Generalized Sheet Transition Conditions Research Articles

Magnetless reflective gyrotropic spatial isolator metasurface

We present the concept of a magnetless reflective gyrotropic spatial isolator (RGSI) metasurface. This is a birefringent metasurface that reflects vertically polarized incident waves into a horizontally polarized waves, and absorbs horizontally polarized incident waves, hence providing isolation between the two orthogonal polarization. We first synthesize the metasurface using surface susceptibility-based generalized sheet transition conditions. We then propose a mirror-backed metaparticle implementation of this metasurface, where transistor-loaded resonators provide the desired magnetless nonreciprocal response. Finally, we demonstrate the metasurface by full-wave simulation results. The proposed RGSI metasurface may be used in various electromagnetic applications, and may also serve as a step towards more sophisticated magnetless nonreciprocal metasurface systems.

Synthesis analysis of frequency selective surface using the generalized sheet transition conditions

Based on the generalized sheet transition conditions (GSTCs), the surface electric/magnetic susceptibilities of frequency selective surface (FSS) are extracted and analyzed. Key factors that affect the FSS performance, including frequency variations, structure shapes, angular dependent, and bandwidth are studied through the susceptibility parameters. Based on the analysis of four typical FSS structures, potential automatic structure designs are suggested and several illustrative examples are given. Finally, the method is compared with the equivalent circuit method.

Analysis of wave scattering from 2D curved metasurfaces using Floquet and Fourier series expansions

An efficient technique for calculating the scattering from curved metasurfaces using the extinction theorem in conjunction with the Floquet and Fourier series expansions is presented. Here, we treat the two-dimensional metasurfaces that have transversal polarizabilities with no variation along the y-axis. The boundary conditions at the metasurface are given by the generalized sheet transition conditions (GSTCs) whose susceptibilities are given in an arbitrary local coordinate system. First, we use the extinction theorem to provide integral equations of the scattering problem. The integral equations involve the Green's functions, tangential electric and magnetic fields and their normal derivatives in regions above and below the metasurface. Then, we employ the Floquet theorem that gives us the analytical periodic Green's functions of each region. Next, we employ the Fourier theorem to expand the tangential fields in terms of unknown Fourier coefficients. The GSTCs and the integral equations provide equations to be solved for the unknowns. The method can calculate scattering from both periodic and non-periodic metasurfaces. The technique is used to analyse different applied problems such as carpet cloaking, illusion, and radar echo width reduction. The method is fast and accurate and can efficiently treat metasurfaces with electrically large curved geometries with dimensions as large as 120 times the wavelength.

Floquet Analysis of Space-Time Modulated Metasurfaces With Lorentz Dispersion

A rigorous semi-analytical Floquet analysis is proposed for a zero-thickness space-time modulated Huygens' metasurface to model and determine the strengths of the new harmonic components of the scattered fields. The proposed method is based on Generalized Sheet Transition Conditions (GSTCs) treating a metasurface as a spatial discontinuity. The metasurface is described in terms of Lorentzian electric and magnetic surface susceptibilities, $\chi_\text{e}$ and $\chi_\text{m}$, respectively, with parameters (e.g. resonant frequency) that are periodically modulated in both space and time. The unknown scattered fields are expressed in terms of Floquet harmonics, for which the amplitudes can be found by numerically solving a set of linear equations, leading to the total scattered fields. Using existing computational techniques, the method is validated using several examples of pure-space and pure-time modulation with different modulation strengths and pumping frequencies. Finally, two cases of spacetime modulation (standing wave perturbation and a traveling wave perturbation) are presented to demonstrate the breaking of Lorentz reciprocity. The proposed method is simple and versatile and able to determine the steady-state response of a space-time modulated Huygen's metasurface that is excited with an oblique plane wave, or a general incident field such as a Gaussian beam.

Parallel Analog Computing Based on a 2×2 Multiple-Input Multiple-Output Metasurface Processor With Asymmetric Response

We present a polarization-insensitive metasurface processor to perform spatial asymmetric filtering of an incident optical beam, thereby allowing for real-time parallel optical processing. To enable massive parallel processing, we introduce a novel Multi Input-Multi Output (MIMO) computational metasurface with an asymmetric optical response that can perform spatial differentiation on two distinct input signals regardless of their polarization. In our scenario, two distinct signals set in x and y directions, parallel and perpendicular to the incident plane, illuminate simultaneously the metasurface processor, and the resulting differentiated signals are separated from each other via appropriate Spatial Low Pass Filters (SLPF). By leveraging Generalized Sheet Transition Conditions (GSTCs) and surface susceptibility tensors, we design an asymmetric meta-atom augmented with normal susceptibilitiesto reach asymmetric optical response at normal beam illumination. Proof-of-principle simulations are also reported along with the successful realization of signal processing functions. The proposed metasurface overcomes major shortcomings imposed by previous studies such as large architectures arising from the need of additional subblocks, slow responses, and most importantly, supporting only a single input with a given polarization. Our results set the path for future developments of material-based analog computing using efficient and easy-to-fabricate MIMO processors for compact, fast, and integrable computing elements without any Fourier lens.

Generalized Brewster effect using bianisotropic metasurfaces.

We show that a properly designed bianisotropic metasurface placed at the interface between two arbitrary different media, or coating a dielectric medium exposed to the air, provides Brewster (reflectionless) transmission at arbitrary angles for both the TM and TE polarizations. We present a rigorous derivation of the corresponding surface susceptibility tensors based on the generalized sheet transition conditions and demonstrate by full-wave simulations the system with planar microwave metasurfaces designed for polarization-independent and azimuth-independent operations. The proposed bianisotropic metasurfaces provide deeply subwavelength matching solutions for initially mismatched media. The reported generalized Brewster effect represents a fundamental advance in optical technology, where it may both improve the performance of conventional components and enable the development of novel devices.

Fundamental Properties and Classification of Polarization Converting Bianisotropic Metasurfaces

We provide a detailed discussion on the electromagnetic modeling and classification of polarization converting bianisotropic metasurfaces. To do so, we first present a general approach to compute the scattering response of such metasurfaces, which relies on a generalized sheet transition conditions based susceptibility model. Then, we review how the fundamental properties of reciprocity, energy conservation, rotation invariance and matching may be expressed in terms of metasurface susceptibilities and scattering parameters, and show how these properties may affect and limit the polarization effects of metasurfaces. Finally, we connect together the metasurface susceptibility model to the structural symmetries of scattering particles and their associated polarization effects. This work thus provides a detailed understanding of the polarization conversion properties of metasurfaces and may prove to be of particular interest for their practical implementation.

Near-Field Focusing With Subwavelength Thickness Metalenses via Electromagnetic Susceptibility Models

The design mentality of an optimal metalens model, based on the electromagnetic susceptibility, a synthesis of subwavelength-thick metasurfaces (MSs) is presented in this paper. First, based on the finite difference method of generalized sheet transition conditions, the surface susceptibility function of the MS with spatial discontinuities can be determined. Then, the paper analyzed the remaining corresponding physical field conditions for the scale of metalens. In order to adapt to the physical limitations encountered in the near-field focusing of the metalens, a standard parabolic phase design is proposed in this paper, and its upsides and downsides of the two-phase processing in different aspects are compared. Using COMSOL software with numerical simulation, it can be seen that the standard design can easily obtain high resolution in the near field, while the focusing effect is more stable when the focal length is small by the parabolic phase design.

An ultrathin metasurface carpet cloak based on the generalized sheet transition conditions

In this paper, we propose an arc-shaped metasurface carpet cloak based on generalized sheet transition conditions. The main idea behind this invisibility is phase compensation through local phase modulation, in which the front of the reflected wave is reshaped just as the incident wave hits the flat mirror. Secondly, we have implemented an arc-shaped metasurface carpet cloak based on a cavity structure unit with a thickness of one fifth wavelength. The cloak can still have a stealth effect in the range of incident angle from 0°to 30°and in the range of frequency from 8 GHz to 13 GHz. The numerical results of the arc-shaped metasurface carpet cloak agree well with the theoretical calculation of GSTCs and it can provide an important reference for the future carpet cloak field.

Goos–Hanchen shift in a metasurface of core–shell nanoparticles

Metasurfaces are periodic subwavelength structures that have found applications in functional devices such as image sensors, cameras, and microscopes. They are able to modulate the amplitude, phase, and polarization of incident light. Reflected light from a surface exhibits a deviation from the rules governed by geometric optics and displaces in directions parallel and perpendicular to plane of incidence. The sharp phase changes at reflection from a metasurface would be useful in enhancing the longitudinal reflection shifts, known as Goos–Hanchen​ (GH) shift. In this article, using generalized sheet transition conditions, we study GH shift in a metasurface composed of spherical metal-oxide core with plasmonic shell nanoparticles in a square array. A detailed analysis reveals that reflection shifts of this type of nanostructures can be tuned delicately by varying the size, core-to-shell ratio and periodicity of particles as well as light wavelength and angle of radiation. Large reflection shifts are achievable in both visible and ultraviolet ranges due to plasmonic resonance of metallic shell. Such sensitivity could be useful in very sensitive beam deflection measurements like in AFM or in reflective UV sensors.

Calculation of Potential Green’s Functions for a Planar Metasurface Excited by an Electric Dipole Using Homogenization Method

One of the rapid and efficient methods to calculate the interaction between electromagnetic fields and periodic surfaces with periodicity much less than the wavelength in the surrounding medium is the homogenization method. In this paper, the Hertzian potential Green’s functions corresponding to electric dipoles which excite a homogenized metasurface are presented. The metasurface includes a periodic array of planar scatterers and is replaced by a thin sheet with equivalent electric and magnetic surface polarization density dyads. The magnetic vector potentials are calculated using the generalized sheet transition conditions on the plane of the metasurface. Also the scalar electric potential corresponding to the structure is calculated with the aid of the Lorentz gauge. These potentials together are necessary to use in the mixed potential integral equation formulation of the method of moment in an electromagnetic problem. Two metasurfaces are investigated to calculate the electric fields; a perfect electric conductor square patch array whose surface polarization densities are calculated analytically, and a Jerusalem cross array whose surface polarization dyads are retrieved from reflection and transmission coefficients.

On the surface susceptibilities and effective parameters of metasurfaces composed of isolated metallic unit‐cells

This paper presents a study into the parameter-retrieval methods of metasurfaces composed of isolated metallic unit-cells. The classical method based on the effective-medium theory is revisited by aiming at the point of effective thickness in use. The second method based on the generalized sheet transition conditions is also investigated and the extracted results are mutually verified with the classical method when the unity thickness is used. It is found that these two sets of effective parameters, surface susceptibilities and unity effective parameters, are mutually equivalent if they are not equal. The retrieved values are justified by those results available in literature.

Modal Analysis of a Parallel-Plate Waveguide Containing an Internal Perforated Sheet

This article considers a structure consisting of a planar metal sheet with periodic square perforations lying between two metal plates. Generalized sheet transition conditions (GSTCs) are used to model the perforated sheet, and standard representations of the fields in the two regions of the structure lead to expressions for determining the propagation constants of the guided waves. Waveguide modes of surface wave type are found to exist on this structure, and their propagation constants are calculated. Agreement between the results of the analytical approach and the finite-element simulations is shown for various values of the perforated screen parameters, showing the analytical method to be both accurate and efficient for design.

Fast Nonuniform Metasurface Analysis in FDTD Using Surface Susceptibility Model

Analysis of nonuniform metasurfaces requires enormous computational resources and even cannot be achieved in some cases, due to their multiscale property. To address this, we propose a fast analysis method in finite difference time domain (FDTD) scheme in this article. Two steps are required: first, nonuniform metasurfaces are modeled as a distribution of surface susceptibilities. Secondly, the surface susceptibility model (SSM) is inserted into FDTD equations in a form of surface polarization currents based on generalized sheet transition conditions (GSTCs). A detailed comparison is made between brute force simulation and our proposed method. Compared with the hours consumed for physical model simulation, surface susceptibility model simulation’s time consumption is in seconds while simultaneously maintaining similar field responses independent of the incident wave’s angle and polarization.

Low‐profile TM incident retrodirective metasurface based on generalized sheet transition conditions and Babinet's principle

AbstractThis article presents a method to design low‐profile TM incident retrodirective metasurface (RMS). The equivalent circuit model based on generalized sheet transition conditions (GSTCs) and modified Babinet's principle are used to design the unit cell of RMS for full reflection phase coverage (FRPC). The slots on the unitcell and the artificial magnetic conductor (AMC) ground are used for TM wave and low‐profile, respectively. The height of the designed RMS is reduced by 50%, compared with previous TM incident RMS. The measured bistatic pattern and efficiency are in good agreement with those of the simulation.

Limitations of the Metasurface Diluted-Slab Model

In this article, we investigate the possibility to model a metasurface, defined as a zero-thickness sheet of surface polarization currents and described by generalized sheet transition conditions (GSTCs), by a thin slab with a subwavelength thickness and usual voluminal medium parameters. First, we elaborate a general equivalence relation between the metasurface and the slab in terms of average electromagnetic fields. Then, we derive the exact relations between the metasurface and slab susceptibilities and validate them by full-wave simulations. Finally, we discuss the simple and insightful diluted-slab model, called here the average field approximation (AFA) formula, illustrate its inappropriateness for strong metasurface field transformations, and establish its range of validity. All of these developments are restricted to the simplest case of a uniform isotropic metasurface under normal plane wave incidence. We conclude, from the complexity of the exact equivalence for this simplest case and from the intrinsic limitations of the AFA, that a metasurface is generally best analyzed by computational schemes incorporating the GSTCs.

Surface Susceptibility Synthesis of Metasurface Skins/Holograms for Electromagnetic Camouflage/Illusions

A systematic numerical framework based on Integral Equations and Generalized Sheet Transition Conditions (IE-GSTCs) is presented in 2D to synthesize closed metasurface holograms and skins for creating electromagnetic illusions of specified objects and as a special case, to camouflaging them against their backgrounds. The versatile hologram surface is modeled using a zero-thickness sheet model of a generalized metasurface expressed in terms of its surface susceptibilities, which is further integrated into the GSTCs and the IE current-field propagation operators. To estimate the effectiveness of the illusions, the notion of a scene constructed by an observer is developed from first principles and a simple mathematical model, referred to as a Structured Field Observation (SFO), based on spatial Fourier transform is proposed. Using numerical examples, it is shown that to recreate the reference desired fields everywhere in space using a closed metasurface hologram/skin, an internal illumination must be applied inside the hologram, in addition to the applied external illumination fields. Finally, several numerical examples are presented for simple, angle-dependent and dynamic illusions. Finally, a dynamic camouflaged region of space, which can freely move inside a given complex scene without being detected by the observer is demonstrated.

Surface Susceptibility Synthesis of Metasurface Holograms for Creating Electromagnetic Illusions

A systematic approach is presented to exploit the rich field transformation capabilities of Electromagnetic (EM) metasurfaces for creating a variety of illusions using the concept of metasurface holograms. A system level approach to metasurface hologram synthesis is presented here, in which the hologram is co-designed with the desired object to be projected. A structured approach for the classification of the creation of EM illusions is proposed for better organization and tractability of the overall synthesis problem. The delineation is in terms of the initial incident (reference) illumination of the object to be recreated (front/back-lit), the position of illusion (posterior/anterior), and the illumination used to create the illusion (front/back). Therefore the classification is based on the specific relationship between the reference object to be recreated, the observer measuring the object, the orientation and placement of the reference and illumination field, and the desired placement of the metasurface hologram creating a virtual image. In the paper a general design procedure to synthesize metasurface holograms is presented based on Integral Equations (IE) and Generalized Sheet Transition Conditions (GSTCs), where the metasurface hologram is described as zero thickness sheet with tensorial surface susceptibility densities. Several selected configurations are chosen to illustrate various aspects of the hologram creation in 2D, along with a novel numerical technique to artificially reverse-propagate the scattered fields, required in the synthesis process. Finally, the impact of the metasurface size and the illumination field strength on the quality of the reconstructed scattered fields is also discussed.

FDTD Simulation of Dispersive Metasurfaces With Lorentzian Surface Susceptibilities

A Finite-Difference Time-Domain (FDTD) simulation of broadband electromagnetic metasurfaces based on direct incorporation of Generalized Sheet Transition Conditions (GSTCs) into a conventional Yee-cell region has been proposed for arbitrary wave excitations. This is achieved by inserting a zero thickness metasurface inside bulk nodes of the Yee-cell region, giving rise to three distinct cell configurations - Symmetric Cell (SC), Asymmetric Cell (AC) and Tight Asymmetric Cell (TAC). In addition, the metasurface is modelled using electric and magnetic surface susceptibilities exhibiting a broadband Lorentzian response. As a result, the proposed model guarantees a physical and causal response from the metasurface. Several full-wave results are shown and compared with analytical Fourier propagation methods showing excellent results for both 1D and 2D field simulations. It is found that the TAC provides the fastest convergence among the three methods with minimum error.

Comparison of Tensor Boundary Conditions With Generalized Sheet Transition Conditions

This paper compares Tensor Boundary Conditions (TBCs), which were introduced to model multilayered dielectric structures, with Generalized Sheet Transition Conditions (GSTCs), which have been recently used to model metasurfaces. It shows that TBCs, with their 3 scalar parameters, are equivalent to the direct-isotropic -- cross-antiisotropic, reciprocal and nongyrotropic subset of GSTCs, whose 16 tangential (particular case of zero normal polarizations) or 36 general susceptibility parameters can handle the most general bianisotropic sheet structures. It further shows that extending that TBCs scalar parameters to tensors and allowing a doubly-occurring parameter to take different values leads to a TBCs formulation that is equivalent to the tangential GSTCs, but without reflecting the polarization physics of sheet media, such as metasurfaces and two-dimensional material allotropes.