Abstract
A previously unnoticed connection between the classical optical theory of a twisted nematic liquid crystal and the two beam dynamical theory of diffraction in the transmission Laue case (as is applied to calculate beam intensities in X-ray, electron and neutron diffraction), has been uncovered. Both physical situations are described by an equation of the form (d/d z)Φ = 2π AΦ, where A is an Hermitian matrix, and Φ is a two component column vector representing beam amplitudes in the diffraction case and light polarization components in the nematic case. The counterpart of the concept of the scattering matrix in diffraction theory is the Jones calculus of crystal optics theory. Anomalous (Borrmann) transmission in crystal diffraction (different absorption of the two Bloch waves) also has a counterpart in elliptical dichroism in crystal optics. Crystal optical theory as formulated by Mauguin in 1911 predates the first formulation by Darwin in 1914 of the dynamical theory of diffraction.
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