An efficient solver for the generalized normal modes of non-uniform open optical resonators

Parry Y. Chen, Yonatan Sivan, Egor A. Muljarov

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Modal expansion is an attractive technique for solving electromagnetic scattering problems. With the one set of resonator modes, calculated once and for all, any configuration of near-field or far-field sources can be obtained almost instantaneously. Traditionally applied to closed systems, a simple and rigorous generalization of modal expansion to open systems using eigenpermittivity states is also available. These open modes are suitable for typical nanophotonic systems, for example. However, the numerical generation of modes is usually the most difficult and time-consuming step of modal expansion techniques. Here, we demonstrate efficient and reliable mode generation, expanding the target modes into the modes of a simpler open system that are known. Such a re-expansion technique is implemented for resonators with non-uniform permittivity profiles, demonstrating its rapid convergence. Key to the method's success is the inclusion of a set of longitudinal basis modes.

Original languageEnglish
Article number109754
JournalJournal of Computational Physics
StatePublished - 1 Dec 2020


  • Mode solver
  • Normal mode expansion
  • Open systems
  • Spatially-varying permittivity

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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