# Floquet-Mode Solutions of Space-Time Modulated Huygens' Metasurfaces

## TL;DR

This paper introduces a Floquet mode analysis method for modeling space-time modulated Huygens' metasurfaces, enabling the calculation of scattered harmonic components through a system of linear equations.

## Contribution

It presents a rigorous, versatile approach using GSTCs and Floquet modes to analyze the steady-state response of modulated metasurfaces with arbitrary parameters.

## Key findings

- Method validated with FDTD simulations
- Accurately predicts harmonic generation
- Applicable to various modulation depths and frequencies

## Abstract

A rigorous Floquet mode 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, $\chi_\text{ee}$ and $\chi_\text{mm}$, respectively, and its resonant frequencies are periodically modulated in both space and time. The unknown scattered fields are then expressed in terms of Floquet modes, which when used with the GSTCs, lead to a system of field matrix equations. The resulting set of linear equations are then solved numerically to determine the total scattered fields. Using a finite-difference time domain (FDTD) solver, the proposed method is validated and confirmed for several examples of modulation depths ($\Delta_p$) and frequencies ($\omega_p$). Finally, the computed steady-state scattered fields are Fourier propagated analytically, for visualization of refracted harmonics. The proposed method is simple and versatile and able to determine the steady-state response of a space-time modulated Huygen's metasurface, for arbitrary modulation frequencies and depths.