An Analytical Approach to the Theory of Internal Conical Refraction

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Abstract
An analytical, quantitative treatment of internal conical refraction is presented. The recently derived angular spectrum representation of electromagnetic fields in biaxial crystals is employed. Explicit expressions for the electric field in the far zone of a conically refracted beam of light are found by applying the principle of stationary phase to the integrals of the representation. A close examination of the expressions for the field in the far zone yields all the known results of internal conical refraction including the Poggendorf dark band. The present treatment, however, goes beyond previous studies since, with our expressions, it is possible to investigate the detailed structure of the conically refracted field.