Computer simulation of images of photonic crystals for hard X rays in a transmission scheme. Near field

We have developed a method of calculation of transmission of hard x-ray radiation through a perfect and well oriented photonic crystal consisting of closely packed spheres of matter. The method is based on using an approximate solution of paraxial equation for small distances. The recurrent formula is obtained for a transmission of radiation on one period of crystal. A computer program is elaborated for a simulation of images of photonic crystals in a near field, particularly, just behind the crystal. The calculation is performed for silica spheres of 500 nm diameter. It is shown that the standard phase contrast technique is not valid for these objects, because a strong change of intensity takes place inside the volume of crystal due to a scattering of radiation by separate spheres.