Bifurcation analysis of a multi-transverse-mode VCSEL

K Green, B Krauskopf

Research output: Working paper

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We study the behaviour of a multi-transverse-mode vertical-cavity surface-emitting laser subject to optical feedback in which the optical modes are coupled through the external round-trip. Starting from a delayed partial differential equation description of the spatial optical mode profiles and the carrier diffusion, we first use eigenfunction expansion techniques to resolve the spatial dependence. The resulting system of delay differential equations is then amenable to a full nonlinear bifurcation analysis by means of numerical continuation techniques. As illustration, we present bifurcation diagrams of a two-mode VCSEL in the plane of feedback strength versus feedback phase. In this way, we identify a number of changes in the structure and bifurcations of the VCSEL's dynamics. In particular, we find coexisting stable steady state solutions, which bifurcate to stable in-phase and anti-phase periodic solutions with vastly differing frequencies. We show how these periodic solutions give rise to quasiperiodic and chaotic laser dynamics.
Original languageEnglish
Publication statusPublished - Feb 2008

Bibliographical note

Sponsorship: K.G. is funded by the Dynamics of Patterns Program of the Netherlands Organisation for Scientific Research (NWO) and the Foundation for Fundamental Research on Matter (FOM).


  • chaos
  • optical feedback
  • semiconductor laser
  • optical mode coupling
  • eigenfunction expansion
  • anti-phase dynamics
  • numerical continuation


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  • Bifurcation analysis of a multi-transverse-mode VCSEL

    Green, K. & Krauskopf, B., Feb 2008, Unknown.

    Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

    1 Citation (Scopus)

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