Beam propagation factor based on the Rényi entropy

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.