Discrete-Fourier-Transform-Based Framework for Analysis and Synthesis of Cylindrical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>Omega</mml:mi></mml:math>-Bianisotropic Metasurfaces
Gengyu Xu, George V. Eleftheriades, Sean V. Hum
Abstract
This paper presents a framework for analyzing and designing cylindrical $\mathrm{omega}$-bianisotropic metasurfaces, inspired by mode matching and digital signal-processing techniques. Using the discrete Fourier transform, we decompose the electromagnetic field distributions into orthogonal cylindrical modes and convert the azimuthally varying metasurface constituent parameters into their respective spectra. Then, by invoking appropriate boundary conditions, we set up systems of algebraic equations, which can be rearranged to either predict the scattered fields of prespecified metasurfaces, or to synthesize metasurfaces, which support arbitrarily stipulated field transformations. The proposed framework facilitates the efficient evaluation of field distributions that satisfy local power conservation, which is one of the key difficulties involved with the design of passive and lossless scalar metasurfaces. It represents a promising solution to circumvent the need for active components, controlled power dissipation, or tensorial surface polarizabilities in many state-of-the-art conformal metasurface-based devices. To demonstrate the robustness and the versatility of the proposed technique, we design several devices intended for different applications and numerically verify them using finite-element simulations.