The concept of conical refraction is another example of an important optical idea with a rich history, the first page of which was written by Hamilton in the early nineteenth century.
The basic idea underpinning conical refraction: when a pencil of light illuminates a biaxial crystal along one of its axes, it evolves into a hollow cone within the crystal and exits as a hollow cylinder.
The subsequent historical development of the idea of conical refraction is well described in the paper you have before you, by Sokolovskii, Carnegie, Kalkandjiev and Rafailov. Potential applications of the fundamental optics come relatively late in the piece, including lasing, quantum computing, cryptography, and bottle beams. I’ll leave it to you to read the paper to find out more!
Hamilton, who also gave us Hamiltonian mechanics and quaternions, wrote the first page of the book of conical refraction. The final page of this book is the paper you have before you. It develops the theory of a dual-cone model for conical refraction, and demonstrates the application of this model to experiments using a visible-light laser. Certain phenomena in conical refraction, such as a dark ring which occurs in the so-called Lloyd plane, are naturally described in terms of the interference between the dual cones which give the model its name. I warmly recommend this paper to your attention.
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