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LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
QDs and optical microcavities:tailoring spontaneous emission
Jean-Michel GERARD
Equipe mixte CEA-CNRS-UJF « Nanophysique et Semiconducteurs »jmgerard@cea.fr
Grateful thanks to B. Gayral (CEA) as well as to
B. Sermage, A. Lemaître, I. Robert, E. Moreau, I. Abram, V. Thierry-Mieg, L. Ferlazzo from CNRS/LPN Marcoussis
Spontaneous emission control : why? (as of ~1982)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
laser diode
Current I
Out
put p
ower
Is
Spontaneousemission Stimulated
emission
I
I
250n
m
Only a tiny fraction ofspontaneous emission is useful!
β ~ 10-5
100000 times decrease of Isexpected for β ~ 1 !
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Two strategies toward improved SE control
Energy
Densityof photon modes
quantumwell
emission
Energy
Energyquantum dots
optical microcavity
kT
Optical microcavity = photon confinement on the wavelength scalediscrete photon modes
If the emitter is coupled to a single mode, β=1
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
β=1 « Thresholdless »-laser
Ideal conversion of electrical signals into optical signals. 1 e- -> 1 photon into the (single) mode. Linear input/output characteristic curve. No additional noise. High cut-off frequency
<n>=1
spontaneousemission
Stimulatedemission
Pout
Proposal :
Kobayashi et al, 1982
Yokoyama, Science 256, 62 (1992)
Björk et al, IEEE-JQE 27, 2386 (91)Pin
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
CQED with QDs : historical background
CQED (80->...)
SE can actually be tailored to a large extent for atoms in electromagnetic
cavities
optical microcavities (90->...)
it is possible to confine opticalphotons on the wavelength scale
in 2D, 1D, 0D
self-assembled QDs (~94->...)
single QD optical spectroscopyreveals atom-like behavior CQED with QDs
(96->...)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Outline
1) Some basic microcavity effects2) QDs as probes of photonic microstructures 3) CQED effects on QDs4) Some application prospects :
single-mode photon sourcesmicrolasers
For a recent review see: Solid state CQED with self-assembled QDs, in Topics in Applied Physics 30, 269 (2003), P. Michler ed. Springer
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
SE angular redistribution in planar microcavities
R
R
R
R
λ/2
emitterin free-space
A. Kastler, Appl. Optics 1,17 (1962)
Application to light emitting diodes : directional emission + high efficiency η~25%(Blondelle et al, Electron. Lett 31, 1286, 1995)
η~2% air
GaAs
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Tailoring the spontaneous emission rateE
Free space modes
atom
Fermi golden rule: exponential decayeunit volumper modes ofdensity 1 ∝τ
One can tailor spontaneous emission dynamics
. Dimensionality, refractive index...
. Coupling to a single mode (0D cavity, or optical selection rule)
e.g. : strong coupling for QWs in planar cavities (Weisbuch et al, PRL 69, 3314, 1992)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Ex: Brorson et al, IEEE JQE 26, 1492 (1990)Emitter in a planar microcavity
ideal metallic mirrorsL
usual case forQWs and QDs
Thickness of the cavity layer nL/λ
Both SE rate enhancement and inhibition expected
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
InAs QD array in a planar microcavity
Very weak effect on QD spontaneousemission dynamics !
Solomon et al, PRL 86, 3903 (2001)
This is expected since the effective cavity length is around 4 λ/n
λ/n
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Strong and weak coupling regimes in 0D cavities
Ω (V)Cavity damping (Q)
SE into other modes
Perfect cavity=> reversible spontaneous emission
hΩ = |d . Ε(r)|
Emitter dipole field per photon
time
Rabi oscillationP(t)1
=>Entangled eigenstates
2hΩ
Energy
|g, 1> |e, 0>
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Strong coupling for a single cesium atom in an optical microcavity
Hood et al, PRL 98
Strong coupling first observed for atoms in the microwave spectral range (superconductors are IDEAL mirrors!)
More recently observed in the optical spectral range
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Strong and weak coupling regimes in 0D cavities
time
dampedRabi oscillation
P(t) 1
Ω (V)Cavity damping (Q)
SE into other modes
Ω >> 1/τdecoherence =>
τ ∼ 2 τdecoh
time
P(t) 1
Ω < 1/τdecoherence => exponential decay« weak coupling regime »
τ ∼ f(Q,V,…)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Two important figures of merit
Ability to confine the e.m. field spatially:
effeff Vn
V 20
max 2:
εωε h
= dd
Actual cavity Equivalent cavityvolume Veff
Ability to store the e.m. energy:
ephoton
e
QQmodmod
1:ω
τωω
∆=↔
∆=
Around 1 eV, Q=1000 <-> τphoton =0.6 ps
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
The « Purcell effect »
Decoherence mostly due to photon escape (low Q) => ∆ωmode >> ∆ωem
ρ(ω)
~1/Q
~ Q
weakcouplingregime
( )2
.1 fdi εωρτ
rr∝
free space
Purcell (1946)Fp=
magnitude for an ideal emitter
.quasi-monochromatic
.spatial matching
.spectral matching
( )V
nQ
cav
free3
243 λπτ
τ=
Fp
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Spontaneous emission rate for a « non-ideal » emitter
2
22
2
max2
mod2
mod
2mod
)(
).()()(4 drE
drE
ErEF
eeme
ep
cav
freerr
rrr
ωωωω
ττ
∆+−∆
=
Spectral detuning spatial detuning dipole misorientation
If the emitter linewidth is not negligible,
( ) ( )
out washediseffect Purcell theand emitter broad afor
)(
em
em
dL
→
→ ∫ ωωωρωρω
« natural » emitter line
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
How to confine light in all 3 dimensions with dielectrics ?
metallic mirrors are too lossy at optical frequencies!
distributed Bragg reflection total internal reflection(DBR, photonic crystal) (e.g. optical fibers)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Some 0D solid-state microcavities1 µm
2 µm 3 µm
V < (λ/n)3V=6 (λ/n)3
V=5 (λ/n)3
3D confined modesbut not perfect « photonic dots » (leaky modes)!
Q ?
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Probing cavity modes with QDs
1.346 1.348 1.350 1.352 1.354
theory:
x10
PL
inte
nsity
(arb
. uni
ts)
Energy (eV)
Systematic probing of cavity modes (no selection rule)J.M. Gérard et al, Appl. Phys. Lett. 61, 459 (1996)
QD internal light source widely used to study microdisks orPC cavities see e.g. D. Labilloy et al, APL 73, 1314 (1998)
diam=4 µm1 µm
GaAs/AlAsmicropillar
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
E. Moreau et al,
APL 79, 2865 (2001)Probing cavity modes with one (few) QDs
1.250 1.255 1.260 1.265
10K1 µm
1 µW 200 µW
PL
Inte
nsity
(lin
. uni
ts.)
energy (eV)
cavitymode
Very strong homogeneous broadening of the single QD emission underhigh excitation conditions => broadband light source!
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Probing cavity modes with QDs (2)
0.0 0.5 1.0 1.5 2.0 2.5 3.00
10
20
30
40: theory
∆E
(meV
)
Pillar Radius (µm)
neff<n
Resonance condition:
planar: L= λ / npillar : L= λ/ neff
L
Appl. Phys. Lett. 61, 459 (1996)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Large diameter micropillars (d>4λ/n)
Same profile for guided mode in GaAs and AlAs layers
⇒No mode coupling at interfaces⇒Fundamental pillar mode built using
neff (GaAs) = neff (AlAs)n (GaAs) n(AlAs)
=> the structure is still a « λ-cavity » for the novelresonant wavelength λ = L . neff (GaAs)
=> Cavity Q unchanged
L
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Probing cavity Q’s
High Q’s can be achieved (Q=5000, τ~3ps)
Q drops at small sizes : intrinsic or extrinsic effect ?
0 2 4 6 8
1 000Q
diameter (µm)
Qplanar
Very weak absorption of the QD array => we probe the « empty » cavity Q (as long as Q<~10000)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Numerical study of the intrinsic Q of GaAs/AlAs micropillarsP. Lalanne et al, APL june 2004
0.2 0.4 0.6 0.8 1 1.2 1.4200
400
600
800
1000
1200
1400
1600
0.4 0.43
diameter (µm)
Q
Strong oscillations in the small diameter limit !
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Small diameter micropillars (d>4λ/n)
(Slightly) different mode profile in GaAs andAlAs layers
⇒ inter-mode coupling at interfaces
⇒ fundamental pillar mode built usingand
L
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
refle
ctiv
ity
neff<nEnergy
Blue shift of the DBR stopband as a result for the lateral confinement
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Energy of the fundamentalpillar mode
refle
ctiv
ity
Energy
Resonant cavity mode = α + β with |α|>>|β|
The component propagates freely through the DBRs
=> interferences and oscillations on Q !
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Numerical study of the intrinsic Q of GaAs/AlAs micropillarsP. Lalanne et al, APL june 2004
0.2 0.4 0.6 0.8 1 1.2 1.4200
400
600
800
1000
1200
1400
1600
0.4 0.43
diameter (µm)
Q
Behavior well understood in a two-mode transfer matrix model
( + )
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Probing cavity Q’s
0 2 4 6 8
1 000Q
diameter (µm)
Q2D
see e.g.T.Rivera et al,APL 74, 911 (1999)
High Q’s can be achieved (Q=5000, τ~3ps)
Q drops at small sizes : scattering by sidewall roughness
Fp = 32 achieved for d=1 µm !
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Some 0D solid-state microcavities1 µm
2 µm 3 µm
V=6 (λ/n)3, Q=12000Fp =150
V=1.2(λ/n)3, Q=13000Fp=810 (Caltech 04)
V=5 (λ/n)3, Q=2100Fp=32
High Q, low volume, 3D confined modes
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Some solid-state CQED experiments
performed with QDs
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
CQED : strong coupling for single QDs?
|ground, 1 photon>
Ωrabi
|excited, 0 photon>
2hΩ
Energy
|g, 1> |e, 0>
InAs QD in solid-state cavity : huge vacuum field (105 V/cm)
large dipole (0.6 e.nm)
hΩ = |d . εmax|
Sizeable vacuum Rabi splitting expected : 2hΩ ~ 50 µeV for V~ 10 (λ/n)3
∆EemitterVRS observable 2hΩ > ∆Ecavity
Here, negligible emitter linewidth⇒the relevant criteria for strong coupling is : 4 hΩ > ∆Ecavity
Andreani et al, PRB 60, 13276 (1999)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Strong coupling for single QDs ? Gérard et al, Physica E9, 131 (2001)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Strong coupling for single QDs ? Gérard et al, Physica E9, 131 (2001)Andreani et al, PRB 60, 13276 (1999)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Fresh news !
The strong coupling regime has been observed by tworesearch groups :
. micropillars + big InGaAs QDs displaying a « giant »oscillator strength (Forchel et al, Würzburg)
. InAs QD in high Q photonic crystal microcavity(Scherer et al, Caltech)
(still unpublished)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Purcell effect on InAs QDs
1946: Purcell’s paper1983: Observation for atoms in cavities (x 500! Haroche et al, ENS Paris)
1997: First observation of the Purcell effect in a solid-state microcavity !
QD array in micropillar x 5 J.M. Gérard et al, PRL 81, 1110 (1998)QD array in microdisk x 18 B. Gayral et al, Physica E7, 641(2000)
x 12 B. Gayral et al, APL 78, 2828 (2001)QD array in PC cavity x 12 T. Happ et al, PRB 66, R041303 (2002)
single QD in microdisk x 6 A. Kiraz et al, APL 78, 3932 (2001)single QD in micropillar > x 3 E. Moreau et al, APL 79, 2865 (2001)
x 4 G. Solomon et al, PRL 86, 3903 (2001)x 5 J. Vuckovic et al, APL 82, 3596 (2003)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Purcell effect for a collection of QDs (d=1 µm, Fp=32)
0 1000 2000
QBs out of resonance QBs in resonance
τ ~ 0.25 ns
τ = 1.05 ns
PL
inte
nsity
(lin
. uni
ts)
time (ps)
1.346 1.348
PL
inte
nsity
(arb
. uni
ts)
PL decay faster only for on-resonance QDs : intrinsic effectSE rate enhancement (x5) much smaller than Fp
PRL 81, 1110 (1998)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
How to understand the magnitude of the Purcell effect
M o d e d ens ityd
E nergy
Random distribution of QDs=> spatial + spectral averaging
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Fp : the relevant figure of merit
0 5 10 15 20 25 30 350
1
2
3
4
5
6 experiment model for 2D dipole
Q=2000d=1.3 µm
Q=960d=1 µm
Q=1600d=0.9 µm
Q=2250d=1 µm
Q=5200d=4.2 µm
τ 0 / τ do
n
Purcell factor FP
+random distribution
Enhancement factordepends as expectedon Fp , not d or Q
Good agreement with theory
PRL 81, 1110 (1998)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Dependence of SE rate enhancement on the spectral detuning
fromSolomon et al, PRL 86, 3903 (2001)
see alsoGraham et al, APL 74, 3408 (1999)
Experiment in good agreement withthe expected spectral dependence
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
SE inhibition in metal-coated micropillars
No inhibition in standrad micropillars, due to leaky modes => gold-coated pillars
M. Bayer et al,
PRL 86, 3168 (2001)
Efficient reduction of the density
of non-resonant modes by the
metallic coating
=> strong SE inhibition (/10)
for out-of-resonance QDs
cavitym
ode energy
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Purcell effect for QDs in microdisks
200 400 600 800 1000 1200 1400 1600 1800
2 µm
Off-resonance
Q=7000
Q=10000
Inte
nsity
(lin
. sca
le)
Time (ps)
Up to x 12 SE rate enhancement
B. Gayral et alAPL 78, 2828 (2001)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Purcell effect in microdisks
0 200 400 600 800
experimentmodels:
Fp+spectral/spatial averaging
+ "jitter" due to relaxation time
Inte
nsity
PL
(lin.
sca
le)
Time (ps)
(30 ps)
B. Gayral et al, APL 78, 2828 (2001)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Purcell effect in a c.w. experiment
1E-4 1E-3 0.01 0.1 1
100
1000
10000
100000
1000000
1E7
out-of-resonance QDs
in-resonance QDs8KP
L in
tens
ity (l
og)
excitation power (log)
PL
B. Gayral et alPhysica E7, 641 (2001)
Saturation due to filling of fundamental QD statesPurcell effect (x18 here!)=> saturation occurs for higher pumping power
Same behavior observed for QDs in PC cavities (Happ et al, PRB 2002)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Few QDs in a micropillar
1.250 1.255 1.260 1.265
10K1 µm
1 µW 200 µW
PL
Inte
nsity
(lin
. uni
ts.)
energy (eV)
cavitymode
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Purcell effect on isolated QDs in a micropillar(Q2D=1000, Q=500, Fp=7)
1E-3
0,01
0,1
Rel
ativ
e In
tens
ity τ ~ 400 ps
τ ~ 1.1 ns
τ ~ 1.3 ns
0 2 4 6 8 10Delay (ns)
SE enhancement > x 3
Cavity Mode
QD1QD3
10 µW100 nW
λ (nm)970 980 990
QD2
Moreau et al,APL 79, 2865 (2001)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Beware !
Unlike experiments on large collections of QDs, quantitative modelling not possible
since the QD location (and τfree) are not precisely known !(see e.g. Gayral et al, PRL 90, 229701, 2003)
Coupling the QD in/out of resonance is a good way to highlight the Purcell effect andto estimate its magnitude
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Purcell effect for a single QD in a microdisk
0 2 4 6 8 10 12 14 16 18 20
0.1
1
T=4K1.75nsec
T=48K1.75nsec
T=31K850psec (resonance)
Inte
nsity
(a.u
.)Time (ns)
Kiraz et al, APL 78, 3932 (2001)UCSB
F>2
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Applications of the Purcell effect
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
(Nearly) single-mode spontaneous emission
ω
ρ(ω)
QD
Purcell effect=
selective enhancement of SE into the resonant mode
F/τfree
γ/τfree(γ∼1) 1≈
+=
γβ
FF J.M. Gérard et al
PRL 81, 1110 (1998)
Very interesting for single photon sources and microlasers !
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
What is a single photon source ?What is a single photon source ?
clicclic
Source able to emit single photons pulses on demand
N.B. : Non-classical state of light⇒Impossible to generate it using a thermal source or a laser
Applications : quantum cryptography, metrology...
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
A single-mode single-photon source
GaAs/AlAs micropillar
20 nmIsolated InAs QD
=> Single-photon emission
⇒ Efficient collection+
single-mode behaviorproposal: J.M. Gérard et B. Gayral,
J Lightwave Technol. 17, 2089 (1999)exp : E. Moreau et al, APL 79, 2865 (2001)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Some properties of this single photon source
<2% !Single photon collection efficiency
44%38%
All photons prepared in the same mode (spatial+ polarization)
~ No two-photon pulses
Key device for the practical implementationof quantum cryptography
air
GaAs
Pelton et al, PRL 89, 233602 (2002)Moreau et al, Physica E 13, 418 (2002)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
SPS efficiency for GaAs/AlAs micropillarsscattering by
sidewall roughness
Q spoiling ε < β
int
int
111
QQQ scat
βε =
+=
J.M. Gérard et al, quant-ph/0207115W. Barnes et al, Eur. Phys. J. D.18, 197 (2002)
0 2 4 6 8
1 000Q
diameter (µm)
scattering by sidewall roughness !
ε < βa careful optimisation of the intrinsiclosses is necessary!
Q2D
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Polarization control in single-mode micropillars
Elliptical cross section
1.4 µm
0.7 µm
1.265 1.270 1.275 1.280
PL In
tens
ity (
lin.)
Energy (eV)
x-polarized
y-polarized
Non degenerate fundamental modeGayral et al, APL 72, 1421, 1998
~ 90% linear polarisation degreeof single QD emission
Moreau et al, APL 79, 2865, 2001
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Indistinguishable single photons and the issue of decoherence
Indistinguishable single photons T2 = 2 T1
Decoherence events
t
t
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
InAs QD SPS : photon coalescence experiment
Santori et al, Nature 419, 594 (2002)
Probability of detection on D1+D2D1 D2
InAs QD in bulk GaAs : T2 (~ 600ps) << 2 T1 (~2 ns)
Here, emission of nearly-Fourier-transform limited single photons by the InAs QD, thanks to the Purcell effect
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Toward « nanolasers »
β ~0.04Ith = 36 µA
Huffaker et al,APL 71, 1449 (1997)
β ~ 10-5β ~ 0.1
Ith = 5 mA Ith = 40 µA
Fujita et al, Electron. Lett. 36, 790 (2000)
Sub µA threshold current expected in the β~1 limit !
Purcell effect at 300K ???
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
QDsThe smallest PC cavities exhibitV’s as low as 0.2 (λ/n)3
Best QD arrays ~ 15 meV linewidthat 300K
Assuming Qcav > Q QDs , the SE rate enhancement factor is :
( )V
nQQDs
cav
free3
243 λπτ
τ= ~ 30
and β > 0.95 !
Probably the best strategy to date for approaching the regime of« thresholdless » lasing at 300K
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Conclusion
Using QDs has been the key for observing CQED effects
Solid-state CQED is a very lively domain
Still many basic effects to be observed !
Important potential applications in optoelectronics andquantum information science
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
What is beyond?
moderate β, huge Q
200 µW at 300Kfor InAs QDs
(ENS/LKB2003)
moderate Q, high βusing the Purcell effect
ex: QDs in 2D PCs
β∼1 in 3D PCs
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Single quantum dot laser?Low temperature required !!!
cavem ωωγτβ
∆>∆⇒>
without
Purcell ef
fectwithPurcell effect
Strong couplingΩ<∆<∆ hemcav ωωIth~10 pA predictedPelton et Yamamoto,PRA 59, 2418 (1999)
Τ
emcav ωω ∆<Ω<∆ h
Weak coupling and lasing
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Semiconductor microdisks2 µm
GaAs disk
GaAlAs pedestal
3D photon confinement using waveguiding + total internal reflexion(whispering gallery modes)
V~ 5 (λ/n)3 !
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
Probing WGMs with QDs
1.2 1.3
unprocessed QB array(weak excitation)
50 µW100 µW
2.5 mW
PL
Inte
nsity
(lin
. uni
ts)
Energy (eV)
B. Gayral et al
APL (1999)
Observation of high Q WGMsGreat sensitivity of Q on sidewall roughnessQ>10000 for wet-etched microdisks
QD internal light source also commonly used to probe PC cavities
see e.g. D. Labilloy et al, APL 73, 1314 (1998)
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
An ideal dielectric microcavity
E. Yablonovitch, PRL, 2238 (1991)
photonic crystal + defect
β = 1
All photons are collected/prepared in a single mode !
Rem: spontaneous emission control= main initial motivation for developping photonic crystals
3D PCs and SPSs
LABORATOIRE DEDE PHOTONIQUEET DE NANOSTRUCTURES
To be done !!
Photonic defect+
SC or diamond nanoX, molecule
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