From snaking to isolas: A one-active-site approximation in discrete optical cavities

R. Kusdiantara*, H. Susanto, A.R. Champneys

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We investigate time-independent solutions of a discrete optical cavity model featuring saturable Kerr nonlinearity, a discrete version of the Lugiato–Lefever equation. This model supports continuous wave (uniform) and localized (discrete soliton) solutions. Stationary bright solitons arise through the interaction of dark and bright uniform states, forming a homoclinic snaking bifurcation diagram within the Pomeau pinning region. As the system approaches the anti-continuum limit (weak coupling), this snaking bifurcation widens and transitions into ⊂ -shaped isolas. We propose a one-active-site approximation that effectively captures the system’s behavior in this regime. The approximation also provides insight into the stability properties of soliton states. Numerical continuation and spectral analysis confirm the accuracy of this semianalytical method, showing excellent agreement with the full model.
Original languageEnglish
Article number103495
JournalWave Motion
Volume134
Early online date18 Jan 2025
DOIs
Publication statusPublished - 1 Apr 2025

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© 2025

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