Vector Helmholtz–Gauss and vector Laplace–Gauss beams
- 15 August 2005
- journal article
- Published by Optica Publishing Group in Optics Letters
- Vol. 30 (16), 2155-2157
- https://doi.org/10.1364/ol.30.002155
Abstract
We demonstrate the existence of vector Helmholtz–Gauss (vHzG) and vector Laplace–Gauss beams that constitute two general families of localized vector beam solutions of the Maxwell equations in the paraxial approximation. The electromagnetic components are determined starting from the scalar solutions of the two-dimensional Helmholtz and Laplace equations, respectively. Special cases of the vHzG beams are TE and TM Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel–Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz–Gauss beams. The general expression of the vHzG beams can be used straightforwardly to obtain vector Mathieu–Gauss and vector parabolic-Gauss beams, which to our knowledge have not yet been reported.Keywords
This publication has 10 references indexed in Scilit:
- Helmholtz–Gauss wavesJournal of the Optical Society of America A, 2005
- New structures in paraxial Gaussian beamsOptics and Spectroscopy, 2004
- Ince–Gaussian beamsOptics Letters, 2004
- Parabolic nondiffracting optical wave fieldsOptics Letters, 2004
- Alternative formulation for invariant optical fields: Mathieu beamsOptics Letters, 2000
- Vector-beam solutions of Maxwell’s wave equationOptics Letters, 1996
- Non-diffractive Vector Bessel BeamsJournal of Modern Optics, 1995
- Bessel-Gauss beamsOptics Communications, 1987
- TM and TE electromagnetic beams in free spaceOptics Letters, 1981
- From Maxwell to paraxial wave opticsPhysical Review A, 1975