Abstract

Free propagation in continuous optical and mechanical systems is generated by the momentum-squared operator and results in a shear of the phase space plane along the position coordinate. We examine three discrete versions of the Fresnel transform in periodic systems through their Wigner function on a toroidal phase space. But since it is topologically impossible to continuously and globally shear a torus, we examine a fourth version of the Fresnel transform on a spherical phase space, in a model based on the Lie algebra of angular momentum, where the corresponding Fresnel transform wrings the sphere.

© 2007 Optical Society of America

Geometry and dynamics of squeezing in finite systems

Kurt Bernardo Wolf and Guillermo Krötzsch
J. Opt. Soc. Am. A 24(9) 2871-2878 (2007)

Geometry and dynamics in the fractional discrete Fourier transform

Kurt Bernardo Wolf and Guillermo Krötzsch
J. Opt. Soc. Am. A 24(3) 651-658 (2007)

Covariant discretization of axis-symmetric linear optical systems

Natig M. Atakishiyev, Shakir M. Nagiyev, Luis Edgar Vicent, and Kurt Bernardo Wolf
J. Opt. Soc. Am. A 17(12) 2301-2314 (2000)

Discrete Bargmann transform

Kenan Uriostegui
J. Opt. Soc. Am. A 36(8) 1367-1373 (2019)

Rotation and gyration of finite two-dimensional modes

Kurt Bernardo Wolf and Tatiana Alieva
J. Opt. Soc. Am. A 25(2) 365-370 (2008)