Generation of isolated asymmetric umbilics in light's polarization

Polarization-singularity C points, a form of line singularities, are the vectorial counterparts of the optical vortices of spatial modes and fundamental optical features of polarization-spatial modes. Their generation in tailored beams has been limited to so-called “lemon” and “star” C points that contain symmetric dislocations in state-of-polarization patterns. In this Rapid Communication we present the theory and laboratory measurements of two complementary methods to generate isolated asymmetric C points in tailored beams, of which symmetric lemon and star patterns are limiting cases; and we report on the generation of so-called “monstar” patterns, an asymmetric C point with characteristics of both lemons and stars.

Figure 1

C-point sphere denoting by color the three morphological regions of C points: lemons (L), monstars (M), and stars (S). The polar coordinates are $2\beta$ and $\gamma$ (for $\delta =0$), as specified by Eq. (1). Inserts show polarization lines corresponding to selected points on the sphere.

Figure 2

Apparatuses to produce C points. (a) Using Laguerre-Gauss spatial modes, which includes a helium-neon laser (L), beam expander with spatial filter, nonpolarizing (BS) and polarizing (PBS) beam splitters, half-wave plate (HWP), quarter-wave plate (QWP), Pancharatnam-Berry phase shifter (PS), polarizer (P), and spatial light modulator (SLM). Inset shows an example of the programming of the SLM. (b) Using Hermite-Gauss spatial modes, with the following additional components: objective lenses (OL) and optical fiber (OF).

Figure 3

Results of theoretical calculations and experimental measurements when using Laguerre-Gauss modes as the spatial mode basis [Eq. (1)]. The first row has the calculated polarization lines, with the radial lines shown in red. The second and third rows show the modeled and measured ellipse fields. The solid lines in the ellipse fields correspond to the predicted orientations of the radial lines. The false color represents the orientation of the ellipses, and the saturation of the color is proportional to the intensity of the beams.

Figure 4

Results of data taken using the Hermite-Gauss spatial basis modes [Eq. (2)]. The first and third rows are the calculated and measured polarization-line maps, with the radial lines shown in red. The second row shows the modeled ellipse fields, with solid lines corresponding to the predicted orientations of the radial lines, white contours denoting intensity contours, and colors denoting ellipse orientation.