Revival and Expansion of the Theory of Coherent Lattices

TL;DR

This paper introduces a novel theoretical framework combining prime number factorization and moiré theory to design and compute complex structured coherent wave interference patterns, including high-order superlattices with various symmetries.

Contribution

It presents a new method for designing structured coherent lattices using prime factorization and moiré theory, enabling the creation of complex interference patterns and superlattices.

Findings

Validated in multibeam interference experiments

Able to design patterns with three-, four-, and fivefold symmetry

Facilitates computation of high-order superlattices

Abstract

An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a robust way to design structured patterns with variable spacing of intensity maxima. In addition, the proposed theoretical framework facilitates an elegant computation of previously unexplored high-order superlattices both for the periodic and quasiperiodic case. A number of beam configurations highlighting prime examples of patterns for lattices with three-, four-, and fivefold symmetry are verified in a multibeam interference experiment.