Suppressing noise-induced intensity pulsations in semiconductor lasers by means of time-delayed feedback

We show by analytical and numerical results that coupling an external Fabry-Perot resonator to a semiconductor laser can efficiently suppress noise-induced intensity pulsations (relaxation oscillations). This constitutes a realization of time-delayed feedback control.

[1]  Uwe Küchler,et al.  Langevins stochastic differential equation extended by a time-delayed term , 1992 .

[2]  Kestutis Pyragas Control of chaos via extended delay feedback , 1995 .

[3]  Agrawal,et al.  Effect of phase-conjugate feedback on the noise characteristics of semiconductor lasers. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[4]  Mindaugas Radziunas,et al.  Semiconductor laser under resonant feedback from a Fabry--Perot: Stability of continuous wave operation , 2006 .

[5]  E Schöll,et al.  Delayed feedback control of noise-induced patterns in excitable media. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Andrey Pototsky,et al.  Correlation theory of delayed feedback in stochastic systems below Andronov-Hopf bifurcation. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  E Schöll,et al.  Comparison of time-delayed feedback schemes for spatiotemporal control of chaos in a reaction-diffusion system with global coupling. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Lutz Schimansky-Geier,et al.  Increase of coherence in excitable systems by delayed feedback , 2007 .

[9]  I. Sendiña-Nadal,et al.  Noise-induced wave nucleations in an excitable chemical reaction. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Kurt Wiesenfeld,et al.  Controlling Stochastic Resonance , 1999 .

[11]  L. Tsimring,et al.  Noise-induced dynamics in bistable systems with delay. , 2001, Physical review letters.

[12]  A. Pikovsky,et al.  Control of oscillators coherence by multiple delayed feedback , 2006 .

[13]  MID-INFRARED LASING INDUCED BY NOISE , 2003 .

[14]  E Schöll,et al.  All-optical noninvasive control of unstable steady states in a semiconductor laser. , 2006, Physical review letters.

[15]  E Schöll,et al.  Delayed feedback as a means of control of noise-induced motion. , 2003, Physical review letters.

[16]  M Radziunas,et al.  Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  W L Ditto,et al.  Noninvasive control of stochastic resonance. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Eckehard Schöll,et al.  Some basic remarks on eigenmode expansions of time-delay dynamics , 2007 .

[19]  CONTROL OF NOISE-INDUCED OSCILLATIONS OF A PENDULUM WITH A RANDOMLY VIBRATING SUSPENSION AXIS , 1997 .

[20]  L Schimansky-Geier,et al.  Coherence resonance near a Hopf bifurcation. , 2005, Physical review letters.

[21]  H. Haken,et al.  Stochastic resonance without external periodic force. , 1993, Physical review letters.

[22]  Giacomelli,et al.  Experimental evidence of coherence resonance in an optical system , 2000, Physical review letters.

[23]  P J Beek,et al.  Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  E Schöll,et al.  Control of unstable steady states by time-delayed feedback methods. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  E Schöll,et al.  Delayed feedback control of stochastic spatiotemporal dynamics in a resonant tunneling diode. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  C. Masoller Noise-induced resonance in delayed feedback systems. , 2002, Physical review letters.

[27]  B Krauskopf,et al.  Excitability and coherence resonance in lasers with saturable absorber. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Gavrielides,et al.  Lang and Kobayashi phase equation. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[29]  E Schöll,et al.  Long-term correlations in stochastic systems with extended time-delayed feedback. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  R. Lang,et al.  External optical feedback effects on semiconductor injection laser properties , 1980 .

[31]  Eckehard Schöll,et al.  Giant improvement of time-delayed feedback control by spatio-temporal filtering. , 2002, Physical review letters.

[32]  B Krauskopf,et al.  Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Eckehard Schöll,et al.  Control of noise-induced oscillations by delayed feedback , 2004 .

[34]  Eckehard Schöll,et al.  Noise-Induced oscillations and their Control in semiconductor superlattices , 2006, Int. J. Bifurc. Chaos.

[35]  M. Cáceres,et al.  Functional characterization of linear delay Langevin equations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  N. Dutta,et al.  Semiconductor Lasers , 1993 .

[37]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .

[38]  Parisi,et al.  Stabilization of an unstable steady state in intracavity frequency-doubled lasers , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[40]  Kestutis Pyragas Continuous control of chaos by self-controlling feedback , 1992 .

[41]  A. Amann,et al.  TIME-DELAY FEEDBACK CONTROL OF NONLINEAR STOCHASTIC OSCILLATIONS , 2005 .

[42]  E Schöll,et al.  Noise-induced front motion: signature of a global bifurcation. , 2006, Physical review letters.

[43]  Eckehard Schöll,et al.  CONTROLLING STOCHASTIC OSCILLATIONS CLOSE TO A HOPF BIFURCATION BY TIME-DELAYED FEEDBACK , 2005 .

[44]  Kestutis Pyragas,et al.  Experimental control of chaos by delayed self-controlling feedback , 1993 .

[45]  Eckehard Schöll,et al.  Mean-field approximation of time-delayed feedback control of noise-induced oscillations in the Van der Pol system , 2005 .

[46]  M. Rosenblum,et al.  Controlling oscillator coherence by delayed feedback. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  E Schöll,et al.  Noise-induced cooperative dynamics and its control in coupled neuron models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  E Schöll,et al.  Noise-induced pattern formation in a semiconductor nanostructure. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  V Flunkert,et al.  Refuting the odd-number limitation of time-delayed feedback control. , 2006, Physical review letters.