Synchronization of semiconductor laser on picosecond pulses

Pascal Besnarda, Olivier Vaudela and Jean-Franccois Hayaua

aFOTON-ENSSAT (CNRS - UMR6082) - Universite de Rennes 1,6 rue de Kerampont, B.P.8051822305 Lannion CEDEX, France

ABSTRACT

We show for the first time to our knowledge, synchronization between two bulk semiconductor lasers on anerratic train of pulses. They occurred erratically at different times, following a Poisson statistical law on thescale of the nanosecond. These pulses are due to excitability using an optically injected bulk semiconductorlaser. Synchronization between two lasers is shown and studied cascading two optical injection schemes. Thedegree of correlation between the two signal outputs is analyzed following the detuning and the injected powerand is related to the standard map of dynamics for optically injected laser, seeded by a continuous wave. Thesynchronization on a single pulse is studied as well as on a regular temporal train of pulses and we show that thebirth of synchronization is obtained for injected power related to a saturation process in the laser. A comparisonto quantum dash and quantum dot laser is discussed.

Keywords: synchronization, optical injection, semiconductor laser, bulk, quantum dots

1. INTRODUCTION

Seeding light from a laser into the cavity of a second one is a simple experiment.1,2 When the coupling isunidirectional, this scheme is called optical injection and is a basic tool for the study of synchronization processbetween oscillators. The dynamics has been extensively described theoretically and experimentally mainly whenthe seeded light is a continuous wave.3–7 It has been also suggested that chaotic signal may be synchronizedthrough optical injection8–12 following the proposal of Pecora and Carroll.13 The chaos is usually generatedthrough optical feedback.14,15 The general idea is to inject light from an extended cavity semiconductor laser(ECL) into the cavity of a second laser. When the injected signal has the same strength as that of the opticalfeedback in the ECL, the injected laser duplicates the first system. The injected laser completely synchronizesthen with anticipation (with a time lag corresponding to the round-trip EC time).16–18 However, more general-ized chaos synchronization can be accomplished through optical injection, which means that it is possible to reachsynchronization for a broad range of parameters such as injected-power level and with/without anticipation.19–22

Similar experiments have been realized with fiber lasers.23,24 It is moreover possible to reach synchronizationon other temporal dynamics.25

Generallized synchronization may be obtained without the help of optical feedback, using restrictively opticalinjection.25,26 This is based on a cascade of two successive optical injections (from master to receiver throughtransmitter). In this architecture, both transmitter and receiver may be set in different regimes7 such as re-laxation, multi-wave frequency, frequency doubling, chaotic regime. . . The synchronization can then be studiedby fixing the operating point of the transmitter and varying that of the receiver (as for example the detuningbetween the transmitter and the receiver or the injected power from the transmitter). One may choose theinverse case by setting the operating point of the receiver and going over that of the transmitter (by varying ofthe injected power from the master and its optical frequency). In this communication, we study synchronizationbetween two lasers when the seeded light is non continuous and characterized as a erractic spiking behaviour.This article is organized as follows: In section 2, the basics principle of optical injection and excitability aredescribed; In section 3, synchronization process is investigated. Finally, a brief conclusion is drawn.

Further author information: (Send correspondence to Pascal Besnard)Pascal Besnard: E-mail: pascal.besnard@enssat.fr, Telephone: +33-2-96-46-90-53, Fax : +33-2-96-37-01-99

Physics and Simulation of Optoelectronic Devices XVII, edited by Marek Osinski, Bernd Witzigmann, Fritz Henneberger, Yasuhiko Arakawa, Proc. of SPIE Vol. 7211,

72110T · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.809949

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Figure 1. Optical injection principle.

2. OPTICAL INJECTION BY A CONTINUOUS-WAVE SIGNAL

2.1 Principle

The principle of an optical injection is sketched in Fig. 1. Laser, which is injected, is usually called the slavelaser (SL) while the other is called the master laser (ML).

In our experiments, the ML is a commercially available, single mode tunable external cavity semiconductorlaser, with a precision of 1 pm (125 MHz at 1.55μm), which gives out a power up to 3 mW . This power canbe increased thanks to a polarization maintaining (PM) optical amplifier (+23 dBm), with a high coefficientisolator (70 dB isolation) that ensures a unidirectional seeding from the master to the slave. The SL is a massiveInP/InGaAsP buried double heterostructure DFB laser chip emitting at 1.55 μm. Its temperature is regulated at25˚C thanks to a Peltier controller. Note that all the experiment is fiber-made with PM components, allowing aperfect reproducibility of the measurements. We don’t give more details about the experiment as the descriptioncan be found in former publications.7,25,27

2.2 Experimental results

Generally, the SL is feeded by a continuous wave. In this case, many phenomena have been classified3–7 followingthe control parameters which are essentially the injected power Pinj and the detuning Δν between the master(νm) and slave (νs) frequencies. Usual values for Δν and Pinj are in the respective intervals [−100;+100 GHz]and [−50; 0 dBm] ([100 nW ; 1 mW ]).Usually, results are presented in the “injected power-detuning” chart (Pinj − Δν), for which the different colorsshow at a glance the different regimes.

2.2.1 Dynamical behaviors

Injection by a continuous wave allows the SL to exhibit different kinds of dynamics:

• Frequency-locking28,29 (mark as “L” in Fig. 2-5): The amplification of the master line is made at theexpense of the slave line and is characterized by a linewidth transfer.27

• Wave-mixing (mark as “1” in Fig. 3-5): Wave-mixing could create an image frequency νs − (νm − νs),symmetric of νm with respect to νs and multiple of them.

• Period doubling (mark as “2” in Fig. 3-5): New frequency lines appear between two lines observed in thewave-mixing regime.

• Period quadrupling (mark as “4” in Fig. 3-5): New frequency lines appear between two lines observed inthe period doubling regime.

• Chaos (mark as “C” in Fig. 3-5): The frequency spectra is characterized by a broad band that could beassimilated to noise.

• Undamped relaxation regime30 (mark as “R” in Fig. 3-5): Characteristics are very similar to wave-mixingbut for which mode spacing is equal to the relaxation oscillation frequency (ROF) of the slave laser. Thisspecific regime is more precisely detailed in Refs. 25 & 31.

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• Excitability. An excitable system is characterized by a large non-linear response to a small but sufficientlylarge perturbation from its stable equilibrium before settling back to the equilibrium. Historically, multi-pulses excitability had been observed in biology with neuronal transmission of information. In this domain,excitability is characterized by a spiking behaviour of the cell potential.32 In optics, excitability hasalready been observed in lasers with saturable absorber33,34 or lasers with optical feedback.35–37 In thisphysical field, excitability is also characterized by a spiking behaviour, by of the optical emitted power.Experimentally, Goulding et al38,39 have recently reported observation of multi-pulses excitability in a1.3μm quantum dot laser. This dynamics will be more precisely described in § 2.2.4.

2.2.2 Experimental mapping

Fig. 2, 3 and 4 present experimental mapping in the chart “injected power-detuning”, respectively for the slavelaser biased at 1.2, 1.7 and 4 times its threshold.

At low pumping rate (see Fig. 2), the injected laser mainly acts as an optical amplifier: We just observedfrequency-locking behavior or an amplification regime, for which two frequencies exist (that of the slave laserand the amplified one of the master).This figure shows moreover a bistability: In the hatched area, the slave laser is only frequency-locked for adecreasing detuning.

When the pumping rate is a little bit further increased (1.7), more regimes like wave-mixing, period dou-bling4,7. . . are observed as shown in Fig. 3.As explained in Ref. 28, the locking area divides in two branches when the injected power is increased from verylow values to about −35 dBm at this pumping rate. Above the intersection of these two areas, the undampedrelaxation regime takes place. This particular operating point is usually called the relaxation hole.As previously mentioned, the phenomenon is bistable as illustrated by Fig. 3(a) and 3(b), following here thevariation of the detuning.

Finally, for the slave laser biased at higher current, i.e. 4 times its threshold, the mapping is qualitativelysimilar to that at 1.7 times the threshold, as presented in Fig. 4.However relaxation hole is obtained for a larger injected power (∼ −16 dBm). At higher bias current, it is moredifficult to perturb the slave laser: More power have to be injected in order to obtain a similar regime.

2.2.3 Discussion

At low pumping rate, the behavior of the SL is closer to that of an amplifier. Increasing the pumping rate orthe gain leads to:

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Figure 4. Experimental mapping of injected SL biased at 4 times its threshold. (a): decreasing detuning; (b): increasingdetuning.

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• More complex maps, due to more regimes.

• A higher sensitivity to optical injection, which means that the locking area appears at lower injected power(−25 dBm at r = 1.2; −45 dBm at r = 1.7; −50 dBm at r = 4.)

• A translation of the different areas towards higher injected powers. This last property is a rule of thumb,which is basically illustrated by the translation of the relaxation hole (−35 dBm at r = 1.7; −15 dBm atr = 4.) Comparison of figures 3(a) and 4(a) shows obviously that area delimiting the different regimes arenot identically shaped and located at the same positions.

Different categories of optical injection can be defined as it is indicated in the experimental map of Fig. 5:

• Very weak optical injection, for which the master line is only amplified.7 It corresponds to power scale forwhich there is purity or impurity transfert,27 or as well for which the laser can be used as a very sensitivedetector.40

• Weak optical injection, for which the locking and wave-mixing occur.

• Moderate optical injection, for which complex dynamics occur like period doubling, chaos. This formerregime starts for an injected power corresponding to the relaxation hole.

• High injected power, for which bistability occurs.

• Very High injected power, for which the SL is always locked.

This last category is only seen numerically.25,31

These experimental mapping allow to highlight the existence of bistabilities29,41,42 for all bias current exploredin this work.

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2.2.4 Excitability behaviour

The experimental scheme allows us to observe multi-pulses excitability in the optically injected slave laser.Fig. 6 presents different exemples of the observed time series obtained for the SL biased at 1.2 times its threshold.Fig. 6(a) shows an exemple of a single pulse (order-1 excitability); Fig. 6(b), respectively (c), presents an exempleof two, respectively three, pulses following by an other one (order-2 and order-3 excitability). Finally, Fig. 6(d)presents an exemple of a multiple pulses behaviour (high order excitability). This results is the first observationof multi-pulses excitability for a 1.55μm DFB bulk laser.To complete these observations, we have mapped, in the “detuning-injected power” plane, the areas where wecan observe excitability spiking behaviour. This map is presented in Fig. 7.

To simplify, in this figure, we have only mapped the injection-locking area and multi-pulses excitability areas.These ones are pictured in grey in the figure. These areas are quite small: No more than 1GHz×2dB. This factexplains why we do not have indicated the parameter values of these observations in Fig. 6: Our measurementdevices are not enough accurate to fully distinguish the different injection points. Ones can also note that themulti-pulses areas’ location are in good agreement with theoretical studies already published.43

The probability density associated to the occurrence of spikes is seen to be close to a Poisson law (characterizedthrough the dispersion index of Fisher). Hence the delay between two pulses follows almost an exponential lawas shown in Fig. 8 and it is unlikely to have a separation higher than 50 ns.

3. SYNCHRONIZATION SCHEME

3.1 Principle

To study synchronization between two DFB semiconductor lasers, we use a cascade of two optical injections, aspresented in Ref. 26 and in Fig. 9.The first injection, between a ML and a transmitter laser (TL), fixes the operating point or dynamics of the TL.

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Figure 10. Multi-pulses excitability synchronization.

The second optical injection, between the TL and a receiver laser (RL), allows the synchronization between TLand RL to be studied for different TL-dynamics.

3.2 Excitability synchronizationFig. 10 presents a time example of excitability synchronization (note that the time lag between TL and RLoptical synchronized outputs have been partially compensated for clarity). One can see that the TL spikingexcitability behaviour is well reproduce by the RL.

Finally, Fig. 11 presents the evolution of calculated cross-correlation index44,45 between TL and RL timesamples. It shows that for a sufficient injected power, it is possible to reach a multi-pulses excitability synchro-nization characterised by a similarity upper to 60%. This value could appear bit low but one can note thatbetween optical pulses apparitions, both lasers operate in a continuous regime for which each instrinsic noise isuncorrelated with the other.

4. CONCLUSION

In this article, we have started by reminding the optical injection principle and the usal results associated, es-pecially generated slave laser dynamics. We have presented the first experimental observation of an excitablebehaviour for a 1.55μm injection-locked bulk semiconductor laser. We have shown different orders caracterizedby emission of one, two or more optical pulses. They occurred erratically at different times, following a Poissonstatistical law on the scale of the nanosecond.Parameters space allowing excitability have also been mapped in a “detuning-injected power” plane. Theseresults are in good agreement with numerical works already published.Then, we have presented a cascade scheme for the study of synchronization using two successive optical injec-tions. This scheme is a useful experimental tool to study synchronization and permits us to realized the firstexperimental multi-pulses excitability synchronization with 1.55μm bulk semiconductor lasers, characterised bya 60% cross-correlation index.

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ACKNOWLEDGMENTS

Authors would like to thank N. Peraud for excitability behaviour characterization and “Laser Physic Group”colleagues for helpful discuss and comments.

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