2 November 2011 Finite optical Hamiltonian systems
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Abstract
In this essay we finitely quantize the Hamiltonian system of geometric optics to a finite system that is also Hamiltonian, but where signals are described by complex N-vectors, which are subject to unitary transformations that form the group U(N). This group can be decomposed into U(2)-paraxial and aberration transformations. Proper irreducible representation bases are thus provided by quantum angular momentum theory. For one-dimensional systems we have waveguide models. For two-dimensional systems we can have Cartesian or polar sensor arrays, where digital images are subject to unitary rotation, gyration or asymmetric Fourier transformations, as well as a unitary map between the two arrays.
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Kurt Bernardo Wolf, Kurt Bernardo Wolf, Natig M. Atakishiyev, Natig M. Atakishiyev, Luis Edgar Vincent, Luis Edgar Vincent, Guillermo Krötzsch, Guillermo Krötzsch, Juvenal Rueda-Paz, Juvenal Rueda-Paz, } "Finite optical Hamiltonian systems", Proc. SPIE 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World, 801161 (2 November 2011); doi: 10.1117/12.902162; https://doi.org/10.1117/12.902162
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