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 k(0) perpendicular to the extraordinary axis (EA) of the particle, the optical torque Gamma caused by a linearly polarized (LP) incident wave always shows the angle dependence Gamma = Gamma(0) sin 2 phi(e). Here, phi(e) is the angle between the EA and the incident electric field, whereas Gamma(0) may take positive or negative values, dependent on n(e),n(o), and the particle size. In the small particle limit, Gamma versus particle radius a displays different power law behaviors, Gamma similar to a(3) and Gamma similar to a(6), for LP and circularly polarized (CP) incident waves, respectively, while for small material birefringence vertical bar Delta n vertical bar = vertical bar n(e)-n(o)vertical bar, linear and square laws, Gamma similar to vertical bar Delta n vertical bar and Gamma similar to vertical bar Delta n vertical bar(2), are found for the LP and the CP incident modes, respectively.