Principal Modes of Maxwell's Equations

This chapter reviews the use of principal modes-states which are maximally correlated between two subspaces and hence form pairs unique up to phase factors-in solving Maxwell's equations and analysing these solutions for nanoparticles and structures. The mathematical structure of this method allows a computationally efficient generalisation ofMie's analytical approach for the sphere to obtain semi-analytical solutions for general geometries with smooth interfaces. We apply this method to investigate a range of single and multiple particle metallic structures in the linear, non-linear and non-local response regimes outside of the quasi-static limit.