Scattering of plane waves by soft obstacles: anomalous diffraction theory for circular cylinders

Abstract

An anomolous diffraction theory is presented to describe the scattering of plane waves by circular cylinders for the general case of oblique incidence and for both real and complex values of particle refractive index in terms of a single Bessel-like function. By comparison with the formal solution of Maxwell’s equations, it is demonstrated that the simple theory well approximates the extinction and absorption efficiencies, particularly for a normally incident wave on a nonabsorbing or weakly to moderately absorbing particle. It is also shown that the simple theory provides the correct small (i.e., x → 0) and large (i.e., x → ∞) particle limits for extinction and absorption efficiencies despite the original premise that the theory requires x ≫ 1. The simple theory is particularly useful for those types of practical problem that require integration over all particle orientations or integration over a distribution of particle sizes, since these integrations tend to smear out the errors associated with the single particle theory.