  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.
