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.
© 2005 Optical Society of America
(030.4070) Coherence and statistical optics : Modes
(080.2720) Geometric optics : Mathematical methods (general)
(260.0260) Physical optics : Physical optics
(350.1370) Other areas of optics : Berry's phase
(350.5500) Other areas of optics : Propagation
Gabriel F. Calvo, "Wigner representation and geometric transformations of optical orbital angular momentum spatial modes," Opt. Lett. 30, 1207-1209 (2005)