A proper generalization of the extended boundary condition method to calculate the transition matrix, T, for electromagnetic scattering from a homogeneous and isotropic body of arbitrary shape, characterized by a periodically time-varying electric permittivity, is presented. The application of the method on a specific example of a spheroidal dielectric particle confirms that time modulation induces strong inelastic scattering, accompanied by energy transfer between the scatterer and the light field, when the difference of the incident wave frequency to a particle optical resonance matches an integer multiple of the modulation frequency. Moreover, it is shown that, for nonspherical scatterers, these effects can be selectively tuned by external means such as the polarization and the propagation direction of the incident light beam. The method is readily implementable in available dynamic multiple-scattering computer codes, and, because of its versatility and computational efficiency, it can offer new opportunities for studying more complex time-varying photonic structures.

An extension of the photonic layer multiple scattering methodology to dynamic spherical scatterers, which exhibit a periodic time-varying response, is presented. The applicability of the method is demonstrated on specific examples of single- and bi-layers of periodically modulated high-refractive-index spherical particles arranged on a square lattice. The results provide compelling evidence for strong and tunable inelastic scattering effects under the triple resonance condition, fulfilled for optical transitions between neighboring high-Q lattice modes of the appropriate symmetry, which originate from multipolar Mie resonances. A consistent interpretation of the underlying mechanisms is provided and potential applications in the design of nonreciprocal devices are discussed.