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

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.

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• Creative Telescoping for Holonomic Functions
• Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields
• Fundamental Laser Modes in Paraxial Optics: From Computer Algebra and Simulations to Experimental Observation
• Solution of the Cauchy Problem for a Time-Dependent Schoedinger Equation
• Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II

Cited by in corpus (2)

• Fundamental Laser Modes in Paraxial Optics: From Computer Algebra and Simulations to Experimental Observation
• Constructing various paraxial beams out of regular and modified Bessel-Gaussian modes