Alternative formulation for invariant optical fields: Mathieu beams
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- 15 October 2000
- journal article
- Published by Optica Publishing Group in Optics Letters
- Vol. 25 (20) , 1493-1495
- https://doi.org/10.1364/ol.25.001493
Abstract
Based on the separability of the Helmholtz equation into elliptical cylindrical coordinates, we present another class of invariant optical fields that may have a highly localized distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. These fields are described by the radial and angular Mathieu functions. We identify the corresponding function in the McCutchen sphere that produces this kind of beam and propose an experimental setup for the realization of an invariant optical field.Keywords
This publication has 9 references indexed in Scilit:
- Self-reconstruction effect in free propagation of wavefieldOptics Communications, 2000
- Generalized propagation-invariant wave fieldsJournal of the Optical Society of America A, 1998
- Propagation invariance and self-imaging in variable-coherence opticsJournal of the Optical Society of America A, 1991
- Realization of general nondiffracting beams with computer-generated hologramsJournal of the Optical Society of America A, 1989
- Nondiffracting optical fields: some remarks on their analysis and synthesisJournal of the Optical Society of America A, 1989
- Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beamsJournal of the Optical Society of America B, 1988
- Diffraction-free beamsPhysical Review Letters, 1987
- Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation ψt t−Δ2ψ=0Journal of Mathematical Physics, 1976
- Generalized Aperture and the Three-Dimensional Diffraction ImageJournal of the Optical Society of America, 1964