We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.
© 1999 Optical Society of America
(000.3860) General : Mathematical methods in physics
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(260.0260) Physical optics : Physical optics
(350.5500) Other areas of optics : Propagation
R. Simon and N. Mukunda, "Gaussian Schell-model beams and general shape invariance," J. Opt. Soc. Am. A 16, 2465-2475 (1999)