Single-interface Casimir torque

Abstract

A different type of Casimir-type interaction is theoretically predicted: a single-interface torque at a junction of an anisotropic material and a vacuum or another material system. The torque acts to reorient the polarizable microscopic units of the involved materials near the interface, and thus to change the internal structure of the materials. The single-interface torque depends on the zero-point energy of the interface localized and extended modes. Our theory demonstrates that the singleinterface torque is essential to understand the Casimir physics of material systems with anisotropic elements and may influence the orientation of the director of nematic liquid crystals. IntroductionCasimir-Lifshitz interactions [1-3] are the most paradigmatic example of quantum effects on the macro scale, and result from the confinement of the quantum-mechanical zero-point fluctuations of the electromagnetic field. Until recently, the study of quantum fluctuation-induced electromagnetic interactions was only of pure theoretical interest. Nevertheless, with the rapid development of micro-and nano-electromechanical systems (MEMS and NEMS) and its great impact in different areas [4,5], the research of Casimir-Lifshitz interactions has become of great practical importance as well. If, on one hand, Casimir interaction phenomena may lead to potentially undesired effects such as 'stiction' [6,7], on the other hand, they may open new and exciting possibilities in the field of micro and nanomechanics [4,[8][9][10][11].The study of Casimir-Lifshitz phenomena was pioneered by Casimir for more than 60 years ago [1]. In his seminal work, Casimir showed that as a result of the electromagnetic field quantum fluctuations, two parallel perfectly conducting plates standing in a vacuum may experience an attractive force pushing the plates toward each other. Following Casimir's prediction, Lifshitz, Dzyaloshinskii, and Pitaevskii extended the theory to the more general case of realistic isotropic dielectric plates, including non-ideal metals [2, 3]. Some years later, this theory was further generalized to anisotropic dielectric plates [12,13]. Interestingly, it was shown that the anisotropy may lead to the emergence of qualitatively different phenomena. It was demonstrated that a pair of parallel anisotropic uniaxial plates-with in-plane optical anisotropy and misaligned optical axes-separated by an isotropic dielectric, may experience a mechanical torque, designated as Casimir torque, that spontaneously forces the rotation of the plates towards the minimum energy position. The Casimir torque in this kind of systems was further investigated in [14][15][16][17][18]. In particular, numerical calculations of the torque were provided in [14][15][16]18], and possible experiments to measure the Casimir torque were proposed in [14,[16][17][18].With the emergence of metamaterials and their intriguing electromagnetic properties, the study of the Casimir-Lifshitz interactions has also been extended to systems with complex structural nanoscopic unities [1...

Optical torque on a two-level system near a strongly nonreciprocal medium

“…The boundary between these two regimes is the frequency ω m , at which the momentum of the SPP modes becomes parallel to the y-axis (bias direction) with θ = ±90 o , as seen in Eq. (20) and Fig. 2 (dashed black line in Fig.…”

“…(16) and the correspond-ing eigenfrequencies in Eq. (20) to derive a closed-form expression for the resonant and non-resonant parts of the optical torque in Eqs. (9).…”

“…In 15,16 , Casimir's theory was then generalized to the case of a system composed of two birefringent plates (i.e., a system with in-plane optical anisotropy) showing, for the first time, the emergence of a fluctuation-induced mechanical torque that makes the plates rotate toward a position with minimum zero-point energy. Further inves-tigations and generalizations are discussed in [17][18][19][20][21][22][23][24] .…”

Lateral optical forces on linearly polarized emitters near a reciprocal substrate

“…The reflection coefficient matrix for an interface between air ( 0 z  ) and a uniaxial material ( 0 z  ) can be found by imposing the continuity of t E and t  J H at the interface. This procedure yields [44]:…”

“…When the medium is either reciprocal or invariant under a parity transformation (   r r), the admittance matrices have the symmetries discussed in Ref. [44].…”