Full Wave Solutions of Multiple Scattering Using Vector Spheroidal Waves and Addition Theorem

In this paper, we develop a hybrid method to calculate the multiple scattering of arbitrary-shape objects, based on the rigorous solutions of Maxwell equations in the form of Foldy-Lax multiple scattering equations (FL). The hybrid method includes three steps: (1) calculating the T matrix of each single object using vector spheroidal waves, (2) vector spheroidal wave transformations, and (3) solving FL for all the objects. We utilize the commercial software HFSS to calculate the T matrix of a single object. From the numerical integration of the scattered fields from HFSS with the vector spheroidal waves, the T matrix is obtained. To perform wave transformations (i.e. addition theorem) for vector spheroidal waves, we develop robust numerical methods. In solving FL, the coherent wave interactions among the objects are considered and the multiple scattering of all the objects is calculated. The hybrid method is applicable for full wave simulations of objects with arbitrary shapes, such as trees with arbitrary-shape branches and leaves.