Method of field expansions for multiply layered media with quasiperiodic interfaces

Periodic structures are foundational in applied optics; however, more permissive forms of periodicity are becoming increasingly important in electromagnetics. Due to both their central importance and the high cost of their production at the nanoscale, numerical approximation of scattering by such structures is very important. In this paper, the author derives, implements, and validates the generalization of the method of field expansions (FEs), a classical high-order perturbation of surfaces (HOPS) algorithm, to numerically simulate multiply layered media scattering in the presence of quasiperiodic interfaces. This interfacial HOPS approach is not only substantially faster for layered media configurations than its volumetric counterparts (e.g., finite difference or finite element methods), but also useful for structures that the classical FE method would find severely challenging (for interfaces with widely disparate periods) or impossible (for profiles with incommensurate periods), due to its enhanced capability of simulating quasiperiodic interfaces. With an implementation of this algorithm, the author investigates the (nonlinear) dispersion relation of surface plasmon resonances on several increasingly difficult, alternately vacuum-silver, multiply layered structures with quasiperiodic interfaces.