Ma. Karam et al., IMPROVEMENT OF THE RAYLEIGH APPROXIMATION FOR SCATTERING FROM A SMALLSCATTERER, IEEE transactions on antennas and propagation, 43(7), 1995, pp. 681-688
An improvement of the Rayleigh approximation for electromagnetic scatt
ering from an arbitrary small scatterer is developed through solving t
he conventional integro-differential equation governing the electric f
ield inside the scatterer. The improvement is represented by an equiva
lent polarizability tenser differing from that used in the Rayleigh ap
proximation in two aspects: i) it is frequency dependent, and ii) it g
ives a scattering amplitude tenser satisfying energy conservation. The
energy conservation is investigated through formulating the extinctio
n, scattering, and absorption losses according to the equivalent polar
izability tenser. Numerical calculations on spheres and spheroids indi
cate that the present extinction loss formulation has a wider validity
range than the extinction loss formulation according to the Rayleigh
approximation.