X-ray diffraction analysis of matter taking into account the second harmonic in the scattering of powerful ultrashort pulses of an electromagnetic field

It is well known that the scattering of ultrashort pulses (USPs) of an electromagnetic field in the X-ray frequency range can be used in diffraction analysis. When such USPs are scattered by various polyatomic objects, a diffraction pattern appears from which the structure of the object can be determined. Today, there is a technical possibility of creating powerful USP sources and the analysis of the scattering spectra of such pulses is a high-precision instrument for studying the structure of matter. As a rule, such scattering occurs at a frequency close to the carrier frequency of the incident USP. In this work, it is shown that for high-power USPs, where the magnetic component of USPs cannot be neglected, scattering at the second harmonic appears. The scattering of USPs by the second harmonic has a characteristic diffraction pattern which can be used to judge the structure of the scattering object; combining the scattering spectra at the first and second harmonics therefore greatly enhances the diffraction analysis of matter. Scattering spectra at the first and second harmonics are shown for various polyatomic objects: examples considered are 2D and 3D materials such as graphene, carbon nanotubes, and hybrid structures consisting of nanotubes. The theory developed in this work can be applied to various multivolume objects and is quite simple for X-ray structural analysis, because it is based on analytical expressions.