Maxwell-Bloch modeling of an x-ray pulse amplification in a 1D photonic crystal

TL;DR

This paper develops a Maxwell-Bloch formalism using FDTD to simulate x-ray emission and amplification in multilayer photonic crystals, accounting for spontaneous emission noise and layer resonances, with applications to XFEL-induced population inversion.

Contribution

It introduces a novel numerical model combining Maxwell-Bloch equations with FDTD for x-ray dynamics in multilayer materials, including noise and layer-specific effects.

Findings

Simulated x-ray amplification in multilayer photonic crystals.

Demonstrated effects of Bragg diffraction on x-ray fluorescence.

Potential for studying non-linear x-ray interactions with matter.

Abstract

We present an implementation of the Maxwell-Bloch (MB) formalism for the study of x-ray emission dynamics from periodic multilayer materials whether they are artificial or natural. The treatment is based on a direct Finite-Difference-Time-Domain (FDTD) solution of Maxwell equations combined with Bloch equations incorporating a random spontaneous emission noise. Besides periodicity of the material, the treatment distinguishes between two kinds of layers, those being active (or resonant) and those being off-resonance. The numerical model is applied to the problem of $K\alpha$ emission in multilayer materials where the population inversion could be created by fast inner-shell photoionization by an x-ray free-electron-laser (XFEL). Specificities of the resulting amplified fluorescence in conditions of Bragg diffraction is illustrated by numerical simulations. The corresponding pulses could be used for specific investigations of non-linear interaction of x-rays with matter.