Time-dependent Bragg diffraction bymultilayer gratings

TL;DR

This paper investigates the time-dependent Bragg diffraction in multilayer gratings, extending coupled-wave and Takagi-Taupin theories to analyze transient responses and time delays in reflection and transmission geometries.

Contribution

It generalizes existing theories to multilayer gratings and calculates the indicial response, revealing how transient times depend on extinction length and grating thickness.

Findings

Time delay depends on extinction length in reflection geometry.

Transient response duration is influenced by grating thickness in transmission.

Extended theoretical framework for multilayer grating diffraction.

Abstract

The time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional photonic crystal [Andr{\'e} J-M and Jonnard P, J. Opt. 17, 085609 (2015)] and also by extending the Takagi-Taupin approach of the dynamical theory of diffraction. The indicial response is calculated. It presents a time-delay with a transient time that is a function of the extinction length for reflection geometry and of the extinction length combined with the thickness of the grating for transmission geometry.