We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T-matrix for modeling arbitrarily shaped micro-sized objects. The emph{T}-matrix elements are calculated using point m
atching between fields calculated using vector spherical wave functions and DDA. When applied to microrotors, their discrete rotational and mirror symmetries can be exploited to reduce memory usage and calculation time by orders of magnitude; a number of optimization methods can be employed based on the knowledge of the relationship between the azimuthal mode and phase at each discrete rotational point, and mode redundancy from Floquets theorem. A reduced-mode T-matrix can also be calculated if the illumination conditions are known.
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 t
rapping 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.
