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Elegant Ince–Gaussian beams

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Abstract

The existence of elegant Ince–Gaussian beams that constitute a third complete family of exact and biorthogonal elegant solutions of the paraxial wave equation is demonstrated. Their transverse structure is described by Ince polynomials with a complex argument. Elegant Ince–Gaussian beams constitute exact and continuous transition modes between elegant Laguerre–Gaussian and elegant Hermite–Gaussian beams. The expansion formulas among the three elegant families are derived.

© 2004 Optical Society of America

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Equations (15)

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