A T matrix method based upon scalar basis functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by the use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

- A derivation of the T matrix for a homogeneous particle is presented.
- The analysis begins with the standard volume integral equation.
- The basis functions are the VSWF translation operators.
- The result is completely equivalent to Waterman's surface integral formulation.