Fundamental Laser Modes in Paraxial Optics: From Computer Algebra and Simulations to Experimental Observation

TL;DR

This paper explores advanced laser modes in paraxial optics, combining computer algebra, simulations, and experimental observations to analyze propagation-invariant solutions and novel focusing effects in weakly varying media.

Contribution

It introduces new multi-parameter laser solutions, demonstrates computer algebra verification, and explores experimental implications of exotic propagation-invariant modes.

Findings

New laser beam solutions with exotic properties

Computer algebra methods for deriving complex formulas

Potential for experimental observation of novel modes

Abstract

We study multi-parameter solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation which include oscillating laser beams in a parabolic waveguide, spiral light beams, and other important families of propagation-invariant laser modes in weakly varying media. A "smart" lens design and a similar effect of superfocusing of particle beams in a thin monocrystal film are also discussed. In the supplementary electronic material, we provide a computer algebra verification of the results presented here, and of some related mathematical tools that were stated without proofs in the literature. We also demonstrate how computer algebra can be used to derive some of the presented formulas automatically, which is highly desirable as the corresponding hand calculations are very tedious. In numerical simulations, some of the new solutions reveal quite exotic properties which deserve further investigation including an experimental observation.