Improvement of the Rayleigh approximation for scattering from a small scatterer

An improvement of the Rayleigh approximation for electromagnetic scattering from an arbitrary small scatterer is developed through solving the conventional integro-differential equation governing the electric field inside the scatterer. The improvement is represented by an equivalent polarizability tensor differing from that used in the Rayleigh approximation in two aspects: (i) it is frequency dependent, and (ii) it gives a scattering amplitude tensor satisfying energy conservation. The energy conservation is investigated through formulating the extinction, scattering, and absorption losses according to the equivalent polarizability tensor. Numerical calculations on spheres and spheroids indicate that the present extinction loss formulation has a wider validity range than the extinction loss formulation according to the Rayleigh approximation