arXiv subjects

Anthony Grbic

Publications and source records attributed to Anthony Grbic.

At least 19 recordsLinked to original sources

arXiv2026

The Swiss Roll Metamaterial Revisited

In this work, we analytically model the Swiss roll metamaterial medium, showing that each unit cell can be thought of as a flux-coupled waveguide terminated in coupled inductors. The equivalent circuit model of the metamaterial accurately predicts its response, including its higher order resonances, even when made of a lossy, finite-thickness conductor. A closed-form solution for the response of this circuit model is then derived by solving a matrix equation of arbitrarily large dimensions. Along the way, we provide a general method for modeling the effective permeability of uniaxial, anisotropic metamaterials formed from axially invariant conducting inclusions.

physics.app-ph↗

arXiv2026

Analysis of Multi-Tone, Multi-Conductor, Spatially Discrete Traveling-Wave Modulated Loop Networks

This work presents a semi-analytical framework for analyzing spatially discrete traveling-wave modulated (SDTWM) loop networks, which exhibit cavity-like behavior and support discrete spatiotemporal modes. We introduce a computationally efficient method, based on the Interpath Relation, to analyze periodic networks using a single unit cell. This allows characterization of driven systems with single-tone, multi-tone, and multi-conductor loop configurations. The framework captures both multi-modal and multi-frequency harmonic interactions, and is extended to compute the spatial Green's functions of such loop networks using analytic array scanning. The analysis of example designs, such as an electrically small antenna and a non-magnetic circulator, is presented. These examples confirm that the proposed approach is computationally efficient and offers physical insight, making it well-suited for the optimization of multifunctional and nonreciprocal SDTWM electromagnetic systems.

physics.app-ph↗

arXiv2026

Wave-based Neuromorphic Circuit Networks: Tunable 2D Transmission-Line Metamaterials

Neuromorphic computing promises fast and energy-efficient information processing for emerging applications such as artificial intelligence. This paper presents neuromorphic processors based on wave-based programmable transmission-line (TLIN) metamaterials. Specifically, 2D reactive electrical networks are proposed, consisting of a grid of interconnected subwavelength TLIN-based unit cells (neurons) with tunable reactive elements. During inference, the input data is encoded using single-tone sources impressed onto the network, and circuit quantities are measured to decode the output prediction. Computation is performed through wave propagation and interference across the grid, with the learned input-output relationships stored in the tunable reactive elements. A key contribution of this work is a scalable training method based on in-situ backpropagation. The adjoint variable method is used to derive a physical (electrical) realization of the backpropagation algorithm that is typically used to compute the gradient of the objective loss function in digital neural networks. This formulation computes the gradient from voltage measurements of two steady-state excitations: the forward pass (inference) and the adjoint pass (error backpropagation). This enables efficient training since it is independent of the number of trainable parameters and avoids the simulation-reality gap. To demonstrate the effectiveness of this approach, wave-based neuromorphic circuit networks are trained for allostery and classification tasks, and the system's robustness to damage is shown. This work paves the way for self-learning systems based on wave-based neuromorphic analog circuit hardware.

physics.app-ph↗

arXiv2026

Leaky-Wave Antenna Analysis using Multi-Modal Network Theory with Open Periodic Boundaries

This paper introduces two methods for analyzing periodic leaky-wave antennas (LWAs) within a new framework denoted as multi-modal network theory (MNT) with open periodic boundaries (OPBs). The approach is hybrid, combining analytical techniques with a commercial full-wave solver. The first method computes the dispersion diagram of periodic LWAs. It is iterative and relies on the full-wave simulation of a single unit-cell of a LWA, coupled with the analytical solution of an eigenvalue problem. This method effectively captures both the phase and attenuation constants of periodic LWAs while using fewer modes than previous methods with commercial frequency-domain solvers. The method is validated by computing the dispersion of classic LWA unit-cells and comparing them to those obtained through full-wave simulations of the full-length antenna and other state-of-the-art methods. The second, also based on OPB-MNT, focuses on LWA analysis in reception. Specifically, it determines the response of a unit-cell to an incident plane wave. To validate this method, we compute the response of LWA with different unit-cell designs. By comparing these results with the corresponding dispersion analysis, we show that the receiving case and the eigenvalue problem are related but not simply time-reversed versions of each other.

physics.optics↗

arXiv2026

Physics-Informed Deep Neural Network Design of Reactively Loaded Metasurfaces

A tandem deep neural network approach is presented for the inverse design of reactively loaded metasurfaces with prescribed far-field radiation characteristics. The proposed approach integrates a deep neural network (DNN) with a physics-based microwave network forward solver. The DNN maps target far-field patterns to distributions of reactive loads across the metasurface unit cells. The predicted distribution of reactive loads is evaluated by the forward solver to compute the resulting radiation pattern and guide the learning process through a cosine-similarity loss function. The forward solver enables a fast evaluation of the metasurface's electromagnetic response, significantly reducing the computational cost required for training. The proposed approach is applied to a metasurface with aperture-coupled unit cells loaded with reactances. Several design examples are presented to demonstrate the accurate synthesis of shaped and steered radiation patterns. Full-wave electromagnetic simulations are performed to validate the accuracy of the designed beamforming metasurfaces.

physics.app-ph↗

arXiv2025

Perfectly Matched Metamaterials

Fully harnessing the vast design space enabled by metamaterials to control electromagnetic (EM) fields remains an open problem for researchers. Inverse-design techniques have shown to best exploit the degrees of freedom available in design, resulting in high-performing systems for wireless communications, sensing and analog signal processing. Nonetheless, fundamental yet powerful properties of metamaterials are still to be revealed. In this paper, we introduce the concept of Perfectly Matched Metamaterials (PMMs). PMMs are passive, inhomogeneous media that perform purely refractive field transformations under different excitations. Their advantage lies in their simplicity, reflectionless behavior and suitability for both analytical and numerical design methods. Unlike Transformation Optics, PMM-based designs are devoid of coordinate transformations. Anisotropic unit cells are configured to control EM fields in a true-time delay manner. Simple analytical designs are reported which demonstrate the broadband capability of PMM devices. Proposed PMMs may find application in wideband beamforming and analog computing, realizing functionalities such as spatial filtering and signal pre-processing.

physics.optics↗

arXiv2025

Inverse Design of Perfectly-Matched Metamaterials Via Circuit-Based Surrogate Models and the Adjoint Method

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 they are embedded within 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.

physics.optics↗

arXiv2024

Characterization of a Displaced Coaxial Feed for Cascaded Cylindrical Metasurfaces

This paper characterizes a realistic feed for cylindrical metasurfaces, allowing it to be included in metasurface design. Specifically, it investigates a coaxial feed which is displaced from the center (off-center) of concentrically-cascaded cylindrical metasurfaces. Formulas are reported to quickly compute the multimodal S-matrix (scattering properties) of a displaced feed from that of the central feed. The theory is rigorously derived based on the addition theorem of Hankel functions for all azimuthal modes. Moreover, the resulting multimodal S-matrix is combined with the multimodal wave matrix theory used to model cylindrical metasurfaces, allowing devices to be designed that realize arbitrary field transformations from a displaced coaxial feed. A design example is reported, which opens new opportunities in the realization of realistic, high-performance cylindrical-metasurface-based devices.

physics.app-ph↗

arXiv2023

Design of Beamforming, Transparent Metasurfaces Using Integral Equations

An accurate method for designing transmissive metasurfaces is presented that provides perfect transmission while transforming the amplitude and phase of the wavefront. The designed metasurfaces consist of three spatially-varying, electric impedance sheets separated by two dielectric substrates. The design method uses integral equations to account for interactions within and between the impedance sheets, allowing for accurate design. In this paper, a comparison between the integral equation method and the local periodicity approximation is presented. The comparison includes one design example for a transmitted field of uniform phase and amplitude. The design using integral equations provides better collimation. Two other examples involving an amplitude tapered transmitted field are reported to show the versatility of the proposed design technique. In all the examples, the metasurface is $7.35\lambda_0$ wide, the focal length is $4\lambda_0$, and has an overall thickness of $0.1355 \lambda_0 $ at the operating frequency of 5GHz. The designs are verified using a commercial finite element electromagnetic solver.

physics.app-ph↗

arXiv2023

A Realistic Coaxial Feed for Cascaded Cylindrical Metasurfaces

In this letter, a realistic coaxial feed is integrated into the design of cascaded cylindrical metasurfaces. This is in contrast to the fictitious current source that is often reported in literature. The S-matrix of the coaxial feed is obtained by way of the mode-matching technique, which is subsequently combined with the S-matrix of the cascaded cylindrical metasurfaces to account for the interaction between the feed and metasurfaces. The integration of a realistic feed into the design process enables practical cylindrical-metasurface-based devices.

physics.app-ph↗

arXiv2022

Unit Cell Design for Aperiodic Metasurfaces

A technique is presented for the design of printed unit cells in aperiodic metasurface environments. The method begins with a solved matrix equation governing electromagnetic scattering from a homogenized metasurface design. The matrix equation is used to find the local, inhomogeneous electric field exciting a printed-circuit unit cell geometry. The local field is then impressed onto the printed circuit geometry and the induced surface current numerically computed. The computed surface current is sampled at the matrix equation discretization. The matrix equation is then used to compute the electric field scattered by the printed-circuit unit cell onto its neighbors using the sampled current in place of the current of the original homogenized unit cell. The printed circuit geometry is optimized to scatter the same field as the homogenized unit cell when excited with the local electric field computed. Two design examples are provided. Both a finite-sized, wide-angle reflecting metasurface, and a metasurface reflectarray designed to scan and collimate an incident cylindrical wave, are realized with printed-circuit unit cells using the proposed approach. It is shown that the local periodicity approximation cannot be used to accurately design the unit cells of either finite-sized metasurface.

physics.app-ph↗

arXiv2021

Design of Planar and Conformal, Passive, Loss-less Metasurfaces that Beamform

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.

physics.optics↗

arXiv2021

Field Synthesis with Azimuthally-Varying, Cascaded, Cylindrical Metasurfaces using a Wave Matrix Approach

In recent years, there has been extensive research on planar metasurfaces capable of arbitrarily controlling scattered fields. However, rigorous studies on conformal metasurfaces, such as those that are cylindrical, have been few in number likely due to their more complex geometry. Here, wave propagation in cascaded cylindrical structures consisting of layers of dielectric spacers and azimuthally-varying metasurfaces (subwavelength patterned metallic claddings) is investigated. A wave matrix approach, which incorporates the advantages of both ABCD matrices and scattering matrices (S matrices), is adopted. Wave matrices are used to model the higher order coupling between metasurface layers, overcoming fabrication difficulties associated with previous works. The proposed framework provides an efficient approach to synthesize the inhomogeneous sheet admittances that realize a desired cylindrical field transformation. Design examples are reported to illustrate the power and potential applications of the proposed method in antenna design and stealth technology.

physics.app-ph↗

arXiv2021

Recent Advances in Bianisotropic Boundary Conditions: Theory, Capabilities, Realizations, and Applications

In recent years, new functionality and unprecedented wavefront control has been enabled by the introduction of bianisotropic metasurfaces. A bianisotropic metasurface is characterized by an electric response, a magnetic response, and an electromagnetic/magnetoelectric response. In general, these metasur-faces consists of an array of metallic or dielectric particles located within a subwavelength thick host medium, and are approximated and modelled as infinitely-thin, idealized sheet boundaries defined along a surface. An appropriate sheet boundary condition which effectively models the tangential field discontinuity due to the array of magnetoelectric inclusions is the Generalized Sheet Transition Condition or GSTC. Several forms of the GSTC appear in literature. Here, we present each interpretation and show how they are related. Synthesis approaches unique to each form are overviewed. By utilizing the GSTC in metasurface design, new possibilities emerge which are not possible with conventional design techniques incorporating only electric or only magnetic responses. Since the metasurfaces are designed using bianisotropic boundary conditions, they must be realized using particles which contain magnetoelectric responses. This review article discusses the design of metasurfaces using the GSTC, and the bianisotropic particles used to realize GSTCs. Further, it discusses new and recent applications that have emerged due to bianisotropy, and future prospects in metasurface design using bianisotropic boundary conditions. The intent is to provide a comprehensive overview of metasurface design involving bianisotropy and for this review article to serve as a starting point for engineers and scientist that wish to introduce bianisotropy into metasurface design.

physics.app-ph↗

arXiv2021

Fast and Accurate Optimization of Metasurfaces with Gradient Descent and the Woodbury Matrix Identity

A fast metasurface optimization strategy for finite-size metasurfaces modeled using integral equations is presented. The metasurfaces considered are constructed from finite patterned metallic claddings supported by grounded dielectric spacers. Integral equations are used to model the response of the metasurface to a known excitation and solved by Method of Moments. An accelerated gradient descent optimization algorithm is presented that enables the direct optimization of such metasurfaces. The gradient is normally calculated by solving the method of moments problem N+1 times where N is the number of homogenized elements in the metasurface. Since the calculation of each component of the N-dimensional gradient involves perturbing the moment method impedance matrix along one element of its diagonal and inverting the result, this numerical gradient calculation can be accelerated using the Woodbury Matrix Identity. The Woodbury Matrix Identity allows the inverse of the perturbed impedance matrix to be computed at a low cost by forming a rank-r correction to the inverse of the unperturbed impedance matrix. Timing diagrams show up to a 26.5 times improvement in algorithm times when the acceleration technique is applied. An example of a passive and lossless wide-angle reflecting metasurface designed using the accelerated optimization technique is reported.

math.NA↗

arXiv2021

All-Dielectric Meta-optics for High-Efficiency Independent Amplitude and Phase Manipulation

Metasurfaces, composed of subwavelength scattering elements, have demonstrated remarkable control over the transmitted amplitude, phase, and polarization of light. However, manipulating the amplitude upon transmission has required loss if a single metasurface is used. Here, we describe high-efficiency independent manipulation of the amplitude and phase of a beam using two lossless phase-only metasurfaces separated by a distance. With this configuration, we experimentally demonstrate optical components such as combined beam-forming and splitting devices, as well as those for forming complex-valued, three-dimensional holograms. The compound meta-optic platform provides a promising approach for achieving high performance optical holographic displays and compact optical components, while exhibiting a high overall efficiency.

physics.optics↗

arXiv2021

Inverse Design of Multi-input Multi-output 2D Metastructured Devices

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.

physics.app-ph↗

arXiv2021

Efficient Computation of Spatially-Discrete Traveling-Wave Modulated Structures

Traveling-wave modulation is a form of space-time modulation which has been shown to enable unique electromagnetic phenomena such as non-reciprocity, beam-steering, frequency conversion, and amplification. In practice, traveling-wave modulation is achieved by applying a staggered time-modulation signal to a spatially-discrete array of unit cells. Therefore, the capability to accurately simulate spatially-discrete traveling-wave modulated structures is critical to design. However, simulating these structures is challenging due to the complex space-time dependence of the constituent unit cells. In this paper, a field relation (referred to as the interpath relation) is derived for spatially-discrete traveling-wave modulated structures. The interpath relation reveals that the field within a single time-modulated unit cell (rather than an entire spatial period) is sufficient to determine the field solution throughout space. It will be shown that the interpath relation can be incorporated into existing periodic method of moments solvers simply by modifying the source basis functions. As a result, the computational domain is reduced from an entire spatial period to a single time-modulated unit cell, dramatically reducing the number of unknowns. In the context of traveling-wave modulation, this enables researchers to efficiently simulate both complex structures with patterned unit cells in addition to continuous structures with infinitesimal unit cells.

physics.app-ph↗