Exact partial wave expansion of optical beams with respect to arbitrary origin

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(K. Dholakia & G. C. Spalding, Eds.) Optical Trapping and Optical Micromanipulation III. 1000 20TH ST, PO BOX 10, BELLINGHAM, WA 98227-0010 USA: SPIE-INT SOC OPTICAL ENGINEERING (2006) .



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.

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