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A rigorous Floquet mode analysis is proposed for a zero thickness space-timemodulated Huygens' metasurface to model and determine the strengths of the newharmonic components of the scattered fields. The proposed method is based onGeneralized Sheet Transition Conditions (GSTCs) treating a metasurface as aspatial discontinuity. The metasurface is described in terms of Lorentzianelectric and magnetic surface susceptibilities, $\chi_\text{ee}$ and$\chi_\text{mm}$, respectively, and its resonant frequencies are periodicallymodulated in both space and time. The unknown scattered fields are thenexpressed in terms of Floquet modes, which when used with the GSTCs, lead to asystem of field matrix equations. The resulting set of linear equations arethen solved numerically to determine the total scattered fields. Using afinite-difference time domain (FDTD) solver, the proposed method is validatedand confirmed for several examples of modulation depths ($\Delta_p$) andfrequencies ($\omega_p$). Finally, the computed steady-state scattered fieldsare Fourier propagated analytically, for visualization of refracted harmonics.The proposed method is simple and versatile and able to determine thesteady-state response of a space-time modulated Huygen's metasurface, forarbitrary modulation frequencies and depths.

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