Publication: Orthonormal mode sets for the two-dimensional fractional Fourier transformation
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2007-05-15
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Optical Society of America
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Abstract
A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincare sphere are studied.
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© 2007 Optical Society of America. T. Alieva (talieva@fis.ucm.es) thanks the Spanish Ministry of Education and Science (project TEC 2005-02180/MIC). M. J. Bastiaans (m.j.bastiaans@tue.nl) appreciates the hospitality at Universidad Complutense de Madrid.
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