Probing the reciprocal lattice associated with a triangular slit to determine the orbital angular momentum for a photon

TL;DR

This paper explores how the diffraction patterns of light passing through a triangular slit reveal the orbital angular momentum of photons, using reciprocal lattice concepts to explain finite diffraction patterns and their relation to crystal structures.

Contribution

It introduces a novel analogy between optical diffraction patterns and crystal reciprocal lattices, providing a new method to analyze photon orbital angular momentum with minimal photon sources.

Findings

Diffraction patterns depend on the topological charge of incident light.

Finite diffraction patterns are explained via reciprocal lattice concepts.

The method offers potential insights into crystallography and photon angular momentum.

Abstract

The orbital angular momentum conservation of light reveals different diffraction patterns univocally dependent on the topological charge of the incident light beam when passing through a triangular aperture. It is demonstrated that these patterns, which are accessed by observing the far field measurement of the diffracted light, can also be obtained using few photon sources. In order to explain the observed patterns, we introduce an analogy of this optical phenomenon with the study of diffraction for the characterization of the crystal structure of solids. We demonstrate that the finite pattern can be associated to the reciprocal lattice obtained from the direct lattice generated by the primitive vectors composing any two of the sides of the equilateral triangular slit responsible for the diffraction. Using the relation that exists between the direct and reciprocal lattices, we provide a conclusive explanation of why the diffraction pattern of the main maxima is finite. This can shed a new light on the investigation of crystallographic systems.