J. Phys. II France
Volume 4, Numéro 2, February 1994
Page(s) 287 - 303
DOI: 10.1051/jp2:1994129
J. Phys. II France 4 (1994) 287-303

Transmission and reflection of a monochromatic beam in a twisted nematic wedge

S. Faetti1, 2, M. Nobili1, 2 and I. Raggi1

1  Dipartimento di Fisica, Università di Pisa, Piazza Torricelli 2, 56100 Pisa, Italy
2  Consorzio Nazionale interuniversitario di Fisica della Materia and Gruppo Nazionale di Struttura della Materia del Consiglio Nazionale delle Ricerche

(Received 12 August 1993, received in final form 18 October 1993, accepted 2 November 1993)

The transmission and reflection of a monochromatic electromagnetic wave in a twisted nematic wedge are investigated. We consider the special case where the characteristic length $\xi$ of the director twist is much higher than the optical wavelength  $\lambda$. By using the perturbative theoretical procedure proposed by Oldano et al., we find an analytic expression for the transmitted and reflected beams at the first order in the perturbative parameter $\varepsilon = 1/\Delta k \xi$, where $\Delta k$ is the difference between the extraordinary and ordinary wavenumbers. The intensity and the polarization of the refracted and reflected beams are related by simple analytic expressions to the normal derivatives of the director at the interfaces and do not depend on details of the bulk director distortion. The theoretical predictions are compared with experimental results obtained using an electric field to twist the director-field. A satisfactory agreement is found between theory and experiment. On the basis of our theoretical results we propose a simple experimental method to measure the twist viscosity coefficient of nematic liquid crystals.

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