Entropic uncertainty relations for electromagnetic beams

TL;DR

This paper derives entropic uncertainty relations for electromagnetic beams using symplectic tomograms of Hermite-Gauss modes, linking optical measurements to quantum-like uncertainty principles.

Contribution

It introduces a method to determine electromagnetic field properties via symplectic tomograms and establishes entropic uncertainty relations specific to Hermite-Gauss beams.

Findings

Derived explicit symplectic tomograms for Hermite-Gauss beams.

Established entropic uncertainty relations for electromagnetic modes.

Numerical examples illustrating the uncertainty bounds.

Abstract

The symplectic tomograms of 2D Hermite--Gauss beams are found and expressed in terms of the Hermite polynomials squared. It is shown that measurements of optical-field intensities may be used to determine the tomograms of electromagnetic-radiation modes. Furthermore, entropic uncertainty relations associated with these tomograms are found and applied to establish the compatibility conditions of the the field profile properties with Hermite--Gauss beam description. Numerical evaluations for some Hermite--Gauss modes illustrating the corresponding entropic uncertainty relations are finally given.