Light scattering by an elongated particle: spheroid versus infinite cylinder

Abstract

Using the method of separation of variables and a new approach to calculations of the prolate spheroidal wave functions, we study the optical properties of very elongated (cigar-like) spheroidal particles. A comparison of extinction efficiency factors of prolate spheroids and infinitely long circular cylinders is made. For the normal and oblique incidence of radiation, the efficiency factors for spheroids converge to some limiting values with an increasing aspect ratio a/b provided particles of the same thickness are considered. These values are close to, but do not coincide with the factors for infinite cylinders. The relative difference between factors for infinite cylinders and elongated spheroids ($a/b \ga 5$) usually does not exceed 20 % if the following approximate relation between the angle of incidence $α(in degrees)$ and the particle refractive index m=n+ki takes the place: $α\ga 50 |m-1| + 5$ where $1.2 \la n \la 2.0$ and $k \la 0.1$. We show that the quasistatic approximation can be well used for very elongated optically soft spheroids of large sizes.