The Dynamics of Semiconductor Optical Amplifiers: Modeling and Applications

Jesper Mørk,

Mads L. Nielsen

and Tommy W. Berg

The Dynamics of

Semiconductor Optical AmplifiersModeling and Applications

July 2003 ■ Optics & Photonics News 43

A semiconductor optical amplifier(SOA) is essentially a semicon-ductor laser with anti-reflection

coated facets that amplifies an injectedlight signal by means of stimulated emis-sion (see Fig. 1). SOAs share many of thefeatures that have made semiconductorlasers the dominant light source for opti-cal communications and numerous otherapplications. These features include smallsize, simple electrical pumping, broadspectral range and opportunities for integration and mass production.

Up to now, however, the erbium-doped fiber amplifier (EDFA), not theSOA, has been the amplifier of choicefor optical communication systems. Thereason is essentially that SOAs are eithertoo fast or too slow. Amplification ofan optical signal consumes carriers,thereby transiently saturating (i.e.,reducing) the gain. If the amplifier doesnot provide approximately the samegain for all the data bits, patterningeffects prevail and the quality of theoptical data signal is significantly dis-torted. To avoid distortion of the signal,the magnitude of gain saturation mustbe sufficiently small, or the amplifierdynamics must be such that transientgain changes do not affect the neighbor-ing bits. This dynamical condition canbe fulfilled when either the recoverytime of the gain is shorter than the bit-period or the recovery time is much

longer than the bit-period so that theamplifier effectively averages the powerover very long bit sequences.

EDFAs typically have recovery timesin the millisecond region, which meansthat they operate in the regime of meanpower saturation. The carrier lifetimes of SOAs, on the other hand, are in theregion of hundreds of picoseconds tonanoseconds, a factor that leads to tran-sient gain variations for data rates in the Gigabit-per-second regime. Severalsolutions to this problem have been pre-sented. Although we will discuss some of them here, for a more complete dis-cussion of the systems aspects of SOAs,we refer readers to an article by Mecozzi and Wiesenfeld.1

Gain saturation and fast responsetimes make SOAs useful in all-optical signal processing applications. In theseapplications, the data signal is processed,e.g. wavelength converted, in opticalform, rather than first being converted toan electrical signal.2, 3 At present, all sig-nal processing in wavelength divisionmultiplexed (WDM) network nodes isaccomplished by terminating incomingoptical signals and then, after paralleliza-tion, carrying out the process electroni-cally. A demand for increased bandwidthcan be accommodated by an increase inthe line rate per wavelength and/or by anincrease in the wavelength channel count.Either approach, however, will lead to

further parallelization in the electronicdomain, which will increase power consumption and the footprint of thesystem. This is strong motivation forintroducing some level of optical signalprocessing in the nodes of high capacityphotonic networks: by keeping signals inthe optical domain, a fast optical schemecould potentially circumvent the need for optical-electronic-optical (OEO) andserial-parallel conversion. It is clear, inany case, that for an all-optical solutionto present a realistic alternative to elec-tronic processing, it would have to bemechanically stable, very compact andsimple to operate; to allow for high-den-sity integration without the risk of ther-mal problems, it would also have to becharacterized by low overall power con-sumption. What’s more, it would have toprovide at least the same functionality asan OEO system at lower cost. Needless tosay, no single optical processing technol-ogy is yet capable of responding to allthese requirements. The functionalitiesthat are simplest to realize by opticalmeans—and thus closest to implementa-tion in real systems—are wavelength conversion and regeneration. IntegratedSOA-based devices are widely recognizedas prime candidates for future all-opticalsystems because of their compact size,low optical and electrical power con-sumption, polarization independenceand high speed.2-4

Semiconductor optical ampli-fiers (SOAs) have a number ofunique properties that open upsignificant opportunities in thearea of fast, all-optical signalprocessing but pose challengesto those who would seek to usethem as linear amplifiers. Thesituation has changed recentlywith the appearance of a newgeneration of SOAs: In thefuture, novel, quantum-dot-based SOAs, because of theirdistinctive dynamical features,may become the linear amplifier of choice.

Figure 1. Qualitative illustration of amplification and saturation in an SOA.

1047-6938/03/07/0042/6-$0015.00 © Optical Society of America

In this article we will discuss the phys-ical properties of SOAs that affect theirsuitability for use as linear amplifiersand switching elements for ultrafast all-optical signal processing. The basicproperties of SOAs can be described byeffective device models: a propagationequation can be used to characterize theevolution of the (complex) electricalfield; and rate equations can be used tomodel carrier dynamics. We will illus-trate the discussion by means of theresults of simulations, referring fordetails on the physical models to thearticles listed in Refs. 2,6 and 7, as wellas to the references cited therein.

The dynamics of SOAsWhen an optical beam is injected into anamplifier, electrons in excited (conduc-tion band) states are depleted because of the stimulated emission processesresponsible for amplifying the inputbeam. The reduction in the density ofexcited electrons has two consequences.First, amplifier gain is reduced and, as aconsequence of the induced change incarrier density in the active region, therefractive index of the waveguide changes(see Fig. 1). In linear amplifier applica-tions of SOAs, the induced gain andindex changes are problematic in that

they may introduce patterning effects anddynamic wavelength changes, or chirp.Yet these same effects become usefulwhen SOAs are used as optically con-trolled switching elements.

Recovery following depletion by aninjected optical pulse is illustrated in Fig. 2, which shows the qualitative evolu-tion of the carrier distributions in theSOA. Within a few picoseconds, a quasi-equilibrium (Fermi-Dirac) distribution at the lattice temperature is established.From this point on, the state of theamplifier—as far as gain and index areconcerned—can be characterized bythe total carrier (electron/hole) density.This density decays, because of the well-known radiative and nonradiative recom-bination processes, on a time scale ofhundreds of picoseconds. Prior to theestablishment of a Fermi-Dirac distribu-tion, the carrier distribution is in a non-equilibrium state governed mainly byspectral hole burning (or, in other words,by a localized reduction in the number ofcarriers at the transition energies) and bycarrier heating, or in other words a tran-sient heating of the electron and holetemperatures.5 The temporal characteris-tics of the processes—as well as theirdependence on operation parameters,such as wavelength and injection cur-

rent—can be characterized throughpump-probe measurements whichemploy femtosecond optical pulses.A generalized rate equation model thataccounts well for such measured gain andindex dynamics in bulk and quantumwell SOAs has been established.6 On the100-fs time scale, instantaneous coherentprocesses, such as two-photon absorptionand optical Kerr effects, are also found tosignificantly influence the response.

The practical importance of the ultra-fast processes depends on the applicationand the time scale in question. It is wellknown that carrier heating and spectralhole burning cause gain suppression andbandwidth limitations in semiconductorlasers. It has also been shown that, for relatively low repetition rates and pulsesshorter than about 10 ps, ultrafast gaindynamics provide the dominant contri-bution to the saturation of pulse gain.For optical switches such as those dis-cussed in the following section, the impli-cation is that the carrier density changeinduced by a pump pulse with fixedenergy is reduced for shorter pulses. Thecontributions of intraband dynamics tothe gain and index changes also increasefor shorter pulses. These opposing effectslead to switching windows with charac-teristics that depend on the pulsewidthand the operation point of the device,and careful optimization is necessary toreap the benefits of the fast processes.

In the presence of an optical signal,the recovery of the carrier density in theactive region is governed by the stimu-lated carrier lifetime; in other words,the lifetime decreases when the opticalpower level is high. This effect can beused to increase the modulation band-width of the SOA by ensuring a highoptical power level, either through thedata/control input beams themselves,in the case of a long amplifier with highgain, or by the application of a separate“holding” beam.8 As it turns out, tounderstand these dynamical features it is important to understand propagationeffects in the SOA.2,9

Optical signal processingAll SOA-based wavelength conversionand regeneration schemes exploit cross-gain modulation (XGM), cross-phasemodulation (XPM) or four-wave mixing.

44 Optics & Photonics News ■ July 2003

SEMICONDUCTOR OPTICAL AMPLIFIERS

Figure 2. Qualitative illustration of the evolution of the carrier distribution (electron den-sity � vs. electron energy E ) in the active region of an SOA. Following stimulated emissioninduced by a short optical pulse, the distribution recovers to equilibrium by carrier-carrierscattering, establishing a Fermi-Dirac distribution function, carrier temperature relaxationand carrier injection.


Figure 3(a) shows the XGM configura-tion: the input data signal at wavelength�1 is combined with a cw probe at thetarget wavelength �2 and the signals arelaunched together into the SOA. The datasignal saturates the SOA gain; this gainmodulation is observed by the cw probe,which is thus imprinted with the inverteddata pattern. An optical band-pass filter is needed at the output to suppress theoriginal data signal at �1. This poses anobstacle to the realization of fast, tunablewavelength converters, because filter tun-ing is obtained thermally or mechani-cally, at speeds which are much slowerthan the tuning speed of lasers. A solu-tion to this problem is to operate theXGM wavelength converter in counter-propagation mode, whereby the cw probeis launched into the SOA from the oppo-site facet, thus making the filter unneces-sary. As will be explained later, however,the use of a counterpropagating data sig-nal and probe severely limits the bit rateat which the converter can be operated.Wavelength conversion by XGM coprop-agation has been demonstrated at speedsas high as 100 Gbit/s.

As a rule of thumb, the maximum bitrate at which wavelength conversion bycopropagation XGM is possible increaseswith the active length of the SOA. Thishas been verified through small signalmeasurements and modeling, which alsoreveals that a moderate amount of inter-nal waveguide scattering loss enhancesthe XGM response.9 Internal loss is not aparameter that can be easily controlled.However, by introducing a lumped lossbetween two or more SOAs (e.g., theunavoidable coupling loss), the benefitsof loss can be exploited and optimized.For counterpropagation XGM, the prop-agation time of the SOA, and thus theSOA length, play an important role. Thisis illustrated in Fig. 4, where the simu-lated small signal XGM bandwidth isshown as a function of SOA length for a constant bias current density of25 kA/cm2. As mentioned above, thebandwidth increases monotonically withlength for copropagation, whereas itpeaks at around 1 mm for counterpropa-gation. For long SOAs, the bandwidthapproximates the expression vg /(2L) = (2 � prop. time)-1, where �g is the groupvelocity, corresponding to a scenario in

which the modulation of the probe islimited by slow depletion of the effectiveprobe gain rather than by gain recovery.The results in Fig. 4 were obtained with adetailed time domain SOA model, takinginto account the inhomogeneous carrierand photon distribution in the activeregion as well as the dynamics of ampli-fied spontaneous emission (ASE).

Although wavelength converters thatexploit XGM are simple, stable, and havebeen demonstrated at high bit rates, theysuffer from several drawbacks that posechallenges to practical application: Asexplained previously, the gain modula-tion of the probe is accompanied byphase modulation; this phase modulationcorresponds to a red-shifted chirp on theleading edge of the inverted pulses and a blue-shifted chirp on the trailing edge.The chirp is generally quite large, sincethe XGM converter relies on maximizingthe carrier density modulation. On fiberwith anomalous dispersion, the combina-tion of data polarity and sign of the chirpgives rise to pulse broadening which limits transmission distance. Moreover,XGM wavelength converters possesseither very limited regenerative capabili-ties or no regenerative capability at all,a factor that limits cascadability. Theseproblems can be addressed by insertingSOAs into an interferometer to exploitXPM. Figure 3(b) shows a Mach-Zehnder

interferometer (MZI) with SOAs in botharms as well as at the input and outputports. The standard mode of operatingthe MZI is by launching the data signalinto one of the two arms (in this case, theupper one). The data signal modulatesthe phase on the part of the cw probetraveling in the upper arm and causes achange from constructive to destructiveinterference (or vice versa) at the output.The duration of the trailing edges of theconverted pulses is governed by the effec-tive carrier lifetime at the output of SOA 1.At high bit rates, the trailing edges mayoverlap significantly with the successivetime slot, which leads to pattern depen-dence and intersymbol interference (ISI).

Launching a delayed and attenuatedcopy of the data signal into the lower armof the interferometer can mask thisinherent speed limitation. This approach,referred to as differential-mode opera-tion, is illustrated in Fig. 3(c), whichshows the phase imposed on the cw probe by a data pulse in the upper(�1) and lower (�2) arm, as well as thephase difference �1 – �2 that defines theswitching window. By comparing theswitching window of standard-modeoperation with that of the differentialscheme, it is clear that the latter is capableof masking the finite gain and phaserecovery times of the individual SOAsand thus reducing pattern effects at high


Figure 3. (a) SOA XGM wavelength converter. The data signal at �1 modulates the gainobserved by the probe at �2. At the output, �1 is suppressed with a band-pass filter (BPF).(b) MZI wavelength converter with SOAs in the interferometer arms and accesswaveguides. In the standard mode of operation, injecting the data signal into one of theinterferometer arms modulates the phase observed by the probe, which is converted toamplitude modulation at the output. In differential mode, launching a delayed and atten-uated replica of the data signal into the other arm opens a narrow switching window (c),enabling operation at higher bit rates.

(a)

(b) (c)

bit rates. This is further detailed in Fig. 5.Figure 5(a) shows a cross-gain modulatedprobe signal, subjected to an RZ data sig-nal at 40 Gbit/s containing a series of sixlogic 1’s, in an SOA with a gain recoverytime larger than the 25-ps time slot. Inthis scenario, the extinction ratio, whichis indicated by the dashed horizontallines, is limited by the logic transition“…1 0 1…”. Figure 5(b) shows the corre-sponding phase of the probe assumedtraveling in the upper SOA (solid curve),and lower SOA (dashed curve) of a MZI,with the latter delayed and attenuated asexplained previously. Focusing on theevolution of the phases during the six 1’s,it is clear that the phase change caused bythe first 1 is about a factor of 2 largerthan the phase shift brought about by thefollowing 1’s. The reason is that the first 1 saturates the SOA, leaving less gain forthe next 1, which is then unable to pro-vide the same phase shift. After a few 1’s,the gain dynamics enters a steady state,as seen in Fig. 5(a). When the differentialscheme shown in Fig. 5(c) is applied, thepatterning is masked because the phasedifference �1 – �2 is governed primarilyby the slope of the phase response andnot by the absolute phase shift. Clearly,the phase contrast of the individual bits isincreased, and this increase in phase con-trast will correspond to a pronouncedincrease of the extinction ratio when the

phase difference is converted to ampli-tude modulation at the output of theinterferometer. A specific pulse energy isrequired to facilitate the phase shift nec-essary for switching. For increasing bitrates, a long string of 1’s corresponds toincreasing average power into the SOAand the SOA is driven toward trans-parency (i.e., zero net material gain).This means that no further gain or phasechange can be introduced and the differ-ential scheme breaks down since the slopeof the phase changes caused by successive1’s will decrease.

The MZI configuration, with or without the peripheral SOAs shown inFig. 3(b), is considered superior to otherclassic interferometric wavelength con-verters (IWC), such as the SOA-basedMichelson (MI) and Sagnac interferome-ters (SI), which to some extent rely oncounterpropagation of data signal andprobe. A variation of the differential MZIscheme, referred to as the delayed inter-ference signal converter (DISC), uses onlya single SOA followed by a passive Mach-Zehnder interferometer. Wavelength con-version using a hybrid implementation of a DISC has been demonstrated at 168 Gbit/s [Ref. 4] and at 100 Gbit/s with a fully integrated device.5

All IWCs provide a transfer functionof the probe which is nonlinear withrespect to the input signal power and

thus approximates a decision gate. Anonlinear transfer function gives rise to a regenerative effect, since the extinctionratio of the converted signal can begreatly improved compared to that of theinput signal, so as to make the convertedsignal less sensitive to the addition of ASEnoise from inline EDFAs in a link. Theeffect is referred to as 2R regeneration(reamplification and reshaping),although IWCs seldom provide net gain.Timing jitter, which accumulates on longfiber links, easily becomes the limitingfactor in high-speed transmission. Tocombat jitter accumulation, the signalmust be retimed periodically. Thisimplies recovering the clock and thenusing it to sample the data. Sampling thedata is a relatively simple task in conjunc-tion with wavelength conversion and 2Rregeneration in an IWC, since data sam-pling can be achieved by simply replacingthe cw probe with a clock signal. Becauserecovering the clock from the incomingdata is much more difficult, a significantamount of attention is being devoted to research into electro-optical and all-optical clock recovery schemes.

Quantum dot SOAsSome of the limitations in bulk andquantum well (QW) SOAs may poten-tially be overcome by use of low dimen-sional structures, such as quantum dots



Figure 5. Simulation of differential scheme showing (a) XGMprobe at 40 Gbit/s along with the logic pattern of the datasignal, (b) phase modulation of the probe traveling in upper(solid ) and lower (dashed ) arm of a MZI, and (c) resultingphase difference governing the switching. A pronouncedreduction of patterning effects is observed.

Figure 4. Simulation of the small-signal 3 dB XGM bandwidthfor the co- (squares) and counterpropagation scheme (circles),demonstrating the superiority of the former. A simplifiedexpression for the counterpropagation bandwidth in the longSOA limit is shown by the dashed line.

SOA length [mm]

copropagating

counterpropagating3 dB

XG

M b

andw

idth

[G

Hz]

Time [ps]


(QDs), as the active medium. Researchon QD devices has focused mainly onlasers. Remarkable results—e.g., in termsof low threshold current densities—havebeen obtained in the realm of lasers, butonly a few results for QD SOAs have beenreported to date.7,10,11

The basic outline of a QD SOA isshown in Fig. 6(a). In principle, thedevice is identical to other SOAs exceptthat the active region consists of a num-ber of QD layers; in this case, two areshown. A practical way of growing highdensities of high quality QDs is by self-assembly through the Stranski Krastanowgrowth technique. In this method, a thinlayer of dot material, the so-called wet-ting layer (WL), is formed beneath theQDs. Because it is mainly through thislayer that charge carriers are fed into theactive states in the dots, the properties ofthe WL are important for the overall per-formance of the device. Figure 6(b) illus-trates the conduction band structure ofa single QD and the WL. In this case, it isassumed that the QD contains two dis-crete electronic states: an excited state(ES) and a ground state (GS). Carrierspresent in the WL are captured into the ES by means of a combination ofphonon- and Auger-assisted processes.Through similar mechanisms, carriersfrom the ES relax to the GS, which isusually the state involved in the amplifi-cation of light.

The discrete nature of the QD systemmeans that, in some respects, the QDSOA may be considered a three level sys-tem. The states above the QD GS act as a nearby reservoir of carriers for the GS.This is very different from the case ofbulk SOAs, which behave more like twolevel systems in which the reservoirstates and the optically active states arestrongly coupled. It is thus easier toobtain complete inversion of the activestates of a QD SOA. The three levelnature of a QD system is similar to thatof an EDFA,1 which suggests that someof the properties associated with EDFAs,such as low noise figure and smalldegree of patterning, might also beachievable in QD SOAs.

The important role of a highlyinverted WL can be understood by con-sidering the linear amplification proper-ties of a QD SOA under high inversion

(i.e., with a high bias current densityapplied). Figure 6(c) shows the calculatedgain and saturation power versus devicelength when a cw signal is injected intothe amplifier. Because of the small valueof modal gain of the QDs grown today, toobtain significant device gain it is neces-sary to consider long devices. The satura-tion output power, P 3dB

out , which causesthe gain to decrease by 3 dB (solid line),is found to be above 20 dBm for alllengths. This value is significantly higherthan the best results reported for bulkand QW SOAs,1 and is caused by thecombination of a highly filled carrierreservoir (the WL) and the small overlapbetween the optical field and the QDs.The highly filled WL and the large energyseparation from the QD GS means thatthe carrier number may decrease signifi-cantly before the gain is affected, and as aresult the saturation power increases.

The device gain (dashed line) is seento increase linearly with length up to 6mm, at which point the ASE starts to sat-urate the gain. At this length, the gain hasreached a maximum of 45 dB. As in thecase of bulk and QW devices, the maxi-mum gain value is limited because of thesaturation caused by ASE—or by lasing,if the antireflection coating of the facetsis not of sufficient quality. It is thus thehigh saturation power of the QD SOAwhich enables the high level of gain.Another effect of the high inversion of a

QD SOA is a low noise figure. When boththe conduction and valence band activestates are completely inverted, the inver-sion factor is close to unity and the noisefigure approaches its lower limit of 3 dB.

The nonlinear properties of QD SOAsoffer unique possibilities for optical sig-nal processing. Figure 7(a) shows the gainrecovery when a QD SOA is saturated by a 150-fs pump pulse. Experimentalresults10 (red dots) and the result of atheoretical rate equation model7 (blackline) are seen to agree very well. The gainrecovers completely less than 0.5 ps aftersaturation by the pump pulse, which issignificantly faster than for bulk devices.Once again, the explanation of the fastrecovery is related to the existence of acarrier reservoir in the upper states.

Figure 7(b) shows the calculateddynamics of the GS (red line), ES (blueline) and WL (green line) carrier densi-ties during the pump-probe experiment.Initially, before the pump pulse enters theamplifier, the two dot states are nearlycompletely inverted and the WL containsa significant amount of carriers. As thepulse excites the material, the GS popula-tion is rapidly depleted through stimu-lated emission. Due to rapid intradotrelaxation on a time scale of 150 fs,carriers from the ES refill the GS, whichexplains the rapid gain recovery. The ESin turn recovers by capture of carriersfrom the WL on a picosecond timescale


Figure 6. (a) Schematic illustration of a QD SOA, including two layers of dots situated onwetting layers (WL). (b) State structure of a single QD, including a QD ground state (GS),a QD excited state (ES) and the WL continuum of states. (c) Device gain (dashed line)and 3 dB saturation input and output power (solid and dotted lines, respectively) as function of device length.

Amplifier length [mm]

Smal

l sig

nal g

ain

[dB]

Pow

er [

dBm

]

0 1 2 3 4 5 6 7 8

P 3dBout

GunsatP 3dB

in

50

40

30

20

10

0

30

20

10

0

-10

-20

-30

ES

GS

WL

WLP

QD

n

(a) (c)

(b)

and the WL recovers by current injectionon a timescale determined by the carrierlifetime of the WL [shown in the inset ofFig. 7(b)]. Thus, despite the fact that theGS gain has recovered completely in lessthan 0.5 ps, it is clear that the recovery ofthe total carrier density is much slowerand essentially limited by the same pro-cesses as for bulk and QW devices.Hence, for the operating conditions usedin this experiment, we cannot expect tobe able to operate the device at speedshigher than those of bulk or QW deviceswithout significant pattern dependence.Thus, if a train of short pulses with a highrepetition rate is injected instead of a single pulse, the overall inversion wouldcontinue to decrease and the devicewould be forced toward transparency.However, if the bias current is increased

to the point where the saturated WL car-rier density is high enough that the QDstates remain inverted, operation at highbit rates without pattern effects should be possible.11 This effect is illustrated in Fig. 7(c). A 100 Gbit/s data stream and acw beam are injected into a QD SOAwith high bias current. Figure 6(c)shows the resulting normalized modu-lation of the cw signal during criticaltransitions between long sequences ofzero-levels and one-levels. The modula-tion is seen to be close to 100% andnearly pattern independent. Eventually,the GS gain does decrease slightly as aconsequence of the high repetition rateof the input signal, but the extinctionratio remains high. Signal processing in a QD SOA has been demonstratedexperimentally at 10 Gbit/s even at

moderate inversion and shows poten-tial for 160 Gbit/s operation.11

Referring back to Fig. 2, gain deple-tion in a QD resembles the process ofspectral hole burning in a bulk or QWdevice. One significant difference is that,for QDs the equilibration time is given by the capture time, i.e., on the order of afew picoseconds, which is to be comparedto the sub-100-fs intraband scatteringtime for bulk or QW active layers. Thismeans that the nonlinearity becomesmuch more efficient for QD materials,enabling new regimes of operation, asdiscussed above.

ConclusionsFuture optical networks may employSOAs as inexpensive linear amplifiers and as nonlinear elements in all-opticalprocessing devices, such as wavelengthconverters and regenerators. The opti-mization of SOAs for these applicationsrequires good models and a detailedunderstanding of the dynamical proper-ties. Interferometric configurations offer possibilities for achieving very fastswitching through exploitation of indexdynamics in the SOA, while new quan-tum dot materials may open up opportu-nities in the area of fundamentalengineering of SOA dynamics.

Jesper Mørk ([email protected]), Mads L. Nielsen andTommy W. Berg are with the Research Center COM,Technical University of Denmark, Lyngby, Denmark.

References

1. A. Mecozzi and J. M.Wiesenfeld, Opt. Photon. News,12(3), 36-42 (2001).

2. K. Stubkjaer, IEEE J. Select. Topics Quantum Electron.6, 1428-35 (2000).

3. B. Dagens, A. Labrousse, S. Fabre, B. Martin, S.Squedin, B. Lavigne, R. Brenot, M. L. Nielsen and M.Renaud, Proc. ECOC 2002, paper PD3.1.

4. S. Nakamura, Y. Ueno and K. Tajima, IEEE Photon.Technol. Lett. 13, 1091-3 (2001).

5. J. Leuthold, B. Mikkelsen, G. Raybon, C. H. Joyner, J. L.Pleumeekers, B. I. Miller, K. Dreyer and R. Behringer,Optical and Quantum Electron. 33, 939-52 (2001).

6. A. Mecozzi and J. Mørk, IEEE J. Sel.. Topics QuantumElectron. 3, 1190-207 (1997).

7. T. W. Berg, S. Bischoff, I. Magnusdottir and J. Mørk,Photon. Technol. Lett. 13, 541-3 (2001).

8. R. J. Manning, A. D. Ellis, A. J. Poustie and K. J. Blow, J.Opt. Soc. Am. B, 14, 3204-16 (1997).

9. M. L. Nielsen, D. J. Blumenthal, J. Mørk, “A transferfunction approach to the small-signal response of sat-urated semiconductor optical amplifiers,” J.Lightwave. Technol.18, 2151-57 (2000).

10. P. Borri, W. Langbein, J. M. Hvam, F. Heinrichsdorff,M.-H. Mao and D. Bimberg, IEEE Photon. Technol.Lett. 12, 594–6 (2000).

11. T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, M.Sugawara, Electron. Lett. 38, 1139-40 (2002).



Figure 7. (a) Pump-probe trace of a QD SOA. (b) Calculated carrierdynamics during the pump-probe experiment. (c) Calculated out-put power (normalized) when a QD SOA is used for wavelengthconversion of a 100Gbit/s input signal.

Time delay [ps]

Delay [ns]

100 Gbit/s

Gai

n ch

ange

�G

[dB

]

-0.5 0.0 0.5 1.0 1.5 2.0

(a)

(b)

(c)

0.0 0.5 1.0 1.5 2.0

ExperimentCalculated

0.00

-0.25

-0.50

-0.75

-1.00

-1.25

-1.50

Time delay [ps]

Gai

n ch

ange

�G

[dB

]

0 2 4 6 8 10

GSESWL

1.0

0.9

0.8

0.7

0.6

Time delay [ps]

P con

v(N

orm

aliz

ed)

0.0 0.1 0.2 0.3 0.4 0.5

1.0

0.8

0.6

0.4

0.2

0.0

1.0

0.9

0.8

0.7

0.6

The Dynamics of Semiconductor Optical Amplifiers: Modeling and Applications

Documents

Transcript of The Dynamics of Semiconductor Optical Amplifiers: Modeling and Applications