Topology of Generic Polarization Singularities in Birefringent Crystals

Abstract

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.

Calibration of Measurement of Multiple Polarization Singularities

“…Many papers acquired good experimental results [13][14][15][16] without eliminating the mismatches caused by the measuring system. But we noticed that most of these successful experiments were measuring the polarization state of fields with sparse PSs.…”

“…While phase singularities (wave dislocated, or optical vortices) are frequently encountered in interference of scalar waves [2,3], they resolve into polarization singularities (PSs) when the vector nature of light is retained [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A large number of papers have studied polarized properties of vector fields [4][5][6][7][8][9][10][11].…”

“…Measuring polarization states is the crucial step in experimental studies of polarization singularities [12]. Experiments have been successful in generating PSs [13][14][15][16]. However fields with crowded PSs present challenges in measuring the polarization states [17][18][19].…”