Ultra-short and ultra-intense X-ray free-electron laser single pulse in one-dimensional photonic crystals

The propagation within a one-dimensional photonic crystal of a single ultra-short and ultra-intense pulse delivered by an X-ray free-electron laser is analysed with the framework of the time-dependent coupled-wave theory in non-linear media. It is shown that the reflection and the transmission of an ultra-short pulse present a transient period conditioned by the extinction length and also the thickness of the structure for transmission. For ultra-intense pulses, non-linear effects are expected: they could give rise to numerous phenomena, bi-stability, self-induced transparency, gap solitons, switching, etc., which have been previously shown in the optical domain.