Rigorous space-time coupled-wave analysis for patterned surfaces with temporal permittivity modulation [Invited]

Material patterns with temporal modulation of permittivity provide an unprecedented platform for active light manipulation and multifunctional devices. The ongoing discovery of new classes of tunable optical materials combined with various multiphysics paradigms demands an appropriate computational tool to characterize and design the wave manipulation patterns with the additional degree of freedom (time). Here we present, for the first time, a fast and accurate numerical technique to compute light propagation through patterned layers with spatial and temporal modulation of permittivity by extending the well-established rigorous coupled-wave analysis framework. We expand the electric and magnetic field components of an arbitrarily shaped space-time unit cell into a basis of spatio-temporal harmonics and compute their modal field profiles as a set of eigenmodes of the unit cell. The relation between the wave amplitudes of the incident, reflected, and transmitted spatio-temporal harmonics are then computed by enforcing the boundary conditions at each interface of the pattern. The validity of the proposed method is rigorously verified against the results of a time-variant finite-difference time-domain technique. The applicability of the method to study dielectric and plasmonic time-modulated metasurfaces is exemplified by considering two metasurfaces with spatially-variant phase and frequency of temporal modulation, based on electro-optical modulation of materials such as silicon and graphene. Utilizing the developed technique, we demonstrate some recently reported phenomena associated with time-modulated metasurfaces, such as anomalous steering of higher-order frequency harmonics, and dynamic optical beam generation. Even though we restrict ourselves to one-dimensional patterns for simplicity, the developed method can be flexibly employed for the design, characterization and optimization of two-dimensional spatio-temporal modulation patterns of arbitrary composition and shape.