Ultrafast Characteristics of Quantum Dot Amplifiers
Paola Borri
Experimentelle Physik II, Universität Dortmund, Germany
present address: School of Bioscience, Cardiff University, Wales (UK)
Samples (TU Berlin) :
Experiment:
• Priv. Doz. Dr. Wolfgang Langbein
• Dipl.-Phys. Stefan Schneider
• Prof. Dr. Ulike Woggon
• Roman L. Sellin
• Dongxun Ouyang
• Dieter Bimberg
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Outline
• Ultrafast optical spectroscopy in semiconductor optical amplifiers:
heterodyne pump-probe experiment
• Measurements in quantum-dot amplifiers:
gain and refractive index dynamics
dephasing time from 300K to 10K
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Semiconductor optical amplifier (SOA)
+
L
p
IC
i
n
light in
Lasing action inhibited by
titling and/or anti-reflection
coating the end facets
light out
Single pass amplification:
Eout = e
2
g(IC): material gain
α: losses
Γ: confinement factor
Γ=
∫
∫
V
+∞
−∞
(Γg −α )L
Ein
2
2
E d 3r
2
3
V: active volume
E d r
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Ultrafast optical spectroscopy in SOA‘s
Pump-probe experiment: ~100fs optical pulses
probe pump
transmitted probe
SOA
τ
without pump:
E0 out = E in e
with pump:
E out = E in e
2
2
2
2
G0 L
G (τ )L
= E in e
2
(G0 + ∆G (τ ))L
Differential transmission intensity:
2
E out
2
E0 out
E out − E0 out
2
=
2
2
E0 out
+1 = e
∆G (τ )⋅ L
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Pump-probe experiment in SOAs
Heterodyne detection:
ωRF1 /2π ~ 80MHz
AOM
ω0
ω1 = ω0+ ωRF1
AOM
waveguide
ωRF2 /2π ~ 79MHz ω2 = ω0+ ωRF2
-
Detection at
ωRF2 or
2ωRF2 -ωRF1
• 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)
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).
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
InGaAs quantum dot optical amplifier
electrical injection
ridge waveguide 5µmxL (0.5, 1mm)
10° tilted facets
+
-
ES
ASE (a.u.)
65meV
GS
p-GaAs
p-A lGaAs
GaAs
GaAs
n-A lG aAs
+ 25K
3 stacked QD layers
35nm GaAs spacers
areal dot density ~2x1010cm-2
n-G aAs
_
InG aAs Q Ds
laser
1.1
1.2
1.3
1.4
Inhomogeneous broadening: 60meV
GS-ES separation: 65meV
Confinement to wetting layer ~220meV
1.5
Energy (eV)
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
State Filling versus Injection Current
gain ∝ fe+fh-1
GS absorption:
transparency
-1
gain(cm )
80
-1
gain(cm )
60
20
0
T=10K
e0
e0
e0
h0
h0
h0
h0
-20
10
40
20
IC(mA)
30
ES
GS
20
e0
saturation
GS gain:
gain
0
e0
e0
e0
e0
h0
h0
h0
h0
Spectral gain at 2, 4, 6, 8, 10, 15, 20, 25mA
e0
abs.
-20
25mA
2mA
1.10
1.15
1.20
1.25
1.30
Energy (eV)
h0
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
ES group
Differential Transmission at 300K
P. Borri, W. Langbein et al. IEEE J. Sel Topics Q. El. 6, 544 (2000); IEEE J. Sel. Topics Q. El. 8, 984 (2002).
∆G(dB)=20*log(1+∆T/T)
g ∝ f e+fh-1
∆G (dB)
10
8
0 mA
∆G (dB)
6
Absorption:
0 mA
1
~1ns
0.1
450±20fs
4
50±1ps
6.3±0.6ps
0
100
200
pump
300
delay (ps)
Transparency:
2
4.5mA
0
-2
1.3±0.2ps
150±20fs
40 mA
0
5
10
15
20
delay (ps)
Fit:
Gain:
∫ A(t')h(t − t')dt'
A(t): pulse intensity autocorrelation
h(t): multi-exponential response function
Ultrafast gain recovery (high-speed applications)
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Ground state vs excited state gain dynamics
g ro u n d s ta te
6
1
8
= 4 5 0 fs
G (d B )
4
2
2
40m A
-2
1
0
2
= 1 5 0 fs
2
4
0m A
0
40m A
2
-4
= 1 .3 p s
= 2 9 0 fs
1
= 3 .8 p s
= 2 .5 p s
= 1 8 0 fs
-8
2
4
P
0mA
1
= 6 .3 p s
0m A
0
e xc ite d s ta te
6
8
0
2
(p s )
40mA
4
P
0mA
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
6
(p s )
40mA
8
Gain dynamics
Optical signal transmission at high bit rate
limited from slow gain recovery of the
excited states
Pulse width:
150 fs
Ground-state gain recovery: ~ 100 fs
Excited-state gain recovery:
~ 5 ps
We measure a fast (< 1ps)
gain recovery of both GS and ES!
T.W. Berg et al., IEEE PTL 13, 541 (2001)
GS 40mA
0
ES 40mA
ES 60mA
∆G (dB)
-1
ES 80mA
-2
-3
-4
0
2
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
4
τP (ps)
6
8
10
Refractive Index Dynamics: The α-Parameter
 dn 


∆Φ ( rad )
4π  dN 
20
log(
)
=
−
⋅
e
α =∆G (dB )
λ  dg 


dN


S. Schneider, P. Borri et al., IEEE JQE accepted (2004)
Pump-induced phase change of the probe
∆Φ = ∆n(2πL/λ) ⇒ refractive index change
gain (40mA) 300K
0.10
9
10
40mA
0.05
8
7
0.00
LEF α
∆Φ (rad)
20mA
-0.05
15mA
7mA
-0.15
5
4
1
-0.10
6
2mA
3
2
absorption (0mA)
0mA
-0.20
1
0
0
4
8
12
100
delay τ (ps)
200
0
50
100
150
200
250
300
τ (ps)
0
10
20
IC (mA)
• at IC< 2mA the LEF is below 1
• LEF increases with increasing IC
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
30
40
300K
∆ G(dB)
3mA
20mA
0
time(ps)
The ultrafast gain recovery depends on
bias current and temperature:
150K
300K
1
IC/Itr10
150K
1
0.5
300K
DOS
0.0
The thermal occupation of the excited
states is quenched at low temperature for
low bias current ⇒ slower gain recovery
3mA
0
150K
Energy (arb. units)
1
-1
1.0
0.1
20mA
-3
occupation probability
Temperature-Dependent Gain Dynamics
2
3
4
5
delay (ps)
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
T=10K
-1
delay(ps)
0
1
20
40
1.0
+
+
τ4
A macroscopic configuration is a
superposition of microstates. The probability
of a specific microstate varies with IC, but
each microstate has a given internal dynamics.
∆G (dB )
0.5
5.5m A
0.0
τ1
τ2
τ3
-0.5
30m A
TPA
-2
After the removal of one e0h0 by the pump
photons microstates with a high number of
carriers in the excited states undergo a fast
relaxation dynamics modeled by τ1=0.33 ±
0.05ps.
0.5
-1
am plitude (dB )
∆G (dB )
0
We have consistently fitted the DTS data with
4 time constants τ1..τ4 of amplitudes A1..A4.
A4
A3
A2
0.0
-0.5
A1
-3
0
10
20
Microstates with only one carrier in the excited
states have only one relaxation channel modeled
by τ2=4±0.3ps, τ3 =35 ± 4ps for a hole, electron.
30
I C (m A )
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Dephasing Time of the 0-X Transition
P. Borri et al., Phys. Rev. Lett. 87, 157401 (2001)
7K
TI FWM field amplitude (a.u.)
25K
630ps
50K
75K
At T=7K the long exponential decay
dominates the dynamics with a
dephasing time of 630 ps corresponding
to only 2µeV homogeneous broadening
170ps
100K
125K
0.2ps
37ps
At 300K the fast 0.2ps dephasing
correspond to 6.6meV homogeneous
broadening!
11ps
200K
6ps
300K
0
1
2
3
τP(ps)
150
Without electrical injection,
the optical transition 0-X
from the crystal ground state
to the ground-state exciton in
the QD is probed
300
450
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
Re(F(|E(t)|)) (arb. units)
Acoustic phonon band Zero phonon line
CdTe on ZnTe QDs
InAs/GaAs QDs
100K
75K
50K
25K
-2
0
2
Energy (meV)
Below 100K, the homogeneous
lineshape consists of a narrow
Lorentzian line, corresponding
L. Besombes et al.
to the long exponential decay,
B. Urbaszek et al. PRB 69, 035304 (2004)
PRB 63, 155307 (2001)
and a broad non-Lorentzian
Similar findings in photoluminescence spectra of single QDs!
band corresponding to the
Theory: pure dephasing from coupling with acoustic phonons
initial fast dephasing.
B. Krummheuer et al. PRB 65 195313 (2002)
R. Zimmermann and E. Runge ICPS26 (2002)
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Dephasing versus Injection Current at Low Temperature
P. Borri et al. Phys. Rev. Lett.89 187401 (2002)
TI FWM (a.u.)
TI FWM field amplitude (a.u.)
10K
n
• With increasing IC the FWM decay is
faster, i.e. the ZPL broadens due to Coulomb
interaction with the injected carriers.
n-1
X -(X )*
30mA
0-X
0
10
delay(ps)
• For IC >14mA the majority of dots is
occupied by two e0h0 excitons. When several
carriers occupy the excited states, the
multiexcitonic transition:
(Xn-1)*
Xn
0mA
1mA
XX-X
2mA
14mA
30mA
0
3mA
20mA
25mA
50
100
delay (ps)
has a strong final state damping due to the
quick relaxation of the (Xn-1)* state (which
we measure in differential transmission).
5mA
200
300
400
• The biexcton to exciton transition (XX-X)
has a much smaller final state damping than
the Xn-(Xn-1)* and is distinguished by the
long FWM decay.
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
Dephasing versus Relaxation of Multiexcitonic Transitions
P. Borri et al. IEEE J. Sel. Topics Q. El. 8, 984 (2002).
Xn-(Xn-1)*
20
220K
295K
γh
15
γ(meV)
pure dephasing
from Coulomb
population
interaction
relaxation
pure dephasing
from phonon
interaction
10
γ1
5
1
1
1
1
=
+
+
T2 2T1 ( I C , T ) T2' ph (T ) T2'ee ( I C )
0
150K
γh = 2=/T2
γ1 = =/T1
25K
γ(meV)
5
At 295K pure dephasing
processes given by phonon and Coulomb
interactions dominate
Xn
0
0
5
10
IC/Itr
15
20
0
5
10
15
20
IC/Itr
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
(Xn-1)*
Dephasing versus Relaxation of Multiexcitonic Transitions
P. Borri et al. IEEE J. Sel. Topics Q. El. 8, 984 (2002).
Xn-(Xn-1)*
20
220K
295K
γh
15
γ(meV)
pure dephasing
from Coulomb
population
interaction
relaxation
pure dephasing
from phonon
interaction
10
γ1
5
1
1
1
1
=
+
+
T2 2T1 ( I C , T ) T2' ph (T ) T2'ee ( I C )
0
150K
γh = 2=/T2
γ1 = =/T1
25K
γ(meV)
5
At 150K the pure dephasing
is given only by phonon interaction
Xn
0
0
5
10
IC/Itr
15
20
0
5
10
15
20
IC/Itr
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
(Xn-1)*
Dephasing versus Relaxation of Multiexcitonic Transitions
P. Borri et al. IEEE J. Sel. Topics Q. El. 8, 984 (2002).
Xn-(Xn-1)*
20
220K
295K
γh
15
γ(meV)
pure dephasing
from Coulomb
population
interaction
relaxation
pure dephasing
from phonon
interaction
10
γ1
5
1
1
1
1
=
+
+
T2 2T1 ( I C , T ) T2' ph (T ) T2'ee ( I C )
0
150K
γh = 2=/T2
γ1 = =/T1
25K
γ(meV)
5
At 25K the broadening is fully given
by the population relaxation
without pure dephasing
Xn
0
0
5
10
IC/Itr
15
20
0
5
10
15
20
IC/Itr
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers
(Xn-1)*
Summary
• 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
Borri, Ultrafast Characteristics of Quantum Dot Amplifiers