Optics and Photonics Society of Iran

In the passing of a plane wave through a spatial periodic structure that we call it transmission grating, the intensity pattern at distinct propagation lengths can be reproduced as it was just after the grating. This effect is known as the Talbot effect or self-imaging phenomenon. At half-way between two successive Talbot distances again self-image of the initial amplitude pattern is produced but with a lateral spatial shift. This kind of image so called as half-Talbot image and its location called as half-Talbot distance.  In addition, in half-way between a Talbot plane and the nearest half-Talbot plane we have another spatially periodic intensity pattern in which its period is equal to the half of the grating period. This kind of patterns is known as quarter-Talbot image or sub-image of the grating. Sometimes, this phenomenon is named as the spatial second harmonic generation. In this work, we will investigate by theoretical details the spatial second harmonic generation in the near filed diffraction from pure amplitude gratings at their corresponding quarter-Talbot distances and the maps of the amplitude and phase of the diffracted light beam are determined for different transmission gratings