Polynomials of Gaussians and vortex-Gaussian beams as complete, transversely confined bases
Abstract
A novel type of discrete basis for paraxial beams is proposed, consisting of monomial vortices times polynomials of Gaussians in the radial variable. These bases have the distinctive property that the effective size of their elements is roughly independent of element order, meaning that the optimal scaling for expanding a localized field does not depend significantly on truncation order. This behavior contrasts with that of bases composed of polynomials times Gaussians, such as Hermite-Gauss and Laguerre-Gauss modes, where the scaling changes roughly as the inverse square root of the truncation order.
Keywords
Cite
@article{arxiv.1802.09132,
title = {Polynomials of Gaussians and vortex-Gaussian beams as complete, transversely confined bases},
author = {Rodrigo Gutiérrez-Cuevas and Miguel A. Alonso},
journal= {arXiv preprint arXiv:1802.09132},
year = {2018}
}
Comments
4 pages, 5 figures, \c{opyright} 2017 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited