A biaxial crystal is a direction dependent refractive index medium most commonly associated with the optical phenomenon of birefringence. A circularly polarised ray upon propagation through such a medium has its constituent s-p polarisation components experience a difference in refractive index and consequently upon exiting the medium separate into two orthogonally polarised beams rays. However there are two directions within such mediums known as the optic axes where there is no longer a difference in phase but a point of singular phase where an incident ray of light upon propagation down the optic axis of a biaxial crystal refracts into a hollow cone of light within the crystal and a hollow cylinder of light upon exiting the medium. This process is known as "internal conical diffraction" and was first theorised in 1832 here in Trinity college by the famous Irish scientist Sir. W.R. Hamilton (more commonly known for his discovery of Quaternions ). External and internal conical refractionwas later experimentally demonstrated by Prof. Lloyd a few years later. No further work was done on this process here in the School of Physics Trinity college until after Hamilton's bicentenary of his birth in 2005 [School of Physics webpage]. This was mainly due to the lack of high optical grade biaxial crystal. However due to the recent ease of access of such media a project funded by SFI was started to investigate this phenomenon further. The expansion of Hamilton's work to incorporate the diffraction of the conical field results in the transformation of a circularly polarised incident Gaussian beam into a superposition of circularly symmetric fields known as Bessel beams of zero and 1st order. In 2009 the first paper published  in over 180 years from Trinity College was published describing experimentally and theoretically the formation of such fields in a by postgraduate researchers Ciaran Phelan and David O'Dwyer under the supervision of Dr. Yury Rakovich, Prof. J. Donegan and Prof J. Lunney. Current research interests into conical diffraction involves the examination and profiling of the phase profile which is know to contain a complex phase component associated with orbital angular momentum of a photon. The formation of micron sized structures using two photon polymerisation process in conjunction with the Tyndall national institute in Cork. Future aims involve using the conical profile as a novel optical trap.
1.Conical refraction - Hamilton
3.Conical refraction - Loyd
4."Conical Diffraction and Bessel beam formation with a high quality Biaxial crystals" C.F.Phelan, D.P.ODwyer, Y.P.Rakovich, J.F.Donegan and J.G.Lunney,20 July 2009, Vol. 17, No. 15 OPT. EXPRESS 12891