Generalized Sheet Transition Condition Research Articles

Unified GSTC-FDTD Algorithm for the Efficient Electromagnetic Analysis of 2D Dispersive Materials

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic wave analysis of complex media. Conventional FDTD analyses of very thin two-dimensional (2D) dispersive materials require overwhelming computing resources because they should use very refined FDTD spatial grids. In this work, we propose a computationally efficient and unified FDTD formulation for 2D dispersive materials based on a combination of the generalized sheet transition condition (GSTC) and the modified Lorentz dispersion model. The proposed FDTD formulation can lead to a significant improvement in computational efficiency compared to the conventional FDTD method, while maintaining high accuracy. Numerical examples validate the improved computational efficiency of the proposed FDTD formulation.

Metasurface characterization based on eigenmode analysis and averaging of electromagnetic fields

A fully numerical homogenization technique for the retrieval of the effective surface susceptibilities of a periodic composite metasurface is developed in this work. We utilize the so-called dual field-flux finite element formulation scheme to accurately calculate the eigenmodes of a composite periodic metasurface, a scheme that possesses a crucial advantage: The capability of evaluating all field components and their derivatives accurately and with the same order of approximation is a requirement for our proposed technique. Next, we derive the generalized sheet transition condition equations for a general bianisotropic metasurface, which correlate the field components on either sides of the metasurface with its surface susceptibilities. At this point, we establish a new field averaging scheme for the acquisition of the average field components of the modes supported by the metasurface. Combining this computational information, we derive a set of linear algebraic equations based on the GSTCs and the average electromagnetic fields and numerically solve it, so as to obtain the effective surface susceptibilities of a bianisotropic metasurface. Comparison with the results of other techniques in the literature shows very good agreement, relatively to the resonance behavior of the returned values and their position at the frequency spectrum. The advantages that distinguish the proposed technique over other related methods are its foundation on the intrinsic modal information of the eigenmodes supported by the metasurface and its independence of any wave excitation schemes or involvement of analytical polarizability calculations.

Simple and Comprehensive Strategy to Synthesize Huygens Metasurface Antenna and Verification

Huygens metasurface (HMS) provides a flexible way to tailor the phases of fields without incurring reflection. Recently, HMS has been used in antenna scenes to convert the incident field into directional radiation. However, most design processes of the HMS antennas are based on the generalized sheet transition condition, which is usually augmented with extra operations for ensuring passivity and losslessness. Here, we propose a simple and comprehensive strategy to design and optimize the HMS antenna. The strategy builds an equivalent model of the HMS antenna and deals with the designs from the perspective of phase optimization, which is simple and straightforward. A fast and efficient algorithm is presented to solve the optimization problem under the framework of alternating direction method of multipliers (ADMM). The phases obtained by this strategy are naturally compatible with the passive and lossless conditions and can be directly implemented by metasurfaces. Furthermore, the strategy imposes constraints on the phase difference of adjacent meta-atoms, thus reducing the performance deterioration caused by aperiodic boundary conditions. The feasibility and superiority of the strategy are verified by full-wave simulation results and experimental measurements of exemplary designs.

Application of cylindrical IE-GSTC to physical metasurfaces

The cylindrical Integral Equation -- Generalized Sheet Transition Condition (IE-GSTC) is validated by applying it to physical metasurfaces, i.e. metasurfaces defined by material properties and dimensions rather than by susceptibility tensor components. The previously reported IE-GSTC, which was formulated for zero thickness GSTC discontinuities, is extended to handle the finite thickness of physical metasurfaces. A simple analytical approach is used to extract the bianisotropic susceptibility tensor of concentric, multilayered, magneto-dielectric shells. Plane wave scattering by a physical metasurface constructed of four segments of multilayered, magneto-dielectric metasurface scatterers is used as an example problem to validate cylindrical IE-GSTC. A second example considers an opening on the cylindrical metasurface, confirming IE-GSTC can handle metasurfaces with openings. Third example is that of plane wave scattering by an eight segment metasurface. Good agreement is obtained between IE-GSTC results and full wave simulation results for all the cases. The paper concludes with a novel technique to handle PEC segments embedded in a cylindrical metasurface.

Recent advances in bianisotropic boundary conditions: theory, capabilities, realizations, and applications

Abstract 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 electro-magnetic/magneto-electric response. In general, these metasurfaces consists of an array of metallic or dielectric particles located within a subwavelength thick host medium, and are approximated and modeled 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 GSTC’s. 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.

Holographic Smart EM Skins for Advanced Beam Power Shaping in Next Generation Wireless Environments

An innovative approachfor the synthesis of inexpensive holographic smart electromagnetic (EM) skins with advanced beamforming features is proposed. The complex multi-scale smart skin design is formulated within the Generalized Sheet Transition Condition (GSTC) framework as a combination of a mask-constrained isophoric inverse source problem and a micro-scale susceptibility dyadic optimization. The solution strategy integrates a local search procedure based on the iterative projection technique (IPT) and a System-by-Design(SbD)-based optimization loop for the identification of optimal metasurface descriptors matching the desired surface currents. The performance and the efficiency of the proposed approach are assessed in a set of representative numerical test cases concerned with different smart skin apertures and target pattern masks.

Simulation of Cylindrical Metasurfaces Using GSTC-MFCM

We present a multifilament current method (MFCM) incorporated with generalized sheet transition condition (GSTC) to simulate 2-D cylindrical metasurfaces with arbitrary cross sections. The GSTC casts in the form of an impedance-type boundary condition to relate the tangential fields on two sides of a cylindrical metasurface. The MFCM is subsequently introduced and formulated by employing the GSTC. The doublet-current unit, including both electric and magnetic filamentary sources, is introduced in order to capture both co- and cross-polarized scattered and transmitted fields from the GSTC characterized cylindrical metasurfaces. Three illustrative examples are presented to validate the proposed simulation technique. The behaviors of filamentary sources in terms of scattered field singularities and the ill-conditioning issue of the constructed matrix are also discussed in detail. In comparison to existing numerical methods, the proposed technique has its merits on simplicity and conciseness.

Homogenized Dyadic Potential Green’s Function for Planar Metasurface Placed at Two Half Spaces Interface Excited by Vertical and Horizontal Ideal Electric Dipole

In this article, dyadic magnetic vector potential Green’s functions corresponding to electric dipole which illuminates homogenized metasurface have been presented. Metasurface is constructed by a periodic arrangement of planar metallic scatterers and located at the interface of two different dielectric half spaces. The metasurface is replaced by a thin sheet with the dyadic equivalent surface distribution of electric and magnetic susceptibilities. These vector potentials have been derived employing generalized sheet transition condition (GSTC) on the plane of the metasurface. The retrieval relations to obtain equivalent surface susceptibilities of such a surface are calculated by means of the calculated reflection and transmission coefficients due to TE polarized plane waves. Also, the transverse and longitudinal scalar electric potentials relative to the problem have been calculated with the aid of the Lorentz gauge. These vector and scalar potentials together are necessary to use in the mixed potential integral equation (MPIE) formulation of the method of moment (MoM) in an electromagnetic problem.

Electromagnetic Simulation of 2.5-Dimensional Cylindrical Metasurfaces With Arbitrary Shapes Using GSTC-MFCM

We present a multifilament current method (MFCM) incorporated with generalized sheet transition condition (GSTC) to simulate 2.5-dimensional cylindrical metasurfaces with arbitrary cross sections for the first time. The chain-type form of GSTC is synthesized and utilized to relate the tangential fields on two sides of a cylindrical metasurface. The MFCM is subsequently introduced and formulated by deploying the GSTC. The doublet-current unit which contains both electric and magnetic line sources with phase terms is deployed in the MFCM for simulating co- and cross-polarized scattered and transmitted fields from GSTC characterized cylindrical metasurfaces. Three illustrative examples regarding different geometries, different metasurface characteristics and different excitations are presented to validate the proposed simulation technique. In comparison to existing numerical methods, the proposed technique has its merits on simplicity and conciseness.

PLRC-FDTD Modeling of General GSTC-Based Dispersive Bianisotropic Metasurfaces

A general bianaisotropic metasurface represented by a generalized sheet transition condition is modeled by the finite-difference time-domain (FDTD) method. The dispersive susceptibilities of the metasurface are approximated by FDTD-compatible rational functions which are incorporated in the update equations by the piecewise linear recursive convolution technique. Compared to the existing methods, the proposed technique requires less arithmetic operations. The method is verified by comparing the results with those of the finite-difference frequency-domain method through simulation of wave propagation in five test cases: generalized refraction metasurface, polarization rotator, Bessel beam generator, orbital angular momentum multiplexer, and reflectionless omega-type metasurface.

Metasurface-loaded dielectric rod leaky wave antenna

This paper introduces an analytical solution for a dielectric rod leaky wave antenna loaded by a metasurface. The advantage of adding metasurface on the dielectric rod is that it introduces an additional degree of freedom in the design of this antenna by controlling the outer boundary condition. Modified Generalized Sheet Transition Condition on a cylindrical geometry is used to model the metasurface on the dielectric rod. The analysis is based on developing the characteristic equation of the proposed structure. This characteristic equation is used to obtain the complex propagation constant of this structure and the corresponding field distribution inside and outside the rod including the resulting radiated fields. Parameters of the metasurface are extracted from the reflection and transmission properties of its elements in infinite periodic structure. An example of a dielectric rod loaded by a metasurface is presented analytically based on the introduced analysis and also simulated numerically for comparison. The effect of different polarizabilities of the loading metasurface on the leaky wave properties of the dielectric rod is discussed.

Analysis of anisotropic metasurfaces using generalized sheet transition condition

This paper presents an analysis of anisotropic metasurfaces using generalized sheet transition condition (GSTC). Unlike previously studied GSTC, the present analysis takes into consideration the coupling between transverse field components. Based on the shape of the metasurface element, coupling between transverse fields can be obtained. This coupling between transverse field components introduces polarization rotation in reflected and transmitted fields. This property can be used to control the wave polarization. Using anisotropic metasurfaces as superstrate for a printed antenna can control the resulting radiation pattern as well as the polarization of the radiated field.