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Beam propagation factor based on the Rényi entropy.

Pablo Vaveliuk¹, Marcone Lopes da Silva

¹Faculdade de Tecnologia, Servicio Nacional de Aprendizagem Industrial SENAI-Cimarec, Avenida Orlando Gomes 1845, Salvador, Bahia, Brazil. pablov@fisica.ufpb.br

|September 17, 2008

Summary

This study introduces a general Rényi beam width measure for arbitrary beam profiles, improving upon previous 1D analyses. This new measure effectively describes beam propagation through paraxial systems, offering advantages over the M(2) factor.

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Area of Science:

Optics and Photonics
Laser Physics
Quantum Optics

Background:

Previous one-dimensional Rényi entropy beam width measures were limited to rectangular symmetry.
Characterizing beam spreading and propagation is crucial in laser systems and optical engineering.

Purpose of the Study:

To derive a generalized Rényi beam width measure applicable to beams with arbitrary symmetry.
To demonstrate the utility of this measure in describing beam propagation through ABCD paraxial systems.
To introduce and discuss the Rényi beam propagation factor.

Main Methods:

Derivation of a generalized Rényi beam width measure based on Rényi entropy.
Analysis of the measure's dependence on the propagation coordinate.
Application to arbitrary ABCD paraxial optical systems.

Main Results:

A general Rényi beam width measure for arbitrary beam profiles was derived.
The square of the measure exhibits quadratic dependence on the propagation coordinate.
The Rényi beam propagation factor was introduced and analyzed.

Conclusions:

The generalized Rényi beam width measure is effective for arbitrary beam symmetries.
This measure provides a robust way to analyze beam propagation in ABCD systems.
The Rényi beam propagation factor offers advantages over the M(2) factor in certain beam spreading scenarios.