Optical trapping, where microscopic particles are trapped and manipulated by light is a powerful technique. The single-beam gradient trap (also known as optical tweezers) is widely used for a large number of biological and other applications. The forces and torques acting on a trapped particle result from the transfer of momentum and angular momentum from the trapping beam to the particle. Despite the apparent simplicity of a laser trap, with a single particle in a single beam, exact calculation of the optical forces and torques acting on particles is difficult, and a number of approximations are normally made. Approximate calculations are performed either by using geometric optics, which is appropriate for large particles, or using small particle approximations. Neither approach is adequate for particles of a size comparable to the wavelength. This is a serious deficiency, since wavelength sized particles are of great practical interest because they can be readily and strongly trapped and can be used to probe interesting microscopic and macroscopic phenomena. The lack of suitable theory is even more acute when the trapping of non-spherical particles is considered. Accurate quantitative calculation of forces and torques acting on non-spherical particles is of particular interest due to the suitability of such particles as microscopic probes. These calculations are also important because of the frequent occurrence of non-spherical biological and other structures, and the possibility of rotating or controlling the orientation of such objects. The application of electromagnetic scattering theory to the laser-trapping of wavelength sized non-spherical particles is presented
