Formulation of the moiré patterns formed by superimposing of gratings consisting topological defects: moiré technique as a tool in singular optics detections

Abstract

The use of moiré pattern of superimposition of linear forked gratings (LFGs) and Fresnel zone plates (ZPs) has already been reported for study of different physical effects. In spite of a considerable number of applications, there is no comprehensive formulation for this kind of moiré pattern. In this work, we introduce a new family of ZPs containing topological defects that we named defected ZP (DZP) and we present a very simple, uniform, and comprehensive formulation for the moiré pattern of superimposition of two LFGs, two DZPs, and superimposition of an LFG on a DZP, using the reciprocal vector approach. For the case of the two LFGs superimposition, we show that the resulting moiré pattern has a starlike shape or is a large-scale LFG pattern. In the case in which two DZPs are superimposed, we show that the resulting moiré pattern has three general forms: large-scale DZP pattern, starlike pattern, and large-scale LFG pattern. In the superimposition of an LFG on a DZP, in special conditions a new spiral ZP having a topological defect is produced in which its defect number related to the superimposed gratings structures. The presented formulation has potential applications in singular optics measurements.