Open AccessThree-dimensional localized Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets in free space
Author(s) -
Fu Deng,
Dongmei Deng
Publication year - 2016
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.24.005478
Subject(s) - hermite polynomials , physics , wave packet , gaussian , airy function , superposition principle , mathematical analysis , optics , classical mechanics , quantum mechanics , mathematics
We have investigated the 3D Airy-Hermite-Gaussian and Airy-Helical-Hermite-Gaussian wave packets by solving the (3+1)D free-space Schrödinger equation in Cartesian coordinates analytically. The complex amplitudes of these wave packets are described by the product of the superposition of two Airy functions, the Hermite-Gaussian functions and the helical Hermite-Gaussian functions. The different 3D spatiotemporal profiles, the photoelastics and vortex rings can be obtained by selecting different values of the following parameters: the mode number, the decay factor and the propagation distance.