Differential and integral Jones matrices for a cholesteric

S. Yu. Nastyshyn, I. M. Bolesta, S. A. Tsybulia, E. Lychkovskyy, M. Yu. Yakovlev, Ye. Ryzhov, P. I. Vankevych, and Yu. A. Nastishin
Phys. Rev. A 97, 053804 – Published 4 May 2018

Abstract

Previous attempts to derive the differential Jones matrix (DJM, N) by Jones [Jones, J. Opt. Soc. Am. 38, 671 (1948)] for a twisted crystal and the integral Jones matrix (IJM, J) 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 N0 and the elementary IJM J0 (to which the cholesteric is split) are those of a uniform nematic and (2) under rotation of the coordinate system, N0 and J0 obey the similarity transformation rule, namely, N=RN0R1 and J=RJ0R1, where R 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 N0d of N0 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 N0 appear to be the wave numbers for the two eigenwaves propagating in the sample. Then the form of N0 reconstructs from its diagonal form N0d. 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 N0 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

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

S. Yu. Nastyshyn1, I. M. Bolesta1, S. A. Tsybulia2, E. Lychkovskyy3, M. Yu. Yakovlev2, Ye. Ryzhov2, P. I. Vankevych2, and Yu. A. Nastishin2,*

  • 1Ivan Franko National University of Lviv, Faculty of Radioelectronics and Informational Technologies, 107 General Tarnavskyi street, Lviv 79017, Ukraine
  • 2Hetman Petro Sahaidachnyi National Army Academy, 32 Heroes of Maidan street, Lviv 79012, Ukraine
  • 3Lviv Danylo Halytsky National Medical University, 69 Pekarska street, Lviv 79010, Ukraine

  • *nastyshyn_yuriy@yahoo.com

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Issue

Vol. 97, Iss. 5 — May 2018

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