Light beams with fractional orbital angular momentum and their vortex structure.

Light emerging from a spiral phase plate with a non-integer phase step has a complicated vortex structure and is unstable on propagation. We generate light carrying fractional orbital angular momentum (OAM) not with a phase step but by a synthesis of Laguerre-Gaussian modes. By limiting the number of different Gouy phases in the superposition we produce a light beam which is well characterised in terms of its propagation. We believe that their structural stability makes these beams ideal for quantum information processes utilising fractional OAM states.

Polarization singularities in 2D and 3D speckle fields.

The 3D structure of randomly polarized light fields is exemplified by its polarization singularities: lines along which the polarization is purely circular (C lines) and surfaces on which the polarization is linear (L surfaces). We visualize these polarization singularities experimentally in vector laser speckle fields, and in numerical simulations of random wave superpositions. Our results confirm previous analytical predictions [M. R. Dennis, Opt. Commun. 213, 201 (2002)] regarding the statistical distribution of types of C points and relate their 2D properties to their 3D structure.

Fractality of light's darkness.

Natural light fields are threaded by lines of darkness. For monochromatic light, the phenomenon is familiar in laser speckle, i.e., the black points that appear in the scattered light. These black points are optical vortices that extend as lines throughout the volume of the field. We establish by numerical simulations, supported by experiments, that these vortex lines have the fractal properties of a Brownian random walk. Approximately 73% of the lines percolate through the optical beam, the remainder forming closed loops. Our statistical results are similar to those of vortices in random discrete lattice models of cosmic strings, implying that the statistics of singularities in random optical fields exhibit universal behavior.

Stokes parameters in the unfolding of an optical vortex through a birefringent crystal.

Following our earlier work [F. Flossmann et al., Phys. Rev. Lett. 95 253901 (2005)], we describe the fine polarization structure of a beam containing optical vortices propagating through a birefringent crystal, both experimentally and theoretically.We emphasize here the zero surfaces of the Stokes parameters in three-dimensional space, two transverse dimensions and the third corresponding to optical path length in the crystal. We find that the complicated network of polarization singularities reported earlier -lines of circular polarization (C lines) and surfaces of linear polarization (L surfaces) - can be understood naturally in terms of the zeros of the Stokes parameters.

Polarization singularities from unfolding an optical vortex through a birefringent crystal.

Optical vortices (nodal lines and phase singularities) are the generic singularities of scalar optics but are unstable in vector optics. We investigate experimentally and theoretically the unfolding of a uniformly polarized optical vortex beam on propagation through a birefringent crystal and characterize the output field in terms of polarization singularities (C lines and points of circular polarization; L surfaces and lines of linear polarization). The field is described both in the 2-dimensional transverse plane, and in three dimensions, where the third is abstract, representing an optical path length propagated through the crystal. Many phenomena of singular optics, such as topological charge conservation and singularity reconnections, occur naturally in the description.