Quantifiable example of complementarity relation between optical orbital angular momentum and angular position

TL;DR

This paper demonstrates a quantifiable complementarity relation between optical orbital angular momentum and angular position using a specially constructed light beam with phase singularity, revealing how their properties are interconnected.

Contribution

It provides a novel, quantifiable example of the complementarity relation between optical OAM and angular position through experimental analysis of phase dislocation and OAM deviation.

Findings

The deformation of the light beam profile relates to its OAM noneigenvalue.

A proportional relation exists between OAM deviation and phase dislocation.

The study offers a measurable example of the complementarity between OAM and angular position.

Abstract

A light beam with phase singularity (PS) characterized with azimuthally symmetric angular positions (APs) can be constructed by the rotationally symmetric superposition of n (n is N) fractional vortex light beams with identical charges. The profile of this light beam deforms after propagation owing to its orbital angular momentum (OAM) noneigenvalue, and the deformation degree can be evaluated by the degree of phase dislocation associated with the PS. The expectation value of the mean deviation of its OAM from its characteristic charge value and the variation of the degree of phase dislocation obey a proportional relation. This light beam offers a quantifiable example of a complementarity relation between the observers of optical OAM and AP, which are the OAM noneigenvalue and intensity AP variation, respectively.