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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
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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
Borri, Ultrafast Characteristics of Quantum Dot Ampli fiers
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
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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)
Borri, Ultrafast Characteristics of Quantum Dot Ampli fiers
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
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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
Borri, Ultrafast Characteristics of Quantum Dot Ampli fiers
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).
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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!
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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:
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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.
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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).
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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)
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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)
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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)*
P. Borri et al. IEEE J. Sel. Topics Q. El. 8, 984 (2002).
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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 150K the pure dephasingis given only by phonon interaction
population relaxation
pure dephasingfrom Coulomb
interactionpure dephasingfrom phononinteraction
Xn (Xn-1)*
P. Borri et al. IEEE J. Sel. Topics Q. El. 8, 984 (2002).
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
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 25K the broadening is fully givenby the population relaxationwithout pure dephasing
population relaxation
pure dephasingfrom Coulomb
interactionpure dephasingfrom phononinteraction
Xn (Xn-1)*
P. Borri et al. IEEE J. Sel. Topics Q. El. 8, 984 (2002).
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
• 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
Summary