Principal modes of Maxwell’s equations

Hourahine, Benjamin and McArthur, Duncan and Papoff, Francesco; Wriedt, Thomas and Eremin, Yuri, eds. (2018) Principal modes of Maxwell’s equations. In: The Generalized Multipole Technique for Light Scattering. Springer Series on Atomic, Optical, and Plasma Physics . Springer International Publishing AG, Berlin. ISBN 9783319748900

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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 of Mie’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.