Includes bibliographical references (page 5539).We measure the temporal evolution of the intensity of an edge emitting semiconductor laser with delayed optical feedback for time spans ranging from 4.5 to 65 ns with a time resolution from 16to 230 ps, respectively. Spectrally resolved streak camera measurements show that the fast pulsing of the total intensity is a consequence of the time delay and multimode operation of the laser. We experimentally observe that the instabilities at low frequency are generated by the interaction among different modes of the laser

Balle, S.

Giudici, M.

Menoni, C. S.

Rocca, Jorge J.

Tredicee, J. R.

Vaschenko, G.

English

We measure the temporal evolution of the intensity of an edge emitting semiconductor laser with delayed optical feedback for time spans ranging from 4.5 to 65 ns with a time resolution from 16to 230 ps, respectively. Spectrally resolved streak camera measurements show that the fast pulsing of the total intensity is a consequence of the time delay and multimode operation of the laser. We experimentally observe that the instabilities at low frequency are generated by the interaction among different modes of the laser

Balle, S., author

Tredicee, J. R., author

Menoni, C. S., author

Rocca, Jorge J., author

Giudici, M., author

Vaschenko, G., author

American Physical Society, publisher

Mountain Scholar (Digital Collections of Colorado and Wyoming)

VOLUME 81, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 21 DECEMBER 1998versity,g5536Temporal Dynamics of Semiconductor Lasers with Optical FeedbackG. Vaschenko,1 M. Giudici,2 J. J. Rocca,1 C. S. Menoni,1 J. R. Tredicce,2,3 and S. Balle31Center for Optoelectronic Computing Systems and Department of Electrical Engineering, Colorado State UniFort Collins, Colorado 805232Institut Non Lineaire de Nice, UMR 129 CNRS-UNSA, 06560 Valbonne, France3Departament de Fı´sica Interdisciplinar, IMEDEA (CSIC-UIB), E-07071 Palma de Mallorca, Spain(Received 12 June 1998)We measure the temporal evolution of the intensity of an edge emitting semiconductor laser withdelayed optical feedback for time spans ranging from 4.5 to 65 ns with a time resolution from 16to 230 ps, respectively. Spectrally resolved streak camera measurements show that the fast pulsinof the total intensity is a consequence of the time delay and multimode operation of the laser. Weexperimentally observe that the instabilities at low frequency are generated by the interaction amongdifferent modes of the laser. [S0031-9007(98)08077-6]PACS numbers: 05.45.+b, 05.40.+ j, 42.60.Miregcis-adeiavicrcc]imsegllecxienesgedicasl—andav-art-wsd-re-wedeardel.is-astten-thin-h aigu-g.then-ltsHLde.ednalmutheath)zerertem.20Nonlinear systems with delayed feedback are of intebecause they can be widely found in economy, biolochemistry, and physics [1]. These systems are in prinple infinite dimensional, and from this point of view, itdifficult to classify thema priori as deterministic dynamical systems because the existence and uniqueness oflution have to be demonstrated for each particular mo[2]. It is also difficult to separate the role of noise from dterminism, because complex solutions display a GaussMarkovian behavior as if they were solutions of a Langeequation [3,4], thus nonconventional measurement teniques are required [5].During the past years, there has been particular intein understanding the dynamical behavior of one susystem: a semiconductor laser with optical feedback.was experimentally shown that weak optical feedbamay induce bistability [6], oscillations, and chaos [7At moderate feedback levels, a special dynamical regoccurs which is characterized by the appearanceaperiodic, fast reductions of the total intensity of the la[8,9], followed by a slower recovery stage. The averatime between such intensity drops is much longer thancharacteristic times of the system itself, so they are calow-frequency fluctuations (LFF).From numerical simulations it was recently proposthat LFF originate from a deterministic chaotic attrator which encompasses a large number of unstable fipoints, either saddle-node points or foci [9–11]. Thchaotic attractor coexists with one or more stable fixpoints. The trajectory, if in the chaotic attractor, waders in phase space around the foci until it approachsaddle. The collision with a saddle gives rise to a larfast excursion in phase space until the evolution recovtowards the foci. Since this process lasts for severallay times, it generates a long-time scale dynamics whcontributes to the lower part of the spectrum, and it wcalled “chaotic itinerancy with a drift” because it involvea drift in the laser frequency. Furthermore, the mode0031-9007y98y81(25)y5536(4)$15.00sty,i-so-el-n-nh-esthItk.eofrealledd-edsd-ae,rse-hswhich assumes single-mode operation of the laservery weak feedback—predicted that the temporal behior of the laser intensity is characterized by pulses deping from zero intensity level and whose amplitude grosteadily until the collision with a saddle takes place leaing to a sudden reduction of the intensity. However,cent measurements of the time-resolved spectrum shothat the laser operates multimode whenever LFF app[12], breaking one of the basic assumptions of the moIn addition, statistical measurements of the intensity dtribution with a sampling oscilloscope showed that the ffluctuations in general take place around an average inity value different from zero [13], thus disagreeing withe model.Here we present measurements of both the totaltensity and the time-resolved spectrum conducted witsingle-shot streak camera which allowed us to unambously identify the physical mechanism of the fast pulsinThese results suggest an alternative interpretation ofprocess at the origin of the intensity drop in a semicoductor laser with optical feedback and confirm the resupresented in [12,13].These measurements are performed on an Hitachi6314MG laser emitting about 630 nm, with a mospacing ofø135 GHz and a threshold current of 24 mAAn antireflection coated microscope objective is placat the laser output to collimate the beam. An extermirror of 30% reflectivity is placed at a distance of 30 cfrom the laser output (delay timet ­ 2 ns), reducing thethreshold of the laser down to 22 mA. Part of the outpbeam is sent to a 2 GHz bandwidth silicon avalancphotodiode. The photodiode signal is monitored withTDS620 digital oscilloscope (500 MHz analog bandwidand it can also be sent to a power spectrum analy(1.5 GHz bandwidth). The remaining portion of the lasoutput is detected by a single-shot streak camera sysThis system is based on a streak tube with an Sphotocathode having a radiant sensitivity of 20 mAyW© 1998 The American Physical SocietyVOLUME 81, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 21 DECEMBER 1998besifgndrayfroon1temwthtictpNethethaatearonththantlsolsethehetiol aakpear.they.lesWetionsityd iniorilswithnsndsiveouricshegec-tinglu-ethimepsps,neat 630 nm and a P-11 phosphorous screen. A fioptics coupled gated image intensifier is used to intenthe output of the streak tube. The intensified imais detected with a two-dimensional, fiber coupled athermoelectrically cooled charge-coupled device arWe operate the camera with different streak speeds,about 4.5 to 65 nsyscreen, to monitor the laser outputdifferent time spans. The resolution of the system isto 230 ps, respectively. The time resolution of the sysand the linearity of the ramp at each speed are testeda mode-locked Ti:sapphire laser. In order to maximizesignal to noise ratio of our measurements the input opof the streak camera is removed, and the laser ouis focused directly onto the photocathode. A cw He-laser is used to determine the minimum sensitivity ofstreak camera. This test rules out any possibilityin our experiments the camera might have been operbelow the level at which a continuous signal can appas a sequence of pulses as a result of a low numbephotoelectrons and a high intensifier gain.In Fig. 1 we show the total intensity as a functiof time observed with the oscilloscope (Fig. 1a) andstreak camera (Fig. 1b). In both cases we notethe average intensity increases steadily with time uit suddenly drops to a minimum value. We can aobserve that in both cases there are fast intensity pupartially filtered in the oscilloscope trace (Fig. 1a) byFIG. 1. Total intensity as a function of time taken with (a) toscilloscope, and (b) the streak camera with a time resoluof about 230 ps. Note the pseudoperiodicity of the signathe round-trip time in the external cavity (,2 ns).r-ye.m6ithesuttedrofetils,ntlimited bandwidth of the detection system. The strecamera measurement shows that the pulses disapimmediately following the drop of the total intensityThese pulses exhibit a marked pseudoperiodicity atround-trip time of the optical field in the external cavitHowever, there also exists pulsing at shorter time scawhich suggests the influence of higher frequencies.repeat the measurements for several values of injeccurrent and feedback strength over hundreds of intendrops in each case. As long as the system operatethe so-called LFF regime, the above qualitative behavremained unaltered. However, the quantitative detachange from one drop to another. In Fig. 2 we shointensity traces covering time spans of 21 ns taken wa time resolution of 70 ps (a)–(c) and time spans of 4.5and 16 ps time resolution (d)–(f). Each trace correspoto a different drop and starts at a different delay relatto the drop. These measurements confirm that up tomaximum time resolution there is no underlying dynamand that Fig. 1b illustrates the relevant behavior of ttotal intensity.In order to analyze the origin of the pulsing occurrinat shorter times than the delay time, we conduct sptrally resolved measurements. We place a 0.3 m gramonochromator (Acton Research VM 503) with a resotion of 0.5 Å in front of the streak camera. Removing thFIG. 2. Temporal evolution of the total intensity taken withe streak camera over different time spans: (a)–(c) 21 ns tspan, 70 ps time resolution; (d)–(f ) 4.5 ns time span, 16time resolution. Different traces correspond to different droand the starting point relative to the drop is changing from oacquisition to the other.5537VOLUME 81, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 21 DECEMBER 1998gtwititilviadeltarsisftediooFplrgymntisalofetebevityinceesastofragesoizetal(seel,ofnge,noteeueomdaloutput slit of the monochromator, we obtain a wavelendispersed beam on the camera photocathode. In thiswe are able to record the time-resolved spectrum, wthe horizontal axis of the streak image correspondingwavelength, at the price of a lower signal to noise radue to the dispersion of the beam. The spectral resoluis ,40 GHz, enough to clearly resolve the resonancesthe internal laser cavity although insufficient to resothe external cavity resonances.Figure 3 displays a typical time-resolved spectrumthe LFF regime taken with the streak camera withresolution of 230 ps in time. We clearly observe thmost of the time the system operates in multiple moof the internal laser cavity, in agreement with the resuof [12], and in general the dominant active modesnot consecutive ones. When a drop of the total intenoccurs (see timesø5 and 35 ns), all modal intensitieare below the photocathode sensitivity. However, aa delay of a few ns, we observe that several diomodes grow from the background. The modal evolutis controlled by the delay time, and until the next dropFIG. 3(color). Typical time-resolved spectrum in the LFregime taken with the streak camera. The time span65 ns with a time resolution ofø230 ps, while the frequencyresolution isø40 GHz. The index indl denotes the pixel onthe CCD array, and the power is in false color, from pur(low power) to bright red (high power).5538hay,thtooonofenatssetyrenfisethe total intensity takes place, there is a transfer of eneamong these modes.Important dynamical information can be gained frothe analysis of the temporal evolution of the relevamodal intensities. As shown in Fig. 4, each modepulsing with a repetition rate controlled by the externcavity round-trip time, but in general the phasepulsation is different for different modes; in particular, thtwo dominant modes over a given time interval operawith different phases. The origin of the oscillations canunderstood as a partial phase locking of the external caresonances within each internal cavity resonance. Sthe modal intensities are pulsing with arbitrary phasone relative to the other, the total intensity displays fpulsing (which looks irregular due to the exchangeenergy among the modes) around a nonvanishing avelevel, in agreement with [13]. Finally, the analysis aleveals that shortly after two or more modes synchrontheir amplitudes to pulse in phase, a drop in the tointensity occurs as soon as the pulses are big enoughbottom panel in Fig. 4). It is worth noting that, in generaafter each drop of the total intensity, both the numbermodes and the respective phase of the pulsing chaand that the dominant modes just after the drop areFIG. 4. Top panel (color): Modal intensity traces for the thrdominant modes in Fig. 3 for times around the first drop. Blcorresponds to the mode at aboutdl ­ 60, green to that ataboutdl ­ 100, and red to the one at aboutdl ­ 150. Thedotted black line corresponds to the background level. Bottpanel: modal correlation defined as the product of the mopowers above the background level.VOLUME 81, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 21 DECEMBER 1998ivftisamehneaoretitgn5cllcithltaanslydaieisteineesesisnothellatedpry,nndandisitys-ct.us,t.n.,,i,d.the dominant ones just before it. However, the repetitfeature is that a total intensity drop happens shortly aseveral modes start pulsing in phase.It is worth noting that as the injection currentincreased, the intensity drops become more frequent,finally the signal in the oscilloscope looks almost randoThis situation is commonly called “coherence collaps(CC). In the CC regime, the signal observed with tstreak camera does not show qualitative differencescompared to the LFF case, although now the sigfluctuates strongly at all times. In fact, the time-resolvspectrum in the CC regime does not show any “dperiods” where all modes are below the sensitivity limitthe streak camera. In addition, it appears that the diffemodes are no longer synchronized, as was the case inLFF regime.The above results disclose the fact that the interacbetween the resonances of the internal cavity is atorigin of the total intensity drops. It is worthwhile notinthat the operating modes are usually not consecutive osuch as multimode instabilities in laser theory [14,1A physical interpretation can be based on a typimultimode laser instability. The system is essentiacontrolled by the delay time, which fixes a resonanfrequency at 21. For one laser mode, the external cavmodes tend to lock in phase during the buildup of taverage total intensity, thus leading to pulses. If the deis long enough the active material can recover beforenext pulse is generated, and another laser mode isto operate and it will grow from noise. The externcavity modes inside the bandwidth of this “new” operatimode tend also to lock in phase, but their locking phawill in general be different from that of the previousexisting mode. In this way several electromagnetic moare able to operate but their nonlinear coupling leadsan instability which gives origin to the drop of the totintensity and to fast variations of the material propertsuch as refractive index. As a consequence, thereshift in frequency and later operation at other unrelalaser modes. The process then initiates again.In conclusion, the fast pulsing observed in the totaltensity with the streak camera is due mainly to the supposition of the intensities of different longitudinal lasmodes and, for each mode, to a phase locking procesthe external resonances. The intensity drops are the rof a multimode instability and the total intensity valuegenerally above the spontaneous emission level. Therepetitiveness of the signal from drop to drop leavesquestion unanswered about the role of noise and the dministic character of this particular system. Heuristicaeernd.”easaldrkfnttheonhees,].alyeyeayheblelgeestolsad-r-rofultn-eter-ywe can say that the whole process seems to be dominby noise. However, the instability giving rise to each droleads to a short stage of determinism during the recovebut it is difficult to establish an unambiguous conclusioabout the role of noise by just measuring the intensity aoperation frequency of the laser.Further details on the coherence collapse regimethe evolution of the system as the injection currentincreased will be published elsewhere.We acknowledge support of the European CommunTMR program, the NSF Optoelectronic Computing Sytem Center, the NSF (ECS 95-02888), CICYT ProjeNo. TIC95-0563, and DGICYT Project No. SAB95-0674We thank S. Hegarthy and J. J. González for their preciolp and G. Huyet for helpful discussions.[1] R. M. 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Temporal dynamics of semiconductor lasers with optical feedback

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Temporal dynamics of semiconductor lasers with optical feedback

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