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A rigorous semianalytical Floquet analysis is proposed for modeling space&#x2013;time-modulated metasurface and determining the scattered fields in terms of their harmonic components. The proposed method is based on generalized sheet transition conditions (GSTCs) treating a metasurface as a spatial discontinuity with zero thickness. The metasurface is described in terms of Lorentzian electric and magnetic surface susceptibilities, both tangential and normal to the surface, with parameters (e.g., resonant frequency) that are periodically modulated in both space and time. The unknown scattered fields are expressed in terms of Floquet harmonics, for which the amplitudes can be found by numerically solving a set of linear equations, leading to the total scattered fields. Using existing computational techniques and a commercial full-wave solver, the method is validated using several examples of pure-space and pure-time modulation with different modulation strengths and pumping frequencies. Finally, two cases of space&#x2013;time modulation (standing wave perturbation and a traveling-wave perturbation) are presented to demonstrate the breaking of Lorentz reciprocity. The proposed method is simple and versatile and able to determine the steady-state response of a space&#x2013;time-modulated metasurface that is excited with an oblique plane wave or a general incident field such as a Gaussian beam.

Floquet Analysis of Space-Time Modulated Metasurfaces With Lorentz Dispersion