%0 Journal Article
%A Wolf, Kurt Bernardo
%A Alieva, Tatiana Krasheninnikova
%T Rotation and gyration of finite two-dimensional modes
%D 2008
%@ 1084-7529
%U https://hdl.handle.net/20.500.14352/51265
%X 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 Poincare sphere. In finite systems, where the emitters and the sensors are in N x N 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.
%~