Methods with discrete sources for electromagnetic scattering by large axisymmetric particles with extreme geometries

•Extension of discrete sources method to large axisymmetric particles.•Use of multiple SVWF with origins in complex plane.•Derivation of the invariant imbedding T-matrix equation.•Analytical method for computing the elements of the T-matrix.

The applicability of the discrete sources method and the null-field method with discrete sources to electromagnetic scattering by large axisymmetric particles with extreme geometries is analyzed. We present the numerical and theoretical improvements of the methods and design the null-field method with multiple spherical vector wave functions as an enhancement of the conventional null-field method for computing the optical properties of large size parameter particles. The numerical performances of the methods with discrete sources are illustrated through simulations in spheroidal and cylindrical particle cases.