Modal Theory for Twisted Waveguides

Fyodor Morozko, Alina Karabchevsky, Andrey Novitsky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Twisted waveguides are promising building blocks for broadband polarization rotation in integrated photonics. They may find applications in polarization-encoded telecommunications and quantum-optical systems. In our work, we develop a rigorous modal theory for such waveguides. To this end, we define an eigenmode of a twisted waveguide as a natural generalization of the eigenmode of a straight waveguide. Using covariant approach for expressing Maxwell’s equations in helical reference frame, we obtain the eigenmode equation which appears to be nonlinear with respect to the eigenvalue, i.e. propagation constant. By analyzing the obtained equations we establish fundamental properties of the eigenmodes and prove their orthogonality. We develop a finite-difference full-vectorial scheme for solving the eigenmode equation and solve it using two approaches: with perturbation theory and using routines for nonlinear eigenvalue problems. By analyzing the obtained propagation constants and modal fields we explain the modal mechanism of polarization rotation in twisted waveguides and explain qualitatively polarization conversion efficiency dependence on twist length. Although photonic applications are of our primary concern, our results are general and apply to twisted waveguides of arbitrary architecture.

Original languageEnglish
Title of host publicationMetamaterials XIII
EditorsKevin F. MacDonald, Isabelle Staude, Anatoly V. Zayats
ISBN (Electronic)9781510651364
StatePublished - 1 Jan 2022
EventMetamaterials XIII 2022 - Virtual, Online
Duration: 9 May 202220 May 2022

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceMetamaterials XIII 2022
CityVirtual, Online


  • Twisted waveguides
  • eigenmode expansion method
  • finite-difference method
  • helical coordinates
  • nonlinear eigenvalue problem
  • polarization conversion

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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