Dispersion interactions in stratified anisotropic and optically active media at all separations

Abstract

We propose a method to calculate dispersion interactions in a system composed of a one dimensional layering of finite thickness anisotropic and optically active slabs. The result is expressed within the algebra of 4 × 4 matrices and is demonstrated to be equivalent to the known limits of isotropic, nonretarded and uniaxial dispersion interactions. The method is also capable of handling dielectric media with smoothly varying anisotropy axes.

Qualitative chirality effects on the Casimir-Lifshitz torque with liquid crystals

“…This result is equivalent to that of Ref. [35] which uses the formalism of Berreman [19], while here the same formalism has been used with the basis suggested by Yeh [20].…”

“…The Casimir-Lifshitz interaction free energy can be obtained from the secular determinant of the modes, whose zeros give the eigenfrequencies of the bound states. [35] However, in its turn the secular determinant itself can be rewritten in terms of the Fresnel reflection coefficients that can be obtained from the transfer matrix formalism. This route then connects the transfer matrix formalism with the Casimir-Lifshitz interactions which we elucidate in what follows.…”

“…However, a cholesteric liquid crystal actually 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].…”

van der Waals torque and force between dielectrically anisotropic layered media

“…Later the complete Lifshitz result, including retardation, for two dielectrically anisotropic half-spaces with an intervening isotropic slab was obtained by Barash [12][13][14][15]. The general Lifshitz theory results for the vdW interactions in stratified anisotropic and optically active media with retardation effects are algebraically unwieldy * Electronic address: binghermes@gmail.com [16], not permitting any final simplification [17]. Further efforts in the investigation of the vdW torque between a pair of single-layered dielectrically anisotropic slabs include a one-dimensional calculation [18], calculations on two ellipsoids with anisotropic dielectric function [19], a pair of dielectric slabs with different conductivity directions [20], and a quantum torque calculation for two specific uniaxial materials (barium titanate and quartz or calcite) [14,15].…”

“…Dielectrically anisotropic multi -layered materials have many examples, appearing in ceramics and clays, such as kaolinite [30] and computations of the vdW forces for multi-layered systems are well-known in the literature [16,[31][32][33][34][35][36]38]. In addition, many common minerals, e.g.…”