Numerical and Analytical Formulizations of the Extended Mie Theory for Solving the Sphere Scattering Problem

Abstract

For biomedical applications of numerical electromagnetics, the basic Mie theory is extended to the scenario where the spherical scatter and the surrounding medium are given electromagnetic properties of biological tissues. The numerical approach and the analytical approach to solve the six partial differential equations of the extended Mie theory are formulized in detail. Using two representative models, we validate the numerical and analytical solutions against the result from the standard finite-difference time-domain (FDTD) method and theoretical data. Both solutions are compared with respect to the accuracy and efficiency. The analytical solution provides more accurate results whereas the numerical solution is considerably more efficient. Therefore, the summarized analytical and numerical formulas of the extended Mie theory are both at choice for applications to numerical bioelectromagnetics.