Two-dimensional Talbot array illuminators with single-step phase grating

Abstract

The purpose of the paper is to pursue solutions to the two-dimensional (2D) Talbot array illuminators (AIL’s). In order to pave the way for the 2D AIL’s, we reshape the formulation for the one-dimensional AIL’s so that it can be referred to for the 2D AIL’s. It is found that there are eight types of 2D single-step phase grating, which lead to eight types of 2D AIL, and they form four conjugate pairs, each of which satisfies the conjugate requirement of diffraction. In practice, we need to consider only one AIL of each conjugate pair, because the given AIL automatically involves the other, owing to the specific structure of the original grating. Moreover, each AIL represents a series of 2D AIL’s, because we are free to assign the structure ratios of the original phase grating. However, the complexity of the 2D AIL offers more design flexibility. We show that some of the data that are simply worthless in the 1D case turn out to be useful in the 2D case. We do not claim to have exhausted the case of 2D AIL’s, as we have confined ourselves only to the case in which the 2D AIL’s have the same periodic structures as those of the original single-step phase gratings.