An investigation of the symmetrical properties in the invariant imbedding T-matrix method for the nonspherical particles with symmetrical geometry

Abstract

The Invariant Imbedding (IIM) T-matrix method is recognized as one of the most promising scattering models since it can perform the scattering simulation of the nonspherical particles in a semi-analytical way. However, because the T-matrix should be updated in each iterative process, its computational efficiency is an important issue in the actual scattering simulation. To alleviate this problem, the symmetrical properties for the nonspherical particles with symmetrical geometries are systematically investigated in this paper. Firstly, the symmetry of the U-matrix (an important matrix in the IIM T-matrix model) is derived for the particles with mirror symmetry with respect to the coordinate planes. In this case, the U-matrix is firstly decomposed into the sine and cosine components, and then its symmetrical properties are obtained by combining the spatial symmetry of the permittivity and the symmetry of the angular functions. In the second part, the symmetry of the U-matrix is derived for the particles with N-folds symmetrical geometry, and based on the symmetrical properties, the method to simplify the T-matrix iteration is further proposed. In this case, it can be found that by using the symmetry of the U-matrix, both the U-matrix and T-matrix can be rearranged into the block diagonal ones, and the calculation of the T-matrix can be decomposed into the iteration of several block sub-matrices, which can cut down the computational amount and memory consumption notably. Also, it can be seen that the derivation process also provides another point of view to understand the symmetry of T-matrix for the particles with N-folds symmetrical geometry.