{'fraction_non_alphanumeric': 0.01778496362166532, 'fraction_numerical': 0.007679870654810024, 'mean_word_length': 5.0513447432762835, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Investigation of various behaviors of near- and far-field diffractions from multiplicatively separable structures in the x and y directions, and a detailed study of the near-field diffraction patterns of 2D multiplicatively separable periodic structures using the contrast variation method

In this paper, first a detailed investigation of the various behaviors of the near- and far-field diffractions from multiplicatively separable (MS) structures in the x and y directions is presented. It is shown that in near-field propagation, the diffraction pattern of a 2D MS structure is same as the product of the corresponding near-field diffractions of the 1D individual components of the structure. For the far-field diffraction, although the resulting diffraction pattern is not equal to the product of the individual 1D structures’ diffraction patterns, we show that it is still a 2D MS pattern. Second, a detailed theoretical investigation of the contrast enhancement effect for the multiplication of two 1D orthogonal intensity patterns (not necessarily periodic) is presented. By merging the above-mentioned facts, we deduced that in near-field diffraction, the contrast of the diffraction pattern of a 2D MS structure is always larger than the contrast of each of the diffraction patterns of the corresponding individual 1D structures. In the second part of this paper, we implement the intensity contrast as a quantity to describe self-images of the 2D MS periodic structures. For the first time, two very important results are obtained based on the contrast enhancement effect. We show that the depth of focus of the self-images increases for the 2D periodic structures in comparing to their corresponding 1D structures. We also predict the 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 the prediction of the 1D or 2D forms of the diffraction pattern and the direction of the 1D pattern strips at given propagation distances from the 2D structure by introducing another intensity-contrast-based parameter. Furthermore, we show that the diffraction pattern of a 2D MS periodic structure depends strongly on the square of the ratio of the 1D structure periods in the x and y directions. These theoretical achievements are verified by some experimental works.