Time-resolved amplified spontaneous emission in quantum dots [original]

Appl. Phys. Lett. 97, 251106 (2010); https://doi.org/10.1063/1.3529447 97, 251106

Time-resolved amplified spontaneous

emission in quantum dots

Cite as: Appl. Phys. Lett. 97, 251106 (2010); https://doi.org/10.1063/1.3529447

Submitted: 26 June 2010 • Accepted: 25 November 2010 • Published Online: 21 December 2010

J. Gomis-Bresco, S. Dommers-Völkel, O. Schöps, et al.

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Time-resolved amplified spontaneous emission in quantum dots

J. Gomis-Bresco,1,a兲S. Dommers-Völkel,2O. Schöps,2Y. Kaptan,2O. Dyatlova,2

D. Bimberg,2and U. Woggon2

1Institut für Optik und Atomare Physik, Technische Universität Berlin, Strasse des 17,

Juni 135, D-10623 Berlin, Germany

2Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36,

D-10623 Berlin, Germany

共Received 26 June 2010; accepted 25 November 2010; published online 21 December 2010兲

In time-resolved experiments at InGaAs/GaAs quantum-dots-in-a-well 共DWELL兲semiconductor

optical amplifiers, pump-probe of the ground state 共GS兲population, and complementary

measurement of the amplified spontaneous emission of the excited state 共ES兲population, we are

able to separate the early subpicosecond dephasing dynamics from the later picosecond population

relaxation dynamics. We observe a 10 ps delay between the nonlinear GS pulse amplification and

the subsequent ES population drop-off that supports the dominance of a direct two dimensional

reservoir-GS capture relaxation path in electrically pumped quantum-dot-DWELL structures.

Nowadays many optoelectronic devices1,2use quantum-

dots-in-a-well 共DWELL兲as active media because they pro-

vide faster gain recovery,3lower threshold current,4and pat-

tern free amplification.5An important application of DWELL

quantum dots 共QDs兲is demonstrated in semiconductor opti-

cal amplifiers 共SOAs兲, i.e., in an electrically pumped wave-

guide where the population inversion created in the QDs by

the current is used to amplify the propagating light. To in-

vestigate the ultrafast optical response of SOA-devices, het-

erodyne pump and probe experiments became a standard tool

to study the effect of doping,6optically induced index of

refraction changes,7or the origin and limits of the relaxation

of carriers in QDs.3,8–14 The understanding and control of the

carrier relaxation pathway in DWELL structures are crucial

to achieve large operation bandwidths for telecommunica-

tions and data applications. In particular, at moderate and

high injection currents the dominating relaxation mechanism

is Coulomb-scattering in a carrier reservoir.11,15 For weak

excitation, where carrier-carrier scattering is less efficient,

residual populations in the higher quantum-dot states are

found and explained in terms of both carrier-phonon and

carrier-carrier interactions.16

Subpicosecond pump-probe 共or other nonlinear-optical兲

experiments monitor both the population decay and the de-

coherence process in the QD gain recovery signals within the

first picoseconds. Simulations of the QD ground state 共GS兲

gain dynamics by solving the semiconductor QD-Bloch

equations of a system composed by the QDs, and a two

dimensional 共2D兲-reservoir 共the wetting layer and the quan-

tum well兲evidenced that dephasing, nonthermal carrier

populations, and Coulomb coupling to the reservoir have to

be taken into account,11 although we can simplify the Bloch

approach and use only a laserlike rate equation model to

interpret the experiments after the first picoseconds.12–14 In

the important case of cumulative amplification of pulse

trains, relaxation only through the excited state would pro-

duce an ultimate breakdown of the gain recovery17 which is

not observed in experiments.12

In the ongoing discussion of the nature of carrier relax-

ation pathways we obviously need an alternative experimen-

tal method independent of pump-probe experiments and free

of coherent effects to test directly the excited state 共ES兲

population after the amplification of a pulse resonant to the

QD GS. In this paper, we propose to monitor the time-

resolved luminescence of the ES that is not affected by co-

herent effects but proportional to the instantaneous ES popu-

lation. We introduce an experimental technique which is

based on complementary pump-probe experiments of the

ground state population and time-resolved amplified sponta-

neous emission 共TRASE兲of the excited state population.

This technique is applied to DWELL-SOAs and allows us to

observe changes of the ES population within the time reso-

lution of the light detector 共6ps兲.

The sample studied is a p-i-n structure witha1mmlong,

␮

m wide waveguide. The active medium consists of 15

layers of molecular beam epitaxy grown QDs-in-a-well with

a nominal areal density of 2⫻1010 cm−2/layer and a nomi-

nal delta p-doping of 5⫻1017 cm−2 共for further sample de-

tails see Ref. 3兲. When pumped electrically, we observe a 33

meV broad 共inhomogeneous broadening兲GS excitonic emis-

sion peak at EGS=965 meV共␭=1.285

␮

m兲. A well resolved

p-shell ES emission peak at 70 meV above the ground state

dominated at injection currents above 70 mA.

We used a Ti:sapphire pumped optical parametric oscil-

lator tuned to the GS transition peak, ␭=1.285

␮

m, corre-

sponding to a photon energy of 965 meV with a pulse width

of 150 fs 共full width at half maximum兲and a repetition rate

of 75.4 MHz. First we determine in femtosecond-pump-

probe experiment the gain recovery dynamics of the QD GS

关Fig. 2共a兲兴. For the complementary TRASE measurement we

coupled the beam into the waveguide and sent the light

coupled out to a streak camera. The streak camera, synchro-

nized with the pulsed laser, allowed us to spectrally disperse

and time resolve both the amplified pulse and the electrolu-

minescence of the SOAs. Normal spontaneous processes in

the SOAs are not time-correlated with the pulsed laser and

are statistically averaged. Amplified spontaneous emission

共ASE兲of the SOA generates a constant background, except

for the population changes related to the amplification pro-

a兲Electronic mail: [email protected].

APPLIED PHYSICS LETTERS 97, 251106 共2010兲

cess. The low light level of the ASE signal and the time

dispersion of the measurement 共we measured only 100 ps out

of 13 ns兲resulted in long acquisition times of typically 30

min.

A typical result of the TRASE measurements is shown in

Fig. 1: the upper panel is a streak camera image of an am-

plified pulse measured at injection currents of 150 mA 共lim-

ited by the temporal resolution of 6 ps兲. Both the ultrafast

recovery dynamics of the GS at that injection current3and

the pump pulse itself are below the temporal resolution of

the streak camera. In the lower panel, we show a streak cam-

era image of the ES spectral window 共red centered zone兲of

the QD DWELL SOA pumped with an injection current of

150 mA and being in the saturation regime. The spectral

integration yields the red centered curve, showing the ES

ASE dynamics within the first 100 ps. The arrival time of the

laser pulse is marked by the green left curve obtained from

spectral integration over the tail of the amplified laser pulse

共green left zone兲. Figure 2proves that the streak camera

images are sensitive to the changes in the ES ASE created by

the amplification of the pulse. We observe a pronounced de-

crease of intensity in the ES TRASE, followed by a partial

fast signal recovery up to a value of 16% of the initial ASE

signal lasting then for about 100 ps. The most important

result is, however, that the minimum of the ES TRASE ap-

pears 10 ps after the GS laser pulse amplification. A hypo-

thetical fast relaxation from the ES to the GS, accompanied

by the slower gain recovery of the ES 共see Refs. 3,18, and

22兲, would produce a fast decrease of the ES population

which is not observed in the TRASE experiment of Fig. 2or

any other measurement with less pump power. To explain the

observed ASE dynamics in TRASE experiments, we apply a

population model and compare the signatures of the different

carrier relaxation paths with the experimental data. The de-

veloped rate equation system is given by

⳵

t=J−NB

␶

冉

1− NW

max

冊

+NW

␶

BW −NB

␶

B,共1兲

⳵

t=NB

␶

冉

1− NW

max

冊

−NW

␶

BW −NW

␶

WG共1−NG兲

+NE

␶

冉

1− NW

max

冊

+NW

␶

冉

1−NE

冊

+NG

␶

冉

1− NW

max

冊

−NW

␶

W,共2兲

⳵

t=NW

␶

冉

1−NE

冊

−NE

␶

冉

1− NW

max

冊

+NG

␶

冉

1−NE

冊

−NE

␶

EG共1−NG兲−NE

␶

,共3兲

FIG. 1. 共Color online兲Upper panel: streak camera image of an amplified

pulse resonant to the GS. Middle panel: spectra of the ASE at 150 mA 共solid

black line兲and the pulse coupled in. Left 共right兲patterned zone marks the

spectral range of upper and lower streak images. Lower panel: streak camera

image of the amplified spontaneous emission centered at the ES emission

and showing the ES ASE 共red centered curve兲and the signal tail of the

pump laser 共green left curve兲.

FIG. 2. 共Color online兲共a兲Pump and probe resonant to the GS and 共b兲

TRASE of the ES emission 关upper red curve, corresponding to the red

centered zone in Fig. 1lower panel 共1015–1039 meV兲兴 and temporal posi-

tion of the amplified pulse 关green lower curve, corresponding to the laser tail

seen in the green left zone in Fig. 1lower panel 共983–988 meV兲兴. We plot

simulations of the expected saturation behavior as a function of the intradot

relaxation time for 共a兲GS and 共b兲ES.

251106-2 Gomis-Bresco et al. Appl. Phys. Lett. 97, 251106 共2010兲

⳵

t=NE

␶

EG共1−NG兲+NW

␶

WG共1−NG兲−NG

␶

−NG

␶

冉

1− NW

max

冊

−NG

␶

冉

1−NE

冊

−gP

冉

NG−1

冊

.共4兲

We model the experimental data by a four-level system

including the carrier population of the QD ground 共NG兲

and excited 共NE兲states, the 2D-reservoir 共quantum well

and wetting layer NW兲, and the GaAs barrier 共NB兲.We

include as parameters the capture times

␶

OriginDestiny.P, the

uncoupled light power, is chosen to satisfy the saturation

regime. The escape times are calculated as

␶

OriginDestiny

␶

DestinyOrigin expEDestiny−EOrigin/kT. The other parameters used

are EG=0 meV, EE=60 meV, EW=120 meV, EB

=130 meV,

␶

WE=

␶

WG=1 ps,

␶

sp=400 ps,

␶

W=20 ps,

␶

=10 ps,

␶

BW=300 ps, g=10, NW

max=20 carriers, and J

=1.4 carriers/ps. The carrier/relaxation rates depend on the

carrier population, but for a fixed injection current, we con-

sider them constant.

Supposing that direct capture and cascadelike capture

are both possible, we plot in Fig. 2the simulations for the

time evolution of the GS 共a兲and ES 共b兲populations as a

function of the intradot relaxation time

␶

EG, but fixing the

capture times

␶

WE and

␶

WG to 1 ps, which is mandatory to

reproduce the ultrafast ground state population recovery

found in literature. We show in Fig. 2共a兲a standard one color

ground state pump and probe at the same experimental con-

ditions used in Figs. 1and 2共b兲: the GS population recovers

fully in 5 ps, feature that is well reproduced by the simula-

tions.

␶

EG is the modified parameter starting from

␶

=1000 ps, i.e., almost completely switching off the intradot,

cascadelike relaxation pathway, and varied then down to

␶

EG=100, 10, 2, and 1 ps intradot carrier relaxation times.

The delay found is not compatible with a cascadelike relax-

ation path because in that case, the ES TRASE decrease

should appear almost immediately after pulse amplification.

Good agreement of the simulations and the experimental re-

sults is obtained for an intradot relaxation of

␶

EG⬎10 ps,

which is 10 times slower than the direct capture time

␶

WG.

Our results contrast with the evidences of cascadelike cap-

ture found in experiments with much lower excitation

density.19,20 Coulomb-scattering is likely to be responsible

for our fast carrier capture and relaxation: the relaxation path

depends on the carrier density.21 It should be mentioned here

that the observed early picosecond ES ASE dynamics in

TRASE experiments differ from the ES-GS pump and probe

results, as, e.g., observed in Ref. 22, confirming the absence

of coherent effects in ASE signals.

In conclusion, in complementary pump-probe experi-

ments of the GS population and TRASE measurement of the

ES population we directly determined the existence of a di-

rect capture relaxation path in a quantum-dot-in-a-well semi-

conductor optical amplifier. We base our conclusion on the

delayed ES population response observed in the saturation

regime and the lack of ultrafast response at lower pump pow-

ers that are incompatible with a dominance of a cascade like

relaxation path.

We acknowledge the funding of this work by Grant No.

SFB 787 of the DFG.

1G. Fiol, D. Arsenijevic, D. Bimberg, A. G. Vladimirov, M. Wolfrum, E. A.

Viktorov, and P. Mandel, Appl. Phys. Lett. 96, 011104 共2010兲.

2C. Meuer, J. Kim, M. Laemmlin, S. Liebich, G. Eisenstein, R. Bonk, T.

Vallaitis, J. Leuthold, A. Kovsh, I. Krestnikov, and D. Bimberg, IEEE J.

Sel. Top. Quantum Electron. 15, 749 共2009兲.

3S. Dommers, V. V. Temnov, U. Woggon, J. Gomis, J. Martinez-Pastor, M.

Laemmlin, and D. Bimberg, Appl. Phys. Lett. 90, 033508 共2007兲.

4D. Bimberg, G. Fiol, M. Kuntz, C. Meuer, M. Laemmlin, and N. N.

Ledentsov, Phys. Status Solidi A 203, 3523 共2006兲.

5T. Akiyama, N. Hatori, Y. Nakata, H. Ebe, and M. Sugawara, Electron.

Lett. 38,1139共2002兲.

6V. Cesari, W. Langbein, P. Borri, M. Rossetti, A. Fiore, S. Mikhrin, I.

Krestnikov, and A. Kovsh, Appl. Phys. Lett. 90, 201103 共2007兲.

7I. O’Driscoll, T. Piwonski, J. Houlihan, G. Huyet, R. J. Manning, and B.

Corbett, Appl. Phys. Lett. 91, 263506 共2007兲.

8P. Borri, F. Romstad, W. Langbein, A. Kelly, J. Mork, and J. Hvam, Opt.

Express 7, 107 共2000兲.

9M. Ishida, N. Hatori, T. Akiyama, K. Otsubo, Y. Nakata, H. Ebe, M.

Sugawara, and Y. Arakawa, Appl. Phys. Lett. 85, 4145 共2004兲.

10T. Piwonski, I. O’Driscoll, J. Houlihan, G. Huyet, R. J. Manning, and A.

V. Uskov, Appl. Phys. Lett. 90, 122108 共2007兲.

11J. Gomis-Bresco, S. Dommers, V. V. Temnov, U. Woggon, M. Laemmlin,

D. Bimberg, E. Malic, M. Richter, E. Schöll, and A. Knorr, Phys. Rev.

Lett. 101, 256803 共2008兲.

12J. Gomis-Bresco, S. Dommers, V. Temnov, U. Woggon, J. Martinez-

Pastor, M. Laemmlin, and D. Bimberg, IEEE J. Quantum Electron. 45,

1121 共2009兲.

13J. Kim, C. Meuer, D. Bimberg, and G. Eisenstein, Appl. Phys. Lett. 94,

041112 共2009兲.

14T. Erneux, E. A. Viktorov, P. Mandel, T. Piwonski, G. Huyet, and J.

Houlihan, Appl. Phys. Lett. 94, 113501 共2009兲.

15R. P. Prasankumar, W. W. Chow, J. Urayama, R. S. Attaluri, R. V. Shenoi,

S. Krishna, and A. J. Taylor, Appl. Phys. Lett. 96, 031110 共2010兲.

16H. Kurtze, J. Seebeck, P. Gartner, D. R. Yakovlev, D. Reuter, A. D. Wieck,

M. Bayer, and F. Jahnke, Phys. Rev. B 80, 235319 共2009兲.

17T. Berg, S. Bischoff, I. Magnusdottir, and J. Mork, IEEE Photonics Tech-

nol. Lett. 13, 541 共2001兲.

18S. Schneider, P. Borri, W. Langbein, U. Woggon, R. Sellin, D. Ouyang,

and D. Bimberg, IEEE Photonics Technol. Lett. 17, 2014 共2005兲.

19T. Müller, F. F. Schrey, G. Strasser, and K. Unterrainer, Appl. Phys. Lett.

83, 3572 共2003兲.

20T. Siegert, S. Marcinkevicius, and Q. X. Zhao, Phys. Rev. B 72, 085316

共2005兲.

21B. Ohnesorge, M. Albrecht, J. Oshinowo, A. Forchel, and Y. Arakawa,

Phys. Rev. B 54, 11532 共1996兲.

22I. O’Driscoll, T. Piwonski, C.-F. Schleussner, J. Houlihan, G. Huyet, and

R. J. Manning, Appl. Phys. Lett. 91, 071111 共2007兲.

251106-3 Gomis-Bresco et al. Appl. Phys. Lett. 97, 251106 共2010兲