Crisis route to chaos in semiconductor lasers subjected to external optical feedback

Abstract

Semiconductor lasers subjected to optical feedback have been intensively used as archetypical testbeds for high-speed (sub-ns) and high-dimensional nonlinear dynamics. By simultaneously extracting all the dynamical variables, we demonstrate that for larger current, the commonly named "quasiperiodic" route is in fact based on mixed external-cavity solutions that lock the oscillation frequency of the intensity, voltage, and separation in optical frequency through a mechanism involving successive rejections along the unstable manifold of an antimode. We show that chaos emerges from a crisis resulting from the inability to maintain locking as the unstable manifold becomes inaccessible.

Routes to Chaos of a Semiconductor Laser Subjected to External Optical Feedback: A Review

“…A description of the principles and implementation of the heterodyne technique can be found in Refs. [14,16]. [17,18].…”

“…Not represented: the heterodyne scheme used to measure the optical phase (please refer to Refs. [14,16]).…”

“…Detailed experimental reports and interpretation of the intensity, phase, and optical spectrum in the various regimes can be found in Refs. [16,17,24,25]; the main points are focused on here.…”

“…The first regime that can be identified experimentally looks quasiperiodic in the time domain (region β). A study of the optical spectra and optical phase [16] reveals that it actually involves an alternation in time between a periodic oscillation located around ECM 1 and another ECM, which depends on feedback level (e.g., ECM −3 or ECM −4). The quasiperiodic appearance in time therefore does not result from a torus that would have developed from two successive Hopf bifurcations of a given ECM, as would be expected in a traditional quasiperiodic (Ruelle-Takens or Curry-Yorke) route [26], but is rather the result of the interaction between two equilibria (ECMs).…”

“…Indeed, when the PD regime is reached in region ε, the RF frequencies still display locking, as I and V show period-doubled oscillation at 3.5 GHz, corresponding to a halving of the frequency (7 GHz) of the last limit cycle of region γ. In addition, a locking occurs at the optical frequency level since the ECMs participating in the dynamics, as revealed by the optical spectrum and phase [16], are also separated by 7 GHz. Specifically, ECMS 3, −4, and −11 participate in the period-doubled dynamics: 3 and −11 are separated by 7 GHz, while 3 and −4, and −4 and −11, are separated by 3.5 GHz.…”