Large Aspect Ratio T-matrix Method

For particles with rotational symmetry, such as circular cylinders and spheroids, the T-matrix method is the most effective one to obtain the scattering properties. In the current T-matrix method, electromagnetic fields are expanded in terms of vector spherical wave functions. The expansion orders in specific cases depend largely on the size parameter and the aspect ratio of the particle. In general, the larger the aspect ratios of particles are, the smaller size parameters this method can deal with. However, a new method has been proposed in order to deal with large particles with large aspect ratios. This method divides a prolate particle into several equal or unequal sub-pieces. For each sub-piece, the corresponding transition matrix can be acquired in terms of the current T-matrix method. Furthermore, scattering coefficients of each sub-piece are related to incident coefficients through these transition matrices and through the addition coefficients. The scattering coefficients of the single particle are composed of the ones of each sub-piece. Eventually, a new transition matrix relating the total scattering fields to incident fields is obtained after a series of arithmetic processes. Therefore, this method can deal with relatively large particles with large aspect ratios.