E - Onera

Harald Schneider | Institute of Ion-Beam Physics and Materials Research | Semiconductor Spectroscopy Division
Rosencher‘s Optoelectronic Day Onéra 24.05.2011
Optical Nonlinearities in Quantum Wells
Harald Schneider
Helmholtz-Zentrum Dresden Rossendorf
Institute of Ion-Beam Physics and Materials Research
Dresden, Germany

Outline
Introduction
Optical Rectification
Harmonic Generation & Two-Photon Absorption
Difference-Frequency Generation
Conclusion
2

Optical nonlinearities in QW: Classification
Our focus today:
Resonant intersubband (intraband) nonlinearities
Not covered (but also interesting):
Interband optical nonlinearities
CB
e2
e1
• Electro-optical effects
e.g., quantum-confined Stark effect
intensity and phase modulators
• Excitonic nonlinearities
Marginally covered:
Mixed interband/intersubband nonlinearities
hh1
lh1
hh2
lh2
VB
3

Optical nonlinearities involving intersubband transitions
Second-order
Optical rectification E. Rosencher et al., APL 55 1597 (1989)
Second-harmonic generation M.M. Fejer et al., PRL 62, 1041 (1989)
Difference-frequency mixing C. Sirtori et al., APL 65, 445 (1994)
Sum-frequency mixing H.C. Liu et al., IEEE JQE 31, 1659 (1995)
Third-order
Four-wave mixing D. Warlod et al., APL 59, 2932 (1991)
Third-harmonic generation C. Sirtori et al., PRL 68, 1010 (1992)
Dc Kerr effect A. Sa’ar et al., APL 61, 1263 (1992)
Two-photon absorption E. Dupont et al., APL 65, 1560 (1994)
4

ITQW Conference
1991 Cargèse
2011 Badesi
5

… often used for nonlinear
wavelength conversion
integrated with quantum
cascade lasers
7
Nature 391, 464 (1998)

Outline
Introduction
Optical Rectification
Harmonic Generation & Two-Photon Absorption
Difference-Frequency Generation
Conclusion
8

Nonlinear susceptibility
(2)
0,max
q T
2
3 2
2
2
0
2
N1
N2
1212
T 2 dephasing time
12 |
1| z
| 2 |
12 2 | z | 2 1| z
|1
More than 10 3 higher nonlinearity than in bulk GaAs
Additional contribution due to T 1 , which is ~10x longer than T 2 !
9

Sainte Chapelle, Paris
Little devil who holds the electron
at its place, thus preventing it from
returning back to the ground state
10

Semiclassical
"rectification efficiency"
(2)
0,max
3
q T2
2
2
0
T 2 dephasing time
storage time
2
N1
N2
1212
More than 10 6 higher efficiency than in GaAs!
11

12
Several periods with thick inter-well barriers

From rectification to detection …
Thin inter-period barriers
dc photocurrent!
13

Optimization
high absorption strength
high escape probability
high capture probability
small tunneling probability
Low-noise QWIP
1: excitation zone
2: drift zone
3: capture zone
4: tunnel barrier zone
no tunneling
no thermal re-emission
high tunneling probability
14

ENERGY (meV)
Parameters and subbands
20 periods
4.8 nm GaAs:Si
45.0 nm AlGaAs x=0.26
4x10 11
1
cm -2 excitation
zone
2
drift zone
1.8 nm GaAs 3
1.8 nm AlGaAs x=0.26 capture
3.0 nm GaAs zone
0.6 nm AlAs 4
1.8 nm AlGaAs x=0.26 tunnel
0.6 nm AlAs barrier
3.6 nm AlGaAs x=0.26 zone
250
200
150
100
50
1
2
3
4
0
0 20 40 60 80 100 120
POSITION (nm)
15
Appl. Phys. Lett. 71, 2646 (1997)

CURRENT (A)
Response at 300 K background temperature
• Photovoltage due to
thermal background
radiation
10 -8
cold shield
T B
=300 K, 45° facet
T B
=300 K, grating
(expected)
10 -7 120x120 µm 2
• Background limited
performance
10 -9
10 -10
65 K
-4 -3 -2 -1 0 1
BIAS VOLTAGE (V)
16

DETECTIVITY (cmHz 1/2 /W)
“Low-Noise” QWIP
• same D * as for conventional QWIPs
• both polarities demonstrated
other polarity
• carrier density
PC QWIP 8 x 10 10 cm -2
“Low-Noise” 4 x 10 11 cm -2
Photoconductive QWIP
" Low-Noise" QWIP in PC mode
fit to all data
10 10 77 K
45° facet geometry
20 periods
8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5
LONG WAVELENGTH CUTOFF (µm)
Physica E 7, 101 (2000)
17

640 x 512 “Low-Noise” QWIP FPA
NETD = 9.6 mK
7.4 - 9.2 µm
f/2, 30 ms, 60 K
18
H. Schneider and H. C. Liu, Quantum Well Infrared Photodetectors, Springer 2007
AIM

Outline
Introduction
Optical Rectification
Harmonic Generation & Two-Photon Absorption
Difference-Frequency Generation
Conclusion
19

Nonlinear susceptibility for SHG
N1
N2
1223
31
(2) 2
2 ,max
~ T2
Dipole moments
µ 12 , µ 23 , µ 31 0
Need asymmetry
SHG in step QWs
Up to 3 orders of magnitude more efficient than in bulk GaAs
20

High-efficiency SHG
conversion possible
provided that we can beat
the losses…
21

Nonlinear susceptibility
(2)
3 ,max
~ NT12T23T3412233441
µ 12 , µ 23 , µ 34 µ 41 0
T 12 , T 23 , T 34 dephasing times
22

Intracavity SHG and THG in quantum cascade lasers
23
T. Moseley et al., Opt. Express 12, 2972 (2004)
C. Gmachl et al., IEEE JQE 39, 1345 (2003)

50 µW
80 K
298 K
6 µW
Efficiency 0.13 mW/W 2 (RT), 0.04 mW/W 2 (80K), 19 mW/W 2 (theory)
Deviation due to higher lateral modes, detuning from resonance, …
24

Two-photon absorption
TPA coefficient
~
, max
N
D
2
12
23T2
12
( 3)
T 2 dephasing time 21
T e dephasing time associated with state 3
Independent of µ 31 (in contrast to SHG)
TPA works with a symmetric QW structure!
T
e
E 2
E 3
E 1
E 3
Semiclassical (analogy with opt. rectification)
"Sequential TPA"
N
D
2step,max
~ 12234
12
T 1 lifetime for 21
T
1
T
2
T
e
E 2
E 1
25

QWIPs with quadratic power dependence
Resonant two-photon QWIP
3
2
1
E 3 - E 2 = E 2 - E 1
Standard QWIP
2
1
• Photocurrent (power) ²
stronger signal if two pulses overlap in time
• photocurrent
power density
26

norm. Photocurrent
Time Resolution of Two-Photon-QWIP
Autocorrelation measurements
using 170 fs mid-IR pulses
• 8:1 peak-to-background-ratio
nearly ideal autocorrelation
for small delay times
8
6
4
2
= 10.4µm
Bias = 1V
T = 77K
Sub-ps time resolution
Influence of intermediate state
on detector response
• Oscillations decrease exponentially
phase relaxation T 2
• Exponential behavior of the "wings“
intersubband relaxation T 1
0
8
6
4
2
0
-1 0 1
Delay Time (ps)
ideal autocorrelation
of 165 fs pulse
IR Phys. Technol. 47, 182 (2005)
27

Photocurrent (a. u.)
Photocurrent (a. u.)
Determining T 1 and T 2 by numerical fits
8
6
well doped
experimental
numerical fit
8
6
modulation doped
experiment
numerical fit
4
2
= 10.4 µm
Bias = 1 V
T = 77 K
4
2
=10.6µm
Bias = 0.2 V
T=70K
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Delay Time (ps)
well doped
mod.
doped
T 1 530 fs 750 fs
T 2 120 fs 240 fs
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Delay Time (ps)
28
Appl. Phys. Lett. 91, 191116 (2007)

Signal (arb. units)
Signal (arb. units)
Quadratic Autocorrelation at Room Temperature
6
4
interferometric
intensity
autocorrelation
300 K
InGaAs/AlGaAs
6.2 nm QW
= 5.4 µm
6
4
EXP
FIT
2
2
0
0
-4 -2 0 2 4 -0.02 0.00 0.02 0.04 0.06
Time (ps)
Time (ps)
Interferometric autocorrelation 6:1 (ideally 8:1)
Intensity autocorrelation 2.2:1 (ideally 3:1)
Fringes
(1-cos) 2 shape
FWHM 3.7 ps
FEL pulse width 2.6 ps
29
H. Schneider et al., Appl. Phys. Lett. 93, 101114 (2008)

Photocurrent (arb. u.)
THz Two-Photon QWIP
8
6
4
2
Interferometric autocorrelation
Intensity autocorrelation
= 42 µm
9.5 K, 0.5 V
18 nm GaAs/AlGaAs QWs
6
4
2
0
-0.4 0.0 0.4
0
-10 -5 0 5 10
Time Delay (ps)
Operation below the Reststrahlenband at 42 µm (7 THz)
FWHM 6.2 ps 4.4 ps FEL pulse width
30
H. Schneider et al., Opt. Express 17, 12279 (2009)

Interferometric autocorrelation of modelocked QCL
C. Y. Wang et al.,
Opt. Express 17, 12931 (2009)
Pulse diagnostics
• Pulse width
• Chirp
• Photon correlation
31

32
Autocorrelation of amplified
spontaneous emission source

Outline
Introduction
Optical Rectification
Harmonic Generation & Two-Photon Absorption
Difference-Frequency Generation
Conclusion
33

34
DFG at around 60 µm

• 3 stacks: DFG region, QCL1 (8.4 µm), QCL2 (9.5 µm)
• 100 nW output power (0.5 µW/W 2 external efficiency) at 78 K
• Up to 100 µW expected after further optimization
35

intensity (counts)
THz/NIR nonlinear optics with exciton levels in quantum wells
THz sideband generation
TiSa
NIR
FEL
FEL
Sideband energies
sample
n = NIR ± n FEL
n = 0,±1,±2,
125000
100000
75000
50000
25000
n=-2
*100
n=-1
*1000
FEL energy 8.9 meV
NIRlaser
/1000
-NIR wavelength 791.9nm
-NIR power 230 kW/cm²
-FEL-power 13 kW/cm²
-efficiency here 0.03%
n=+1
*1000
n=+2
n=+4
n=+3
*1000
*1000
0
1540 1550 1560 1570 1580 1590 1600 1610
energy (meV)
• Best efficiency if THz energy is resonant with 1s-2p intraexcitonic transition
36
M. Wagner et al., Appl. Phys. Lett. 94, 241105 (2009)

Absorption (-log(T))
hh(1s)
hh(2s/p)
lh(1s)
High-field physics with FEL: Excitons dressed by THz beams
Autler-Townes (AT) effect for intra-excitonic transitions
e 2
weak ……. strong THz field
e 1
hh 1
lh 1
exciton
9 meV
hh(2p)
ħ THz
hh(1s)
hh-exciton
Rabi frequency
E 21
/
Observation of AT splitting
• interband absorption under
intense THz pumping of
hh(1s) – hh(2p) transition
3
2
1
0
3
NIR Energy (meV)
1560 1580 1600
0
130
220
330
650
THz
Peak
Intensity
(kW/cm²)
37
M. Wagner et al., Phys. Rev. Lett. 105, 167401 (2010)
2

NIR photon energy (meV)
energy splitting (meV)
Dependence on THz frequency and intensity
1572
1568
130 kW/cm²
4.4 kV/cm
6
4
measured
linear fit
1564
1560
4 6 8 10 12 14 16 18 20
THz photon energy (meV)
Anticrossing
experiment
model
unperturbed exciton
• As expected from
the two-level model
also quantitatively!
• Deviations at very
high intensities
2
0
0 5 10 15 20 25 30
(THz peak intensity) 1/2 (kW/cm 2 ) 1/2
On-resonance energy splitting
(THz peak intensity) 1/2
electric field
38
M. Wagner et al., Phys. Rev. Lett. 105, 167401 (2010)

Conclusion
QW = great system for constructing huge optical nonlinearities
• Dipole moments on the order of the QW width
• Model system with taylorable (2) , (3)
• Custom-design of resonances for enhanced nonlinearity
But still much room for improvements…
• New geometries, e.g., photonic crystal structures for higher efficiency?
• New concepts, e.g., shorten the "radiatíve lifetime" using a microresonator?
• Other nonlinearities, e.g., two photon emission?
Jamais la nature ne nous trompe; c’est toujours nous
qui nous trompons.
Jean-Jacques Rousseau
39