Conical Diffraction: Complexifying Hamilton's Diabolical Legacy

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


The propagation of light along singular directions in anisotropic media teems with rich asymptotic phenomena that are poorly understood. We study the refraction and diffraction of light beams through crystals exhibiting biaxial birefringence, optical activity, and dichroism. The optical properties and length of the crystal are related to the beam’s width, wavenumber, and alignment, by just three parameters defined by the effect of the crystal on a paraxial plane wave.

Singular axes are crystal directions in which the refractive indices are degenerate. In transparent biaxial crystals they are a pair of optic axes corresponding to conical intersections of the propagating wave surface. This gives rise to the well understood phenomenon of conical diffraction. Our interest here is in dichroic and optically active crystals. Dichroism splits each optic axis into pairs or rings of singular axes, branch points of the complex wave surface. Optical activity destroys the optic axis degeneracy but creates a ring of wave surface inflection points. We study the unknown effect of these degeneracy structures on the diffracted light field, predicting striking focusing and interference phenomena. Focusing is understood by the coalescence of real geometric rays, while geometric interference is included by endowing rays with phase to constitute complex rays. Optical activity creates a rotationally symmetric cusped caustic surface threaded by an axial focal line, which should be easy to observe experimentally. Dichroism washes out focusing effects and the field is dominated by exponential gradients crossing anti-Stokes surfaces.

A duality is predicted between dichroism and beam alignment for gaussian beams: both are described by a single parameter controlling transition between conical and double refraction. For transparent crystals we predict simple optical angular momentum effects accompanied by a torque on the crystal. We also report new observations with a biaxial crystal that test the established theory of conical diffraction.
Date of Award3 Oct 2007
Original languageEnglish
Awarding Institution
  • University of Bristol
SupervisorMichael V Berry (Supervisor)

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