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Modes in n-dimensional first-order systems

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Abstract

The evolution of the Hermite–Gaussian modes in one dimensional centered nonlossless sytems is a well known result.1 Using the generalized Hermite polynomials used by Arnaud2 we can easily prove by induction the corresponding result for any finite dimensional first order system, including misalignment and the corresponding normalization terms. Phase conjugators are easily incorporated into the analysis. Various properties of the generalized Hermite polynomials are proved. Biorthogonality of the modes is demonstrated. The higher order modes are not periodic, i.e. they have no self consistent solutions except the separable one dimensional solutions. Some applications involving the Hermite–Gaussians are also presented.

© 1993 Optical Society of America

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