Alex Turpin, Yury V. Loiko, Todor K. Kalkandjiev, Jordi Mompart
In 1832 Hamilton predicted that a collimated light beam propagating through a biaxial crystal parallel to one of its optical axes refracts as a slanted cone within the crystal and emerges as a hollow light cylinder, this optical effect being named as conical refraction (CR). The diffractive solution of CR presented by Belsky and Khapalyuk in 1978 and the corresponding re-formulation carried out by Berry in 2004 rekindled this old and almost forgotten phenomenon. In this article, we review the CR phenomenon following different approaches that allow understanding light propagation in biaxial crystals, including the case of multiple crystals in cascade. We then focus on the description of the singular properties of the CR beams, presenting some examples such as optical bottle beams and beams carrying orbital angular momentum. All these features are used to introduce some of the most appealing applications of CR in the fields of optical trapping, free-space optical communications, polarization metrology, super-resolution imaging, two-photon polymerization, and lasers.