Publication: Rotation and gyration of finite two-dimensional modes
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2008-02-01
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Optical Society of America
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Abstract
Hermite-Gauss and Laguerre-Gauss modes of a continuous optical field in two dimensions can be obtained from each other through paraxial optical setups that produce rotations in (four-dimensional) phase space. These transformations build the SU(2) Fourier group that is represented by rigid rotations of the Poincare sphere. In finite systems, where the emitters and the sensors are in N x N square pixellated arrays, one defines corresponding finite orthonormal and complete sets of two-dimensional Kravchuk modes. Through the importation of symmetry from the continuous case, the transformations of the Fourier group are applied on the finite modes.
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© 2008 Optical Society of America. T. Alieva acknowledges the Spanish Ministry of Education and Science for financial support (project TEC 2005- 02180/MIC). K. B. Wolf acknowledges the support of the SEP-CONACYT (México) project IN102603 “Óptica Matemática.” The authors are grateful to the UCM/ UNAM Collaboration Agreement for making this joint work possible. We appreciate Guillermo Krötzsch for assistance with the graphics, and Luis Edgar Vicent for Figs. 2 and 5.
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