A general technique for synthesizing both planar and conformal beamforming metasurfaces is presented that utilizes full-wave modeling techniques and rapid optimization methods. The synthesized metasurfaces consist of a patterned metallic cladding supported by a finite-size grounded dielectric substrate. The metasurfaces are modeled using integral equations which accurately account for mutual coupling and the metasurface's finite dimensions. The synthesis technique consists of three phases: a direct solve phase to obtain an initial metasurface design with complex-valued impedances satisfying the desired far-field beam specifications, a subsequent optimization phase that converts the complex-valued impedances to purely reactive ones, and a final patterning phase to realize the purely reactive impedances as a patterned metallic cladding. The optimization phase introduces surface waves which facilitate passivity. The metasurface is optimized using gradient descent with a semi-analytic gradient obtained using the adjoint variable method. Three examples are presented: a low-profile directly-fed metasurface antenna with near perfect aperture efficiency, a scanned-beam reflectarray design with controlled sidelobes, and a conformal metasurface reflectarray. The far-field and near-field performance of the metasurfaces are verified and the bandwidth and loss tolerance of the metasurfaces are investigated.

In this work, an optimization-based inverse design method is provided for multi-input multi-output (MIMO) metastructured devices. Typically, optimization-based methods use a full-wave solver in conjunction with an optimization routine to design devices. Due to the computational cost this approach is not practical for designing electrically-large aperiodic metastructured devices. To address this issue, a 2-D circuit network solver using reduced order models of the metastructure’s unit cells is introduced. The circuit network solver is used in conjunction with a gradient-based optimization routine that uses the adjoint variable method to solve large-scale optimization problems like those posed by metastructured devices. To validate the inverse design method, a planar beamformer and an analog signal processor for aperture field reconstruction are designed and validated with full-wave simulations.

Lossless, reciprocal bianisotropic metasurfaces have the ability to control the amplitude, phase, and polarization of electromagnetic wavefronts. However, producing the responses that are necessary for achieving this control with physically realizable surfaces is a challenging task. Here, several design approaches for bianisotropic metasurfaces are reviewed that produce physically realizable metasurfaces using cascaded impedance sheets. In practice, three or four impedance sheets are often used to realize bianisotropic responses, which can result in narrowband designs that require the unit cells to be optimized in order to improve the performance of the metasurface. The notion of a metasurface quality factor is introduced for three-sheet metasurfaces to address these issues in a systematic manner. It is shown that the quality factor can be used to predict the bandwidth of a homogeneous metasurface, and it can also be used to locate problematic unit cells when designing inhomogeneous metasurfaces. Several design examples are provided to demonstrate the utility of the quality factor, including an impedance matching layer with maximal bandwidth and a gradient metasurface for plane wave refraction. In addition to these examples, several metasurfaces for polarization control are also reported, including an isotropic polarization rotator and an asymmetric circular polarizer.

In this work, perfectly-matched metamaterials (PMMs) are described and combined with inverse design to realize broadband devices. PMMs are discretized metamaterials with anisotropic unit cells selected from a constrained design space, referred to as perfectly-matched media. PMMs exhibit the unique property that all their unit cells are impedance-matched to each other as well as to the host medium in which they are embedded under all excitations. As a result, PMM devices rely on reflectionless refractive effects to achieve a prescribed function. This property enables true time delay performance and promises broadband capabilities. Two design examples are presented to demonstrate the potential of inverse-designed PMMs: a compact, broadband beam-collimator with a prescribed amplitude taper and a multi-input multi-output beamformer exhibiting zero scan loss.

Transmissive and reflective all-dielectric metastructures will be presented that offer tailored polarization con- versions and spectral responses. The metastructures consist of stacked deeply subwavelength, high contrast gratings of different fill factors and rotations. Broadband metastructures that perform a given polarization conversion over a wide continuous bandwidth will be shown, as well as multiband metastructures that perform a common polarization conversion over different bands. Multifunctional metastructures that realize different polarization conversions over different bands will also be reported at the conference. Unlike earlier stacked grating geometries, the transmissive metastructures do not require antireflection layers since impedance matching is incorporated into their design. The subwavelength gratings are modeled as homogeneous anisotropic layers, allowing an overall metastructure to be treated as a stratified dielectric medium. Quasi-static analysis is used to homogenize the subwavelength gratings and represent them with effective dielectric constants. Plane-wave transfer matrix techniques are employed to model the interactions between gratings, allowing for rapid design and optimization. In the metastructures, higher-order Floquet harmonics are bound to the gratings due to their subwavelength periodicities. As a result, only zeroth-order coupling between the gratings needs to be considered. The multifunctional performance and compactness (wavelength-sized thickness) of the proposed devices will find use at millimeter-wave wavelengths and beyond. Two example designs are described in this paper. Measured performance of prototypes will also be reported at the conference and various fabrication approaches reviewed. This work demonstrates the flexibility with which cascaded subwavelength gratings can realize unprecedented polarization control with varied spectral responses.

A broadband half-wave plate is demonstrated based on cascaded alumina/air subwavelength gratings. Stacked subwavelength gratings can be well-approximated by homogeneous anistropic layers, permitting analysis by plane wave transfer matrix techniques and rapid design optimization. The example waveplate, fabricated using ceramic stereolithography, shows broadband phase performance and low loss over the K a frequency band (26.5 – 40 GHz). Analytic calculations show excellent agreement with measured reflection coefficients, validating the design approach.