Transcript N. Livneh et al., Nano Letters(2011)
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 I out ( )/I in ( )>(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 sin TM 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 sin TM SPP modes E 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 sin TM SPP modes E H • Slit-Cavity resonances
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EOT in nanoslit arrays: Possible mechanisms
TE SPP modes E TE H • • EOT in TE with a thin dielectric layer No propagating (or standing) modes in subwavelength slits • No SPP in TE polarization •Waveguide modes
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Bragg Cavity Model for EOT
• Fabry-Perot Cavity: high resonant transmission with very highly reflective mirrors Standing optical modes High transmission constructive forward interference
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Bragg Cavity Model for EOT
• Inside the slit array: periodic Bragg (Bloch) modes for
g > k
, there are modes with m
≠ 0 g
2
d
m H e mj x
z prop z
]
y
ˆ • 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
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I. Schwarz et al., preprint arXiv 1011.3713
Bragg Cavity Model for EOT
Mapping to FP (waveguide) physics: Analytic condition for standing Bragg modes 2
k z prop w
2 12 2 23 2
l
ij
Are phases accumelated upon collision with the boundary
The nanophotonics and quantum fluids group
n eff
(
k z prop
) 2
g
2
k
Bragg Cavity Model for EOT
TE TM Very good agreement with full numerical calculations.
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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 g 0 .
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 g 0 .
Weak coupling
: g 0 < 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 g 0 . Strong coupling : g 0 >>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 g 0 . Strong coupling for excitons in planar microcavities – exciton polaritons “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 Possible applications : ◦ Photodetectors ◦ ◦ ◦ Solar cells Lasing medium Single Photon sources InAs/CdSe type I The nanophotonics and quantum fluids group The nanophotonics and quantum fluids group N. Livneh et al., Nano Letters(2011) 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 1.4 TE 1.3 1.2 1 0.5 1.1 1 0 10 Emission angle 20 No angular dependence – as expected 0 N. Livneh et al., Nano Letters(2011) The nanophotonics and quantum fluids group Angular emission spectrum – Nanoslit array 10 Emission angle The nanophotonics and quantum fluids group 1.4 TE emission 1.3 1.2 15 10 1.1 5 1 0 10 Emission Angle 20 0 Strong angular dependence, directional emission (follow EOT disp.) N. Livneh et al., Nano Letters(2011) Directional emission with divergence of 3.4 o 20 fold emission enhancement to this angle Photon emission rate: 20 15 10 5 3.4 o nanoslit array sample reference sample 1.4 1.3 1.2 1.1 1 0 10 Emission Angle 15 10 5 20 0 0 0 5 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 N. Livneh et al., Nano Letters(2011) The nanophotonics and quantum fluids group 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 0 o → stronger emission to 0 o Near field in 0 o (structure mode) Near field in 15 o The nanophotonics and quantum fluids group Physical explanation – Purcell effect The dipole emission rate into a cavity mode is given by Experimental values: Numerical model: 20 15 10 5 3.4 o nanoslit array sample reference sample purcell factor 0 -2 0 2 4 6 8 emission to 0 o due to a Small modal volume N. Livneh et al., Nano Letters(2011) The nanophotonics and quantum fluids group 10 12 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 Excitation and Nanocrystal Quantum Dots Photoluminescence Two photon upconversion process The nanophotonics and quantum fluids group M. Harats et al., Optics Express (2011) Two photon absorption induced fluorescence H 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 I The induced upconversion is: I UC N I 2 I 2 Polymer layer Al h Al Al Al d a Glass substrate Al 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 The nanophotonics and quantum fluids group Thank you 2 Using Dynamical Diffraction (1) , near-field intensities are extracted. An averaged unit cell enhancement is calculated by: calc PFCB d r (1) M. M. J. Treacy, Phys. Rev. B, 66(19):195105, Nov 2002. enhancement per wavelength is taken into account: avg calc P dsamples
Experimental results wavelength dependence
Analysis