  Superconductors exhibit a nonlinear interaction with an applied light, which
can resonantly excite the collective amplitude (Higgs) mode. Here we study
light-induced dynamics of layered superconductors, where each layer is coupled
to adjacent layers via the Josephson coupling and the first few layers near the
surface are driven by an in-plane-polarized light. We study the system under
the assumption that the interlayer Coulomb interactions are sufficiently
screened out and that the phase-difference mode becomes available in the
low-energy regime. We find that interlayer transport is induced via excitations
of the collective amplitude and phase-difference modes, even when the applied
electric field is parallel to the planes. We provide analytic calculations as
well as numerical simulations of the real-time dynamics, and investigate the
influence on the light-induced interlayer Josephson current and intralayer
third-harmonic generation.
