Transition matrix of a nonspherical particle in the non-local optical response theory

Abstract

In this paper, we present two methods for deriving the transition matrix of a nonspherical particle in the non-local optical response theory, which is important for particles of size below about 10 nm. The key point in our analysis is the separation of the internal field into a transverse and a longitudinal component. The first method for T-matrix calculation relies on the null-field equation for the total field inside the particle, the null-field equation for the longitudinal field outside the particle, and the integral representation of the scattered field. The second method uses a projection scheme for the additional boundary condition instead of the null-field equation for the longitudinal field. When the non-local effects are neglected, the transition matrix becomes the transition matrix in the local optical response theory, while for spherical particles, the transition matrix is analytically equivalent to the transition matrix derived by the extended Mie scattering theory that considers non-local optical response. The numerical results obtained by the T-matrix method are in good agreement with the results delivered by the discrete sources method which also considers non-local optical response.