Maxwell-Bloch modeling of an x-ray-pulse amplification in a one-dimensional photonic crystal

We present an implementation of the Maxwell-Bloch (MB) formalism for study 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 Maxwell equations combined with Bloch incorporating random spontaneous noise. Besides periodicity material, distinguishes between two kinds layers, those being active (or resonant) and off-resonance. numerical model applied to problem $K\alpha$ in where population inversion could be created by fast inner-shell photoionization free-electron-laser (XFEL). Specificities resulting amplified fluorescence conditions Bragg diffraction illustrated simulations. corresponding pulses used specific investigations non-linear interaction x-rays matter.