Karim Achouri

General Metasurface Synthesis Based on Susceptibility Tensors

A general method, based on susceptibility tensors, is proposed for the synthesis of metasurfaces transforming arbitrary incident waves into arbitrary reflected and transmitted waves. The proposed method exhibits two advantages: 1) it is inherently vectorial, and therefore better suited for full vectorial (beyond paraxial) electromagnetic problems; 2) it provides closed-form solutions, and is therefore extremely fast. Incidentally, the method reveals that a metasurface is fundamentally capable to transform up to four independent wave triplets (incident, reflected, and refracted waves). In addition, this paper provides the closed-form expressions relating the synthesized susceptibilities and the scattering parameters simulated within periodic boundary conditions, which allows one to design the scattering particles realizing the desired susceptibilities. The versatility of the method is illustrated by examples of metasurfaces achieving the following transformations: generalized refraction, reciprocal and nonreciprocal polarization rotation, Bessel vortex beam generation, and orbital angular momentum multiplexing.

Metasurface Spatial Processor for Electromagnetic Remote Control

We introduce the concept of metasurface spatial processor, whose response is remotely and coherently controlled by the superposition of an incident wave and a control wave through the metasurface. The conceptual operation of this device is analogous to that of both a transistor and a Mach-Zehnder interferometer, while offering much more diversity in terms of electromagnetic transformations. We demonstrate here two metasurfaces that perform the operations of remotely controlled electromagnetic switching and amplification. However, the proposed concept may be readily extended to many other devices, such as remotely controlled transformers providing generalized refraction, birefringence, orbital angular momentum, pulse dispersion engineering, nonreciprocity, and multiple wave processing.

Nonreciprocal Nongyrotropic Magnetless Metasurface

We introduce a nonreciprocal nongyrotropic magnetless metasurface. In contrast to previous nonreciprocal structures, this metasurface does not require a biasing magnet, and is therefore lightweight and amenable to integrated circuit fabrication. Moreover, it does not induce Faraday rotation, and hence does not alter the polarization of waves, which is a desirable feature in many nonreciprocal devices. The metasurface is designed according to a Surface-Circuit-Surface architecture and leverages the inherent unidirectionality of transistors for breaking time reversal symmetry. Interesting features include transmission gain as well as broad operating bandwidth and angular sector operation. It is finally shown that the metasurface is bianisotropic in nature, with nonreciprocity due to the electric-magnetic coupling parameters, and structurally equivalent to a moving uniaxial metasurface.

Simulation of Metasurfaces in Finite Difference Techniques

We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in finite difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the metasurface as a virtual structure, located between nodal rows of the Yee grid, using an FD version of generalized sheet transition conditions. In contrast to previously reported approaches, the proposed method can handle sheets exhibiting both electric and magnetic discontinuities, and represents therefore a fundamental contribution to computational electromagnetics. It is presented here in the framework of the FD frequency domain method, but also applies to the FD time domain scheme. The theory is supported by five illustrative examples.

Dielectric Resonator Metasurface for Dispersion Engineering

We introduce a practical dielectric metasurface design for microwave frequencies. The metasurface is made of an array of dielectric resonators held together by dielectric connections thus avoiding the need of a mechanical support in the form of a dielectric slab and the spurious multiple reflections that such a slab would generate. The proposed design can be used either for broadband metasurface applications or monochromatic wave transformations. The capabilities of the concept to manipulate the transmission phase and amplitude of the metasurface are supported by the numerical and experimental results. Finally, a half-wave plate and a quarter-wave plate have been realized with the proposed concept.

Metasurface Synthesis for Time-Harmonic Waves: Exact Spectral and Spatial Methods (Invited Paper)

Two exact approaches to synthesize metasurfaces for time-harmonic waves are discussed. The first approach is a spectral approach based on wave momentum conservation. Here, the spectral approach is applied to scalar and paraxial wave transformations. This approach effectively allows the arbitrary translation of the transformation plane parallel to the metasurface. The second approach is a direct-space approach based on the extraction of the susceptibility tensors of the metasurface elements. This approach is applied to vectorial field transformation and can be used for single or multiple transformations. An example of wave transformation by a metasurface is illustrated for each of the two approaches.

Spacetime processing metasurfaces: GSTC synthesis and prospective applications

The paper presents the general concept of spacetime processing metasurfaces, synthesized by generalized sheet transition conditions (GSTCs). It is shown that such metasurfaces can perform multiple simultaneous spatio-temporal processing transformations on incident electromagnetic waves. A time-reversal space-generalized-refraction metasurface and a multi-time-space-differentiating metasurfaces are presented as applications of the general spacetime processing metasurface concept.

Comparison of two synthesis methods for birefringent metasurfaces

Birefringent metasurfaces are two-dimensional structures capable of independently controlling the amplitude, phase, and polarization of orthogonally polarized incident waves. In this work, we propose an in-depth discussion on the mathematical synthesis of such metasurfaces. We compare the two methods, one that is rigorous and based on the exact electromagnetic fields involved in the transformation and one that is based on approximate reflection and transmission coefficients. We next validate the synthesis technique in metasurfaces performing the operations of a half- and quarter-wave plates, polarization beam splitting, and orbital angular momentum multiplexing and present the corresponding microwave experimental demonstrations.

All-pass metasurfaces based on interconnected dielectric resonators as a spatial phaser for real-time analog signal processing

A spatial phaser based on all-pass metasurfaces using Interconnected dielectric resonators is proposed for real-time-analog signal processing (R-ASP). The structure is simple to fabricate and is constructed from a single dielectric layer using standard laser hole drilling processing. Its all-pass transmission response along with its transmission delay characteristics are also demonstrated using rigorous coupled-wave analysis (RCWA).

Susceptibility Derivation and Experimental Demonstration of Refracting Metasurfaces Without Spurious Diffraction

Refraction represents one of the most fundamental operations that may be performed by a metasurface. However, simple phase-gradient metasurface designs suffer from restricted angular deflection due to spurious diffraction orders. It has been recently shown, using a circuit-based approach, that refraction without spurious diffraction, or diffraction-free, can fortunately be achieved by a transverse (or in-plane polarizable) metasurface exhibiting either loss–gain, nonreciprocity, or bianisotropy. Here, we re-derive these conditions using a medium-based—and hence, more insightful—approach based on generalized sheet transition conditions and surface susceptibility tensors, and experimentally demonstrate for the first time, beyond any doubt, two diffraction-free refractive metasurfaces that are essentially lossless, passive, bianisotropic, and reciprocal.