Floquet Theory for Light-Driven Rotation of Dipolar and Multipolar Particles

Abstract

Nano- or micro-particle rotation driven by light has been well known in the fields of optical manipulation and optical physics since the end of the last century. It is viewed as a sort of angular-momentum transfer from light to material, but its microscopic analysis based on the Hamiltonian or the equation of motion has been less developed. We model this rotation with a simple setup of an electrically dipolar or multipolar particle irradiated by circularly polarized laser and comprehensively analyze the Langevin-type equation of motion by using the Floquet theory for dissipative classical systems and the mode separation method. Furthermore, we numerically compute the time evolution of the particle. As a result, we accurately estimate the dependence of the laser-frequency, laser-intensity, particle mass, temperature, and friction (dissipation) on the laser-driven rotation. We determine the ``nonequilibrium phase diagram'' of the laser-driven rotation in a broad parameter regime, which consists of three regimes: the rotation frequency $\Omega\propto\omega^{-1}$, $\Omega\propto\omega^{-3}$, or $\Omega=\omega$ ($\omega$ is the laser frequency). Comparing our theoretical result with some experiments, we show that the result of the overdamped Langevin equation is qualitatively consistent with the experiments.