Edge-effect contribution to the extinction of light by dielectric disks and cylindrical particles

The extinction efficiency factor associated with the scattering of a plane electromagnetic wave impinging on a basal face of a dielectric disk or a cylindrical particle is investigated by employing the physical-geometric optics hybrid (PGOH) method and the discrete-dipole approximation (DDA) method. It is found that the derived extinction efficiency factor from the PGOH is a function of the thickness of the disk, or the length of the cylinder, and the refractive index, but is independent of the diameter and shape of the cross section of the basal face of the particle. Furthermore, the oscillations of the extinction efficiency factor versus the thickness or length of the particle do not diminish if the particle is not absorptive. The values of the extinction efficiency factor simulated from the DDA method are quite different from those computed from the PGOH, although the size parameter of the particle is in the commonly recognized geometric optics regime. To explain the difference, the concept of the edge effect associated with the tunneling rays in the semiclassical scattering theory is generalized from the case of spherical particles to that of nonspherical particles based on the localization principle. Accordingly, the edge-effect contribution can be distinguished and removed from the extinction cross section calculation by the DDA method. The remaining part of the extinction cross section, associated with the interference between the transmitted rays and incident rays, agrees well with the results computed from the PGOH, and the agreement illustrates the presence of the edge effect in the case of nonspherical particles with surfaces that have no curvature along the incident direction. It is found that the asymptotic extinction efficiency factor may not necessarily converge to 2, but it depends on the specific physical processes of the interference between diffracted and transmitted light and of the edge effect.