From weak to strong coupling of
quantum emitters in metallic nano-slit
Bragg cavities
Ronen Rapaport
Acknowledgments
Graduate Students:
Nitzan Livneh
Moshe Harats
Itamar Rosenberg
Ilai Schwartz
Collaborations:
Adiel Zimran, Uri Banin – Chemistry, Hebrew Univ.
Ayelet Strauss, Shira Yochelis, Yossi Paltiel – Applied Physics Hebrew Univ.
Loren Pfeiffer – EE, Princeton University
Gang Chen – Bell Labs
Support: -EU FP7 Marie Currie
-ISF (F.I.R.S.T)
-Wolfson Family Charitable Trust
-Edmond Safra Foundation
The nanophotonics and quantum fluids group
Outline
• Extraordinary transmission (EOT) in nanoslit arrays
• EOT in nanoslit array exposed – Bragg Cavity Model
• Two level system in a cavity – the weak and strong coupling limits
• 3 Examples of control and manipulations of light-matter coupling:
1. WCL – linear: the Purcell effect and controlled directional emission of quantum dots
2. WCL – nonlinear: enhancement of optical nonlinearities: Two photon
absorption induced fluorescence
3. SCL : Strong exciton-Bragg cavity mode coupling: Bragg polaritons
The nanophotonics and quantum fluids group
Extraordinary Transmission (EOT) in
subwavelength metal Hole/slit arrays
Resonant Extraordinary Transmission – output light intensity
(at resonant wavelengths) larger than the geometrical ratio of
open to opaque areas
Iout ()/Iin()>(open area)/(total area)
Channeling of energy through the subwavelength openings!
The nanophotonics and quantum fluids group
EOT in nanoslit arrays: Possible mechanisms
TM
k x  k sin   
2

TM
sin  
E
H
EOT of more than 5
EOT

Full numerical EM simulations: give full account
◦ No clear physical picture.
The nanophotonics and quantum fluids group
EOT in nanoslit arrays: Possible mechanisms
TM
k x  k sin   
2

TM
sin  
E
SPP modes
H

Surface Plasmon Polaritons (SPPs)
Unit cell near field
The nanophotonics and quantum fluids group
EOT in nanoslit arrays: Possible mechanisms
TM
k x  k sin   
2

TM
sin  
E
H
• Slit-Cavity resonances
The nanophotonics and quantum fluids group
SPP modes
EOT in nanoslit arrays: Possible mechanisms
TE
SPP modes
E
H
TE
• EOT in TE with a thin dielectric layer
• No propagating (or standing)
modes in subwavelength slits
• No SPP in TE polarization
•Waveguide modes
The nanophotonics and quantum fluids group
Bragg Cavity Model for EOT
• Fabry-Perot Cavity: high resonant
transmission with very highly reflective mirrors
Standing optical modes  constructive forward interference
 High transmission
The nanophotonics and quantum fluids group
Bragg Cavity Model for EOT
• Inside the slit array: periodic Bragg (Bloch)
modes
for g > k, there are modes with m ≠ 0
H (r )   Hmj e
i[( kx  gm) x  kzprop z ]
2
g
d
yˆ
m
• Outside the slit array: For g > k, only
the mode with m = 0 is propagating
We can have Standing m ≠ 0 Bragg waves in the structure!
Constructive interference with m=0 mode  EOT
The nanophotonics and quantum fluids group
I. Schwarz et al., preprint arXiv 1011.3713
Bragg Cavity Model for EOT
Mapping to FP (waveguide) physics: Analytic condition for standing Bragg modes
2k
prop
z
w  212  223  2 l
neff
The nanophotonics and quantum fluids group
ij Are phases accumelated
upon collision with the boundary
(k zprop ) 2  g 2

k
Bragg Cavity Model for EOT
TE
TM
Very good agreement with full numerical calculations.
The nanophotonics and quantum fluids group
I. Schwarz et al., preprint arXiv 1011.3713
Bragg Cavities
• “one mirror” cavities
• easily integrated with various
active/passive media
• small mode volume
• easily controllable Q-factor
The nanophotonics and quantum fluids group
TLS in a cavity – weak and strong coupling
At resonance, the relative strength of the Two Level
System (TLS) - cavity interaction is determined by:
•the photon decay rate of the cavity κ,
•the TLS non-resonant decay rate γ,
•the TLS–photon coupling parameter g0.
The nanophotonics and quantum fluids group
TLS in a cavity – weak and strong coupling
At resonance, the relative strength of the Two level
System (TLS) - cavity interaction is determined by:
•the photon decay rate of the cavity κ,
•the TLS non-resonant decay rate γ,
•the TLS–photon coupling parameter g0.
Weak coupling: g0<<max(κ,γ)
The emission of the photon by the TLS is
an irreversible process.
Resonant enhancement of spontaneous
emission rate into cavity modes.
Purcell effect
The nanophotonics and quantum fluids group
TLS in a cavity – weak and strong coupling
At resonance, the relative strength of the Two level
System (TLS) - cavity interaction is determined by:
•the photon decay rate of the cavity κ,
•the TLS non-resonant decay rate γ,
•the TLS–photon coupling parameter g0.
Strong coupling: g0>>max(κ,γ)
The emission of a photon is a
reversible process.
Vacuum Rabi splitting
The nanophotonics and quantum fluids group
TLS in a cavity – weak and strong coupling
At resonance, the relative strength of the Two level
System (TLS) - cavity interaction is determined by:
•the photon decay rate of the cavity κ,
•the TLS non-resonant decay rate γ,
•the TLS–photon coupling parameter g0.
Strong coupling for excitons in planar microcavities – excitonpolaritons
“Dynamical” Exciton – polariton BEC in a microcavity
See J. Kasprzak, et al., Nature, 443 (2006) 409-414.
The nanophotonics and quantum fluids group
1. Weak coupling of Quantum dots to Bragg
cavity modes – directional emission
Nanocrystal quantum dots - NQDs


Nanometric light source:
◦ Essentially a TLS
◦ Tunable emission wavelength
◦ High quantum efficiency
Core
Possible applications:
◦ Photodetectors
◦ Solar cells
◦ Lasing medium
◦ Single Photon sources
Shell
Lumo
Homo
Type I
InAs/CdSe type I
The nanophotonics and quantum fluids group
The nanophotonics and quantum fluids group
N. Livneh et al., Nano Letters(2011)
samples

Reference sample –
quantum dots on a glass
substrate

Quantum dots in a polymer
layer on the nano-slit array

Quantum dot self-assembled
monolayer on the nano-slit
array
The nanophotonics and quantum fluids group
N. Livneh et al., Nano Letters(2011)
Angular emission spectrum - Reference
Wavelength [m]
1.4
1
TE
1.3
0.5
1.2
0
1.1
1
0
10
20
Emission angle
No angular dependence – as
expected
The nanophotonics and quantum fluids group
N. Livneh et al., Nano Letters(2011)
Angular emission spectrum – Nanoslit array
TE
1.3
0.5
1.2
0
1.1
1
0
1.4
1
10
Emission angle
20
Wavelength [m]
Wavelength [m]
1.4
TE emission
1.3
15
1.2
10
1.1
5
1
0
10
Emission Angle
20
0
Strong angular dependence,
directional emission (follow EOT disp.)
The nanophotonics and quantum fluids group
N. Livneh et al., Nano Letters(2011)

20
nanoslit array sample
reference sample
15
10
1.4
3.4o
Wavelength [m]

Directional emission
with divergence of 3.4o
20 fold emission
enhancement to this
angle
Photon emission rate:
Norm. intensity [a.u]

15
1.2
10
1.1
5
1
5
0
1.3
0
5
0
10
Emission Angle
10
QD emission angle
The interaction with the
structure is in the single
quantum-dot (photon?) level
 Second order correlation
measurements g(2) on the way

The nanophotonics and quantum fluids group
N. Livneh et al., Nano Letters(2011)
20
0
15
Physical explanation – Purcell effect
Purcell effect: The emission rate of a dipole in a cavity into
a cavity mode is enhanced.
 Our structure acts as a Bragg cavity with an eigenmode at
0o → stronger emission to 0o

Near field in 0o (structure mode)
The nanophotonics and quantum fluids group
Near field in 15o
Physical explanation – Purcell effect

The dipole emission rate into a cavity mode is given by
Experimental values:
Norm. intensity [a.u]
Numerical model:
20
nanoslit array sample
reference sample
purcell factor
15
10
3.4o
5
0
-2
0
2
4
6
8
10
12
emissionenhances
angle
Despite a low Q factor, the nanoslit array QD
significantly
the
emission to 0o due to a Small modal volume
The nanophotonics and quantum fluids group
N. Livneh et al., Nano Letters(2011)
14
Angular emission spectrum – QD monolayer
The nanophotonics and quantum fluids group
N. Livneh et al., Nano Letters(2011)
Towards directional emission of a single
QD -
The nanophotonics and quantum fluids group
2. enhancement of optical nonlinearities:
Two photon absorption induced fluorescence
Experimental configuration
The nanophotonics and quantum fluids group
Excitation and
Nanocrystal Quantum
Dots Photoluminescence
M. Harats et al., Optics Express (2011)
Two photon
upconversion
process
Two photon absorption induced fluorescence
QD absorption:
 ( )- the intensity enhancement factor in the
nanoslit array
Using the resonant enhancement of EM
fields in the nanoslit array results with
I   I     (2) I
The induced upconversion is:
IUC  Neh   I   (2) 2 I 2
Polymer layer
H
Al
Al
h
Al
d
Al
Al
a
Glass substrate
The nanophotonics and quantum fluids group
M. Harats et al., Optics Express (2011)
Two photon absorption induced fluorescence
TPA and induced upconverted fluorescence in
semiconductor NQDs in TE polarization in
metallic nanoslit arrays with a maximal
enhancement of ~400
The nanophotonics and quantum fluids group
M. Harats et al., Optics Express (2011)
3. Strong exciton-Bragg cavity mode coupling:
Bragg exciton-polaritons in GaAs QW’s
Second order bragg resonance

The signature of strong coupling: vacuum Rabi splitting
(avoided crossing)
The nanophotonics and quantum fluids group
Calculated angular absorption spectrum –
no excitons
TM
The nanophotonics and quantum fluids group
Angular absorption spectrum – with excitons
TM
Clear vacuum Rabi
Splitting (~4meV).
Clear avoided crossings
The nanophotonics and quantum fluids group
Angular absorption spectrum – TE
TE
TE
The nanophotonics and quantum fluids group
Thank you
The nanophotonics and quantum fluids group
2
Experimental results wavelength dependence
Using Dynamical Diffraction(1), near-field intensities are
What’s happening
in the
noted by
the red circles?
extracted.
An averaged
unitwavelengths
cell enhancement
is calculated
by:
 calc 

I (r )d r
unit  cell
 PFCB

dr
unit  cell
(1) M. M. J. Treacy, Phys. Rev. B, 66(19):195105, Nov 2002.
Analysis
As we used a pulse with a spectral width (P ( )), the
enhancement per wavelength is taken into account:
This is good agreement between calc
the(experimental
and theoretical
) P ( ) d 

 avg ( ) results
 P ( ) d 