Lorentz Beams

Details Lorentz Beams Lorentz Beams

2005-10-13

arxiv.org/abs/physics/0510123v1

J. Opt. A: Pure Appl. Opt. 8 (2006), 406-414

Physics

Optics

11 pages, 1 figure, submitted to Journal of Optics A

Scientific paper

10.1088/1464-4258/8/5/007

A new kind of tridimensional scalar optical beams is introduced. These beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. Closed-form expression of free-space propagation under paraxial limit is derived and pseudo non-diffracting features pointed out. Moreover, as the slowly varying part of these fields fulfils the scalar paraxial wave equation, it follows that there exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original Lorentz beam to a Gaussian apodization function. Although the existence of Lorentz-Gauss beams can be shown by using two different and independent ways obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different approach, which makes use of Lie's group theory, and which possesses the merit to put into evidence the symmetries present in paraxial Optics.

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