Calculation of generalized Lorenz-Mie theory based on the localized beam models

- In this work, we introduce the proper pre-factors to the Bessel functions, BSCs and the angular functions. With this improvement, all the quantities involved in the numerical calculation are scaled into a reasonable range of values so that the algorithm can be used for computing the physical quantities of the GLMT.
- The algorithm is not only an improvement in numerical technique, it also implies that the set of basic functions involved in the electromagnetic scattering (and sonic scattering) can be reasonably chosen.
- The algorithms of the GLMT computations introduced in previous references suggested that the order of the n and m sums is interchanged. In this work, the sum of azimuth modes is performed for each partial wave. This offers the possibility to speed up the computation, since the sum of partial waves can be optimized according to the illumination conditions and the sum of azimuth modes can be truncated by selecting a criterion discussed in Section 3.3.
- Numerical results show that the algorithm is efficient, reliable and robust, even in very exotic cases. The algorithm presented in this paper is based on the original localized approximation and it can also be used for the MLA calculation with slight modification.

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 (GLMT). The numerical calculation of relevant physical quantities is a challenge for its practical applications due to the limit of computer resources. The study presents an improved algorithm of the GLMT calculation based on the localized beam models. The BSCs and the angular functions are calculated by multiplying them with pre-factors so as to keep their values in a reasonable range. The algorithm is primarily developed for the original localized approximation (OLA) and is further extended to the modified localized approximation (MLA). Numerical results show that the algorithm is efficient, reliable and robust.