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17 February 2003 Elliptic propagation invariant optical fields: Mathieu beams
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Proceedings Volume 4833, Applications of Photonic Technology 5; (2003)
Event: Applications of Photonic Technology 5, 2002, Quebec City, Canada
The interest in propagation invariant optical fields (PIOF's) is due to the fact that, under optimal conditions, they propagate long distances without significant change of their transverse intensity distribution. These kind of wavefields were first identified and described in terms of Bessel function. Based on the separability of the Helmholtz equation in elliptic cylindrical coordinates we have demonstrated that there exist another class of PIOF's. The lowest order mode may have a highly localised distribution along one of the transverse directions and a sharply peaked quasi-periodic structure along the other. Higher order modes are composed of elliptical vortices and the corresponding intensity profiles are formed by propagation-invariant confocal elliptical rings. These fields are described by the Mathieu-Hankel functions which are exact solutions of Helmholtz equation and for this reason we have called them Mathieu beams. We demonstrate that Bessel beams are a particular case of Mathieu beams, which have a broader fan of interesting features. Since the Mathieu functions form a whole set of exact travelling wave solutions of the Helmholtz wave equation they can be used to describe a class of PIOF's. The McCutchen theorem provides the relation between the general class of PIOF's and these new beams.
© (2003) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Sabino Chavez-Cerda, Marcelo David Iturbe Castillo, and Julio Cesar Gutierrez-Vega "Elliptic propagation invariant optical fields: Mathieu beams", Proc. SPIE 4833, Applications of Photonic Technology 5, (17 February 2003);


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