Floquet–Mie Theory for Time-Varying Dispersive Spheres

Abstract

Exploring the interaction of light with time-varying media is an intellectual challenge that, in addition to fundamental aspects, provides a pathway to multiple promising applications. Time modulation constitutes here a fundamental handle to control light on entirely different grounds. That holds particularly for complex systems simultaneously structured in space and time. However, a realistic description of time-varying materials requires considering their material dispersion. The combination thereof has barely been considered but is crucial since dispersion accompanies materials suitable for dynamic modulation. As a canonical scattering problem from which many general insights can be obtained, a self-consistent analytical theory of light scattering by a sphere made from a time-varying material exemplarily assumed to have a Lorentzian dispersion is developed and applied. The eigensolutions of Maxwell's equations in the bulk are discussed and a dedicated Mie theory is presented. The proposed theory is verified with full-wave simulations. Peculiar effects are disclosed, such as energy transfer from the time-modulation subsystem to the electromagnetic field, amplifying carefully structured incident fields. Since many phenomena can be studied on analytical grounds with the proposed formalism, it represents an indispensable tool that enables exploration of electromagnetic phenomena in time-varying and spatially structured finite objects of other geometries.