Applied Physics B

, Volume 121, Issue 3, pp 315–336 | Cite as

Fundamental laser modes in paraxial optics: from computer algebra and simulations to experimental observation

  • Christoph Koutschan
  • Erwin Suazo
  • Sergei K. Suslov
Article

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.

Mathematics Subject Classification

Primary 35C05 35Q55 Secondary 68W30 81Q05 

Supplementary material

340_2015_6231_MOESM1_ESM.nb (9.9 mb)
Supplementary material 1 (nb 10104 KB)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Christoph Koutschan
    • 1
  • Erwin Suazo
    • 2
  • Sergei K. Suslov
    • 3
  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  2. 2.School of Mathematical and Statistical SciencesUniversity of Texas of Rio Grande ValleyEdinburgUSA
  3. 3.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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