New class of nondiffracting beams: Mathieu beams

Julio Cesar Gutierrez-Vega; Ramon M. Rodriguez-Dagnino; Marcelo David Iturbe Castillo; Sabino Chavez-Cerda

doi:10.1117/12.424720

12 April 2001 New class of nondiffracting beams: Mathieu beams

Julio Cesar Gutierrez-Vega, Ramon M. Rodriguez-Dagnino, Marcelo David Iturbe Castillo, Sabino Chavez-Cerda

Proceedings Volume 4271, Optical Pulse and Beam Propagation III; (2001) https://doi.org/10.1117/12.424720
Event: Photonics West 2001 - LASE, 2001, San Jose, CA, United States

Abstract

We present a new class of invariant optical fields that we named Mathieu beams because they are described by radial and angular Mathieu functions. The angular spectrum of these beams when mapped on the McCutchen sphere gives the clue to create them in the laboratory. The corresponding experimental setup is described and the results obtained corroborated our theoretical predictions. The experimental parameters can be easily adjusted to obtain a variety of transverse intensity patterns that range from cosine to Bessel. There are two main families of higher order Mathieu beams, one of them are confocal elliptically ringed and can present phase rotating characteristics that are interesting for creating elliptical rotating waves. The other family of these high order beams have bowtie shapes. Mathieu beams are a variant of superposition of uniform conical waves, i.e. Bessel beams, and for these reason they have also the capability of self-reconstruction after finite obstructions.

Citation Download Citation

Julio Cesar Gutierrez-Vega, Ramon M. Rodriguez-Dagnino, Marcelo David Iturbe Castillo, and Sabino Chavez-Cerda "New class of nondiffracting beams: Mathieu beams", Proc. SPIE 4271, Optical Pulse and Beam Propagation III, (12 April 2001); https://doi.org/10.1117/12.424720

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KEYWORDS

Bessel beams

Superposition

Wave propagation

Nondiffracting beams

Optical spheres

Beam propagation method

Photography

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