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Borri, Ultrafast Characteristics of Quantum Dot Ampli fiers

Paola Borri Experimentelle Physik II , Universität Dortmund, Germany

present address: School of Bioscience, Cardiff University, Wales (UK)

• Priv. Doz. Dr. Wolfgang Langbein • Dipl.-Phys. Stefan Schneider

• Prof. Dr. Ulike Woggon

• Roman L. Sellin • Dongxun Ouyang

• Dieter Bimberg

Samples (TU Berlin) :Experiment:

Ultrafast Characteristics of Quantum Dot Amplifiers

Borri, Ultrafast Characteristics of Quantum Dot Amplifiers

• Ultrafast optical spectroscopy in semiconductor optical amplifiers:

heterodyne pump-probe experiment

• Measurements in quantum-dot amplifiers:gain and refractive index dynamicsdephasing time from 300K to 10K

Outline


p

n

L

i

Semiconductor optical amplifier (SOA)

Lasing action inhibited by titling and/or anti-reflection coating the end facets

Single pass amplification:

light in light out

( ) 22

inLg

out EeE α−Γ=g(IC): material gainα: lossesΓ: confinement factor

+

IC

-

2 3

2 3

VE d r

E d r+∞

−∞

Γ = ∫∫

V: active volume


Ultrafast optical spectroscopy in SOA‘sPump-probe experiment:

SOA

τ

transmitted probepumpprobe

( ) ( )( )LGG

in

LG

inouteEeEE ττ ∆+== 0

222

LG

inouteEE 0

22

0 =

( )2 2 2

0

2 2

0 0

1 G Lout out out

out out

E E Ee

E E

τ∆ ⋅−= + =

Differential transmission intensity:

without pump:

with pump:

~100fs optical pulses


Pump-probe experiment in SOAs

K. Hall et al., Optics Lett.17, 874 (1992)A. Mecozzi et al. Optics Lett. 21, 1017 (1996) P. Borri et al. Optics Comm. 169, 317 (1999).

waveguide

Detection at ωRF2 or

2ωRF2 -ωRF1

AOMω1 = ω0+ ωRF1

ωRF1 /2π ~ 80MHz

AOM

ωRF2 /2π ~ 79MHz ω2 = ω0+ ωRF2

ω0

-

Heterodyne detection:

• co-polarized and co-propagating pulses• sensitive to electric field Idet∝ ΕrefΕsignal (gain and refractive index dynamics)• able to measure third-order coherent signal (four-wave mixing ⇒ dephasing time)


3 stacked QD layers35nm GaAs spacersareal dot density ~2x1010cm-2

1.1 1.2 1.3 1.4 1.5

+

_

n-GaAs

n-A lGaAs

GaAs GaAs

p-A lGaAsp-GaAs

InGaAs QDs

ES

GS

laser

65meV

AS

E (

a.u.

)

Energy (eV)

25K

Inhomogeneous broadening: 60meVGS-ES separation: 65meVConfinement to wetting layer ~220meV

+

-

electrical injectionridge waveguide 5µmxL (0.5, 1mm)

10° til ted facets

InGaAs quantum dot optical amplifier


State Filling versus Injection Current

Spectral gain at 2, 4, 6, 8, 10, 15, 20, 25mA

1.10 1.15 1.20 1.25 1.30

-20

0

20

40

60

80

10 20 30

-20

0

20

T=10K

abs.

gain

gai

n(cm

-1)

ESGS

2mA

25mA

Energy (eV)

gai

n(cm

-1)

IC(mA)

GS absorption:

e0

h0

e0

h0

e0

h0

GS gain:

e0

h0

e0

h0

e0

h0

saturation

e0

h0

e0

h0

ES group

gain ∝ fe+fh-1

e0

h0

transparency


Differential Transmission at 300K

0 5 10 15 20

-2

0

2

4

6

8

10

0 100 200 300

0.1

1

6.3±0.6ps

450±20fs

4.5mA

1.3±0.2ps150±20fs

40 mA

0 mA

∆G (

dB)

delay (ps)

0 mA

~1ns

50±1ps

∆G (

dB)

delay (ps)

∆G(dB)=20* log(1+∆T/T)

Fit: ( ) ( ) 'dt'tth'tA −∫A(t): pulse intensity autocorrelationh(t): multi-exponential response function

Gain:

Transparency:

g ∝ f e+fh-1

pump

Absorption:

Ultrafast gain recovery (high-speed applications)

P. Borri, W. Langbein et al. IEEE J. Sel Topics Q. El. 6, 544 (2000); IEEE J. Sel. Topics Q. El. 8, 984 (2002).


0 2 4 6 8

-2

0

2

4

6

0 2 4 6 8

-8

-4

0

4

8

�P (p s )

g ro u n d s ta te

�2= 1 .3 p s

�1= 1 5 0 fs

�2= 6 .3 p s

�1= 4 5 0 fs

0 m A

4 0 m A�G (

dB)

�1= 1 8 0 fs

�2= 2 .5 p s

�2= 3 .8 p s

4 0 m A

0 m A

�1= 2 9 0 fs

e xc ite d s ta te

�P (p s )

Ground state vs excited state gain dynamics

0mA 40mA 0mA 40mA


Gain dynamics

Pulse width: 150 fs

T.W. Berg et al., IEEE PTL 13, 541 (2001)

Ground-state gain recovery: ~ 100 fs

Excited-state gain recovery: ~ 5 ps

Optical signal transmission at high bit ratelimited from slow gain recovery of the

excited states

0 2 4 6 8 10

-4

-3

-2

-1

0

ES 80mA

ES 60mA

ES 40mA

GS 40mA

∆G (

dB)

τP (ps)

We measure a fast (< 1ps)gain recovery of both GS and ES!


Refractive Index Dynamics: The α-Parameter

=

dN

dgdNdn

λπα 4

- )(

)()log(20

dBG

rade

∆∆Φ⋅−=

0 4 8 12 100 200

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

∆Φ (

rad)

delay τ (ps)

gain (40mA)

absorption (0mA)

0 50 100 150 200 250 300

1

1040mA

20mA

15mA

7mA

2mA

0mA

LE

F α

τ (ps)

300K

S. Schneider, P. Borri et al., IEEE JQE accepted (2004)

Pump-induced phase change of the probe ∆Φ = ∆n(2πL/λ) ⇒ refractive index change

0 10 20 30 400

1

2

3

4

5

6

7

8

9

IC (mA)

• at IC< 2mA the LEF is below 1• LEF increases with increasing IC


Temperature-Dependent Gain Dynamics

The ultrafast gain recovery depends onbias current and temperature:

-1 0 1 2 3 4 5

1 10

0.1

1

-3

0

3mA

20mA

20mA

3mA

300K

150K

∆G(d

B)

delay (ps)

time(

ps)

IC/I

tr

150K 300K

The thermal occupation of the excitedstates is quenched at low temperature for

low bias current ⇒ slower gain recovery

0.0

0.5

1.0

300K

150K

DOS

occu

patio

n pr

obab

ility

Energy (arb. units)

P. Borri et al. IEEE J. Sel. Topics Q. El. 8, 984 (2002).

Ultrafast gain-recovery once the excited states are occupied with several carriers:


Low-Temperature Gain Dynamics

-0.5

0.0

0.5

1.0-1 0 1 20 40

-3

-2

-1

0

0 10 20 30

-0.5

0.0

0.5

τ4

τ3

τ2

τ1

T PA

++

de lay(ps )

5 .5m A

∆G(d

B)

∆G

(dB

)

30m A

A1

A2

A3

A4

ampl

itude

(dB

)

IC(m A )

A macroscopic configuration is asuperposition of microstates. The probabilityof a specific microstate varies with IC, buteach microstate has a given internal dynamics.

We have consistently fitted the DTS data with4 time constants τ1..τ4 of amplitudes A1..A4.

After the removal of one e0h0 by the pumpphotons microstates with a high number ofcarriers in the excited states undergo a fastrelaxation dynamics modeled by τ1=0.33 ±0.05ps.

T=10K

Microstates with only one carrier in the excitedstates have only one relaxation channel modeledby τ2=4±0.3ps, τ3 =35 ± 4ps for a hole, electron.


Dephasing Time of the 0-X Transition

0 1 2 3 150 300 450

300K

0.2ps

6ps

100K

200K 11ps

125K

75K

50K

25K

7K

37ps

170ps

630ps

TI F

WM

fie

ld a

mp

litu

de (

a.u.

)

τP(ps)

At T=7K the long exponential decaydominates the dynamics with adephasing time of 630 ps correspondingto only 2µeV homogeneous broadening

At 300K the fast 0.2ps dephasingcorrespond to 6.6meV homogeneousbroadening!

P. Borri et al., Phys. Rev. Lett. 87, 157401 (2001)

Without electrical injection,the optical transition 0-Xfrom the crystal ground stateto the ground-state exciton inthe QD is probed

See also: D. Birkedal et al., PRL 87, 227401 (2001);M. Bayer and A. Forchel, PRB 65, 041308(R) (2002);C. Kammerer et al. PRB 66, 041306(R) (2002).


Fourier Transform of the TI-FWM: Homogeneous Lineshape

Below 100K, the homogeneouslineshape consists of a narrowLorentzian line, correspondingto the long exponential decay,and a broad non-Lorentzianband corresponding to the

initial fast dephasing.

-2 0 2

100K

75K

50K

25K

Re

(F(|

E(t

)|))

(a

rb.

un

its)

Energy (meV)

Theory: pure dephasing from coupling with acoustic phononsB. Krummheuer et al. PRB 65 195313 (2002)R. Zimmermann and E. Runge ICPS26 (2002)

Zero phonon lineAcoustic phonon band

Similar findings in photoluminescence spectra of single QDs!

L. Besombes et al.PRB 63, 155307 (2001)

CdTe on ZnTe QDs InAs/GaAs QDs

B. Urbaszek et al. PRB 69, 035304 (2004)


Dephasing versus Injection Current at Low Temperature

• With increasing IC the FWM decay isfaster, i.e. the ZPL broadens due to Coulombinteraction with the injected carriers.

• For IC >14mA the majority of dots isoccupied by two e0h0 excitons. When severalcarriers occupy the excited states, themultiexcitonic transition:

0 50 100 200 300 400

10K

XX-X

0-X

14mA

20mA25mA

5mA

3mA

2mA

1mA

0mA

30mA

TI

FW

M f

ield

am

plitu

de (

a.u.

)

delay (ps)

0 10

Xn-(Xn-1)*

30mA

delay(ps)

TI F

WM

(a.

u.)

Xn (Xn-1)*

has a strong final state damping due to thequick relaxation of the (Xn-1)* state (whichwe measure in differential transmission).

• The biexcton to exciton transition (XX-X)has a much smaller final state damping thanthe Xn-(Xn-1)* and is distinguished by thelong FWM decay.

P. Borri et al. Phys. Rev. Lett.89 187401 (2002)


0

5

10

15

20

0 5 10 15 20

0

5

0 5 10 15 20

γ1

γh

295K

γ(m

eV)

γ(m

eV)

150K

IC/I

tr

220K

25K

IC/I

tr

Dephasing versus Relaxation of Multiexcitonic Transitions

γh = 2=/T2

γ1 = =/T1

Xn-(Xn-1)*

)(

1

)(

1

),(2

11'

2'

212 CC ITTTTITTeeph

++=

At 295K pure dephasingprocesses given by phonon and Coulombinteractions dominate

population relaxation

pure dephasingfrom Coulomb

interactionpure dephasingfrom phononinteraction

Xn (Xn-1)*



0

5

10

15

20

0 5 10 15 20

0

5

0 5 10 15 20

γ1

γh

295K

γ(m

eV)

γ(m

eV)

150K

IC/I

tr

220K

25K

IC/I

tr


γh = 2=/T2

γ1 = =/T1

Xn-(Xn-1)*

)(

1

)(

1

),(2

11'

2'

212 CC ITTTTITTeeph

++=

At 150K the pure dephasingis given only by phonon interaction




Xn (Xn-1)*



0

5

10

15

20

0 5 10 15 20

0

5

0 5 10 15 20

γ1

γh

295K

γ(m

eV)

γ(m

eV)

150K

IC/I

tr

220K

25K

IC/I

tr


γh = 2=/T2

γ1 = =/T1

Xn-(Xn-1)*

)(

1

)(

1

),(2

11'

2'

212 CC ITTTTITTeeph

++=

At 25K the broadening is fully givenby the population relaxationwithout pure dephasing




Xn (Xn-1)*



• At 300K:

• Ultrafast (~100fs) gain recovery dynamics in InGaAs QD amplifiers

• Large homogeneous broadening (10-20meV) i.e fast dephasing due to

phonon and Coulomb interactions (dominantly pure dephasing)

• Gain recovery is slower (~ps) at low temperature and injection current:

fast gain recovery dominated by dots with several carriers in the excited

states (i.e. multiexcitons)

• Dephasing (of multiexcitonic transitions) dominated by population

relaxation dynamics < 30K

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