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.

Figure 1

In random vector fields $C$ points are classified by the streamlines of their immediate surroundings into stars (S), monstars (M, short for lemon-stars), and lemons (L). The polarizations may be either right handed or left handed, but $C$ points of opposite handedness are always separated by an $L$ line.

Figure 2

Apparatus used to generate random vector speckle fields: HeNe laser incident on a Wollaston prism (WP) to doubly illuminate a ground glass screen (GG). A polarizing beam splitter (BS) recombines the two beams. The cross sections behind the ground glass screen were imaged with lens (L2) after the rotating polarizer (POL) onto a CCD camera mounted on a motorized stage.

Figure 3

Examples of four $C$ points and nearby polarization streamlines as measured in our experiment. Part I is lemon type, part II is star, part III is monstar, and part IV is a cross section near a star-monstar transformation.

Figure 4

Experimentally observed $C$ lines (a) and associated $L$ surfaces (b), with [right (left)-handed] stars [green (blue)], monstars (black), and lemons [red (yellow)]. (c) Shows an expanded region of (a), highlighting a loop and the neighboring $L$ surface, the roman numerals highlight cross sections of interest, for which the streamlines are shown in Fig. 3.