A note on the spherical harmonic expansion of the Mie scattering kernel

Three methods of obtaining the Mie scattering function are considered and compared . Legendre polynomials and Clebsh-Gordon coefficients are employed and an exact expression for the expansion of the Mie kernel in spherical harmonics is given . 1 . Introduction The absorption and scattering of electromagnetic radiation by a sphere of arbitrary size and refractive index is an exactly solvable problem with an extensive literature [1-3] . The angular variation of intensity of the scattered light is the radial component of the Poynting vector of the radiation and has the form, for unpolarised light Is(0) = S'l I(0)Il, (1) where Ii is the incident intensity and the scattering kernel S 11 is expressible as S,1(0) 1 r (2n+1) (2m+1)~ 2xZ n(n+l) m(m+1) [`q" m (x)F„,m cos6+B„, m(x)G„,m cosB], (2)