Nonlinear Schrödinger equation for integrated photonics

Kevin Bach Gravesen*, Asger Brimnes Gardner, Emil Zanchetta Ulsig, Eric J. Stanton, Mikkel Torrild Hansen, Simon Thorndahl Thomsen, Lucas Ahler, Nicolas Volet

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


The foundations of nonlinear optics are revisited, and the formalism is applied to waveguide modes. The effects of loss and dispersion are included rigorously along with the vectorial nature of the modes, and a full derivation of a new version of the nonlinear Schrödinger (NLS) equation is presented. This leads to more general expressions for the group index, for the group-index dispersion (GVD), and for the Kerr coefficient. These quantities are essential for the design of waveguides suitable for, e.g., the generation of optical frequency combs and all-optical switches. Examples are given using the silicon nitride material platform. Specifically, values are extracted for the coefficients of the chi-3 tensor based on measurements of Kerr coefficients and mode simulations.

Original languageEnglish
JournalJournal of the Optical Society of America B: Optical Physics
Pages (from-to)1451-1456
Number of pages6
Publication statusPublished - Jun 2024


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