TY - JOUR

T1 - Fundamental laser modes in paraxial optics

T2 - from computer algebra and simulations to experimental observation

AU - Koutschan, Christoph

AU - Suazo, Erwin

AU - Suslov, Sergei

N1 - Funding Information:
This research was partially carried out during our participation in the Summer School on “Combinatorics, Geometry and Physics” at the Erwin Schrödinger International Institute for Mathematical Physics (ESI), University of Vienna, in June 2014. We wish to express our gratitude to Christian Krattenthaler for his hospitality. The first-named author was supported by the Austrian Science Fund (FWF): W1214, the second-named author by the Simons Foundation Grant #316295 and by the National Science Foundation Grant DMS-1440664, and the third-named author by the AFOSR Grant FA9550-11-1-0220. We are grateful to Eugeny G. Abramochkin, Sergey I. Kryuchkov, Vladimir I. Man'ko, and Peter Paule for valuable comments and to Miguel A. Bandres for kindly pointing out the reference [] to our attention. Suggestions from the referees are much appreciated. Last but not least, we would like to thank Aleksei P. Kiselev for communicating the interesting articles [–].
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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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U2 - 10.1007/s00340-015-6231-9

DO - 10.1007/s00340-015-6231-9

M3 - Article

AN - SCOPUS:84948379680

VL - 121

SP - 315

EP - 336

JO - Applied Physics B: Lasers and Optics

JF - Applied Physics B: Lasers and Optics

SN - 0946-2171

IS - 3

ER -