Abstract
Previous attempts to derive the differential Jones matrix (DJM, by Jones [Jones, J. Opt. Soc. Am. 38, 671 (1948)] for a twisted crystal and the integral Jones matrix (IJM, by Chandrasekhar and Rao [Chandrasekhar and Rao, Acta Crystallogr. A 24, 445 (1968)] for a cholesteric liquid crystal resulted in Jones matrices, which are valid for the spectral range except the selective light reflection band. We argue that the limitation of their validity is rooted in two key assumptions used in both approaches, namely, (1) local (nonrotated) DJM and the elementary IJM (to which the cholesteric is split) are those of a uniform nematic and (2) under rotation of the coordinate system, and obey the similarity transformation rule, namely, and , where is the rotation matrix. We show that both of these assumptions are of limited applicability for a cholesteric, being justified only for weak twist. In our approach, the DJM and IJM are derived for a cholesteric without these assumptions. To derive the cholesteric DJM, we have established the relation between the diagonal form of and Mauguin solutions [Mauguin, Bull. Soc. Fr. Mineral. Crystallogr. N° 3, 71 (1911)] of Maxwell equations for eigenwaves propagating in the cholesteric. Namely, the eigenvalues of appear to be the wave numbers for the two eigenwaves propagating in the sample. Then the form of reconstructs from its diagonal form . Our DJM and IJM, derived for a general case of any ellipticity value of the eigenwaves, correspond to an optically anisotropic plate possessing gyrotropy, linear birefringence, and Jones dichroism. In the limiting approximations of circularly polarized eigenwaves and that corresponding to the Mauguin regime, the DJM and IJM reduce to those known from the literature. We found that the form of the transformation rule for the local DJM under rotation of the coordinate system depends on the regime of light propagation, being different from the similarity transformation rule alluded to above, but reduces to it at weak twist corresponding to the Mauguin regime.
- Received 26 January 2018
DOI:https://doi.org/10.1103/PhysRevA.97.053804
©2018 American Physical Society