  A fully dynamic theoretical approach to layered optomagnonic structures,
based on a time Floquet scattering-matrix method, is developed. Its
applicability is demonstrated on a simple design of a dual photonic-magnonic
cavity, formed by sandwiching a magnetic garnet thin film between two
dielectric Bragg mirrors, subject to continuous excitation of a perpendicular
standing spin wave. Some remarkable phenomena, including nonlinear
photon-magnon interaction effects and enhanced inelastic light scattering in
the strong-coupling regime, fulfilling a triple-resonance condition, are
analyzed and the limitations of the quasistatic adiabatic approximation are
established.
