Results of computer simulations of the transmission of an X-ray beam through a two-dimensional photonic crystal as well as the propagation of an X-ray beam in free space behind the photonic crystal are reported. The photonic crystal consists of a square lattice of silicon cylinders of diameter 0.5 µm. The amount of matter in the path of the X-ray beam rapidly decreases at the sides of the cylinder projections. Therefore the transmission is localized near the boundaries, and appears like a channeling effect. The iterative method of computer simulations is applied. This method is similar to the multi-slice method that is widely used in electron microscopy. It allows a solution to be obtained with acceptable accuracy. A peculiarity in the intensity distribution inside the Talbot periodzTin free space was found when the intensity is approximately equal to the initial value at a distance 0.46zT, and it is shifted by half a period at distance 0.5zT. The reason for this effect is the existence of a periodic phase of the wavefunction of radiation inside the intensity peaks. Simulations with zero phase do not show this effect. Symmetry rules for the Talbot effect are discussed.
Holographic design of a two-dimensional photonic crystal of square lattice with pincushion columns and large complete band gaps
