Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam

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Abstract
Expanding on developments presented in an earlier paper, theoretical expressions for the scattering coefficients of a homogeneous, absorbing, spherical particle irradiated by a fifth-order Gaussian beam are presented for the special case of the particle center located on the propagation axis of the beam. For this case, evaluation of two-dimensional surface integrals, required in computing the scattering coefficients for the most general particle location, is reduced to a computationally more efficient one-dimensional integral. For a typical size parameter α=πd/λ=17, the CPU time required for calculation of scattering coefficients is reduced by a factor of ∼1500 by using the simplified coefficient expressions. In addition, computation of electromagnetic field components is reduced from double summation to single summation expressions, further simplifying the field calculations.