Diabolic effects on nuclear rotational state population in two-neutron transfer

Experimental umbilic diabolos in random optical fields

The intensity of a random optical field consists of bright speckle spots (maxima) separated from dark areas (minima and optical vortices) by saddle points. We show that hidden in this complicated landscape are umbilic points--singular points at which the eigenvalues Lambda (+/-) of the Hessian matrix that measure the curvature of the landscape become degenerate. Although not observed previously in random optical fields, umbilic points are the most numerous of all special points, outnumbering maxima, minima, saddle points, and vortices. We show experimentally that the directions of principal curvature, the eigenvectors Psi (+/-), rotate about intensity umbilic points with positive or negative half-integer winding number, in accord with theory, and that Lambda (+) and Lambda (-) generate a double cone known as a diabolo. At optical vortices the curvature of the amplitude is singular, and we show from both theory and experiment that for this landscape Psi (+/-) rotate about vortex centers with a positive integer winding number. Diabolos can be classified as elliptic or hyperbolic, and we present initial results for the measured fractions of these two different types of umbilic diabolos.

Diabolo creation and annihilation

A point of circular polarization embedded in a paraxial field of elliptical polarization is a polarization singularity called a C point. At such a point the major axis a and minor axis b of the ellipse become degenerate. Away from the C point this degeneracy is lifted such that surfaces a and b form nonanalytic cones that are joined at their apex (the C point) to produce a double cone called a diabolo. Typically, during propagation diabolo pairs are created or annihilated. We present rules based on geometry and topology that govern these events, provide initial experimental confirmation, and enumerate the allowed configurations in which diabolos can be created or annihilated.