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Quantum Dots in Photonic Structures
Lecture 10: QD-microcavity in weak coupling
regime
Jan Suffczyński
Wednesdays, 17.00, SDT
Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego
Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki
Reminder - microdisc cavity
Total internal reflection
Lord Rayleigh, “The problem of the whispering
gallery,” Philosophical Magazine’1910.
Photonic Crystal cavity
formed by a point defect
O. Painter et. al.,
Science (1999)
CdSe QDs attached to a glass m-sphere
Picture: M.V.Artemyev, I. Nabiev
CdSe QDs attached to a glass m-sphere
Here: CdSe-shell
on glass m-sphere
R=3.1 mm
Wavelength (nm)
mode separation > GQD
room temperature emission
Nano Lett. 1, 309 (2001)
Coupled QD - micropillar systems
Motivation – enhancement of photon
extraction efficiency
sin max = 1/n
quantum dot
• Low photon
extraction efficiency
from unstructured
crystal
Motivation
S. Strauf, Nature Photonics 2010
Motivation
Desired: production method of coupled QD-cavity systems „on demand”
Quality factor of a planar cavity
For a planar microcavity:
Reflectivity
ru
rl
ncav
dcav
Quality factor of a planar cavity
For a planar microcavity
(GaAs/AlAs example):
Reflectivity
ru
Effective
cavity length
rl
Effective
refractive
index of DBR
Effective
mirror
length
Effective number
of mirror pairs
ncav
dcav
Quality factor of a planar cavity
The reflectivity of a DBR consisting of m mirror pairs
(n0 equals 1 for the top mirror and
n0 = nGaAs for the bottom mirror)
AlAs/GaAs planar
microcavity sample with
20/24 mirror pairs in
the upper/lower DBR
Impact of the cavity on the
spontaneous emission rate
Planar cavity (top view)
Emitter
Planar cavity
A condition for a sizable Purcell
effect: fully 3D cavity
D
The idea:
Lateral structuring of a planar
cavity
From 2D to 3D photonic crystal
Planar
microcavity =
1D confinement
of the light
Pillar microcavity=
3D confinement of
the light
DBR made of ZnSSe and MgS/ZnCdSe supperlattices
Lohmeyer et al.
Quality factor of the micropillar
Evolution of the microresonator resonance with diameter
T. Rivera et al., APL ’1999
Two main effects of the diameter reduction:
 blueshift of the fundamental mode
 linewidth increase due to the higher optical losses
Quality factor of the micropillar
 Q constant for large
pillar diameters =
Rivera et al.’1999
close to the Q of the
planar cavity
 The degradation of Q below a certain critical diameter  losses
due to the scattering by the roughness of the microresonators
sidewalls + intrinsic losses
Quality factor of the micropillar: loss sources
1
𝑄
~
Top view
Photon
Escape 
Rate
1
𝑄(𝑟)
=
„Planar”
losses
1
+
+
„Sidewall”
losses
1
𝑄𝑖𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 (𝑟) 𝑄𝑎𝑏𝑠
+
1
𝑄𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑖𝑛𝑔 (𝑟)
r dr
dr: typically ~ 10 nm
Scattering losses proportional to the transverse mode intensity at
the microresonator edge:
𝐽0 2 (𝑐𝑜𝑛𝑠𝑡 ∗ 𝑟)
1
|𝐸 𝑟 |2
~
~ϵ
𝑄𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑖𝑛𝑔 (𝑟)
𝑟
𝑟
Sidewall roughness
Sidewall roughness
GaAs/AlAs DBRs
Roughness
of the order of tens of nm
Quality factor of the micropillar: loss sources
Q decraese with
pillar diameter dominant
contribution
from egde
scattering losses
Reitzenstein et al.
Quality factor of the micropillar:
implications for the Purcell factor
3 𝑄l3
𝐹𝑝 =
4𝜋 2 𝑉
The same Q planar
Low losses
High lossses
Gayralet al.
Non-linear dependence of Fp on Q factor in the limit of
small pillar diameters
Quality factor of the micropillar:
implications for the Purcell factor
4000
3 𝑄l3
𝐹𝑝 =
4𝜋 2 𝑉
Purcell factor
6
5
3500
3000
2500
The same Q planar
Low losses
High lossses
4
3
2000
1500
2
1000
1
500
0
0
0
1
2
3
4
Pillar diameter (mm)
5
Quality Factor
7
Q factor oscillations
Prediction:
Lalanne et al.’2004
The appearance of strong oscillations for high-Q
micropillars in the small diameter regime
Q factor oscillations
Prediction:
Observation:
experiment
calculation
Lalanne et al
The appearance of strong oscillations for high-Q
micropillars in the small diameter regime
Lecamp et al.’2007
Q factor oscillations
Oscillations attributed to a
coupling of the fundamental mode
to higher-order pillar modes
Basic idea:
+
+
Fundamental Mode Energy (mev)
Micropillar eigenmodes vs diameter
PL Intensity (arb. units)
(a)
d = 2.9 mm
(b)
d = 1.9 mm
(c)
d = 1.4 mm
(d)
d = 0.9 mm
(e)
d = 0.7 mm
2040
2050
2060
2070
2080
2090
2100
2110
2090
2080
2070
2060
2050
0
1
2
3
4
5
Pillar diameter ( mm )
Photon Energy (meV)
T. Jakubczyk et al.
Blueshift of the mode with decreasing diameter evidenced
in photoluminescence
Photoluminescence - Micropillar eigenmodes
Experiment
Simulation
Extended transfer matrix method:
•
•
Material absorption included
Equal emission intensity of each line assumed
(a)
d = 2.9 mm
(b)
PL Intensity (arb. units)
PL Intensity (arb. units)
(a)
d = 2.9 mm
d = 1.9 mm
(c)
d = 1.4 mm
(d)
d = 0.9 mm
(e)
d = 0.7 mm
2040
2050
2070
2080
d = 1.9 mm
(c)
d = 1.4 mm
(d)
d = 0.9 mm
(e)
d = 0.7 mm
Experiment
Simulation
2060
(b)
2090
Photon Energy (meV)
2100
2110
2040
2050
Simulation
Simulation (absorption considered)
2060
2070
2080
2090
2100
2110
Photon Energy (meV)
T. Jakubczyk et al.
Purcell enhancement of spontaneous
emission
Spontaneous emission rate
FP
Purcell Factor
Reminder: Fermi’s Golden Rule
• Spontaneous emission rate is not an inherent property of the emitter
• Sponteanous emission rate proportional to:
Dipol moment
Density of
of the emitter Electric field intensity
photon states
at emitter position
at emitter wavelength
Γ ∝ 𝜌(𝜔)·|𝐝·𝐄 𝐫emitter
mirror
Spontaneous emission inhibited
2
|
mirror
Spontaneous emission enhanced
l - cavities
l - cavities
Purcell factor in realistic case
Quality factor
Effective mode volume
The observation of cavity QED phenomena relies on
• high Q/ Veff
• spatial and spectral matching
Purcell factor in realistic case
FP
Purcell factor in realistic case
FP
1
1
QD-micropillar system – the first realization
Out of cavity reference QDs
In cavity – out
of resonance
In cavity – on
resonance
Measurements on QD ensamble
J. M. Gérard et al. ’ PRL1998
Enhancement or suppression of QD
spontaneous emission
QD in
micropillar
QD in planar
microcavity
QD in
micropillar
with coated
sidewalls
Bayer et al 2001
Decay rate as a function of detuning
389 ps
Photon Counts (arb. units)
91 ps
63 ps
75 ps
Detuning (meV):
s
2.8
0.6
0.0
-0.7
-200
0
200
Time (ps)
400
600
T. Jakubczyk et al.
Decay rate as a function of detuning
Temperature (K)
3
21
65
389 ps
500
450
91 ps
350
300
250
200
150
100
50
0
-2
-1
0
1
2
3
4
Photon Counts (arb. units)
Decay Time (ps)
400
75 ps
Detuning (meV):
s
Detuning (meV)
• Strong enhancement of the
decay rate at zero-detuning
63 ps
2.8
0.6
0.0
-0.7
-200
0
200
Time (ps)
400
600
Decay rate as a function of detuning
Temperature (K)
3
21
65
500
• Strong enhancement of the
decay rate at zero-detuning
450
Decay Time (ps)
400
350
300
Reference QDs
Far detuned QDs
in cavity
QD in cavity
250
200
150
100
50
0
-2
-1
0
1
2
3
4
Detuning (meV)
T. Jakubczyk et al.
Decay rate as a function of detuning
Temperature (K)
3
21
65
500
• Strong enhancement of the
decay rate at zero-detuning
• Shortening of the decay time
does not depend on
temperature
• Far detuned QDs have similar
decay time to reference QDs
450
Decay Time (ps)
400
350
300
Reference QDs
Far detuned QDs
in cavity
QD in cavity
250
200
150
100
50
0
-2
-1
0
1
2
3
4
Detuning (meV)
T. Jakubczyk et al.
Decay rate as a function of detuning
Temperature (K)
3
21
65
500
• Strong enhancement of the
decay rate at zero-detuning
• Shortening of the decay time
does not depend on
temperature
• Far detuned QDs have similar
decay time to reference QDs
450
Decay Time (ps)
400
350
300
Reference QDs
Far detuned QDs
in cavity
QD in cavity
250
200
150
100
50
0
-2
-1
0
1
2
3
4
Detuning (meV)
FP 
1
a
 0
 

 0   5.7  0.5
 leak 
  cav
T. Jakubczyk et al.
Deterministic and scalable method for production of
coupled QD-cavity devices
2 mm
SEM image
QD coupled to the mode of the micropillar microcavity:
an ideal case
Spatial matching: QD at the spatial
maximum of the cavity optical mode
QD
Spectral matching: QD emission
energy = Optical cavity
fundamental mode energy
Emission
micropillar
QD
M
Energy
Towards deterministic coupling
- Control of the spatial positions of individual QDs?
100 nm
AFM image
Towards deterministic coupling
- Control of the spatial positions of individual QDs?
- Yes.
Towards deterministic coupling
- Control of the energy emission of individual QDs?
- No.
PL
~ 50 meV
~ µeV
Bragg
mirrors
1.34
1.32
1.36
1.40
1.38 1.48
Energy (eV)
 Probability of random spatial and spectral matching of the QD to the
cavity mode for 2 mm pillar smaller than 1/1000
Spatial matching
Technology so far
QD in photonic crystal cavity – coupled „on demand” (Imamoglu’s
group, Science’2005, Nature’2007):
Quantum nature of a strongly coupled single
quantum dot-cavity system
K.Hennessy & al., Nature 2007
 Many steps
 Precision of spectral matching 6 meV
 Only one coupled device on the sample
Deterministic and scalable method for
production of coupled QD-cavity devices
• Spectral and spatial QD-cavity matching in a
single step
• Many coupled systems on the same sample
• One or more QDs coupled to the same mode
Experimental setup
emission analysis
spectrometer
spectral matching
CCD
laser
laser
532 nm 750 nm
PL
sample
at 10 K
1,344
1,352
)
Energie (eV
1,360
x
z
y
shutter
focus control
spatial matching
Photolithographic method in situ
Sample preparation:
• InAs/GaAs QD layer MBE grown between AlAs/GaAs Bragg mirrors
• Positive photoresist spin coated on the sample surface
Low density InAs/GaAs
QD layer
24 pairs
}
}
20 pairs
Positive
photoresist
Bragg mirrors AlAs/GaAs:
two dimensional optical cavity
Photolithographic method in situ
Positive
photoresist
Sample at
T= 10 K
planar
InAs/GaAs
QD layer
cavity
y
x
Piezoelectric x-y stages
Photolithographic method in situ
µ-PL excitation at
750 nm
signal
µ-PL
scanning
Sample at
T= 10 K
microskope
Spectrometer + CCD
Spectra acquisition
Positive
photoresist
planar
InAs/GaAs
QD layer
cavity
y
x
Piezoelectric x-y stages
Photolithographic method in situ
Spatial coupling
6
µm
5
1500
15
1210
12
910.0
9
4
6
610.0
3
310.0
0
10.00
photoluminescence XY mapping

7
6
µm
5
c)
QD position determination with
50 nm accuracy
Photolithographic method in situ
µ-PL excitation at
750 nm
signal
‘Green’ beam co-linear
with ‘red’ beam
Spectrometer + CCD
Spectra acquisition
photoresist exposure at
532 nm
Optical
Lithography
Sample at
T= 10 K
microskope
Positive
photoresist
planar
InAs/GaAs
QD layer
cavity
y
x
Piezoelectric x-y stages
Spectral matching
q =0
qmax
EX
planar
cavity
a)
1.345
1.350 1.355
Energy (eV)
1.360
Pillar mode energy (eV)
PL intensity
 QD emission energy = Optical cavity fundamental mode energy
1.360
1.355
1.350
EX
R
1.345
0.5
1.0
1.5
Pillar radius (µm)
Photo of the sample surface: Ni masks
5 µm
Increasing exposure time
2.0
Pillar radius R
(m m )
Spectral matching
1.5
1.0
pillar
radius R
0.5
30
60
Exposure time (s)
 Pillar radius calibration
90
2 µm
 Spectral and spatial QD-cavity matching:
a single step process!
Pillar etching
Signal
Photoresist
exposured
Resist development
Nickel mask deposition
Etching:
Lift-off
Pillar with a QD placed in
the mode maximum
QD-cavity coupling „on demand”
- weak coupling
Pillar radius R=0.85 µm
pillar 1
after pillar
etching
PL Intensity
32K
M
10K
during
lithography
10K
x10
A. Dousse, L. Lanco, J. Suffczyński, E. Semenova, A. Miard,
A. Lemaitre, I. Sagnes, C. Roblin, J. Bloch and P. Senellart,
Phys. Rev. Lett. 101, 267404 (2008)
Selected QD
1.352 1.354
Energy (eV)
Controlled Purcell efect
I sat  nXsat  FP ()
PL Intensity at saturation vs
QD – cavity mode detuning:
nXsat 
1
1  2(1  Fp ())
1
 2Q 

1  

 c 
2

2
C. Böckler et al., Appl. Phys. Lett.,
92, 091107 (2008)
1.0
Normalized PL
intensity at saturation
FP Fp
0.8
Measured: Fp= 9 ± 3
0.6
Expected: Fp= 9.5
(for R = 0.85µm and Q=1500)
0.4
 Purcell factor as predicted
0.2
-0.5
0.0
0.5
1.0
Detuning  (meV)
Scalability of the technique
Etched mikropillars –
SEM image:
Many coupled systems on the same sample
R=1.9 µm
pillar 4
R=1.9 µm
pillar 5
R=1.7 µm
39K
M
37K
M
40K
10K
10K
10K
M
10K
10K
1350
1352
Energy (meV)
selected QD
10K
1350 1352
Energy (meV)
selected QD
1352
After pillar etching
PL intensity
pillar 3
1354
Energy (meV)
selected QD
m-PL during
lithography
1.352
Standard deviation:
0.6 meV
1.348
Actual mode energy (eV)
Scalability of the technique - precision
1.348
1.352
Target mode energy (eV)