Wigner representation and geometric transformations of optical orbital angular momentum spatial modes
G.F Calvo
Optics Letters 30, 1207-1209 (2005)
MOLAB authors
Fernández Calvo, Gabriel. 
Abstract
An exact Wigner representation of optical spatial modes carrying orbital angular momentum is found in closed form by exploiting the underlying SU(2) Lie-group algebra of their associated Poincaré sphere. Orthogonality relations and observables of these states are obtained within the phase space picture. Development of geometric phases on mode transformations is also elucidated.