Nonlinear Optical Eigenmodes

Graeme Docherty-Walthew, Michael Mazilu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


In linear optics, the concept of a mode is well established. Often these modes correspond to a set of fields that are mutually orthogonal with intensity profiles that are invariant as they propagate through an optical medium. More generally, one can define a set of orthogonal modes with respect to an optical measure that is linear in intensity or quadratic/Hermitian in the fields using the method of Optical Eigenmodes (OEi). However, if the intensity of the light is large, the dipole response of an optical medium introduces nonlinear terms to Maxwell’s equations. In this nonlinear regime such terms influence the evolution of the fields and the principle of superposition is no longer valid and consequently, the method of Optical Eigenmodes breaks down. In this work, we define Optical Eigenmodes in the presence of these nonlinear source terms by introducing small perturbation fields onto a nonlinear background interaction and show how this background interaction influences the symmetries associated with the eigenmodes. In particular, by introducing orbital angular momentum (OAM) to the Hilbert space of the perturbation and background fields, we observe conservation laws and symmetries for which we derive associated operators.
Original languageEnglish
Title of host publicationComplex Light and Optical Forces XIII
EditorsJesper Glückstad, David L. Andrews, Enrique J. Galvez
PublisherSociety of Photo-Optical Instrumentation Engineers
Number of pages7
Publication statusPublished - 1 Mar 2019
EventComplex Light and Optical Forces XIII (SPIE OPTO) - Moscone Center, San Francisco, United States
Duration: 2 Feb 20197 Feb 2019
Conference number: 10935

Publication series

NameProceedings of SPIE
PublisherSociety of Photo-optical Instrumentation Engineers
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceComplex Light and Optical Forces XIII (SPIE OPTO)
Abbreviated titleSPIE OPTO
Country/TerritoryUnited States
CitySan Francisco
Internet address


  • Optical eigenmodes
  • Nonlinear optics
  • Structured eliminination
  • Optical angular momentum


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