Involve: A Journal of Mathematics

  • Involve
  • Volume 3, Number 3 (2010), 259-271.

Coexistence of stable ECM solutions in the Lang–Kobayashi system

Ericka Mochan, Davis Buenger, and Tamas Wiandt

Full-text: Open access

Abstract

The Lang–Kobayashi system of delay differential equations describes the behavior of the complex electric field and inversion N inside an external cavity semiconductor laser. This system has a family of special periodic solutions known as external cavity modes (ECMs). It is well known that these ECM solutions appear through saddle-node bifurcations, then lose stability through a Hopf bifurcation before new ECM solutions are born through a secondary saddle-node bifurcation. Employing analytical and numerical techniques, we show that for certain short external cavity lasers the loss of stability happens only after the secondary saddle-node bifurcations, which means that stable ECM solutions can coexist in these systems. We also investigate the basins of these ECM attractors.

Article information

Source
Involve, Volume 3, Number 3 (2010), 259-271.

Dates
Received: 15 September 2009
Revised: 6 August 2010
Accepted: 19 August 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733317

Digital Object Identifier
doi:10.2140/involve.2010.3.259

Mathematical Reviews number (MathSciNet)
MR2739518

Zentralblatt MATH identifier
1211.34105

Subjects
Primary: 37G35: Attractors and their bifurcations 37M20: Computational methods for bifurcation problems 78A60: Lasers, masers, optical bistability, nonlinear optics [See also 81V80]

Keywords
delay differential equations bifurcations Lang–Kobayashi equations

Citation

Mochan, Ericka; Buenger, Davis; Wiandt, Tamas. Coexistence of stable ECM solutions in the Lang–Kobayashi system. Involve 3 (2010), no. 3, 259--271. doi:10.2140/involve.2010.3.259. https://projecteuclid.org/euclid.involve/1513733317


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