Hamilton's diabolical singularity

The transformation of a narrow beam into a hollow cone when incident along the optic axis of a biaxial crystal, predicted by Hamilton in 1832, created a sensation when observed by Lloyd soon afterwards. It was the prototype of the conical intersections now popular in quantum chemistry. But the fine structure of the light cone contains many subtle features, slowly revealed by experiment, whose definitive explanation, involving new mathematical asymptotics, has been achieved only recently, along with definitive experimental test of the theory. Radically different phenomena, being intensively studied now, arise when chirality and absorption are incorporated in addition to biaxiality.