Principal modes of Maxwell’s equations

Research output: Chapter in Book/Report/Conference proceedingChapter


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.
Original languageEnglish
Title of host publicationThe Generalized Multipole Technique for Light Scattering
EditorsThomas Wriedt, Yuri Eremin
Place of PublicationBerlin
PublisherSpringer International Publishing AG
Number of pages33
ISBN (Print)9783319748894, 9783319748900
Publication statusPublished - 3 Apr 2018

Publication series

NameSpringer Series on Atomic, Optical, and Plasma Physics
ISSN (Print)1615-5653
ISSN (Electronic)2197-6791


  • principal modes
  • phase factors
  • Maxwell's equations

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  • Research Output

    The effect of oxidation on the far-field scattering of aluminium patch antennae from visible to UV

    McArthur, D. & Papoff, F., 1 Jul 2019, In : International Journal of Optics. 2019, p. 1-5 5 p., 9687803.

    Research output: Contribution to journalArticle

    Open Access
  • Cite this

    Hourahine, B., McArthur, D., & Papoff, F. (2018). Principal modes of Maxwell’s equations. In T. Wriedt, & Y. Eremin (Eds.), The Generalized Multipole Technique for Light Scattering (Springer Series on Atomic, Optical, and Plasma Physics). Berlin: Springer International Publishing AG.