Abstract
We model a cholesteric liquid crystal as a planar uniaxial multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated calculation of the Casimir-Lifshitz torque. Numerical results differ appreciably from the case of nematic liquid crystals, which can be treated like bloc birefringent media. In particular, we find that the torque deviates considerably from its usual sinusoidal behavior as a function of the misalignment angle. In the case of a birefringent crystal faced with a cholesteric liquid one, the Casimir-Lifshitz torque decreases more slowly as a function of distance than in the nematic case. In the case of two cholesteric liquid crystals, either in the homochiral or in the heterochiral configuration, the angular dependence changes qualitatively as a function of distance. In all considered cases, finite pitch length effects are most pronounced at distances of about 10 nm.
Highlights
Casimir-Lifshitz interactions [1,2] are macroscopic dispersion forces that arise from quantum mechanical and thermal fluctuations of the electromagnetic field
We verified our calculations by reproducing earlier results obtained by implementations of the Barash formula [32,62,63]
To understand the effects of cholesteric chirality on the Casimir-Lifshitz torque, we modeled a cholesteric liquid crystal as a uniaxial planar multilayer system
Summary
Casimir-Lifshitz interactions [1,2] are macroscopic dispersion forces that arise from quantum mechanical and thermal fluctuations of the electromagnetic field. The electromagnetic susceptibilities of the materials involved must be known—either theoretically or experimentally—as a function of frequency in a sufficiently broad range Another requirement to evaluate the Casimir-Lifshitz interaction is solving Maxwell’s equations for the given geometric configuration of the interacting bodies. A cholesteric liquid crystal consists of a sequence of many thin, planar, uniaxially oriented layers, whose orientation varies periodically in space with a periodicity given by the cholesteric pitch [34] This type of layered system has been shown to be amenable to the transfer matrix method [19] as electromagnetic waves in layered anisotropic media can be described by an algebra of 4 × 4 matrices [35].
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