Finite optical Hamiltonian systems

Kurt Bernardo Wolf; Natig M. Atakishiyev; Luis Edgar Vincent; Guillermo Krötzsch; Juvenal Rueda-Paz

doi:10.1117/12.902162

2 November 2011 Finite optical Hamiltonian systems

Kurt Bernardo Wolf, Natig M. Atakishiyev, Luis Edgar Vincent, Guillermo Krötzsch, Juvenal Rueda-Paz

Proceedings Volume 8011, 22nd Congress of the International Commission for Optics: Light for the Development of the World; 801161 (2011) https://doi.org/10.1117/12.902162
Event: International Commission for Optics (ICO 22), 2011, Puebla, Mexico

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.

Citation Download Citation

Kurt Bernardo Wolf, Natig M. Atakishiyev, Luis Edgar Vincent, Guillermo Krötzsch, and 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); https://doi.org/10.1117/12.902162

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