Chiral conical diffraction

The geometrical and wave optics are explored for light emerging from a slab of transparent biaxial crystal with optical activity (chirality), for an incident beam directed along the optic axis. The geometrical optics, here derived from Hamilton's principle, is dominated by a circularly symmetric cusped caustic surface ('spun cusp') threaded by an axial focal line. In wave optics, formulated exactly in the paraxial approximation in terms of integrals previously obtained by Belsky and Stepanov and here derived using a unitary evolution operator, the field is determined by two dimensionless parameters. The geometrical features are decorated by interference, here explored in the focal image plane (where the Poggendorff rings of the non-chiral case are in sharpest focus) and along the axis. Asymptotic approximations are derived in terms of the geometrical optics rays (including interference and evanescent waves), near the spun cusp, and uniformly across the caustic surface far from the cusp.