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Compact formulation of the beam shape coefficients for elliptical Gaussian beam based on localized approximation.

It has been proved that localized approximation (LA) is the most efficient way to evaluate the beam shape coefficients (BSCs) in generalized Lorenz-Mie theory. The BSCs are usually expressed in the form of multiple summations of an infinite series of terms, which is cumbersome to calculate, and the infinite series is frequently slowly convergent. In this paper, we present a compact expression of the BSCs for an elliptical Gaussian beam based on the LA that is more convenient and efficient for numerical computations. A comparison with the integral LA is made, showing the reliability, stability, and efficiency of the presented formulation.