Rigorous justification of the cylindrical localized approximation to speed up computations in the generalized Lorenz–Mie theory for cylinders

To speed up the numerical computation of beam shape coefficients in the generalized Lorenz–Mie theory (GLMT) for cylinders, a cylindrical localized approximation has recently been introduced [J. Opt. Soc. Am. A14, 3014 (1997)], in analogy with the localized approximation used for the GLMT for spheres. A rigorous justification of this cylindrical localized approximation is presented.