From weak to strong coupling of quantum emitters in metallic nano-slit Bragg cavities

From weak to strong coupling of quantum emitters in metallic nano-slit

Bragg cavitiesRonen Rapaport

The nanophotonics and quantum fluids group

AcknowledgmentsAcknowledgmentsGraduate Students:Nitzan LivnehMoshe HaratsItamar RosenbergIlai Schwartz

Collaborations:Adiel Zimran, Uri Banin – Chemistry, Hebrew Univ.Ayelet Strauss, Shira Yochelis, Yossi Paltiel – Applied Physics Hebrew Univ. Loren Pfeiffer – EE, Princeton UniversityGang Chen – Bell Labs

Support: -EU FP7 Marie Currie-ISF (F.I.R.S.T) -Wolfson Family Charitable Trust-Edmond Safra Foundation


OutlineOutline• 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


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)

Extraordinary Transmission (EOT) in Extraordinary Transmission (EOT) in subwavelength metal Hole/slit arrayssubwavelength metal Hole/slit arrays

Channeling of energy through the subwavelength openings!


EOT in nanoslit arrays: Possible mechanisms EOT in nanoslit arrays: Possible mechanisms

sin2sin kkx

TM

EOT

EOT of more than 5

Full numerical EM simulations: give full account◦No clear physical picture.

EH

TM



SPP modes

TM

EH

TM sin2sin kkx

Unit cell near field

Surface Plasmon Polaritons (SPPs)



SPP modes

TM

EH

TM sin2sin kkx

• Slit-Cavity resonances



SPP modes

TE

• EOT in TE with a thin dielectric layer• No propagating (or standing) modes in subwavelength slits• No SPP in TE polarization•Waveguide modes

E HTE


Bragg Cavity Model for EOTBragg Cavity Model for EOT

• Fabry-Perot Cavity: high resonant transmission with very highly reflective mirrors

Standing optical modes constructive forward interference High transmission



[( ) ] ˆ( )prop

x zi k gm x k zmj

m

H r H e y

• Inside the slit array: periodic Bragg (Bloch) modesfor g > k, there are modes with m ≠ 0

dg 2

• 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

I. Schwarz et al., preprint arXiv 1011.3713



12 232 2 2 2propzk w l Are phases accumelated

upon collision with the boundaryij

Mapping to FP (waveguide) physics: Analytic condition for standing Bragg modes

2 2( )propz

eff

k gn

k



TE TM

Very good agreement with full numerical calculations.

I. Schwarz et al., preprint arXiv 1011.3713


Bragg CavitiesBragg Cavities

• “one mirror” cavities

• easily integrated with various active/passive media

• small mode volume

• easily controllable Q-factor


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.

TLS in a cavity – weak and strong coupling TLS in a cavity – weak and strong coupling


At resonance, the relative strength of the Two level



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






Strong coupling: g0>>max(κ,γ)

The emission of a photon is a reversible process.

Vacuum Rabi splitting






Strong coupling for excitons in planar microcavities – exciton-polaritons

See J. Kasprzak, et al., Nature, 443 (2006) 409-414.

“Dynamical” Exciton – polariton BEC in a microcavity



1. Weak coupling of Quantum dots to Bragg1. Weak coupling of Quantum dots to Braggcavity modes – directional emissioncavity modes – directional emissionNanocrystal quantum dots - NQDsNanocrystal quantum dots - NQDsNanometric light source:◦Essentially a TLS◦Tunable emission wavelength◦High quantum efficiency

Possible applications:◦Photodetectors◦Solar cells◦Lasing medium◦Single Photon sources

ShellCore

Type I

ShellCore

Type I

Lumo

Homo

Lumo

Homo

InAs/CdSe type I

The nanophotonics and quantum fluids group N. Livneh et al., Nano Letters(2011)


samplessamples

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

N. Livneh et al., Nano Letters(2011)


Angular emission spectrum - ReferenceAngular emission spectrum - Reference

0 10 201

1.1

1.2

1.3

1.4

Emission angle

Wav

elen

gth

[m

]

0

0.5

1TE

No angular dependence – as expected



Angular emission spectrum – Nanoslit arrayAngular emission spectrum – Nanoslit array

0 10 201

1.1

1.2

1.3

1.4

Emission angle

Wav

elen

gth

[m

]

0

0.5

1TE

0 10 201

1.1

1.2

1.3

1.4

Emission angle

Wav

elen

gth

[m

]

0

0.5

1TE

0 10 201

1.1

1.2

1.3

1.4

Emission Angle

Wav

elen

gth

[m

]0

5

10

15TE emission

Strong angular dependence, directional emission (follow EOT disp.)



Directional emission with divergence of 3.4o

20 fold emission enhancement to this angle

Photon emission rate:

The interaction with the structure is in the single quantum-dot (photon?) level

Second order correlation measurements g(2) on the way

0 5 10 150

5

10

15

20

QD emission angleN

orm

. int

ensi

ty [a

.u]

nanoslit array samplereference sample

3.4o

0 10 201

1.1

1.2

1.3

1.4

Emission Angle

Wav

elen

gth

[m

]

0

5

10

15



Physical explanation – Purcell effectPhysical 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) Near field in 15o


Physical explanation – Purcell effectPhysical explanation – Purcell effectThe dipole emission rate into a cavity mode is given by

-2 0 2 4 6 8 10 12 140

5

10

15

20

QD emission angle

Nor

m. i

nten

sity

[a.u

]

nanoslit array samplereference samplepurcell factor

3.4o

Experimental values:

Numerical model:

Despite a low Q factor, the nanoslit array significantly enhances the emission to 0o due to a Small modal volume



Angular emission spectrum – QD monolayerAngular emission spectrum – QD monolayer



Towards directional emission of a single Towards directional emission of a single QD - QD -


2. enhancement of optical nonlinearities: 2. enhancement of optical nonlinearities: Two photon absorption induced fluorescenceTwo photon absorption induced fluorescence

Experimental configuration Excitation and Nanocrystal Quantum Dots Photoluminescence

Two photon upconversion process

M. Harats et al., Optics Express (2011)


Two photon absorption induced fluorescenceTwo photon absorption induced fluorescence

( )

(2) 2 2UC e hI N I I

- the intensity enhancement factor in the nanoslit array

Using the resonant enhancement of EM fields in the nanoslit array results with

The induced upconversion is:

(2)I I I

Glass substrate

Polymer layer

Al Al Al Al Ald a

H

h


QD absorption:


TPA and induced upconverted fluorescence in semiconductor NQDs in TE polarization in metallic nanoslit arrays with a maximal enhancement of ~400

Two photon absorption induced fluorescenceTwo photon absorption induced fluorescence



3. Strong exciton-Bragg cavity mode coupling: 3. Strong exciton-Bragg cavity mode coupling: Bragg exciton-polaritons in GaAs QW’sBragg exciton-polaritons in GaAs QW’s

The signature of strong coupling: vacuum Rabi splitting (avoided crossing)

Second order bragg resonance


TM

Calculated angular absorption spectrum –Calculated angular absorption spectrum – no excitonsno excitons


Angular absorption spectrum – with excitonsAngular absorption spectrum – with excitons

Clear vacuum RabiSplitting (~4meV).Clear avoided crossings

TM


Angular absorption spectrum – TEAngular absorption spectrum – TE

TE

TE


Thank youThank you

Experimental results - wavelength dependence

Using Dynamical Diffraction(1), near-field intensities are extracted. An averaged unit cell enhancement is calculated by:

(1) M. M. J. Treacy, Phys. Rev. B, 66(19):195105, Nov 2002.

( )unit cell

calcPFCB

unit cell

I r d r

d r

What’s happening in the wavelengths noted by the red circles?

2

Analysis

As we used a pulse with a spectral width ( ), the enhancement per wavelength is taken into account:

( )P

( ) ( )( )

( )calc

avg

P d

P d

This is good agreement between the experimental and theoretical

results

Documents

From weak to strong coupling of quantum emitters in metallic nano-slit Bragg cavities