Numerical simulation of a mode-locked quantum dot external cavity laser

www.ietdl.org

4&

Published in IET OptoelectronicsReceived on 7th May 2013Revised on 18th August 2013Accepted on 23rd September 2013doi: 10.1049/iet-opt.2013.0040

Special Issue on Semiconductor Lasers andIntegrated Optoelectronics

4The Institution of Engineering and Technology 2014

ISSN 1751-8768

Numerical simulation of a mode-locked quantum dotexternal cavity laserNuran Dogru1, Mike J. Adams2

1Department of Electrical and Electronics, University of Gaziantep, 27310 Gaziantep, Turkey2School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK

E-mail: [email protected]

Abstract: The mode-locked characteristics of a quantum dot hybrid soliton pulse source (QD-HSPS) utilising a linearly chirpedfibre Bragg grating (FBG) are investigated using the time-domain solution of coupled wave equations and rate equations. Theeffect of carrier dynamics on the output pulse of the QD-HSPS is also described. The numerical results indicate that thespontaneous coupling factor, carrier recombination time in QD and the length of the laser strongly affect the systemoperation, whereas there is no significant effect of carrier recombination in the wetting layer or of the carrier emission fromthe QD to the wetting layer or of the relaxation time from the wetting layer to the QD. Furthermore, it is also shown that byusing the optimum parameters a QD-HSPS utilising a linearly chirped Gaussian-apodised FBG produces considerably shorterpulses when compared with a multi-quantum-well HSPS (MQW-HSPS) utilising linearly and non-linearly chirped gratings,along with an increase in the mode-locking frequency range.

1 Introduction

Active and passive mode-locking of laser diodes arewell-established techniques for generating picosecondpulses at wavelengths about 1.55 μm [1, 2]. Thesewavelengths are of primary interest for telecommunicationsapplications. A hybrid soliton pulse source (HSPS) hasbeen developed as a pulse source for a soliton transmissionsystem, and a chirped fibre Bragg grating (FBG) has beenutilised as an external cavity in this system [3, 4]. Themodel consists of a multi-quantum-well (MQW) laser, anoptical fibre and an FBG. An external cavity activelymode-locked configuration permits the incorporation ofappropriate intra-cavity dispersion compensation such thatthe pulse characteristics can be optimised [5]. The use ofchirped FBGs to compensate for the dispersion of fibrelinks [3] is a well-known approach. We have previouslyreported [6–9] the frequency range of mode-locking of anHSPS utilising linearly and non-linearly chirped FBGs.These results showed that an extreme increase in themode-locking frequency range to 1.8–3.4 GHz (that is, over1.6 GHz) was obtained by using a linearly chirped,tanh-apodised FBG [6, 8], whereas transform-limited pulseswere generated over a repetition frequency range of850 MHz (2.1–2.95 GHz) using a linearly chirped,Gaussian-apodised FBG [3]. Later, we also reported that thenon-linear (sinusoidally) chirped, Gaussian-apodised gratingproduced shorter pulses than the linearly chirped grating. Italso extended mode-locking over a much larger centrefrequency range (2.1–3.2 GHz), when compared with therange of a linearly chirped, Gaussian-apodised grating [9].Therefore an HSPS utilising a sinusoidally chirped FBG is

a candidate source for many applications such as opticaltime division multiplexing, dense wavelength divisionmultiplexing and soliton propagation. However, the use ofquantum dot (QD) semiconductor mode-locked lasers hasattracted much more attention recently for generation ofultra-short optical pulses [5, 10–15], owing to inherent QDproperties, such as fast carrier dynamics, broadband gain,low-spontaneous emission levels and a low-thresholdcurrent density. These properties motivate us to utilise QDlasers in an HSPS and to observe how the QD laser affectsthe mode-locking frequency range and generation of shortpulses. Hence, in this paper, the mode-locked characteristicsof an HSPS based on a QD laser are investigated for thefirst time to our knowledge, and the results are comparedwith those of an MQW laser. Furthermore, the effect of thecarrier dynamics on the output pulses is also investigated.

2 Numerical methods

The geometry is similar to the one reported in [8, 9], but herea QD laser is used instead of an MQW laser. The structure ofHSPS based on QD laser is shown in Fig. 1.One facet of diode is high reflectivity (HR) coated for

improved cavity Q and the other antireflection coated (AR)to allow coupling to the external cavity and suppress FabryPerot modes. The output power is measured through thegrating.The effective refractive index variation of the Bragg grating

along the propagation direction (z) is given as

n(z) = nco + Dn(z) 1+ m cos2p

L(z)z

( )[ ](1)

IET Optoelectron., 2014, Vol. 8, Iss. 2, pp. 44–50doi: 10.1049/iet-opt.2013.0040

Fig. 2 Schematic energy band diagram of the QD laser

Fig. 1 Schematic of HSPS with linearly chirped FBG

www.ietdl.org

where nco is the unperturbed effective index of the fibre, Δn(z)represents the dc index change, spatially averaged over agrating period and m is the modulation index of the grating.The z-dependent grating period Λ(z) is linearly chirped andis taken as

L(z) = Lo +1

2nco

dlodz

z (2)

where Λo = λo/2nco is the pitch of the unchirped Bragggrating at the operating wavelength λo. The grating pitch isassumed to be linearly chirped such that the operatingwavelength λo corresponds to the centre of the grating andthe wavelength is chirped by C = dλo/dz around the centre.The time-domain propagation equations for the forward-

and backward-propagating electric fields F(z,t) and R(z,t)are written as

dF

dz= −j d+ 2k(z)

m− 1

2

df

dz

( )F − jk(z)R (3)

dR

dz= j d+ 2k(z)

m− 1

2

df

dz

( )R+ jk(z)F (4)

where κ(z) is the coupling coefficient between the forwardand reverse waves, δ is the deviation of the propagationconstant β from the Bragg condition (δ = β− βo = β− π/Λo)and j is the grating chirp. The loss in the fibre and gratingcan be neglected since the fibre is a few centimetres long.The term inside the parentheses in (3) and (4) is referred toas the dc ‘self-coupling’ coefficient, σ(z) [16]. For eachlaser section σ(z) represents the gain and loss of the laserdiode (σ(z) = −g(z,t)/2 + αl/2 + δ). g is the gain, αl is theinternal loss of laser diode and δ is taken as δ = 2πΔn/λowhere Δn is the change in refractive index of laser mediumbecause of carrier density.For a Gaussian-apodised profile, the coupling coefficient is

assumed to be

k(z) = kp exp−4 ln 2

FWHM2g

z2( )

(5)

where κp is the peak value of the Gaussian distribution of thecoupling constant and FWHMg is the full-widthhalf-maximum of this distribution of the coupling constantand is taken as Lg/3 throughout the calculations [16]; Lg isthe grating length.Fig. 2 shows the schematic energy band diagram of the QD

laser. Here, the excited state in the QD and Pauli blocking ofthe ground state (GS) levels are neglected. As seen in thefigure, the QD laser includes a wetting layer (WL) and oneconfined state, that is, GS. The WL state acts as a commonreservoir [17–19], and the dot state couples to the WL.The laser cavity is divided into ML equal sections with

Dz = vgDt. For each time step, the forward and backwardfields are calculated from the transfer matrix. In each


section of the laser, the carrier density is calculated fromthe rate equations as follows

dNw

dt= I

qV− Nw

td− Nw

twr+ Nq

te(6)

dNq

dt= Nw

td− Nq

te− Nq

tr− NGvga

Nq

N− 1

( )S (7)

where I(t) is the injection current, V is the active layer volume,q is the electron charge, Nw(z,t) is the carrier density of theWL, Nq is the carrier density of the GS (QD), N is thequantum dot density, td is the carrier relaxation time intothe QD, twr is the carrier recombination time (radiative andnon-radiative) in the WL, te is the carrier emission timefrom the QD to the WL, tr is the carrier recombination time(radiative and non-radiative) in the QD, S(z,t) is the photondensity (proportional to |F |2 + |R|2), a is the differentialgain and Г is the optical confinement factor. These sectionsalso include coupling between the carrier density and therefractive index through the linewidth enhancement factor,and can be written as

Dn = − lo4p

GaaoDNq(z, t) (8)

ΔNq(z, t) is the change in the carrier density and α is thelinewidth enhancement factor. Here, it is assumed that onlya single discrete GS for electrons and a corresponding GSfor holes are formed inside the QD and that the chargeneutrality always holds in each QD. Inhomogeneousbroadening is also neglected.For each time step, new field values are calculated, and the

boundary conditions are applied. The effect of the non-zeroAR coating reflectivity of the laser is included in the model.The fibre and grating sections are passive, as they have noloss, but they include the effects of the grating. Forsimplicity, the group velocity vg is kept constant throughoutthe cavity and the parameters of the grating are scaled bythe refractive index of the laser.Although the AR-coated face provides maximum field

transfer to the fibre, it is not perfectly transmissive, and forall practical purposes, the field reflection coefficient of theAR coating is taken as 0.01. The coefficient η representsthe coupling loss between the laser and the fibre modes,and its magnitude is assumed to be 0.8 for both thelaser-to-fibre and the fibre-to-laser field transfer.In our simulation, InAs–InP (113)B QD laser emitting at

1.55 μm is used. To reach the standards of long haultransmission, 1.55 μm InAs QD lasers grown on InPsubstrates have been developed [20]. A grating length is4 cm with a peak reflectivity of 0.5 and the operatingfrequency is 2.5 GHz. The other parameters can be found inTable 1. The values of these parameters were obtained in

45& The Institution of Engineering and Technology 2014

Table 1 Laser diode parameters

carrier emission time fromQD to WL

te = 1.1 × 10−7 s field coupling factor η = 0.8

spontaneous emission timefrom WL

twr = 500 ps field reflectivity of AR coating 0.01

spontaneous emission timefrom GS

tr = 1 ns field reflectivity of HR coating 0.9

carrier relaxation time td = 2.5 ps refractive index of unmodifiedfibre core

nco = 1.46

QD dot density N = 6 × 1016 cm−3 operating wavelength λ = 1.55 μmcavity length L = 2.45 mm (250 μm for MQW) length of grating 4 cmcavity width W = 120 μm (1 μm for MQW) mode-locking frequency 2.5 GHzgain material refractive index nr = 3.27 (3.3 for MQW) differential gain a = 4.6 × 10−14 cm2 (10 × 10−16 cm2

for MQW)optical confinement factorfor the QD

Γ = 0.025 (0.1 for MQW) gain saturation parameter ɛ = 0 (2 × 10−7 cm3 for MQW)

spontaneous coupling factor β = 10−4 (5 × 10−5 for MQW) linewidth enhancement factor α = 0.4 (2 for MQW)cavity internal losses αi = 6 cm−1 (25 cm−1 for MQW)

www.ietdl.org

[21–25]. Some MQW laser parameters are also included inTable 1 for use later in this paper.As mentioned before, a mode-locked HSPS utilising a

linearly chirped, Gaussian-apodised FBG has disadvantagesgiving a narrow mode-locking range and generating widerpulses when compared with the linearly chirped,tanh-apodised and sinusoidally chirped, Gaussian-apodisedFBG. For that reason, here we investigate an HSPS utilisinga linearly chirped, Gaussian-apodised FBG where the HSPSuses an InAs–InP (113)B QD laser to see the effect of theQDs on the mode-locking frequency range and the shortpulses.The grating is modelled with transfer matrix that calculates

the grating parameters for the HSPS system. The calculatedparameters are then fed back into the HSPS model tocalculate the output of the mode-locked HSPS at the desiredfrequency. To determine suitable values for the dc and rfcurrents, a simulation was performed to calculate outputpulses, spectra and time-bandwidth products (TBPs) of thepulses over a wide-frequency range for each value of dcand rf currents.The required pulse width depends on the operating bit-rate

of the transmission system. Pulse widths are typically chosento occupy ∼1/5th of the operating bit period, giving a rangefrom 20 to 80 ps, for systems operating from 10 to 2.5 Gb/s[26]. The optimum pulse shape for a standard solitontransmission system would have a sech2 shape to match thesoliton shape. Gaussian-shaped pulses are also acceptable.The TBP of the pulse must lie in the range from 0.3 to 0.5,where the boundary values are the TBP values of sech2 andGaussian pulses, respectively.For stable mode-locking to occur, the dynamics of the

semiconductor section must counteract the dispersion of thegrating, so that a pulse can replicate itself after one roundtrip of the cavity. As the optical pulse travels through thesemiconductor section and is amplified, it will modifythe carrier density in the laser, which in turn modifies therefractive index. Self-phase modulation occurs because ofthe changing refractive index, which chirps the frequency ofthe optical pulse. This chirp can be considered to beapproximately linear across the centre of the pulse, and canhave either sign (or be zero) depending on whether carrierdepletion from stimulated emission is larger or smaller thanthe injected carrier density. A linearly chirped Braggreflector can provide a linearly varying penetration depthand this grating produces an almost constant dispersion,which can be counteracted by a linear chirp in thesemiconductor laser. The linear variation in penetration


depth allows only one stable operating point for a specificeffective cavity length. When actively mode-locked, themodulation frequency applied to the laser diode specifiesthe required effective cavity length, and for any value ofthis cavity length there is only one possible operatingwavelength. The chirped reflector therefore stabilises theoutput of the HSPS. Another advantage of having apenetration depth which varies over a large spatial length isthat the device can have a large variation in effective cavitylengths, and therefore operate over a large modulationfrequency range.On applying a linear chirp across the reflector, the effective

cavity length becomes wavelength-dependent. When themode-locking repetition frequency is changed, the deviceself-tunes its wavelength to give the correct cavity length tomaintain the resonance with the modulation frequency.When the mode-locking repetition frequency is increased,the effective cavity length decreases, and the output movesto longer wavelengths.In our approach, first the effect of the spontaneous coupling

factor (β), the carrier recombination in the WL (twr), thecarrier emission from the QD to the WL (te), the relaxationtime (td), the carrier recombination in the QD (tr) and thelaser cavity length of a mode-locked HSPS will bepresented. Subsequently, the mode-locked characteristics ofthe HSPS based on a QD laser will be examined andcompared with those of a source based on an MQW laser.

3 Numerical results and discussion

In our simulations, the threshold current was found 19 mA.The simulation results also showed that thetransform-limited pulses were generated for a widerfrequency range (1.8–3.1 GHz) if values of dc = 21 mA andrf = 80 mA were used. Therefore these current values wereused in the following results unless otherwise stated. In thesimulation, the current was assumed to be constant alongthe length of the laser.The relaxation time (td) from the WL to the QD has an

insignificant effect on the output pulses up to 30 ps giving apulse width change from 27.9 to 29.9 ps as td is increasedfrom 2.5 to 30 ps. After 30 ps, the pulse width slightlyincreases with increasing td.The effects of twr and te on the output pulse are given in

Fig. 3 when β is taken to be zero. It can be observed in thefigure that whether the values of twr and te are assumed tobe the standard values or to be infinitely large, the results


Fig. 4 Effect of cavity length on pulse width for β= 0

Fig. 5 Effect of cavity length on pulse width for β= 1 × 10−4

Fig. 3 Effect of twr, te and β on output pulse width

For the solid line, twr = te = ∞, and for the dashed line, twr = 500 ps andte = 110 ns

www.ietdl.org

are the same. These results show that carrier recombination inthe WL twr and the carrier emission from the QD to the WL tehave no significant effect on the mode-locked output pulses.Therefore these parameters are neglected here.The pulse width with respect to the mode-locking

frequency for zero β and for a β value of 1 × 10−4 is alsogiven in Fig. 3. As seen in the figure, transform-limitedpulses are generated between 1.8 and 3.1 GHz, giving afrequency range of 1.3 GHz for a β value of zero, whereasfor β = 1 × 10−4, transform-limited pulses are obtainedbetween 1.5 and 2 GHz, giving a frequency range of500 MHz. It can be also observed from the figure that thepulse width decreases from 37.7 to 27.1 ps for β = 0 andfrom 67.3 to 61.3 ps for β = 1 × 10−4 as the mode-lockingfrequency increases. As seen in the results, the range wheretransform-limited pulses are generated decreases, and themode-locking frequency range is shifted to lowerfrequencies for β = 1 × 10−4. Low-repetition-rate ( <2 GHz)mode-locked semiconductor lasers are useful for RFphotonics, photonic-assisted analogue-to-digital converters,and other applications in which the combination ofaffordable low-speed electronics and ultrafast optics can beleveraged [27, 28]. Owing to the relatively low-thresholdcurrent and internal absorption loss, the QD external cavitymode-locked lasers become feasible at low-repetition ratesbelow 10 GHz, corresponding to long laser cavity lengths,in contrast to in bulk/quantum well (QW) lasers [12].Grillot et al. [24] showed that for longer cavity lengths

(L∼ 0.25–0.3 cm), the lasing wavelength remains almostconstant at the GS transition about 1.54 μm. When thecavity length is decreased below 0.2 cm, the lasingwavelength shifts down to 1.49 μm, which corresponds tothe QD excited-state lasing wavelength for a 0.1 cm longcavity. Therefore output pulses of the mode-locked HSPSwere investigated for 0.1, 0.245 and 0.3 cm long lasers, asdescribed below.Fig. 4 shows the pulse widths of the output pulses for

different values of the laser length for zero β. As seen inthe figure, transform-limited pulses are generated only at themode-locking frequencies of 1.1 GHz and between 1.9 and2.4 GHz (500 MHz) for a 0.3 cm long cavity. It can be alsoobserved from the figure that the mode-locking frequencyrange where transform-limited pulses are produced isincreased for the 0.1 and 0.245 cm cavity lengths giving amaximum range of 2.6 GHz (between 4.1 and 6.7 GHz) and1.3 GHz (between 1.8 and 3.1 GHz), respectively.The effect of laser length on mode-locked pulses for

β = 1 × 10−4 is shown in Fig. 5. Transform-limited pulsesare generated only between 1.4 and 1.7 GHz (300 MHz) for


a cavity with a length of 0.3 cm. The maximummode-locking frequency range becomes 1 GHz (between4.9 and 5.9 GHz) and 500 MHz (between 1.5 and 2 GHz)for cavity lengths of 0.1 and 0.245 cm, respectively.The numerical results also showed that the carrier

recombination time tr in the QD significantly affects theoutput pulses of QD-HSPS. Transform-limited pulses areproduced only between 1.8 and 2.5 GHz for a tr value of0.8 ns for zero β. For a tr value of 5 ns, transform-limitedpulses are generated only between 2.9 and 3.4 GHz andonly at the mode-locking frequency of 2.1 GHz.Transform-limited pulses are generated all of themode-locking frequencies for standard value of tr = 1 ns asexplained earlier.As seen from the results, β, tr and the laser cavity length

both strongly affect the operation of the HSPS system.Since the mode-locking frequency range increases for a βvalue of zero, the following results were obtained for β = 0and standard laser parameters, given in Table 1.Fig. 6 shows the relationship between pulse width and

mode-locking frequency for HSPSs with either QD/linearlychirped Gaussian-apodised grating or MQW/linearlychirped Gaussian-apodised grating lasers. To compare theresults, β is also taken to be zero for the MQW laser. Theother MQW laser diode parameters can be found in Table 1as mentioned before. The parameters for the FBG modelare the same both kinds of laser diodes. As seen in thefigure, transform-limited pulses are generated between 1.8and 3.1 GHz, giving a pulse width of 28.8 ps, a TBP of0.44, and a spectral width of 15.3 GHz at the fundamentalfrequency of 2.5 GHz for the QD laser. This range is foundto be 1 GHz for the MQW laser (between 2 and 3 GHz).A typical transform-limited output pulse having a pulsewidth of 45.4 ps, a TBP of 0.393 and a spectral width of


Fig. 6 Pulse width as a function of mode-locking frequency for QDand MQW lasers

Fig. 7 Pulse width (solid line) and peak power (dashed line) asa function rf current for the dc current of 21 mA and frequency of2.5 GHz

Fig. 8 Pulse width (solid line) and peak power (dashed line) asa function of dc current for the rf current of 80 mA and frequencyof 2.5 GHz

Fig. 9 Pulse width of QD-HSPS as a function of mode-lockingfrequency for all rf and dc currents

Fig. 10 TBP of QD-HSPS as a function of mode-locking frequencyfor all rf and dc currents

www.ietdl.org

8.7 GHz is obtained at the fundamental frequency for theMQW laser. It can be observed in the figure that the pulsesgenerated with the QD laser are considerably shorter thanthose generated with the MQW laser and that themode-locking frequency range is correspondingly increased.Fig. 7 shows the change in the pulse width and peak power

as a function of the rf current. The pulse width decreases asthe rf current is increased, as expected because of theinjection of more carriers into the laser diode during thetimespan of the input pulse. The peak powers of the pulsesare approximately inversely proportional to the pulsewidths. This was also the case in the experimental results of[29, 30]. Similar results were also obtained in [7, 8].However, here it is notable that the HSPS with the QDand utilising a linearly chirped, Gaussian-apodised FBGagain produces considerably shorter pulses, in the range of19–39 ps, whereas the pulses range from 40 to 78 ps foran MQW/linearly chirped tanh-apodised grating system[6, 8]; from 40 to 70 ps for an MQW/linearly chirped,Gaussian-apodised grating system [29]; and from 34 to57 ps for an MQW/sinusoidally chirped, Gaussian-apodisedgrating system [9].The effect of the dc current on the pulse width and the peak

power is given in Fig. 8. The peak powers of the pulsesincrease as the dc bias current increases, because morecarriers are injected into the laser diode as noted in [7, 31].As seen in the figure, the pulse width is slightly sensitiveto the dc current, yielding a pulse width range from 29 to30 ps as the dc current is increased from 18 to 29 mA.This range has been found to be from 41 to 70 ps for anMQW/linearly chirped, tanh-apodised grating system [6, 8];from 40 to 85 mA for an MQW/linearly chirped,


Gaussian-apodised grating system [29]; and from 33 to 49ps for an MQW/sinusoidally chirped, Gaussian-apodisedgrating system [9].Fig. 9 shows the variation of pulse widths with

mode-locking frequency for all tested dc and rf levels forHSPS with QD laser. Note that the simulation programmetakes a considerable amount of time to run, so thefrequency was changed from 1.7 to 3.7 GHz. In thisfrequency range, the device produces shorter pulses in the20–114 ps range. However, the MQW/sinusoidally chirped,Gaussian-apodised FBG produced shorter pulses in the25–72 ps range at modulation frequencies between 2 and3.4 GHz [9]; the pulses range from 31 to 97 ps between 1.8


Table 2 Comparison of the QD-HSPS with MQW-HSPS (laser length is 250 μm for MQW laser and 2.45 mm for QD laser)

Grating types Frequency range for constantdc and constant rf current

Pulse range for constant dcand constant rf current

Pulse range for allfrequency, dc and rfcurrents

References

MQW: linearly chirpedtanh-apodised

dc = 6 mA; rf = 20 mA1.8–3.4 GHz

dc = 6 mA; rf = 20 Ma38–69 ps

range = 1.8–3.4 GHz31–97 ps

[6, 8]

MQW: linearly chirpedGaussian-apodised

dc = 6 mA; rf = 20 mA2.2–3 GHz

dc = 6 mA; rf = 20 mA38–53 ps

range = 1.8–3.1 GHz30–80 ps

[3, 29]

MQW: sinusoidal chirpedGaussian-apodised

dc = 6 mA; rf = 22 mA2.1–3.2 GHz

dc = 6 mA; rf = 22 mA28–53 ps

range = 2–3.4 GHz25–72 ps

[9]

QD: linearly chirpedGaussian-apodised

dc = 21 mA; rf = 80 mA1.8–3.1 GHz

dc = 21 mA; rf = 80 mA27–44 ps

range = 1.7–3.7 GHz20–114 ps

MQW – multi-quantum well; QD – quantum dot.

www.ietdl.org

and 3.4 GHz for an MQW/linearly chirped, tanh-apodisedgrating [6] and from 30 to 80 ps for an MQW/linearlychirped Gaussian-apodised grating between 1.8 and 3.1GHz [29].Fig. 10 shows the TBP of the simulated pulses for the same

conditions explained above. The TBP of the pulses are in the0.3–05 range showing that all these pulses aretransform-limited and suitable for soliton transmissionsystems.Table 2 also lists a comparison of the QD-HSPS with an

MQW-HSPS utilising a linearly chirped, tanh-apodisedFBG; a linearly chirped, Gaussian-apodised FBG; and asinusoidally chirped Gaussian-apodised FBG. Pulsedurations and mode-locking frequency ranges are includedin the comparison.The results show that the HSPS based on a QD is superior

to that based on an MQW because of its production of shorterpulses, along with an increase in the mode-locked frequencyrange.A near-zero linewidth enhancement factor (α) and a

negligible wavelength chirp make QD lasers particularlyattractive for achieving pulses that are closer totransform-limited under mode-locked operation than thosegenerated by bulk/QW devices [12].

4 Conclusions

In this study, first a QD-HSPS model utilising a linearlychirped, Gaussian-apodised FBG was developed byconsidering the effects of carrier dynamics on the output ofa QD-HSPS. Subsequently, mode-locking characteristics ofthe QD-HSPS were investigated and also compared withthe mode-locking characteristics of an MQW-HSPS. Theresults obtained from our model revealed that the outputpulses are affected by several parameters in the followingway: the spontaneous coupling factor, carrier recombinationtime in the QD and the length of the laser strongly affectedthe system operation, whereas there was no significanteffect of carrier recombination in the WL or of the carrieremission from the QD to the WL or of the relaxation timefrom the WL to the QD. Further refinements to the model,such as the inclusion of inhomogeneous broadening andexcited-state transitions, and relaxation of the assumption ofcharge neutrality in the QD, are beyond the scope of thepresent work but offer scope for future work.Our results also indicate that using the QD-HSPS it is

possible to (i) increase the mode-locking frequency rangeand (ii) generate considerably short pulses when comparedwith the MQW-HSPS. To obtain these properties, in viewof the above results, the optimum QD laser has


† zero β,† 0.1 and 0.245 cm cavity lengths,† rf current 80 mA,† dc current 21 mA, and† the other standard parameters described in the text.

These properties make it an attractive source of picosecondpulses with widely tunable wavelengths and repetition ratesfor a wide range of high-speed optical communication,optical interconnect and signal processing applications.

5 References

1 Heck, M.J.R., Bente, E.A.J.M., Smalbrugge, B., et al. ‘Observation ofQ-switching and mode-locking in two-section InAs/InP (100)quantum dot lasers around 1.55 μm’, Opt. Express, 2007, 15,pp. 16292–16301

2 Kaiser, R., Hüttl, B.: ‘Monolithic 40-GHz mode-locked MQW DBRlasers for high speed optical communications systems’, IEEE J. Sel.Top. Quantum Electron., 2007, 13, pp. 125–135

3 Ozyazici, M.S., Morton, P.A., Zhang, L.M., Mizrahi, V.: ‘Theoreticalmodel of the hybrid soliton pulse source’, IEEE Photonics Technol.Lett., 1995, 7, pp. 1142–1144

4 Morton, P.A., Mizrahi, V., Andrekson, P.A.Jr., et al.: ‘Mode-lockedhybrid soliton pulse source with extremely wide operating frequencyrange’, IEEE Photonics Technol. Lett., 1993, 5, pp. 28–31

5 McRobbie, A.D., Cataluna, M.A., Zolotovskaya, S.A., Livshits, D.A.,Sibbett, W., Rafailov, E.U.: ‘High power all-quantum-dot basedexternal cavity mode-locked lasers’, Electron. Lett., 2007, 43,pp. 812–813

6 Dogru, N.: ‘Extremely increasing the operating frequency range ofmode-locked hybrid soliton pulse source’, Chin. Phys. Lett., 2006, 23,pp. 838–841

7 Dogru, N.: ‘Mode-locked performance of hybrid soliton pulse sourceutilizing fiber grating external cavity’, Opt. Commun., 2006, 260,pp. 227–231

8 Dogru, N.: ‘Effect of grating parameters on mode-locked external cavitylasers’, IEEE J. Sel. Top. Quantum Electron., 2009, 15, pp. 644–652

9 Dogru, N.: ‘Sinusoidally chirped fiber Bragg grating for mode-lockedapplication’, J. Opt. Soc. Am. B, 2012, 29, pp. 161–169

10 Xia, M., Thompson, M.G., Penty, R.V., White, I.H.: ‘External cavitymode-locked quantum-dot laser diodes for low repetition rate,sub-picosecond pulse generation’, IEEE J. Sel. Top. QuantumElectron., 2011, 17, pp. 1264–1271

11 Thompson, M.G., Rae, A.R., Penty, R.V., White, I.H.: ‘InGaAsquantum-dot mode-locked laser diodes’, IEEE J. Sel. Top. QuantumElectron., 2009, 15, pp. 661–672

12 Shi, L.W., Chen, Y.H., Xu, B., Wang, Z.C., Jiao, Y.H., Wang, Z.G.:‘Status and trends of short pulse generation using mode-locked lasersbased on advanced quantum-dot active media’, J. Phys. D, Appl.Phys., 2007, 40, pp. R307–R318

13 Rafailov, E.U., Cataluna, M.A., Sibbett, W.: ‘Mode-locked quantum dotlasers’, Nature Photonics, 2007, 1, pp. 395–401

14 Kim, J., Choi, M.T., Delfyett, P.J.: ‘Pulse generation and compressionvia ground and excited states from a grating coupled passivelymode-locked quantum dot two section diode laser’, Appl. Phys. Lett.,2006, 89, pp. 261106–261109


www.ietdl.org
15 Gee, G., Alphone, S., Connoly, J., Delfyett, P.J.: ‘High power
mode-locked external cavity semiconductor laser using inversebow-tie semiconductor optical amplifiers’, IEEE J. Sel. Top. QuantumElectron., 1998, 4, pp. 209–215

16 Erdogan, T.: ‘Fiber grating spectra’, J. Lightwave Technol., 1997, 15,pp. 1277–1294

17 Sugawara, M., Mukai, K., Nakata, Y., Ishikawa, H., Sakamato, A.:‘Effect of homogeneous broadening of optical gain on lasing spectrain self-assembled InxGa1-xAs/GaAs quantum dot lasers’, Phys. Rev. B,2001, 61, pp. 7595–7603

18 Huang, H., Deppe, D.: ‘Rate equation model for nonequilibriumoperating conditions in a self-organized quantum dot laser’, IEEEJ. Quantum Electron., 2001, 37, pp. 691–698

19 Markus, A., Chen, J., Provost, O.G.-L.J., Paranthoen, C., Fiore, A.:‘Impact of intraband relaxation on the performance of a quantum-dotlaser’, IEEE J. Sel. Top. Quantum Electron., 2003, 9, pp. 1308–1314

20 Caroff, P., Paranthoen, C., Platz, C., et al. ‘High gain and low thresholdInAs quantum dot lasers on InP’, Appl. Phys. Lett., 2005, 87,pp. 243107-1–243107-3

21 Veselinov, K., Grillot, F., Bekiarski, A., Loualiche, S.: ‘Modeling ofthe two-state lasing and the turn-on delay in 1.55 μm InAs/InP(113)B quantum dot lasers’, IEE Proc., Optoelectron., 2006, 153,pp. 308–311

22 Veselinov, K., Grillot, F., Miska, P., et al. ‘Carrier dynamics andsaturation effect in (113)B InAs/InP quantum dot lasers’, Opt.Quantum Electron., 2006, 38, pp. 369–379


23 Veselinov, K., Grillot, F., Cornet, C., et al. ‘Analysis of the double laseremission occurring in 1.55 μm InAs-InP (113)B quantum-dot lasers’,IEEE J. Quantum Electron., 2007, 43, pp. 810–878

24 Grillot, F., Veselinov, K., Gioannini, M., et al. ‘Spectral analysis of1.55 μm InAs-InP (113)B quantum-dot lasers based on a multipopulationrate equations model’, IEEE J. Quantum Electron., 2009, 45, pp. 872–878

25 Veselinov, K., Grillot, F., Gioannini, M., et al. ‘Lasing spectra of1.55 μm InAs/InP (113)B quantum dot lasers: theoretical analysis andcomparison with the experiments’, Opt. Quantum Electron., 2008, 40,pp. 227–237

26 Morton, P.A.: ‘Compact sources of ultrashort pulses, edited by Irl NDuling III’ (Cambridge Studies in Modern Optics, 1995)

27 Cheung, S., Baek, J.-H., Scott, R.P., et al. ‘1-GHz monolithicallyintegrated hybrid mode-locked InP laser’, IEEE Photonics Technol.Lett., 2010, 18, pp. 1793–1795

28 Valley, G.: ‘Photonic analog-to-digital converters’, Opt. Express, 2007,15, pp. 1955–1982

29 Sayin, M., Ozyazici, M.S., Dogru, N.: ‘Theoretical model of themode-locked hybrid soliton pulse source’, Opt. Eng., 2007, 46,pp. 064201–064209

30 Morton, P.A., Mizrahi, V., Harvey, G., et al. ‘Packaged hybrid solitonpulse source results and 270 Tbit/km/s soliton transmission’, IEEEPhotonics Technol. Lett., 1995, 7, pp. 111–113

31 Morton, P.A., Mizrahi, V., Tanbun-Ek, T., et al. ‘High-powermode-locked hybrid soliton pulse source using two-section laserdiodes’, Opt. Lett., 1994, 19, pp. 725–727


Documents

Numerical simulation of a mode-locked quantum dot external cavity laser