Uniform-over-size approximation of the internal fields for scatterers with low refractive-index contrast

Abstract

We improved the Wentzel-Kramers-Brillouin (WKB) approximation for calculating the electric field inside a scatterer. The new method, named WKBr, additionally takes into account refraction (rotation) of the incident rays at the particle-medium interface. For large particles the WKBr is equivalent to the geometric optics in the limit of relative refractive index m approaching 1. Thus, the resulting accuracy is determined by (m − 1) uniformly for all particle sizes, in contrast to the original WKB, which accuracy deteriorates with increasing size. We extensively studied several versions WKBr for the case of a homogeneous sphere. These versions additionally account for Fresnel transmission and wavefront focusing for rays entering the scatterer, combination of intersecting rays, and the vanishing of the electric field in the shadow region. While keeping the same order of errors with varying (m − 1), they significantly reduce the errors for moderate values of m (from 1.1 to 1.3). Further, we tested the WKB and WKBr as an initial guess in the iterative solution of the linear system in the framework of the discrete dipole approximation (DDA). It allowed us to accelerate the DDA solution without compromising the final accuracy. The acceleration becomes more pronounced with increasing size, while the WKBr becomes clearly superior to the WKB. Moreover, the new initialization of the iterative solver extends the practical applicability of the DDA to size parameter equal to 250, 160, and 140 for m = 1.1, 1.2, and 1.3, respectively. They could not be reached previously due to the stagnation of the iterative solution. We expect similar DDA acceleration for particles of other shapes. One can easily test it for the case of the WKB, since it is already implemented in the open-source ADDA code.