Accuracy of internal fields in volume integral equation simulations of light scattering

We studied the accuracy of volume integral equation simulations of internal fields in small particles illuminated by a monochromatic plane wave as well as the accuracy of the scattered fields. We obtained this accuracy by considering scattering by spheres and comparing the simulated internal and scattered fields with those obtained by Mie theory. The accuracy was measured in several error norms (e.g., mean and root mean square). Furthermore, the distribution of the errors within the particle was obtained. The accuracy was measured as a function of the size parameter and the refractive index of the sphere and as a function of the cube size used in the simulations. The size parameter of the sphere was as large as 10, and three refractive indices were considered. The errors in the internal field are located mostly on the surface of the sphere, and even for fine discretizations they remain relatively large. The errors depend strongly on the refractive index of the particle. If the discretization is kept constant, the errors depend only weakly on the size parameter. We also examined the case of sharp internal field resonances in the sphere. We show that the simulation is able to reproduce the resonances in the internal field, although at a slightly larger refractive index.