the length, width, and spacing dimensions may be larger in some embodiments.

[0051] The specific dimensions of the pillars 125, including the heights and interelement spacing (gaps), are selected as a function of the target operational bandwidth, as described in detail in the patents and patent publications incorporated herein by reference. For example, for operation with optical radiation having a wavelength of 905 nanometers, the gap filled with the tunable dielectric material between adjacent pillars 125 forming a unit cell may be approximately 150 nanometers. The height of the pillars 125 may be approximately 400 nanometers and provide a second order resonance. [0052] FIG. 1 D illustrates a side perspective view of the simplified block diagram of the reflective layer 110 and the resonant layer 120 of the two-dimensional optical metasurface 100. The illustrated view is rotated such that the rows of reflector patches 115 and pillars 125 extend from the bottom of the page toward the top of the page. As previously described, the reflector patches 115 extend lengthwise in the direction of the rows, while the pillars 125 extend widthwise in the direction of the rows. The relative dimensions of the pillars 125 and the reflector patches 115 are selected such that there are two rows of reflector patches 115 beneath each row of pillars 125.

[0053] FIG. 2 illustrates an example diagram of a control layer 200 of a two-dimensional optical metasurface with passive matrix addressing, according to one embodiment. A controller may be connected to voltage control lines on the rows 210 and the columns 220 of the unit cells of resonators (e.g., to the metallic optical pillars of each resonant unit cell). The control lines of the control layer 200 may be integrated within the substrate of a metasurface or within a separate dielectric layer between the substrate and the reflective layer. The control lines may electrically connect to the reflector patches, which are in turn connected to pillars by the conductor vias in the dielectric via layer. The passive matrix control line address scheme facilitates two-dimensional, M x N addressing of M rows 210 and N columns 220 of metallic optical pillars. Beam steering or other spatial phase modulation ( ) by the metasurface, illustrated as wavefronts 250, is expressible in terms of a function of row modulations f(x) and a function of column modulations g(y), such that = f(x) + g(y).

[0054] FIG. 3 illustrates an example diagram of a control layer 300 of a two-dimensional optical metasurface with active matrix addressing, according to one embodiment. The active-matrix control system includes rows and columns of transistors. Each transistor is connected to a unique metallic optical pillar through a corresponding reflector patch and conductor via. The control lines of the control layer 300 may be integrated within the substrate of a metasurface or within a separate dielectric layer between the substrate and the reflective layer. The active-matrix control system may drive a voltage on one or more rows and use column select lines to turn on the transistors associated with specific pillars. The active matrix architecture enables the resonant unit cells of the metasurface to exhibit a unique pattern of phase responses (0) as a function of the row drive (x) and the column select (y), expressible as 0 = f(x,y), as illustrated at 350.

[0055] As described herein, each resonant unit cell includes two metallic optical pillars spaced apart by a subwavelength gap that is filled (partially, fully, or overflowing) with a tunable dielectric material that has a tunable refractive index. The tunable refractive index of the tunable dielectric material of each resonant unit cell is selected by creating a voltage differential between the two metallic optical pillars of the unit cell. The voltage differential is used to tune the phase (and/or amplitude) of incident optical radiation (e.g., laser light). Each resonant unit cell can be less than half of the optical wavelength in size in the inplane direction of the incident optical radiation to enable large field-of-view beam steering without grating lobes. Configuring the dimensions of the resonant unit cell (e.g. , the widths of two metallic optical pillars and the gap therebetween) to be less than one-half of the wavelength (A/2) in the in-plane direction of the incident optical radiation prevents diffraction from the resonant unit cell. The dimensions of the resonant unit cell can be larger (e.g., up to as large as the wavelength) in the out-of-plane or lateral direction while still maintaining a large beam steering field of view without introducing diffraction. The unit cell size can be relaxed (e.g., have dimensions that are larger than one-half of the wavelength (A/2) in the in-plane direction and/or more than one wavelength in the out-of- plane or lateral direction) in applications in which the incidence angle is close to normal to the plane of the metasurface.

[0056] FIG. 4 illustrates a side-view diagram of the layers of a portion of a tunable optical metasurface 400 with active-matrix addressing, according to one embodiment. In the illustrated cross-sectional view, a single row of optical resonators is formed by the metallic optical pillars 425 in the resonator layer 420. The pillars 425 extend vertically relative to a substrate layer (not shown) and lengthwise into the page. A dielectric via layer 450 includes conductor vias 455 that connect the pillars 425 to reflector patches 415 within a reflective layer 410. As illustrated, the reflector patches 415 are staggered or offset with respect to one another such that the reflector patches 415 for every other pillar 425 are not visible in the cross-sectional view. The illustrated example includes a second via layer 460 with conductor vias 465 to connect the pillars 425 to the control lines and transistors 475 within the control layer 470.

[0057] The active matrix architecture enables the resonant unit cells of the metasurface 400 to exhibit a unique pattern of phase responses (O) as a function of the row drive (x) and the column select (y), expressible as <t> = f(x,y). The incident fields and k-vector of the wavefront of the optical radiation 490 are depicted. The metasurface 400 may be used for arbitrary phase modulation of the incident optical radiation 490 for beam steering, lensing, or another optical functionality. [0058] As illustrated, the active matrix addressing scheme includes a transistor 475 beneath each resonant unit cell. In some embodiments, each resonant unit cell includes only a single transistor connected to one of pillars, with the other pillar connected to a fixed voltage. In other embodiments, each resonant unit cell includes two transistors, with one transistor connected to each metallic optical pillar such that each metallic optical pillar can be driven with a unique voltage. While an absolute voltage is applied to each metallic optical pillar, the phase of each resonant unit cell depends on the voltage difference between adjacent metallic optical pillars.

[0059] According to various embodiments, the dielectric via layer 450 also functions as a waveguide layer in between the resonator layer 420 and the reflector layer 410. The thickness of the waveguide layer is such that destructive interference of the fields is created at the bottom of the optical resonator (e.g., the gap between row-adjacent optical metallic pillars), thus confining most of the optical energy to the vertical pillars, and minimal leaking into the waveguide layer.

[0060] The resonant unit cells are tuned via the refractive-index tunable material 485 between adjacent metallic optical pillars 425. Liquid crystal, for example, may be used which has a high refractive index tuning range. As described herein, a differential voltage is applied between adjacent metallic optical pillars 425, which rotates the liquid crystals in that resonant unit cell, changing the refractive index experienced by the x component of the optical electric field. This consequently changes the effective length of the metallic optical pillars 425, and hence the phase experienced by the incident optical radiation 490 at that location on the metasurface. Since the resonant unit cells are resonant, changes in the phase are coupled to changes in the amplitude response in many embodiments, as is typical of Lorentz-type resonators. In such embodiments, each metallic optical pillar 425 is programmed with a unique voltage (hence phase) such that a desired spatial phase gradient is achieved. This gradient can be used for beam steering or other optical functionality such as focusing, collimating, or any arbitrary optical transformation.

[0061] Again, the metallic optical pillars 425 can be implemented in conventional CMOS manufacturing processes, such as those based on copper damascene metallization, deposition processes, etching processes, lithography processes, patterning processes, chemical mechanical planarization processes, and the like. Other metals besides copper, such as aluminum, silver, and gold, can also be used to form the metal core of each metallic optical pillar. Copper is attractive because it is widely used in the semiconductor industry to make transistors interconnects with the dimensions required to implement these resonant unit cells. In addition, copper has excellent optical properties across near-IR and short-wave IR wavelengths.

[0062] FIG. 5A illustrates an example diagram of optical fields 590 within the tunable dielectric material 585 in the gap between a pair of metallic optical pillars 525 and 526 forming an optical resonator, with underlying reflector patches 515 and 516. In the illustrated example, the heights of the metallic optical pillars 525 and 526 are selected for second-order resonance with two magnetic field anti-nodes 590. According to various embodiments, and as illustrated, each metallic optical pillar 525 and 526 includes a metal core 527 and 528 and a passivation coating 521 and 522.

[0063] The passivation coating 521 and 522 may be deposited as a single or uniform layer that covers the sidewalls and top wall of each metallic optical pillar 525. The passivation coating 521 and 522 may be, for example, a thin silicon nitride (SiN) layer to passivate a metal core 527 and 528 of each metallic optical pillar 525. The passivation coating 521 and 522 may operate to prevent diffusion of the metal of the metallic optical pillars 525 and 526 from diffusing into the tunable dielectric material (e.g., liquid crystal) and/or prevent corrosion of the metallic optical pillars 525 and 526. The passivating coating 521 and 522 may be SiN, SiCN, aluminum oxide, or another suitable passivation material.

[0064] The passivation coating 521 and 522 may be optically transparent for wavelengths within the operational bandwidth of the metasurface and/or reflective to complement the underlying reflective conductive metal core 527 and 528 (e.g., copper). The passivation coating 521 and 522 may alternatively (or additionally) include silicon carbide nitride, silicon carbide, aluminum oxide (AIOx), hafnium oxide (HfO2, silicon oxide (SiO2), aluminum nitride (AIN), boron nitride (BN), and/or another passivating dielectric material. A transistor 575 within a control layer is connected to the pillar 525 via the reflector patch 515 and the intervening conductor vias 555 and 565 within the dielectric via layers 550 and 560. A controller can drive the pillar 525 to a target voltage via the transistor 575 to create a voltage differential within the optical resonator formed by the gap between pillars 525 and 526. The refractive index of the tunable dielectric material 585 may be adjusted to a target refractive index based on the applied voltage differential between the pillars 525 and 526.

[0065] FIG. 5B illustrates the tunable dielectric material 585 between two pillars 525 and 526 aligned in a first direction to provide a first refractive index within the optical resonator without any applied voltage (e.g., zero-volt differential, at 501 ), according to one embodiment.

[0066] FIG. 5C illustrates the tunable dielectric material 585 between the pillars 525 and 526 aligned in a second direction to provide a second refractive index within the optical resonator with an applied voltage of 5 volts, at 502, according to one embodiment. [0067] FIG. 5D illustrates a graph 599 of a phase response of the resonant unit cell with respect to applied voltage values, according to one embodiment. It is appreciated that the phase response and range of voltages may vary based on the specific dimensions of the pillars 525 and 526, the width of the gap forming the optical resonator that is filled with the tunable dielectric material 585, and/or the specific material (e.g., liquid crystal) used as the tunable dielectric material 585.

[0068] FIG. 6A illustrates a top-view diagram of the portion of a tunable optical metasurface 600 with offset rows of pillars 625, according to one embodiment. Each resonant unit cell 621 consists of two metallic optical pillars 625 and 626. Each metallic optical pillar 625 and 626 is connected with a conductive via 655 and 656 to one of the reflector patches 615 and 616. The metasurface 600 operates only on transverse magnetic (TM) polarization. Therefore, the x component of the electric field (perpendicular to the lengthwise or long sidewalls and parallel with the widthwise or short sidewalls) couples in the resonant unit cell 621 metallic optical pillars 625 and 626. The gaps or slots 603 between the metallic optical pillars 625 and 626 in the y direction do not couple to this field since the field is parallel to walls of the metal pillars (e.g., copper), and hence excluded from the slots 603. As shown in the cross-sectional view of Figure 4, each reflector patch 615 connects to an underlying transistor (e.g., by conductor vias 465 in a second via layer 460 in FIG. 4).

[0069] The reflector layer 610 of reflector patches 615 and 616 includes off-resonance gaps 612 in the x-axis. The off-resonance gaps 612 provide electrical isolation between adjacent reflector patches 615 and 616 in the same row. The off-resonance gaps 612 have a width dimension selected to be off-resonant from the incident field, limiting the amount of field leaking into the reflector patches 615 and 616 of the reflector layer 610. Additionally, electrical isolation gaps 613 or channels in the y-axis are created to electrically isolate adjacent reflector patches 615 and 616 in adjacent rows. The optical field does not couple into the electrical isolation gaps 613 because the E-field is parallel to the metal walls of the reflector patches 615 and 616, so the dimensions of the electrical isolation gaps 613 may be different (e.g., smaller) than those of the off-resonance gaps 612 which are more carefully selected to be non-resonant.

[0070] FIG. 6B illustrates an example diagram of an offset off-resonance gap 612 between adjacent reflector patches 615 of the reflector layer 610 to reduce or eliminate coupling between reflector patches 615 in the same row, according to one embodiment. Electrical isolation gaps 613 may be used to electrically isolate reflector patches 615 that are in different rows without consideration to avoid resonance. As described herein, reflector patches 615 of one row are staggered or offset with respect to the reflector patches 615 in adjacent rows to ensure that the off-resonance gaps 612 are staggered and not aligned with one another.

[0071] FIG. 6C illustrates an example diagram of an aligned off-resonance gap in a reflector layer of the tunable optical metasurface, according to one embodiment. Electrical isolation gaps 613 electrically isolates reflector patches 615 that are in different rows. The reflector patches 615 of one row are aligned with respect to the reflector patches 615 in adjacent rows. Off-resonance gaps 612 operate to reduce coupling between reflector patches in the same row.

[0072] FIG. 6D illustrates an example diagram of optical fields in a resonator layer of a tunable optical metasurface with offset rows of pillars, according to one embodiment. As illustrated, the metallic optical pillars 625 and 626 are part of a first resonant unit cell. A first optical field 623 is illustrated between the metallic optical pillars 625 and 626. The illustrated example includes staggered or offset pillars 625 and 626. Accordingly, the metallic optical pillars 627 and 628 of the second resonant unit cell are offset, staggered, or misaligned with respect to the metallic optical pillars 625 and 626 of the first resonant unit cell. As such, the second optical field 624 in the second resonant unit cell is also staggered or offset with respect to the first optical field 623.

[0073] FIG. 7A illustrates a top-view diagram of the portion of a tunable optical metasurface 700 with row-aligned pillars 725, according to one embodiment. Each resonant unit cell 721 comprises two metallic optical pillars 725 and 726. Each metallic optical pillar 725 and 726 is connected with a conductive via 755 and 756 to one of the reflector patches 715 and 716. The metasurface 700 operates only on transverse magnetic (TM) polarization. Therefore, the x component of the electric field (perpendicular to the lengthwise or long sidewalls and parallel with the widthwise or short sidewalls) couples in the resonant unit cell 721 metallic optical pillars 725 and 726. The gaps or slots 703 between the metallic optical pillars 725 and 726 in the y direction do not couple to this field since the field is parallel to walls of the metal pillars, and hence excluded from the slots 703. As shown in the cross-sectional view of Figure 4, each reflector patch 715 connects to an underlying transistor (e.g., by conductor vias 465 in a second via layer 460 in FIG. 4).

[0074] The reflector layer 710 of reflector patches 715 and 716 includes off-resonance gaps 712 in the x-axis. The off-resonance gaps 712 provide electrical isolation between adjacent reflector patches 715 and 716 in the same row. The off-resonance gaps 712 have a width dimension selected to be off-resonanctfrom the incident field, limiting the amount of field leaking into the reflector patches 715 and 716 of the reflector layer 710. Additionally, electrical isolation gaps 713 or channels in the y-axis are created to electrically isolate adjacent reflector patches 715 and 716 in adjacent rows. The optical field does not couple into the electrical isolation gaps 713 because the E-field is parallel to the metal walls of the reflector patches 715 and 716, so the dimensions of the electrical isolation gaps 713 may be different (e.g., smaller) than those of the off-resonance gaps 712 which are more carefully selected to be non-resonant.

[0075] FIG. 7B illustrates an example diagram of the off-resonance gap in the reflector layer of the tunable optical metasurface to reduce or eliminate coupling between resonant unit cells, according to one embodiment. Electrical isolation gaps 713 may be used to electrically isolate reflector patches 715 that are in different rows without consideration to avoid resonance. As described herein, reflector patches 715 of one row are staggered or offset with respect to the reflector patches 715 in adjacent rows to ensure that the off- resonance gaps 712 are staggered and not aligned with one another.

[0076] FIG. 70 illustrates an example diagram of optical fields in a row-aligned resonator layer of a tunable optical metasurface with row-aligned pillars, according to one embodiment. As illustrated, the metallic optical pillars 725 and 726 are part of a first resonant unit cell. A first optical field 723 is illustrated between the metallic optical pillars 725 and 726. The illustrated example includes column-aligned pillars. Accordingly, the metallic optical pillars 727 and 728 of the second resonant unit cell are aligned with respect to the metallic optical pillars 725 and 726 of the first unit cell. As such, the second optical field 724 in the second resonant unit cell is also aligned with respect to the first optical field 723.

[0077] FIG. 8 illustrates an example diagram of another example of a metasurface 800, according to one embodiment. In the illustrated example, the metasurface 800 includes multiple tiles 801 , 802, 803, and 804. Each tile 801 , 802, 803, and 804 includes multiple metallic optical pillars 825 that have lengths that are multiple wavelengths in the out-of- plane direction (vertical axis). The horizontal axis includes a pitch or interelement spacing of the metallic optical pillars 825 that is less than the diffraction limit (e.g., one-half of an operational wavelength). The illustrated metasurface 800 can be used to generate grating lobes in the vertical direction. For example, the metasurface 800 may be used to comb discrete beams along the vertical axis that can then be steered together. The metasurface 800 does not generate grating lobes in the horizontal axis because the interelement spacing of the metallic optical pillars 825 is below the diffraction limit. Each metallic optical pillar 825 is connected to an underlying elongated reflector patch 815 by a conductor via 855.

[0078] FIG. 9 illustrates an example of an active-matrix driver architecture 900 with a tiled aperture, with each tile 901 representing a diffraction-limited building block of individually addressable elements, according to one embodiment. As the aperture size of a metasurface increases, the number of elements grows as the square of the linear dimension. Furthermore, all or many of the voltage-controlled or tunable elements (e.g., metallic optical pillars) may need to be updated for every change in the phase modulation pattern (e.g., for a given steering angle). In some embodiments in which the metasurface is based on liquid crystal tuning of copper pillars, the typical switching speed is 50 microseconds, and the entire array is updated on this time scale.

[0079] The illustrated active-matrix driver architecture 900 reduces the complexity, power and/or size of the driver electronics by decoupling the aperture size from the angular resolution. The angular resolution in each axis is determined by the number of individually addressed resonant unit cells in each axis. The aperture size for a particular optical design is often much bigger than the diffraction limited aperture dictated by the angular resolution requirement. Each tile 901 can share the same set of source drivers, such as digital-to-analog converters 981 or “DACs” for column addressing and gate drivers 982 for row addressing). The active-matrix architecture 900 for a tiled metasurface, including the various control lines, capacitors, and/or transistors, along with the DACs 981 and gate drivers 982 are referred to herein as part of a controller or control layer of the metasurface.

[0080] Alternatively, a unit cell architecture can be implemented with passive matrix addressing. In this case, each unit cell may have two pillars, including a first pillar driven by wires propagating in the x-axis (carrying row driving voltages) and another pillar connected to wires propagating in the y-axis (carrying column driving voltages). If the unit cell is below the diffraction limit, the light will experience scattering (phase delay) from both pillars. Therefore, an optical function of the form phi = f(x) + f(y) can be implemented. [0081] FIG. 10A illustrates an example diagram of a top view of the XY plane of a tunable optical metasurface 1000, according to one embodiment. In the illustrated example, the unit cell 1080 includes four metallic optical pillars, including one metallic optical pillar 1025 that is connected to a continuous control line 1005 that provides a drive voltage (x voltage). All the metallic optical pillars connected to the continuous control line 1005 (illustrated with the connection dots) are driven to the same voltage via the continuous control line 1005.

[0082] FIG. 10B illustrates an example diagram of a first cross-sectional side view 1001 of the XZ plane of the tunable optical metasurface 1000 of FIG. 10A at the indicated “cut A” location, according to one embodiment. As illustrated, each metallic optical pillar 1025 is connected to an underlying reflector patch 1015 by a conductor via 1055 and to a control line and/or transistor in the “Y voltage layer” 1075. [0083] FIG. 10C illustrates an example diagram of a second cross-sectional side view 1002 of the XZ plane of the tunable optical metasurface of FIG. 10A at the indicated “cut B” location, according to one embodiment. As illustrated, every other (alternating) metallic optical pillar 1026 is connected to a continuous reflector patch 1016 by conductor vias 1055 in the dielectric via layer 1050.

[0084] FIG. 10D illustrates the optical fields 1018 and 1019 between metallic optical pillars 1025 in the resonator layer from the perspective of the top view of the XY plane of the tunable optical metasurface 1000 of FIG. 10A, according to one embodiment.

[0085] This disclosure has been made with reference to various exemplary embodiments, including the best mode. However, those skilled in the art will recognize that changes and modifications may be made to the exemplary embodiments without departing from the scope of the present disclosure. While the principles of this disclosure have been shown in various embodiments, many modifications of structure, arrangements, proportions, elements, materials, and components may be adapted for a specific environment and/or operating requirements without departing from the principles and scope of this disclosure. These and other changes or modifications are intended to be included within the scope of the present disclosure.

[0086] This disclosure is to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope thereof. Likewise, benefits, other advantages, and solutions to problems have been described above with regard to various embodiments. However, benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature or element. The following claims are also included as part of this disclosure.