Correlations in semiconductor ring lasers in the bidirectional regime

Abstract

We study the influence of spontaneous emission noise in a two-mode model for semiconductor ring lasers, biased in the bidirectional static emission regime. The analysis is carried out by linearizing the model close to a stable stationary solution, and considering effect of noise as stochastic perturbations expressed by Langevin forces. At a linear level, pertubations concerning the total intensity and carrier inversion dynamics decouple from the energy distribution processes between the two modes. This fact permits a full analytic analysis, well confirmed by numerical simulations of the complete non linear system. The analysis shows that semiconductor ring lasers have peculiar noise properties. On one side the total intensity and carrier density show a noise spectrum characterized by a resonance induced by the typical field-medium exchange processes (relaxation oscillations) and the global phase invariance induced by the Goldstone mode, so as far as those variables are concerned, it behaves as a standard single-mode Fabry-Perot semiconductor laser. Besides, the degree of freedom associated to the simultaneous presence of two counterpropagating modes allows for a further process of energy exchange between the two modes. Our analysis unveils that such process presents a resonance peak as well, influenced mainly by the backscattering parameters, and can be excited in the bidirectional regime as a ’noisy precursor’ of a Hopf bifurcation.

The present work represents the development of reliable tools for the simulation and analytical analysis of a model for semiconductor ring lasers. Reliability is tested by a thoughout comparison between simulation and calculations. Future developments will range from quantitative evaluation of two-times correlations functions, to applications to rotation sensing, to analysis of the stochastic jumps induced by noise in the bistable regime.