Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities

AV Yulin, AR Champneys

Research output: Working paperWorking paper and Preprints

180 Downloads (Pure)

Abstract

This paper continues an investigation into a one-dimensional lattice equation that models the light field in a system comprised of a periodic array of pumped optical cavities with saturable nonlinearity. The additional effects of a spatial gradient of the phase of the pump field are studied, which in the presence of loss terms is shown to break the spatial reversibility of the steady problem. Unlike for continuum systems, small symmetry-breaking is argued to not lead directly to moving solitons, but there remains a pinning region in which there are infinitely many distinct stable stationary solitons of arbitrarily large width. These solitons are no-longer arranged in a homoclinic snaking bifurcation diagrams, but instead break up into discrete isolas. For large enough symmetry-breaking, the fold bifurcations of the lowest intensity solitons no longer overlap, which is argued to be the trigger point of moving localised structures. Due to the dissipative nature of the problem, any radiation shed by these structures is damped and so they appear to be true attractors. Careful direct numerical simulations reveal that branches of the moving solitons undergo unsual hysteresis with respect to the pump, for sufficiently large symmetry breaking.
Original languageEnglish
Publication statusPublished - 12 Jan 2010

Bibliographical note

Additional information: Preprint of a paper submitted to AIMS journal publications

Sponsorship: This work was supported by EPSRC grant EP/D079357/1

Keywords

  • moving solitons
  • lattice equation

Fingerprint Dive into the research topics of 'Snake-to-isola transition and moving solitons via symmetry-breaking in discrete optical cavities'. Together they form a unique fingerprint.

Cite this