Vector formalism for circularly symmetric laser beams

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Describing the propagation of light beams, particularly circularly symmetric ones, can be complex.
• Existing methods may lack simplicity or direct applicability for power optimization.

Purpose of the Study:

• To introduce a novel finite dimensional vector formalism for analyzing beam propagation.
• To develop a practical method for calculating beam amplitude and optimizing power transfer.

Main Methods:

• Development of a finite dimensional vector formalism.
• Explicit derivation of a propagation matrix operator.
• Analysis of power transport to circular and annular targets.

Main Results:

• The formalism effectively describes the propagation of circularly symmetric beams.
• A propagation matrix operator is provided to determine beam amplitude at any plane.
• A simple solution is found for maximizing power delivery to a target by optimizing beam shape.

Conclusions:

• The presented vector formalism offers a simple and effective approach to beam propagation analysis.
• The derived matrix operator facilitates amplitude prediction and power optimization.
• This work provides a powerful tool for optical system design and beam shaping applications.