W. Kaminsky and B. Kahr: Crystal Optics and the Symmetry Principle: An Update. Symmetry 2000, I. Hargittai and L. Torvard, eds. Portland Press, Lond.
The Neumann-Minnergerode-Curie Symmetry Principle, that the properties of a system are invariant to its symmetry operations, is a cornerstone of physical science whose origin is in the classification of crystals according to their effects on transmitted light. This classification began with the pioneering studies of the polarization dependence of refraction, linear birefringence, by David Brewster (1781-1868) and Jean-Baptiste Biot (1774-1862) in 1812. But, ignored in their analysis was the angular displacement of linearly polarized light, optical rotation, in some materials, discovered just the year before by Dominique Arago (1786-1853) and interpreted by Biot, also in 1812. REmarkably, in the year 2000 the complete experimental characterization of crystals taking account of both linear birefringence and optical rotation (circular birefringence) has not been accomplished. In this essay we trace the roots of the symmetry principle in the science of crystal optics, explain why optical properties of some dissymmetric crystals have been so confounding, and provide a plan for finishing the work of Brewster and Biot that takes optical rotation into account. Along the way we illustrate the so-called chiroptical or girative crystal symmetries with optical rotation. While this information has frequently been tabulated, the symmetries of gyration tensors have rarely been illustrated pictorally. A complete presentation that emphasizes the three dimensionality of the subject based on experimental data and which is suited to a general audience of symmetry enthusiasts has not yet been available.