Electromagnetic wave scattering by a small impedance particle of arbitrary shape

Scattering of electromagnetic (EM) waves by one small (ka ≪ 1) impedance particle (body) D of arbitrary shape, embedded in a homogeneous medium, is studied. Physical properties of the particle are described by its boundary impedance. The problem is of interest because scattering of light by colloidal particles, or by dust in the air is an example of the scattering theory discussed in this paper. An analytic formula is obtained for the EM field in the far zone without usage of boundary integral equation. If a monochromatic incident field of frequency ω is E0(x, ω), then the scattered field v in the zone r : = |x| ≫ a, where a = 0.5diamD is the characteristic size of D  , is calculated by the formula v=[∇eikr4πr,Q], where [A, B] is the cross product of two vectors, (Q, ej) is the dot product, ej, 1 ≤ j ≤ 3, are orthonormal basis vectors in R3R3, Qj:=(Q,ej)=−iζ|S|ωμ0τjp(∇×E0(O))p, over the repeated index p summation is understood from Eqs. (1) to (3), ζ is the boundary impedance and |S| is the surface area of the particle, O ∈ D is the origin, the tensor τjp : = δjp − |S|− 1 ∫ S Nj(s)Np(s)ds, where Nj(s) is the j-th component of the unit normal N(s) to the surface S at the point s ∈ S, k = ω(ε0μ0)1/2 is the wave number.