Recent intense interest in nanoparticle materials and nanoparticle-based contrast enhancement agents for biophysical applications gives new relevance to Mie scattering theory in its original context of application. The Mie theory still provides the most exact treatment of scattering from single nanoparticles of the noble metals. When recast in terms of modern electrodynamic formalism, the theory provides a concise closed-form representation for the scattered fields and also serves as a vehicle to elaborate the formal electrodynamic technique. The behavior of the Debye truncation condition for the multipole expansion is illustrated with numerical examples, clearly showing the features of the transition between the Rayleigh, dipole and higher order multipole approximations for the scattered fields. The classical Mie theory is an approximation in that only the transverse field components are included in the calculation. Extensions to the classical theory which include the effects of longitudinal fields are discussed and illustrated numerically. The example of scattering from multilayer composite particles is used to examine the feasibility of engineering spectral features of the scattering cross-section to target the requirements of specific applications.
Multipole expansion of Bessel and Gaussian beams for Mie scattering calculations
