Investigation of various behaviors of the near and far field diffractions from multiplicatively

In this paper, rstly a detailed investigation on various behaviors of the near and far eld diractions from multiplicatively separable (MS) structures in the x and y directions is presented. It is shown that in the near led propagation, diraction pattern of a 2D MS structure is same as the product of the corresponding near eld diractions of the 1D individual components of the structure. For the far eld diraction, although the resulted diraction pattern is not equal to the product of the individual 1D structures' diraction patterns but we show that it still is a 2D MS pattern. Secondly, a detailed theoretical investigation on the contrast enhancement eect for the multiplication of two 1D orthogonal intensity patterns (not necessarily periodic) is presented. By merging of the mentioned facts, we deduced that in the near eld diraction, the contrast of the diraction pattern of a 2D MS structure is always larger than the contrast of each of the diraction patterns of the corresponding individual 1D structures. At the second part of the paper we implement the intensity contrast as a quantity to describe self-images of the 2D MS periodic structures. For the rst time, two most important results are obtained based on the contrast enhancement eect. We show that the depth of focus of the self-images increases for the 2D periodic structures in comparing to their corresponding 1D structures. Also, we predict existence of additional self-images in addition to the Talbot images located at the least common multiple of each of the individual 1D Talbot distances for the 2D MS periodic structures. In addition, in this work we present a very straightforward manner for prediction of 1D or 2D form of the diraction pattern and the direction of the 1D pattern's strips at given propagation distances from the 2D structure by introducing another intensity contrast based parameter. Furthermore, we show that the diraction pattern of a 2D MS periodic structure depends strongly to the square of ratio of 1D structures' periods in x and y directions.These theoretical achievements are veried by some experimental works.

Fourier Optics, near and far field diffraction, 2D multiplicatively separable structures