A new approach to solution of the light scattering problems for particles with a symmetry plane by using the field expansions in wave functions

Solving the light scattering problem for particles with the middle symmetry plane (e.g., spheroids), by applying the exact methods based on the field expansions in basis functions, leads to the linear systems with half matrix elements equal to zero. We suggest an approach that allows one to replace such a system with two ones having a twice smaller size, which significantly reduces the computational time. The approach is applied to the recently derived solution to the light scattering problem for homogeneous spheroids with the field expansions in spheroidal functions. The approach can be used in the case of the field expansions in spherical and other functions as well as for other scatterers, e.g., finite length cylinders, Chebyshev particles with the even parameter $n$, and so on, including both homogeneous and layered ones.