Feasibility of calculating morphology-dependent resonance peaks by numerical methods

Abstract

We investigate the feasibility of numerically calculating morphology-dependent resonance (MDR) peaks. To do so, one has to calculate the scattering intensities numerically and determine how difficult it is to numerically predict the position and the magnitude of the MDR peaks. However, at present, in practice it is impossible to calculate MDR peaks with a personal computer because so much computing time is required. Therefore the surface values of the Debye potential and its derivative for a homogeneous sphere are obtained from Mie's analytical solution and then used in integral equations to give the scattering intensities at a specific position of infinity by numerical integrations. It is shown that if a sufficient number of surface elements are used, the MDR peaks are exactly calculated for a homogeneous sphere with refractive index of 1.5, 1.4, and 1.3 up to a size parameter of 20. One can conjecture the number of finite and boundary elements necessary to numerically compute accurate scattering intensities. It should be also noted that the number of surface elements necessary for exact integration shows peaks similar to MDR peaks with respect to the size parameter. Therefore one will need many more elements at the size parameter at which the MDR occurs. (C) 2003 Optical Society of America.