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1. Coexisting periodic attractors in injection locked diode lasers

Author

Gavrielides, A., Kovanis, V., Varangis, P. M., Erneux, T., and Lythe, G.

Subjects
Nonlinear Sciences - Chaotic Dynamics
Abstract

We present experimental evidence for coexisting periodic attractors in a semiconductor laser subject to external optical injection. The coexisting attractors appear after the semiconductor laser has undergone a Hopf bifurcation from the locked steady state. We consider the single mode rate equations and derive a third order differential equation for the phase of the laser field. We then analyze the bifurcation diagram of the time periodic states in terms of the frequency detuning and the injection rate and show the existence of multiple periodic attractors., Comment: LaTex, 14 pages, 6 postscript figures included

Published
1997
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10. Impact of the carrier relaxation paths on two-state operation in quantum dot lasers

Author

Sokolovskii, G.S., Dudelev, V.V., Kolykhalova, E.D., Soboleva, K.K., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., Viktorov, E.A., Erneux, T., Witzigmann, Bernd, Osiński, Marek, Henneberger, Fritz, and Arakawa, Yasuhiko

Abstract

We study InGaAs QD laser operating simultaneously at ground (GS) and excited (ES) states under 30ns pulsed-pumping and distinguish three regimes of operation depending on the pump current and the carrier relaxation pathways. An increased current leads to an increase in ES intensity and to a decrease in GS intensity (or saturation) for low pump range, as typical for the cascade-like pathway. Both the GS and ES intensities are steadily increased for high current ranges, which prove the dominance of the direct capture pathway. The relaxation oscillations are not pronounced for these ranges. For the mediate currents, the interplay between the both pathways leads to the damped large amplitude relaxation oscillations with significant deviation of the relaxation oscillation frequency from the initial value during the pulse.

Published
2015

11. Slow passage through thresholds in quantum dot lasers

Author

Viktorov, E.A., Erneux, T., Kolykhalova, E.D., Dudelev, V.V., Danckaert, J., Soboleva, K.K., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., Sokolovskii, G.S., Viktorov, E.A., Erneux, T., Kolykhalova, E.D., Dudelev, V.V., Danckaert, J., Soboleva, K.K., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., and Sokolovskii, G.S.

Abstract

A turn on of a quantum dot (QD) semiconductor laser simultaneously operating at the ground state (GS) and excited state (ES) is investigated both experimentally and theoretically. We find experimentally that the slow passage through the two successive laser thresholds may lead to significant delays in the GS and ES turn ons. The difference between the turn-on times is measured as a function of the pump rate of change and reveals no clear power law. This has motivated a detailed analysis of rate equations appropriate for two-state lasing QD lasers. We find that the effective time of the GS turn on follows an -1/2 power law provided that the rate of change is not too small. The effective time of the ES transition follows an -1 power law, but its first order correction in ln is numerically significant. The two turn ons result from different physical mechanisms. The delay of the GS transition strongly depends on the slow growth of the dot population, whereas the ES transition only depends on the time needed to leave a repellent steady state.

Published
2016

13. Dropout dynamics in pulsed quantum dot lasers due to mode jumping

Author

Sokolovskii, G.S., Viktorov, E.A., Abusaa, M., Danckaert, J., Dudelev, V.V., Kolykhalova, E.D., Soboleva, K.K., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., Erneux, T., Sokolovskii, G.S., Viktorov, E.A., Abusaa, M., Danckaert, J., Dudelev, V.V., Kolykhalova, E.D., Soboleva, K.K., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., and Erneux, T.

Abstract

We examine the response of a pulse pumped quantum dot laser both experimentally and numerically. As the maximum of the pump pulse comes closer to the excited-state threshold, the output pulse shape becomes unstable and leads to dropouts. We conjecture that these instabilities result from an increase of the linewidth enhancement factor α as the pump parameter comes close to the excitated state threshold. In order to analyze the dynamical mechanism of the dropout, we consider two cases for which the laser exhibits either a jump to a different single mode or a jump to fast intensity oscillations. The origin of these two instabilities is clarified by a combined analytical and numerical bifurcation diagram of the steady state intensity modes.

Published
2015

14. Impact of the carrier relaxation paths on two-state operation in quantum dot lasers

Author

Witzigmann, Bernd, Osiński, Marek, Henneberger, Fritz, Arakawa, Yasuhiko, Sokolovskii, G.S., Dudelev, V.V., Kolykhalova, E.D., Soboleva, K.K., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., Viktorov, E.A., Erneux, T., Witzigmann, Bernd, Osiński, Marek, Henneberger, Fritz, Arakawa, Yasuhiko, Sokolovskii, G.S., Dudelev, V.V., Kolykhalova, E.D., Soboleva, K.K., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., Viktorov, E.A., and Erneux, T.

Abstract

We study InGaAs QD laser operating simultaneously at ground (GS) and excited (ES) states under 30ns pulsed-pumping and distinguish three regimes of operation depending on the pump current and the carrier relaxation pathways. An increased current leads to an increase in ES intensity and to a decrease in GS intensity (or saturation) for low pump range, as typical for the cascade-like pathway. Both the GS and ES intensities are steadily increased for high current ranges, which prove the dominance of the direct capture pathway. The relaxation oscillations are not pronounced for these ranges. For the mediate currents, the interplay between the both pathways leads to the damped large amplitude relaxation oscillations with significant deviation of the relaxation oscillation frequency from the initial value during the pulse.

Published
2015

15. Synchronization properties of network motifs:Influence of coupling delay and symmetry

Author

D'Huys, O., Vicente, R., Erneux, T., Danckaert, J., and Fischer, I.

Abstract

We investigate the effect of coupling delays on the synchronization properties of several network motifs. In particular, we analyze the synchronization patterns of unidirectionally coupled rings, bidirectionally coupled rings, and open chains of Kuramoto oscillators. Our approach includes an analytical and semianalytical study of the existence and stability of different in-phase and out-of-phase periodic solutions, complemented by numerical simulations. The delay is found to act differently on networks possessing different symmetries. While for the unidirectionally coupled ring the coupling delay is mainly observed to induce multistability, its effect on bidirectionally coupled rings is to enhance the most symmetric solution. We also study the influence of feedback and conclude that it also promotes the in-phase solution of the coupled oscillators. We finally discuss the relation between our theoretical results on delay-coupled Kuramoto oscillators and the synchronization properties of networks consisting of real-world delay-coupled oscillators, such as semiconductor laser arrays and neuronal circuits.

Published
2008

16. Dynamical properties of mutually delayed coupled semiconductor lasers

Author

Erzgräber, H., Lenstra, D., Krauskopf, B., Fischer, I., Morthier, G., Erneux, T., Pessa, M., Electro-Optical Communication, and Stimuli-responsive Funct. Materials & Dev.

Subjects
Propagation time, delay differential equations, numerical continuation, Delay differential equation, Laser, Semiconductor laser theory, law.invention, Nonlinear system, Coupling (physics), Numerical continuation, Control theory, law, mutually coupled lasers, Quantum electrodynamics, Semiconductor optical gain, Mathematics
Abstract

We theoretically investigate the dynamical properties of a system of two semiconductor lasers that are mutually coupled via their optical fields. An intrinsic feature of the coupling is its time delay which generically arises from the finite propagation time of the light form one laser to the other. In our system the coupling time is in the sub-ns range, which is of the same order of magnitude as the period of laser's internal relaxation oscillations. We model this system with Lang-Kobayashi-type rate equations where we account for the mutual coupling of the two lasers by a delay term. The resulting set of nonlinear delay differential equations is analyzed by using recently developed numerical continuation. We consider the case of two nearly identical lasers with symmetrical coupling conditions but different frequencies, and present an analysis of the coupled laser modes (CLMs) of the system.

Published
2004

17. Dynamics and bifurcations of a semiconductor laser with short external cavity

Author

Krauskopf, B., Green, Kirk, Erzgräber, H., Lenstra, D., Morthier, G., Erneux, T., Pessa, M., and Electro-Optical Communication

Subjects
Physics, Dynamical systems theory, Phase (waves), Physics::Optics, Mechanics, Laser, law.invention, Semiconductor laser theory, Numerical continuation, law, Control theory, Oscillation (cell signaling), Relaxation (physics), Semiconductor optical gain
Abstract

We present a theoretical study into the dynamics and bifurcations of a semiconductor laser subject to delayed optical feedback, as modelled by the Lang-Kobayashi equations. For the case of a short external cavity, of the order of a few centimeters, there is a limited number of external cavity modes (ECMs), which makes it possible to apply advanced techniques from dynamical systems, such as the continuation of ECMs and their bifurcations, and the computation of unstable manifolds. From the physical point of view, a short cavity is characterized by the fact that the delay time in the external cavity is of the same order of magnitude as the period of the relaxation oscillation of the laser. In this regime the optical feedback phase is known to play an important role. We provide a detailed overview of how the dynamics depends on the feedback phase, which is in good agreement with recent experimental measurements.

Published
2004
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18. The effect of slow passage in the pulse-pumped quantum dot laser

Author

Panajotov, Krassimir, Sciamanna, Marc, Valle, Angel, Michalzik, Rainer, Sokolovskii, G.S., Abu Saa, M., Danckaert, J., Dudelev, V.V., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., Viktorov, E.A., Erneux, T., Panajotov, Krassimir, Sciamanna, Marc, Valle, Angel, Michalzik, Rainer, Sokolovskii, G.S., Abu Saa, M., Danckaert, J., Dudelev, V.V., Deryagin, A.G., Novikov, I.I., Maximov, M.V., Zhukov, A.E., Ustinov, V.M., Kuchinskii, V.I., Sibbett, W., Rafailov, E.U., Viktorov, E.A., and Erneux, T.

Abstract

In recent years, quantum-dot (QD) semiconductor lasers attract significant interest in many practical applications due to their advantages such as high-power pulse generation because to the high gain efficiency. In this work, the pulse shape of an electrically pumped QD-laser under high current is analyzed. We find that the slow rise time of the pulsed pump may significantly affect the high intensity output pulse. It results in sharp power dropouts and deformation of the pulse profile. We address the effect to dynamical change of the phase-amplitude coupling in the proximity of the excited state (ES) threshold. Under 30ns pulse pumping, the output pulse shape strongly depends on pumping amplitude. At lower currents, which correspond to lasing in the ground state (GS), the pulse shape mimics that of the pump pulse. However, at higher currents the pulse shape becomes progressively unstable. The instability is greatest when in proximity to the secondary threshold which corresponds to the beginning of the ES lasing. After the slow rise stage, the output power sharply drops out. It is followed by a long-time power-off stage and large-scale amplitude fluctuations. We explain these observations by the dynamical change of the alpha-factor in the QD-laser and reveal the role of the slowly rising pumping processes in the pulse shaping and power dropouts at higher currents. The modeling is in very good agreement with the experimental observations.

Published
2014

20. Turn-on delay of QD and QW laser diodes: What is the difference?

Author

Sokolovskii, G S, primary, Dudelev, V V, additional, Kolykhalova, E D, additional, Deryagin, A G, additional, Maximov, M V, additional, Nadtochiy, A M, additional, Kuchinskii, V I, additional, Mikhrin, S S, additional, Livshits, D A, additional, Viktorov,, E A, additional, and Erneux, T, additional

Published
2013
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22. Dynamics of passively Q-switched microchip lasers

Author

Peterson, P., Gavrielides, A., Sharma, M.P., and Erneux, T.

Subjects
Optical waveguides -- Research, Semiconductor lasers -- Research, Semiconductor chips -- Usage, Business, Computers, Electronics, Electronics and electrical industries
Abstract

A study has been conducted to investigate self-pulsing in passively Q-switched microchip lasers. To study this further, laser equations were formulated in dimensionless form and the analytical properties of the laser intensity oscillations such as self-pulsing, bifurcation points and maximum intensity were determined. Findings indicated that the laser oscillations appear through a quasi-vertical Hopf bifurcation located slightly above the lasing threshold.

Published
1999

28. Mode structure of quantum dot semiconductor lasers

Author

Lenstra, D., Morthier, G., Erneux, T., Pessa, M., Lenstra, Daan, Tanguy, Yann, Muszalski, Jan, Houlihan, John, Huyet, Guillaume, Pearce, Emma J., Smowton, Peter Michael, Hopkinson, Mark, Morthier, Geert, Erneux, Thomas, Pessa, Markus, Lenstra, D., Morthier, G., Erneux, T., Pessa, M., Lenstra, Daan, Tanguy, Yann, Muszalski, Jan, Houlihan, John, Huyet, Guillaume, Pearce, Emma J., Smowton, Peter Michael, Hopkinson, Mark, Morthier, Geert, Erneux, Thomas, and Pessa, Markus

Abstract

An analysis of the transverse and longitudinal mode structure of broad area quantum dot lasers emitting at 1060nm is presented. In particular, temperature is shown to play an important role in the stabilisation of the transverse mode structure of the devices. In addition, the investigation of the the interaction between these transverse modes, through the measurement of the spatial intensity correlation, shows that the laser retains some modal properties in the unstable regime. Finally, measurements of spectral correlations between longitudinal mode groups display a strong dependency on their respective transverse mode structures indicating the importance of spatial overlap.

30. Strong delayed negative feedback.

Author

Erneux T

Abstract

In this paper, we analyze the strong feedback limit of two negative feedback schemes which have proven to be efficient for many biological processes (protein synthesis, immune responses, breathing disorders). In this limit, the nonlinear delayed feedback function can be reduced to a function with a threshold nonlinearity. This will considerably help analytical and numerical studies of networks exhibiting different topologies. Mathematically, we compare the bifurcation diagrams for both the delayed and non-delayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit., Competing Interests: The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Erneux.)

Published
2024
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31. Two-color bursting oscillations.

Author

Kelleher B, Tykalewicz B, Goulding D, Fedorov N, Dubinkin I, Erneux T, and Viktorov EA

Abstract

Neurons communicate by brief bursts of spikes separated by silent phases and information may be encoded into the burst duration or through the structure of the interspike intervals. Inspired by the importance of bursting activities in neuronal computation, we have investigated the bursting oscillations of an optically injected quantum dot laser. We find experimentally that the laser periodically switches between two distinct operating states with distinct optical frequencies exhibiting either fast oscillatory or nearly steady state evolutions (two-color bursting oscillations). The conditions for their emergence and their control are analyzed by systematic simulations of the laser rate equations. By projecting the bursting solution onto the bifurcation diagram of a fast subsystem, we show how a specific hysteresis phenomenon explains the transitions between active and silent phases. Since size-controlled bursts can contain more information content than single spikes our results open the way to new forms of neuron inspired optical communication.

Published
2017
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32. Stability of steady and periodic states through the bifurcation bridge mechanism in semiconductor ring lasers subject to optical feedback.

Author

Friart G, Van der Sande G, Khoder M, Erneux T, and Verschaffelt G

Abstract

With the development of new applications using semiconductor ring lasers (SRLs) subject to optical feedback, the stability properties of their outputs becomes a crucial issue. We propose a systematic bifurcation analysis in order to properly identify the best parameter ranges for either steady or self-pulsating periodic regimes. Unlike conventional semiconductor lasers, we show that SRLs exhibit both types of outputs for large and well defined ranges of the feedback strength. We determine the stability domains in terms of the pump parameter and the feedback phase. We find that the feedback phase is a key parameter to achieve a stable steady output. We demonstrate that the self-pulsating regime results from a particular Hopf bifurcation mechanism referred to as bifurcation bridges. These bridges connect two distinct external cavity modes and are fully stable, a scenario that was not possible for diode lasers under the same conditions.

Published
2017
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33. Relaxation and square-wave oscillations in a semiconductor laser with polarization rotated optical feedback.

Author

Friart G, Weicker L, Danckaert J, and Erneux T

Abstract

The rate equations for a laser with a polarization rotated optical feedback are investigated both numerically and analytically. The frequency detuning between the polarization modes is now taken into account and we review all earlier studies in order to motivate the range of values of the fixed parameters. We find that two basic Hopf bifurcations leading to either stable sustained relaxation or square-wave oscillations appear in the detuning versus feedback rate diagram. We also identify two key parameters describing the differences between the total gains of the two polarization modes and discuss their effects on the periodic square-waves.

Published
2014
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34. Slow-fast dynamics of a time-delayed electro-optic oscillator.

Author

Weicker L, Erneux T, D'Huys O, Danckaert J, Jacquot M, Chembo Y, and Larger L

Subjects
Computer Simulation, Algorithms, Models, Theoretical, Oscillometry methods
Abstract

Square-wave oscillations exhibiting different plateau lengths have been observed experimentally by investigating an electro-optic oscillator. In a previous study, we analysed the model delay differential equations and determined an asymptotic approximation of the two plateaus. In this paper, we concentrate on the fast transition layers between plateaus and show how they contribute to the total period. We also investigate the bifurcation diagram of all possible stable solutions. We show that the square waves emerge from the first Hopf bifurcation of the basic steady state and that they may coexist with stable low-frequency periodic oscillations for the same value of the control parameter.

Published
2013
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35. Bifurcation to fronts due to delay.

Author

Erneux T, Kozyreff G, and Tlidi M

Subjects
Mathematical Concepts, Nonlinear Dynamics, Time Factors, Feedback, Systems Theory
Abstract

The stability of a steady-state front (kink) subject to a time-delayed feedback control (TDFC) is examined in detail. TDFC is based on the use of the difference between system variables at the current moment of time and their values at some time in the past. We first show that there exists a bifurcation to a moving front. We then investigate the limit of large delays but weak feedback and obtain a global bifurcation diagram for the propagation speed. Finally, we examine the case of a two-dimensional front with radial symmetry and determine the critical radius above which propagation is possible., (This journal is © 2010 The Royal Society)

Published
2010
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