Near-field diffraction of a hexagonal array at fractional Talbot planes

Abstract

Hexagonal array structure is not only a nature-preferred basic structure widely exists in nature, but also is an important pattern that has been widely used in optoelectronics field. Talbot effect and fractional Talbot effect is one of the most basic optical phenomena that has received extensive investigations both because it is a fundamental Fresnel diffraction effect and also because of its wide applications. As one of the most application of the Talbot effect, Talbot array illuminators have been extensively studied since Lohmann and Thomas put forward for the first time. One-dimensional and two-dimensional orthogonal Talbot array illuminators are in-depth investigated and can be designed and manufactured based on the theory of the fractional Talbot effect. A hexagonal array is a periodic nonorthogonal array that cannot be represented by orthogonal array. Thus, it is difficult to analyze the diffraction field of hexagonal arrays at fractional Talbot planes. Previous studies have shown that light distribution at Talbot distance can be considered multiple copies of the original aperture by shifting and superimposing. In this paper, qualitative analysis of a hexagonal array is carried out at fractional Talbot planes based on the fractional Talbot theory. Theory and experiment analysis show that diffraction patterns at 1/6 and 1/3 Talbot distance are consist of nine equally spaced copies of the original aperture, and each copy is shifted by 2a and a (a represent the side length of the hexagon) from another copy, respectively. Experimental results are in good agreement with the theoretical analysis.