Temporal analog of Bragg gratings

Recently, scalar coupled-wave theory has been employed to analyze a medium with periodic time-varying permittivity, providing simple expressions and, consequently, straightforward insights into the parametric amplification mechanism. Here, we combine such an approach with the Möbius transformation method to investigate the dispersion and optical response of a finite "time-slab" of the aforementioned medium. We demonstrate the temporal analog of a Bragg grating, discuss the differences with its spatial counterpart, and examine nontrivial scenarios of the permittivity's time-modulation, such as chirping and apodization. Furthermore, we propose a highly selective and, moreover, single-spatial-interface optical sensor, based on phase delineation.