Space-Time Cross-Mapping and Application to Wave Scattering

Abstract: Causality creates an asymmetry between space and time, even though the wave equation treats them on equal footing. In this work, we leverage this asymmetry to construct a cross-mapping between space and time. This cross-mapping is applied to simplify scattering in space-varying media, by eliminating the infinite reflections between interfaces. The method is shown to transform the implicit transfer matrix method into an explicit method for the analysis of electromagnetic field scattering by a stratified medium.