This work reports on light scattering by a homogeneous dielectric sphere with a periodically time-varying radius. The off-shell inelastic scattering T matrix, which describes the dynamically changing particle, is evaluated using the Floquet method, and some remarkable phenomena, emerging in the strong- and weak-coupling regimes, are discussed. In particular, the limits of validity of the approximate quasistatic solution are established through comparison with the results of fully dynamic calculations, and the scattering in the strong-coupling regime is analyzed in terms of the general behavior of parametrically driven oscillators. Additionally, the influence of damping of the sphere vibrations on the optical spectra is also investigated.

A time Floquet transfer-matrix method for the description of acoustic wave propagation through dynamic stratified structures, modulated by another, low-frequency, pump acoustic wave, is reported. The method is applied to a specific example of a GaAs/AlAs periodic superlattice, subject to a spatiotemporal modulation induced by an evanescent pump wave with frequency in the lowest acoustic band gap of the structure. By means of systematic numerical calculations, we provide compelling evidence for the occurrence of significant nonreciprocal transmission of an acoustic signal with frequency in a high-order acoustic band gap, through inelastic multiple-scattering processes. Our results indicate a promising route to design nonreciprocal acoustic devices.