We analyse van der Waals interactions between a pair of dielectricallyanisotropic plane-layered media interacting across a dielectrically isotropicsolvent medium. We develop a general formalism based on transfer matrices toinvestigate the van der Waals torque and force in the limit of weakbirefringence and dielectric matching between the ordinary axes of theanisotropic layers and the solvent. We apply this formalism to study thefollowing systems: (i) a pair of single anisotropic layers, (ii) a singleanisotropic layer interacting with a multilayered slab consisting ofalternating anisotropic and isotropic layers, and (iii) a pair of multilayeredslabs each consisting of alternating anisotropic and isotropic layers, lookingat the cases where the optic axes lie parallel and/or perpendicular to theplane of the layers. For the first case, the optic axes of the oppositelyfacing anisotropic layers of the two interacting slabs generally possess anangular mismatch, and within each multilayered slab the optic axes may eitherbe the same, or undergo constant angular increments across the anisotropiclayers. In particular, we examine how the behaviors of the van der Waals torqueand force can be "tuned" by adjusting the layer thicknesses, the relativeangular increment within each slab, and the angular mismatch between the slabs.
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