Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the...

Several approximate methods for modeling the electromagnetic (em) scattering properties of nonspherical particles are examined and evaluated. Although some of the approaches are applicable to arbitrary shapes we confine our attention here mainly to spheres and cylinders, for which exact solutions are available for comparisons. Evaluations include comparisons of the computed angular phase function, total extinction efficiency, and backscatter efficiency. Approximate methods investigated include the Rayleigh-Gans (RG) approximation, the Wentzel-Kramers-Brillouin or WKB approximation [and the closely related eikonal approximation (EA)], diffraction theory, and the second-order Shifrin iterative technique. Examples using spheres indicate that for weakly absorbing particles of moderate- to large-size parameters with a real refractive index near unity (i.e., the optically soft case), all models work well in representing the phase function over all scattering angles, with the Shifrin approximation showing the best agreement with the exact solutions. For larger refractive indices, however, the Shifrin approximation breaks down, whereas the WKB method continues to perform relatively well for all scattering angles over a wide range of particle sizes, including those appropriate in both the RG (small particle) and the diffraction (large particle) limits. The relationship between the WKB, eikonal, and anomalous diffraction descriptions of particle extinction is discussed briefly. Backscatter is also discussed in the context of the WKB model, and two modifications to improve the description are included: one to add an internal-reflected internal wave and the other to add a multiplicative scaling factor to preserve the correct backscatter result for strong absorption in the geometric optics limit. A major conclusion of the paper is that the WKB method offers a viable alternative to the more widely used RG and diffraction approximations and is a method that offers significant improvement in accuracy with only a slight increase in mathematical complexity.