title: Rotation and gyration of finite two-dimensional modes.
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 Poincaré sphere. In finite systems, where the emitters and the sensors are in NxN 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.
authors.affiliation: Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Morelos, Mexico. bwolf@fis.unam.mx
authors.forename: Kurt Bernardo
authors.initials: KB
authors.lastname: Wolf
authors.forename: Tatiana
authors.initials: T
authors.lastname: Alieva