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Dual-wavelength mode-locked quantum-dot

laser, via ground and excited state transitions:

experimental and theoretical investigation

Maria Ana Cataluna,1,* Daniil I. Nikitichev,1 Spiros Mikroulis,2 Hercules Simos,2

Christos Simos,2 Charis Mesaritakis,2 Dimitris Syvridis,2 Igor Krestnikov,3

Daniil Livshits,3 and Edik U. Rafailov1

1 University of Dundee, School of Engineering, Physics and Mathematics, Dundee, DD1 4HN, UK

2University of Athens, Department of Informatics and Telecommunications Panepistimiopolis Ilisia, Athens, Greece

3Innolume GmbH, Konrad-Adenauer-Allee 11, Dortmund, Germany

*m.a.cataluna@dundee.ac.uk

Abstract: We report a dual-wavelength passive mode locking regime where

picosecond pulses are generated from both ground (λ = 1263nm) and

excited state transitions (λ = 1180nm), in a GaAs-based monolithic two-

section quantum-dot laser. Moreover, these results are reproduced by

numerical simulations which provide a better insight on the dual-

wavelength mode-locked operation.

©2010 Optical Society of America

OCIS codes: (140.4050) Mode-locked lasers; (140.5960) Semiconductor lasers; (250.5590)

Quantum-well, -wire and -dot devices; (320.7120) Ultrafast phenomena.

References and links

1. E. U. Rafailov, M. A. Cataluna, and W. Sibbett, “Mode-locked quantum-dot lasers,” Nat. Photonics 1(7), 395–

401 (2007).

2. A. Markus, J. X. Chen, C. Paranthoen, A. Fiore, C. Platz, and O. Gauthier-Lafaye, “Simultaneous two-state

lasing in quantum-dot lasers,” Appl. Phys. Lett. 82(12), 1818–1820 (2003).

3. M. A. Cataluna, E. U. Rafailov, A. D. McRobbie, W. Sibbett, D. A. Livshits, and A. R. Kovsh, “Ground and

excited-state modelocking in a two-section quantum-dot laser,” in 18th Annual Meeting of the IEEE Lasers and

Electro-Optics Society, LEOS 2005, Tech. Dig. LEOS 2005), 870–871.

4. M. A. Cataluna, W. Sibbett, D. A. Livshits, J. Weimert, A. R. Kovsh, and E. U. Rafailov, “Stable mode locking

via ground- or excited-state transitions in a two-section quantum-dot laser,” Appl. Phys. Lett. 89(8), 081124

(2006).

5. J. R. Liu, Z. G. Lu, S. Raymond, P. J. Poole, P. J. Barrios, and D. Poitras, “Dual-wavelength 92.5 GHz self-

mode-locked InP-based quantum dot laser,” Opt. Lett. 33(15), 1702–1704 (2008).

6. A. Leitenstorfer, C. Fürst, and A. Laubereau, “Widely tunable two-color mode-locked Ti:sapphire laser with

pulse jitter of less than 2 fs,” Opt. Lett. 20(8), 916–918 (1995).

7. C. W. Luo, Y. Q. Yang, I. T. Mak, Y. H. Chang, K. H. Wu, and T. Kobayashi, “A widely tunable dual-

wavelength CW Ti:sapphire laser with collinear output,” Opt. Express 16(5), 3305–3309 (2008).

8. C. Song, W. Xu, Z. Luo, A. Luo, and W. Chen, “Switchable and tunable dual-wavelength ultrashort pulse

generation in a passively mode-locked erbium-doped fiber ring laser,” Opt. Commun. 282(22), 4408–4412

(2009).

9. H. Yoshioka, S. Nakamura, T. Ogawa, and S. Wada, “Dual-wavelength mode-locked Yb:YAG ceramic laser in

single cavity,” Opt. Express 18(2), 1479–1486 (2010).

10. J. Kim, M.-T. Choi, and P. J. Delfyett, “Pulse generation and compression via ground and excited states from a

grating coupled passively mode-locked quantum dot two-section diode laser,” Appl. Phys. Lett. 89(26), 261106

(2006).

11. E. A. Viktorov, P. Mandel, A. G. Vladimirov, and U. Bandelow, “Model for mode locking in quantum dot

lasers,” Appl. Phys. Lett. 88(20), 201102 (2006).

12. M. Sugawara, N. Hatori, H. Ebe, M. Ishida, Y. Arakawa, T. Akiyama, K. Otsubo, and Y. Nakata, “Modelling

room-temperature lasing spectra of 1.3 self-assembled InAs/GaAs quantum-dot lasers: Homogeneous broadening

of optical gain under current injection,” J. Appl. Phys. 97(4), 043523 (2005).

13. M. Sugawara, T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and H. Ishikawa, “Quantum-dot semiconductor optical

amplifiers for high-bit-rate signal processing up to 160 Gb/s−1 and a new scheme of 3R regenerators,” Meas. Sci.

Technol. 13(11), 1683–1691 (2002).

14. D. B. Malins, A. Gomez-Iglesias, S. J. White, W. Sibbett, A. Miller, and E. U. Rafailov, “Ultrafast

electroabsorption dynamics in an InAs quantum dot saturable absorber at 1.3 µm,” Appl. Phys. Lett. 89(17),

171111 (2006).

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07 June 2010 / Vol. 18, No. 12 / OPTICS EXPRESS 12832

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15. E. A. Viktorov, M. A. Cataluna, L. O’Faolain, T. F. Krauss, W. Sibbett, E. U. Rafailov, and P. Mandel,

“Dynamics of a two-state quantum dot laser with saturable absorber,” Appl. Phys. Lett. 90(12), 121113 (2007).

1. Introduction

In recent years, mode-locked quantum-dot (QD) lasers have shown great promise as compact

ultrashort-pulse laser sources [1], due the useful combination of ultrafast absorption recovery

with the possibility of broad gain/absorption bandwidth and low threshold current values.

Furthermore, QD materials exhibit a set of discrete energy levels, and as such laser emission

can occur via ground-state (GS), excited-state (ES) or via both GS and ES transitions

simultaneously [2]. Exploiting this potential in ultrashort-pulse generation, we have

previously reported the first demonstration of mode-locking via ground or excited state

transitions in a quantum-dot laser [3,4]. Nevertheless, the GS mode-locking regime did not

coexist with the ES regime, and it was necessary to change the bias conditions (gain current

and absorber reverse bias) in order to switch between one mode-locking regime and the other.

More recently, dual-wavelength mode-locking was reported for a single-section InP-based QD

laser diode, with pulses being generated simultaneously at 1543 and 1571nm [5]. However,

these spectral bands are not ascribed to the ES/GS transitions – the authors point out the

hypothesis that the energy-level splitting corresponds to the Rabi oscillation frequency.

Furthermore, due to the absence of a saturable absorber section or external mode-locking

stimulus, the mechanism for the pulse generation in this single-section laser is not yet fully

understood.

Dual-wavelength mode-locked laser sources have been traditionally developed and

investigated with other solid-state materials, most notably in Ti:Sapphire [6,7], fiber [8] and

most recently, ceramic lasers [9]. Research in this area has been motivated by the variety of

applications for dual- and multiple-wavelength ultrashort pulses, such as time-domain

spectroscopy, nonlinear optical frequency conversion and wavelength division multiplexing.

In this context, the compactness, lower cost and direct electrical pumping associated with

semiconductor lasers are very attractive features for reducing the footprint and complexity of

the aforementioned applications, with the potential to also open up new avenues in ultrafast

optical processing and optical interconnects.

In this paper, we report a dual-wavelength passive mode-locking regime where pulses are

generated from both GS (λ = 1263nm) and ES (λ = 1180nm) transitions, from a two-section

QD laser diode - the widest spectral separation (83nm) ever observed in a dual-wavelength

mode-locked non-vibronic laser [6]. We also present numerical simulations obtained by

means of a theoretical model based on the delay differential equation approximation, which

are in good qualitative agreement with the above behavior.

2. Device structure and experimental setup

The QD structure used in the laser device was grown by molecular beam epitaxy on a GaAs

substrate. The active region incorporated 5 layers of InAs QDs. A two-section QD laser diode

was fabricated with a ridge waveguide 6µm wide, a total length of 2mm, while the saturable

absorber was 300µm long, and was located near the back facet. The front and back facets

were anti-reflection (~3%) and high-reflection (~95%) coated, respectively.

The laser was operated at room temperature (20°C), with its temperature

thermoelectrically controlled via a Peltier cooler. The gain section was pumped with a low-

noise current source and the absorber section was connected to a voltage source. The

threshold current increased between 48mA and 180mA for reverse bias voltage values

between 2V and 10V, while the slope efficiency decreased from 0.35mW/mA to 0.24mW/mA

for the same voltage range. The pulse durations in both GS and ES spectral bands were

measured by a non-collinear autocorrelator based on second-harmonic generation. The

spectral characteristics were measured by a spectrometer and mode-locking performance was

further investigated with an RF spectrum analyzer in combination with a high-speed 29GHz

photodiode.

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3. Experimental results and discussion

The dual-wavelength mode locking regime was obtained for current levels in the gain section

between 330 and 430mA, and values of reverse bias between 6 and 10V in the saturable

absorber section. A map depicting the different mode-locking regimes is represented in Fig. 1.

It is noteworthy to point out that mode-locking involving solely the ES transition is observed

both before and after the dual-wavelength mode-locking regime.

Fig. 1. Mapping of the different operating regimes observed in this laser. The dashed region

corresponds to the dual-wavelength mode-locking regime here described (GSML + ESML).

Legend: GSML – ground-state mode-locking; ESML – excited-state mode-locking; GSCW -

ground-state continuous wave operation.

The central emission wavelengths were 1180nm and 1263nm for ES and GS, respectively

[Fig. 2(a)]. Due to the different refractive index for the two wavelengths, this spectral

separation was translated into a difference in pulse repetition rates for ES and GS, which were

19.6GHz and 20.1GHz respectively [Fig. 2(b)].

Fig. 2. (a) Optical spectrum and (b) RF spectrum characteristic of the dual-wavelength mode-

locked regime, for a reverse bias of 6V and an injection current of 425mA (the red line in a)

depicts the Gaussian fit to the ES and GS spectral bands). In the RF spectrum, the observed

power difference between GS and ES is a result of the different optical power level and pulse

duration for each of the pulse trains, as elucidated in the text.

In Fig. 3, the autocorrelation traces obtained for the ES and GS are shown, evidencing

pulse durations of 8.6ps for the ES and 5.9ps for the GS bands, obtained for a reverse bias of

6V and an injection current of 425mA. The pulses were both highly chirped, exhibiting time-

bandwidth products (TBWP) of 6.7 for the GS and 9 for the ES. These pulse durations and

TBWPs are similar to those previously observed in separate GS/ES mode-locking [4,10].

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Fig. 3. Autocorrelation traces for (a) pulses generated via GS mode-locking; (b) pulses

generated via ES mode-locking (for a reverse bias of 6V and an injection current of 425mA).

It is important to stress that, although not equal, the average power was of the same order

for GS and ES (in the range of ~20-30mW), which we believe to be an important factor in

achieving a stable pulsed operation for both, owing to the dynamics of absorption saturation in

a passively mode-locked laser. For instance, under the bias conditions examined in Figs. 2 and

3, the average power for the GS was PGS = 21.3 mW and for the ES was PES = 32.1 mW. The

difference of ~10dB between the GS and ES peaks, as shown in the RF spectrum [Fig. 2(b)],

can be accounted for as follows. According to the Fourier analysis properties of a Gaussian

pulse train, the amplitude of its Fourier transform depends on both the power of the pulse, as

well as its duration - the broader the pulse, the higher the RF peak. The power ratio between

ES and GS corresponds to PES/PGS = 1.5, while the pulses generated via the ES are broader by

a factor of 1.46 than the GS pulses, for the same conditions. As such, the amplitude of the

Fourier transform for the ES will be ~2.2 times higher (~3.5 dB difference) than that

corresponding to the GS, which can justify a difference of approximately ~7 dB (the double)

in the electrical power spectrum. Importantly, a difference of ~8dB is also obtained from the

numerical simulations as depicted in Fig. 5(b) on the next section, corresponding to the pulses

represented in Fig. 5(a) (in the figure, the pulses are shown normalized). The remaining

difference between the experimental observation (~10 dB) and the above calculations (~7 dB),

can be due to experimental conditions, such as variations in the average power, the RF

spectrum analyser settings and its characteristic frequency response (flatness).

4. Theoretical model and numerical simulations

The theoretical model proposed in the paper is based on the delay differential equation

approximation and aims to predict the basic operating behavior of a GaAs-based monolithic

two-section quantum-dot laser. The particular goal was to highlight the underlying physical

mechanisms that govern the dual-wavelength mode-locked operation. The equations have

been previously reported in the literature, but it is the first time to our knowledge that they are

combined in a single model that takes into account both GS and ES emission with individual

delay equation for each state.

The theoretical analysis is focused on the dual-wavelength mode-locked operation

observed in the experiments as well as the clarification of the underlying physical mechanisms

which control this operating regime. Furthermore, the different operation regimes are

reproduced by the model and briefly reported in this paper. The numerical model is based on

the delay differential equation approximation [11] to describe the cavity effects enhanced with

multipopulation rate equations to account for the dynamics of quantum dot material [12]. An

active (gain) and a passive (absorber) sections as well as a bandwidth limiting element are

included. Moreover, a ring-cavity geometry with unidirectional operation is assumed. The

evolution of the fields in the gain and absorbing sections follows the delay equation [11]:

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(1)( )/2 (1

+ +

)( )/2

( )

1

() ( )

ggdqqd

i L g ti L q t

n

ndn

pp

A t

∂

∂

e A tA t

t

ατατ

κ

τ

τ

τ

+−−

=−−

(1)

where An(t) is the slow envelope of the field for state n (GS, ES). g and q are the gain and

absorbing coefficients for the active and passive section respectively, αg and αq are the

corresponding linewidth enhancement factors, and Lg and Lq, are the corresponding round trip

propagation lengths in the gain and absorbing section, respectively. Moreover, τd is the round-

trip delay time of the cavity, κ is the round-trip attenuation factor and τp

the bandwidth limiting element.

The quantum dot model describes the dot energy distribution with a multi-population rate

equation set, accounting only for the electron dynamics (excitonic representation) [12]. The

model includes three energy states, the wetting layer (WL) which is the common carrier

reservoir, the excited state which captures the electrons from WL and the ground state. The

carrier density rate equations for each state of the gain section are:

−1 is the bandwidth of

,

( )

t

j

WL

∂

ESWL WL

mean

WL ES

τ

j

ES WL

τ

spon WL

τ

nnnn

I

t eV

−

−

∂

=+−−

∑

(2)

2

,

( )

t

( )

t

jjjjjj

j

ES

∂

WL GS ESESES

gES ES

jjj

ES WL

τ

spon ES

τ

WL ES

τ

GS ES

τ

ES GS

τ

n G nnnnn

v gA

t

−

−−−

∂

=+−−−−

(3)

2

,

( )

t

( )

t

jjjj

j

GS

∂

ES GSGS

g GSGS

jj

spon GS

τ

ES GS

τ

GS ES

τ

nnnn

v gA

t

−−

∂

=−−−

(4)

where

( )

t is the carrier density of the wetting layer, and

WL

n

j

ES

n

,

j

GS

n

are the carrier density of

the j-th dot group for the excited and ground state, respectively;

τ

times for the electron transition from excite to ground state and from ground to excited state,

respectively;

WL ES

τ

−

,

WL ES

τ

−

,

ES WL

τ

−

are the carrier capture and escape time, respectively, for

the transition between the wetting layer and the dots [13]. The spontaneous emission rates are

calculated through the carrier lifetime for each state:

j

ES

g

and

j

GS

g

are the

corresponding gain coefficients.

j

ES GS

−

and

j

GS ES

τ

−

are the the j-th dot group characteristic

meanj

,

spon WL

τ

,

,

spon ES

τ

and

,

spon GS

τ

. The

transition times from state n1 to n2 depend on the state occupation probability

ττ

−−

=−

the injected current. Similar expressions to (2) – (4) stand for the absorbing section as well,

enhanced by additional sweep-out terms (as in [14]) in order to take into account the

dependence of the absorber dynamics on the applied negative voltage due to thermionic and

tunneling carrier escape mechanisms.

The gain (and similarly the absorption) coefficient for the state n and for the dot group j at

the frequency ω is given by [12]:

j

nP , and they

are calculated by

0

n

12122

/ (1)

jj

nnnnP

[13]. Finally, V is the active region volume and I is

( , )

ω

(21)()( )

ω

jjjjj

n

n

ngnn

j

n

D

ω

ℏ

g tFPGL

ω

=−

(5)

where the coefficient Fg includes the volume quantum dot density, the transition matrix

element and constants. Dn is the degeneracy of the state,

G ω

accounts for inhomogeneous broadening of the gain

due to the dot size fluctuation and it is described by a Gaussian distribution [13]; the

homogeneous broadening of the gain is assumed to be a Lorentzian distribution and it is

j

n

ω is the central frequency if the j-th

dot group for state n. The term ()

jj

n

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described by

=

gain/absorption coefficient in (1) is given by the summation over all quantum dot groups and

states. The values of the most significant parameters are given below. The spontaneous

recombination times are

,

spon WL

τ

= 5 ns,

,

spon ES

τ

τ

−

= 8 ps,

GS ES

τ

−

= 18 ps,

WL ES

τ

−

maximum of the inhomogeneous broadening is 50 meV and the corresponding width of the

homogeneous broadening is 16.5 meV. The linewidth enhancement factor for the gain and

absorber are αg = 2 and αq = 2. The degeneracy of the states are DES = 4 and DGS = 2. The

interband transition matrix element is 2.7 × 10−49 eV Kg. Finally the quantum dots volume

density is

D

N

= 3.7 × 1022 m−3.

Since the main purpose of the numerical evaluation is not to obtain a complete mapping of

the specific laser configuration but to focus on the dual-wavelength mode-locked operation,

some of the parameters are fitted to match the simultaneous GS-ES operation regime.

At the region near the threshold of the GS (IG = 1.1Ith – 2.0Ith) stable mode-locked

operation is observed, strongly dependent on the absorber voltage value. At low values of

reverse bias voltages in the absorber section (i.e. V < 6 V) continuous wave (CW) operation,

including regions with intensity fluctuations, at the GS is observed (slow absorber). However,

at higher bias values (i.e. V > 6 V) stable GS mode-locking (GS-ML) is revealed due to the

fast absorption recovery time, assisted by the sweep-out effect. A typical GS-ML time trace

calculated at I = 1.2Ith and V = 10 V with a pulse width close to 3 ps is depicted in Fig. 4. A

slight asymmetry in the pulse is attributed to the fast absorption saturation responsible for

pulse leading edge shaping. Additionally, the calculated optical spectrum has a free spectral

range (FSR) corresponding to a repetition rate frequency in the order of 20 GHz. Furthermore,

for current values higher that 2.0Ith and up to 2.7Ith, GS-CW wave or GS-ML is observed for

different values of the absorber voltage.

( )

G ω

j

n L ω [12].

j

nP is the state occupation probability given by:

/(2( ))

jj vol

D

jj

nnnn

PnD N

[12] where

vol

D

N

is the volume dot density. The total

= 500 ps and

τ

,

spon GS

τ

= 2 ns; the transition

times are

0

ES GS

00

= 2 ps,

0

ES WL

−

= 10 ps. The full width at half

vol

Fig. 4. (a) Time trace for pulse generated from GS mode-locking and (b) the corresponding

optical spectrum.

According to our calculations, at low gain currents ES is almost unpopulated. However, at

current values of IG = 2.7Ith - 2.8Ith GS emission saturates, ES carrier population increases and

gradually ES lasing is observed. The onset of ES emission is accompanied with a stable ES-

ML for reverse bias voltages larger than 6 V due to the respective decrease of the absorber

recovery time, as it has already been mentioned above. In the range of gain current between

2.8Ith and 3.4Ith, ES ML coexists with unstable GS-CW operation.

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Fig. 5. (a) Time traces for pulses generated from simultaneous GS-ES mode-locking and (b) the

corresponding simulated RF spectrum.

In agreement with the experiments, a region with stable dual-wavelength mode-locking

occurs at a relatively narrow current range (IG = 3.4Ith - 3.7Ith) and for bias voltages higher

than 7 V. The calculated pulse time traces of this regime are shown in Fig. 5. The GS and ES

pulses are shifted to each other in accordance with out-of-phase dynamics between the two

states. This effect can be attributed to the asymmetric power exchange during capture/escape

carrier transitions which result to nonlinear amplitude-phase coupling [15]. The generated

pulses from the stable dual-wavelength mode-locked operation are broadened [Fig. 5(a)] for

both GS (∆τ = 6.5 ps) and ES pulse (∆τ = 9 ps) compared to the GS-ML, due to the high gain

current value needed for the appearance of lasing from the ES. The relatively narrow regime

of dual-wavelength mode-locked operation can be attributed to the dynamics between the two

competitive states due to the carrier intraband capture/escape process between them, giving

rise to instabilities. At gain currents beyond 3.8Ith, ES-ML is observed while at even higher

current values (i.e. I > 4.2Ith) ES-CW is observed. In both cases emission from GS is

suppressed.

The theoretical computations are in good qualitative agreement with the experimental

results. The main trends of the experimental mapping are clearly reproduced by the model.

Some differences exist in transitions between distinct operating regions where generally

unstable operation occurs. In these regions, the model shows quasi-CW operation with fast

fluctuations of the output power, condition that cannot be experimentally observed.

5. Conclusion

In this paper we report the first experimental and theoretical investigation of a dual-

wavelength passive mode-locking regime where pulses are generated from both ES (λ =

1180nm) and GS (λ = 1263nm), in a two-section GaAs-based QD laser. The spectral

separation (83nm) is the widest ever observed in a dual-wavelength mode-locked non-

vibronic laser. Additionally, numerical simulations are presented by means of a theoretical

model based on the delay differential equation approximation, which reproduce the dual-

wavelength mode-locking regime. The exploitation of this mode-locked regime could enable a

range of applications extending from time-domain spectroscopy, through to optical

interconnects, wavelength-division multiplexing and ultrafast optical processing.

Acknowledgements

The work was funded within the Seventh Framework Program “FAST-DOT”, through Grant

No. 224338. M. A Cataluna acknowledges also financial support through a Royal Academy of

Engineering/EPSRC Research Fellowship.

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