Radiation torque on a birefringent sphere caused by an electromagnetic wave

We present an exact ab initio calculation of the optical torque on a spherical uniaxially birefringent particle of arbitrary size illuminated by plane electromagnetic wave of arbitrary polarization mode and direction of propagation. The calculation is based on the extended Mie theory and the Maxwell stress tensor formalism. The expression for evaluating radiation torque is derived for arbitrary (absorbing and lossless) isotropic surrounding medium. The dependence of the optical torque on the incident angle, the polarization mode, the material birefringence, as well as the particle size, has been systematically investigated. For normal illumination, namely, with the incident wave vector k₀ perpendicular to the extraordinary axis (EA) of the particle, the optical torque Γ caused by a linearly polarized (LP) incident wave always shows the angle dependence Γ=Γ₀ sin 2φ_e. Here, φ_e is the angle between the EA and the incident electric field, whereas Γ₀ may take positive or negative values, dependent on n_e,n_o, and the particle size. In the small particle limit, Γ versus particle radius a displays different power law behaviors, Γ∼a³ and Γ∼a⁶, for LP and circularly polarized (CP) incident waves, respectively, while for small material birefringence ∣Δn∣=∣n_e−n_o∣, linear and square laws, Γ∼∣Δn∣ and Γ∼∣Δn∣², are found for the LP and the CP incident modes, respectively.