2 November 2011 Finite optical Hamiltonian systems
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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.
© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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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