Symmetry and the generation and measurement of optical torque

A key element in the generation of optical torque in optical traps, which occurs when electromagnetic angular momentum is transferred from the trapping beam to the trapped particle by scattering, is the symmetries of the scattering particle and the trapping beam. We discuss the effect of such symmetries on the generation and measurement of optical torque in optical tweezers, and some consequent general principles for the design of optically driven micromachines.