Zero Thickness Surface Susceptibilities and Extended GSTCs-Part I: Spatially Dispersive Metasurfaces

• Published in: IEEE transactions on antennas and propagation Vol. 71; no. 7; pp. 5909 - 5919
• Main Authors: Rahmeier, Joao Guilherme Nizer, Smy, Tom J., Dugan, Jordan, Gupta, Shulabh
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: All-dielectric metasurfaces; Boundary conditions; Dispersion; Electric dipoles; electromagnetic metasurfaces; electromagnetic propagation; Electromagnetics; Frequency response; Frequency-domain analysis; generalized sheet transition conditions (GSTCs); Lorentz oscillator model; Magnetic domains; Magnetic susceptibility; Metasurfaces; Polynomials; Sheet modelling; spatial dispersion; surface susceptibility tensors; Surface waves; Thickness; Unit cell
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2022.3164169

A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero-thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, <inline-formula> <tex-math notation="LaTeX">\boldsymbol {k_{||}} </tex-math></inline-formula> with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the standard generalized sheet transition conditions (GSTCs) accounting for spatial dispersion. Using two simple examples of a short electric dipole and an all-dielectric cylindrical puck unit cells, which exhibit purely tangential surface susceptibilities and reciprocal/symmetric transmission and reflection characteristics, the proposed concept is numerically confirmed in 2-D. A Lorentzian representation with angle-dependent parameters is further proposed and found to accurately model the complex temporal-spatial frequency response via their electric and magnetic susceptibilities of two unit cell examples-a metallic dipole and a dielectric puck resonator. For both the cases, the appropriate spatial boundary conditions are derived.