Three point sources are located at the vertices of an equilateral triangle of radius 2.5 wavelengths (632.8 nm, red laser). Scalar diffraction shows the intensity and phase at each point on 2d cross-sections of the 3d volume (static time). Polar diffraction is of two kinds: radial (the polarization is directly away from the center at each vertex) and azimuthal (the polarization is tangential-left/counter-clockwise to the circle at each vertex). Negative twists turn the polarization clockwise between each vertex instead (i.e. in the opposite direction around the center). Note that since the polarization has an orientation but no arrowhead, it is the same every 180 degrees. Therefore, half-twists of the polarization around the center will also bring the vector back into alignment at the first vertex. These patterns are of interest optically and computationally because they contain both phase and polarization singularities, saddle-points, and bifurcations, in addition to a wide variety of polarization states.
Below is a montage of all 8 polarized results for the XY plane at z = 5.0 wavelengths. Click the plot for a larger image (and then click again to zoom your browser to full size):