Partial wave decomposition of incident beams is the first task to be performed to impose boundary conditions at the particle interface in the calculation of the scattering of spherical particles. The coordinate's origin must be in the center of the particle and not at high symmetry positions of the beam. This can be a quite complicated problem, especially when a full vectorial diffraction description of the electromagnetic fields and highly focused laser beams are required where the paraxial limit fails. Traditional approximation techniques have been used to proceed forward and to obtain numerical results. The main fault relies on a radial dependence of the beam shape coefficients, which limits the validity of such approximations. Here we prove that the radial dependence will emerge from the solid angle integration in this way obtaining an exact, closed expression, without any approximation, for the beam shape coefficients, for an arbitrary beam shape, origin and polarization, the special case of a Gaussian beam is presented.

Date Published: 30 August 2006
PDF: 6 pages
Proc. SPIE 6326, Optical Trapping and Optical Micromanipulation III, 63260J (30 August 2006); doi: 10.1117/12.680898

Published in SPIE Proceedings Vol. 6326:
Optical Trapping and Optical Micromanipulation III
Kishan Dholakia; Gabriel C. Spalding, Editor(s)