We report a camera system, associated motorized opto-mechanics, and data handling routines for imaging the three-dimensional structure of singularities within scalar and vector optical fields. Using Fourier techniques to analyse a series of cross-sectional images, we measure either the relative phase or state of polarization of monochromatic fields and analyse this for the identification and mapping of their associated singularities.

An optical vortex incident on a birefringent crystal unfolds into a complex topological structure of lines of circular polarization (C-lines) and surfaces of linear polarization (L-surfaces). The incident beam splits into two orthogonally polarized beams of ordinary and extraordinary polarization. Extraordinary refraction causes a shift of the extraordinarily polarized beam even under normal incidence. This shift together with the different phase velocities of both beams is the origin of an intriguing pattern of polarization singularities. We measure spatially resolved the full set of Stokes parameters after the beam passed the crystal to determine experimentally the spatial structure of the polarization singularities in three dimensions, two spatial directions (x,y) and one (Λ) corresponding to the relative phase retardation between ordinary and extraordinary beam. The observed unfolding of the initial phase singularity is the most generic case of the generation of polarization singularities in uniaxial or biaxial birefringent crystals. It can be describe in a very general way in terms of Stokes parameters where the polarization singularities arise naturally from the zeros of the Stokes parameters.

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.

We have investigated experimentally the evolution of the intensity distribution of an initial off-axis vortex with topological charge 1 in a Laguerre–Gaussian background beam. It was found that the non-generic dislocation surface of the Laguerre–Gaussian beam destroyed and new vortices are created during propagation in agreement with calculations. The innermost vortex moves to the centre of the beam, in contrast to the other vortices, which propagate to the periphery. The motion of the innermost vortex is explained by a model employing phase and intensity gradients where the changes of the background beam during propagation are taken into account.

We have calculated the propagation dynamics of an initial off-axis vortex with topological charge 1 in Laguerre–Gaussian background beams (LG10andLG70), which are examples of background beams with non-generic dislocation surfaces, on which the real and imaginary parts of the light field are zero. When initially a vortex with broad core (e.g., r-vortex) is embedded in the background beam, the dislocation surfaces are destroyed during propagation and two vortices with opposite charge are created per dislocation surface in planes perpendicular to the propagation direction. For a vortex with narrow core (e.g., point vortex) diffraction is important and leads to the birth of more than two vortices per dislocation surface. These results are also valid for other background beams with dislocation surfaces, e.g., Hermite–Gaussian and Ince–Gaussian beams. We investigated experimentally the spatial evolution of the intensity distribution of an initial off-axis vortex with narrow core and topological charge 1 in LG10andLG70 background beams. The experimental results are in good agreement with the calculated intensity distributions.