Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers

Abstract : Using advanced continuation techniques for dynamical systems, we elucidate the bifurcations leading to asymptotically stable square-wave pulsing and polarization mode switching in semiconductor lasers with mutual time-delayed and polarization rotating coupling. We find that the increase of coupling strength leads to a cascade of Hopf bifurcations on a mixed-mode steady state up to a transcritical bifurcation on a so-called pure-mode steady state where both lasers emit with the injected polarization state. From these successive Hopf bifurcations emerge time-periodic solutions that have a period close to the laser relaxation oscillation for weak coupling but a period close to twice the time delay for large coupling strength. The wave form of the time-periodic solutions also evolves from harmonic pulsing up to square-wave pulsing as has been observed recently in experiments.
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Submitted on : Tuesday, August 28, 2012 - 12:09:06 PM
Last modification on : Tuesday, May 16, 2017 - 4:05:37 PM

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Marc Sciamanna, Martin Virte, Cristina Masoller, Athanasios Gavrielides. Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2012, 86 (1), pp.016218-1-7. ⟨10.1103/PhysRevE.86.016218⟩. ⟨hal-00725920⟩

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