Lyapunov exponents of quantum dot laser systems under optical feedback: influence of cavity length

Abstract

Abstract Performance of quantum dot lasers subject to optical feedback is numerically studied in this work from Lang-Kobayashi and multi-population rate-equation models. The approach adopted to study the characteristics of the laser response is based on the calculation of the Lyapunov exponents of the system and revealed the existence of chaos in shorter devices. Influence of the time-delay of the reflected back electrical field has also been addressed. Keywords semiconductor laser system, Lyapunov exponents, quantum dotsResumo O desempenho de lasers de pontos quânticos quando submetidos a realimentação óptica é estudado numericamente neste trabalho, a partir dos modelos de equações de taxa de Lang-Kobayashi e de multi-populações. A abordagem adotada para estudar as características da resposta laser é baseada no cálculo dos expoentes de Lyapunov do sistema, e revelou a existência de caos em dispositivos curtos. A influência da constante de atraso do campo elétrico refletido para a cavidade também é incluída na análise.Palavras-chave sistema laser semicondutor, expoentes de Lyapunov, pontos quânticos

A Survey on the Nonlinear Analysis of Quantum Dot Semiconductor Lasers

“…As explained in section 3, another approach for characterizing the occurrence of chaos in QD lasers is the calculation of the spectrum of Lyapunov exponents, what has been considered in recent conferences papers. In [39], the influence of the laser cavity length on the sensitivity to optical feedback from an external mirror was revisited; calculations revealed that the dynamical system representing the operation of longer devices (1 mm length) does not present any positive Lyapunov exponent, whereas for shorter lasers (700 and 600 µm) there is one positive exponent along the 140 th direction of the phase space (that representing the electrical field intensity in the laser cavity). Additionally, it was also studied the influence of the external cavity length in the sensitivity to initial conditions for short laser devices; the conclusion was that the longer the external cavity the sooner adjacent trajectories start to deviate from each other.…”