Large-sphere limits of the Mie-scattering functions

Abstract

For x/n ≫ 1, the following relations between the Mie-scattering functions a_n (x,m) and b_n(x,m) are satisfied: a₁ (x,m) = b₂ (x,m) = a₃ (x,m) = ⋯ = a_n−1(x,m) = b_n(x,m) and b₁(x,m) = a₂ (x,m) = b₃ (x,m) = ⋯ = b_n−1 (x,m) = a_n(x,m) for arbitrary refractive index m. By use of these relations, the Van de Hulst and Deirmendjian conjectures about the x → ∞ behavior of the scattering functions or their linear and bilinear combinations, as well as several new relations, are rigorously proved.

© 1973 Optical Society of America

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