  A rigorous semi-analytical Floquet 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, $\chi_\text{e}$ and
$\chi_\text{m}$, respectively, 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, 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
spacetime 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-time modulated Huygen's metasurface that is
excited with an oblique plane wave, or a general incident field such as a
Gaussian beam.
