Extending the Spectral Integral Method to Solving 3-D Electromagnetic Scattering From a Smooth Sphere

Previous works have shown that due to its high-order accuracy with exponential convergence, the spectral integral method (SIM) significantly outperforms the traditional surface integral equation (SIE) for computing electromagnetic (EM) scattering from 2-D homogeneous objects with smooth boundaries (e.g., infinitely long circular cylinders) in terms of memory and time cost. This work extends SIM to the computation of EM scattering from smooth 3-D spheres filled with metal or homogeneous dielectric materials. Starting from the traditional SIE, the unknown spatial-domain equivalent electric and magnetic currents on the sphere surface are expanded by truncated vector spherical harmonics (VSH) series with unknown coefficients. Then the dyadic Green’s functions (DGFs) directly interact with VSH and thus are transformed into their spherical-harmonic spectral coefficients by surface integrals. Consequently, the conventional spatial-domain convolutional integrals in the SIE are transformed into multiplications of VSH spectral coefficients. Finally, to maintain the reliability of the SIM solution, the discretized equations are constructed by sampling the field values at the perturbed spherical Fibonacci grids (SFGs). To justify the computation accuracy and implementation efficiency of SIM applied to EM scattering from metal and dielectric spheres, a few numerical experiments were conducted, comparing it to the traditional SIE method. It is found that SIM only needs the spatial sampling density (SD) of 4 points per wavelength (PPW) to achieve reliable computation results while the traditional SIE usually requires an SD of 25 PPW to reach the same accuracy. In addition, the dependence of the required number of VSH modes to accurately represent the scattered fields on the distance between the excitation source and the scatterer is also studied.