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16 August 2010 Propagation characteristics of Cartesian Parabolic-Gaussian beams
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We study the propagating and shaping characteristics of the novel one-dimensional Cartesian Parabolic-Gaussian beams. The transverse profile is described by the parabolic cylinder functions and are apodized by a Gaussian envelope. Their physical properties are studied in detail by finding the 2n-order intensity moments of the beam. Propagation through complex ABCD optical systems, normalization factor, beam width, the quality M2 factor and its kurtosis parameter are derived. We discuss its behavior for different beam parameters and the relation between them. The Cartesian Parabolic-Gaussian beams carry finite power and form a biorthogonal set of solutions of the paraxial wave equation in Cartesian coordinates.
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D. Lopez-Mago, M. A. Bandres, and J. C. Gutiérrez-Vega "Propagation characteristics of Cartesian Parabolic-Gaussian beams", Proc. SPIE 7789, Laser Beam Shaping XI, 77890Q (16 August 2010);

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