RIGOROUS JUSTIFICATION OF THE LOCALIZED APPROXIMATION TO THE BEAM-SHAPE COEFFICIENTS IN GENERALIZED LORENZ-MIE THEORY .1. ON-AXIS BEAMS

Generalized Lorenz-Mie theory describes electromagnetic scattering of an arbitrary light beam by a spherical particle. The computationally m ost expensive feature of the theory is the evaluation of the beam-shap e coefficients, which give the decomposition of the incident light bea m into partial waves. The so-called localized approximation to these c oefficients for a focused Gaussian beam is an analytical function whos e use greatly simplifies Gaussian-beam scattering calculations. A math ematical justification and physical interpretation of the localized ap proximation is presented for on-axis beams.