Light scattering by small particles: an ellipsoidal model that uses a quasistatic approach

To describe light scattering by small nonspherical particles, we have constructed an ellipsoidal model using a quasistatic approximation. The semiaxes of the model ellipsoid are determined based on the requirement that the volumes of initial and model particles are equal, as well as the ratios of their maximum longitudinal and transverse dimensions. This ensures the closeness of the optical properties of initial and model particles. This approach has been applied to parallelepipeds, cylinders, and cones. The range of applicability has been determined by comparing the results of numerical calculations with approximate and rigorous methods. As a rigorous method, we have chosen the discrete dipole approximation (DDA), which is applicable to arbitrary nonspherical particles. We have shown that, for parallelepipeds and cylinders, the applicability range of the model is rather wide with respect to different parameters of the problem. At the same time, the model is less suitable for cones, and it should be completely avoided for oblate particles in the case when a plane TM wave is incident on particles perpendicularly to their symmetry axis. In general, the proposed approximation yields more accurate results and has a large range of applicability upon a decrease in the relative refractive index and an increase in the semiaxis ratio of the “effective” ellipsoid, $a_{\mathrm{ef}}/b_{\mathrm{ef}}$, i.e., for strongly prolate and strongly oblate transparent particles.