Discrete Numerical Approach to the Fredholm Integral Method for Evaluating Scattering by Irregular Dielectric Particles

A new approach to the implementation of the Fredholm integral method (FIM) was developed to evaluate scattering by irregular dielectric particles. In this paper, particles are modeled discretizing their volume with cells according to their weighted contents. The approach to FIM presented in this paper represents a departure from earlier work where the numerical integration is no longer based on expansion in a set of polynomials but on direct spatial integration. This approach which still involves contour integration method uses quandrantal contour in combination with a conditioning weighting function to control the magnitude of the integrand due to the power of the radial variable in the integrand being odd. The strength of our approach lies on the fact that computations are performed in the spatial frequency domain. As a result, the angular scattering pattern is strongly connected to the spatial Fourier transform of the scatterer; hence, for electrically small particles the angular spectrum is relatively smooth and the number of pivots required for integration is relatively low. This technique is well suited to the treatment of scattering from irregular inhomogeneous dielectric particles since only the distribution in space of the dielectric constants needs to be defined. Numerical results also confirm the inadequacy of effective medium theories in evaluating scattering characteristics of inhomogeneous particles.