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

1. From weak to strong coupling of quantum emitters in metallic nano-slit Bragg cavities Ronen Rapaport

2. 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

3. 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

4. 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!

5. EOT in nanoslit arrays: Possible mechanisms TM TM E EOT of more than 5 H EOT • Full numerical EM simulations: give full account • No clear physical picture.

6. EOT in nanoslit arrays: Possible mechanisms TM SPP modes TM E H • Surface Plasmon Polaritons (SPPs) Unit cell near field

7. EOT in nanoslit arrays: Possible mechanisms TM SPP modes TM E H • Slit-Cavity resonances

8. EOT in nanoslit arrays: Possible mechanisms TE SPP modes • EOT in TE with a thin dielectric layer • No propagating(or standing) • modes in subwavelength slits • No SPP in TE polarization • Waveguide modes E H TE

9. Bragg Cavity Model for EOT • Fabry-Perot Cavity: high resonant transmission with very highly reflective mirrors Standing optical modes  constructive forward interference  High transmission

10. Bragg Cavity Model for EOT • Inside the slit array: periodic Bragg (Bloch) modes • for g > k, there are modes with m ≠ 0 • Outside the slit array: For g > k, only the mode with m = 0 is propagating • We can have Standingm ≠ 0 Bragg waves in the structure! • Constructive interference with m=0 mode  EOT I. Schwarz et al., preprint arXiv 1011.3713

11. Bragg Cavity Model for EOT Mapping to FP (waveguide) physics: Analytic condition for standing Bragg modes

12. Bragg Cavity Model for EOT TE TM Very good agreement with full numerical calculations. I. Schwarz et al., preprint arXiv 1011.3713

13. Bragg Cavities • “one mirror” cavities • easily integrated with various active/passive media • small mode volume • easily controllable Q-factor

14. 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.

15. 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

16. 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

17. 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. “Dynamical” Exciton – polariton BEC in a microcavity Strong coupling for excitons in planar microcavities – exciton-polaritons See J. Kasprzak, et al., Nature, 443 (2006) 409-414.

18. 1. Weak coupling of Quantum dots to Braggcavity 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

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

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

21. Angular emission spectrum - Reference TE No angular dependence – as expected N. Livneh et al., Nano Letters(2011)

22. TE TE emission Angular emission spectrum – Nanoslit array TE Strong angular dependence, directional emission (follow EOT disp.) N. Livneh et al., Nano Letters(2011)

23. Directional emission with divergence of 3.4o • 20 fold emission enhancement to this angle • Photon emission rate: 3.4o • 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)

24. 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) Near field in 15o

25. Physical explanation – Purcell effect • The dipole emission rate into a cavity mode is given by 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 N. Livneh et al., Nano Letters(2011)

26. Angular emission spectrum – QD monolayer N. Livneh et al., Nano Letters(2011)

27. Towards directional emission of a single QD -

28. 2. enhancement of optical nonlinearities: Two photon absorption induced fluorescence Experimental configuration Excitation and Nanocrystal Quantum Dots Photoluminescence Two photon upconversion process M. Harats et al., Optics Express (2011)

29. Two photon absorption induced fluorescence Polymer layer H h Al Al Al Al Al Glass substrate d a QD absorption: - 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: M. Harats et al., Optics Express (2011)

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

31. 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)

32. Calculated angular absorption spectrum – no excitons TM

33. Angular absorption spectrum – with excitons TM • Clear vacuum Rabi • Splitting (~4meV). • Clear avoided crossings

34. Angular absorption spectrum – TE TE TE

35. Thank you

36. Using Dynamical Diffraction(1), near-field intensities are extracted. An averaged unit cell enhancement is calculated by: Experimental results - wavelength dependence What’s happening in the wavelengths noted by the red circles? (1) M. M. J. Treacy, Phys. Rev. B, 66(19):195105, Nov 2002.

37. Analysis As we used a pulse with a spectral width ( ), the enhancement per wavelength is taken into account: This is good agreement between the experimental and theoretical results