pubs.acs.org/NanoLett
Surface Plasmon Mediated Strong Exciton-Photon Coupling in Semiconductor Nanocrystals D. E. Go´mez,*,†,‡ K. C. Vernon,†,‡ P. Mulvaney,§ and T. J. Davis†,‡ †
CSIRO, Materials Science and Engineering, Private Bag 33, Clayton, Victoria, 3168, Australia, ‡ CSIRO, Future Manufacturing Flagship, Gate 5 Normanby Road, Clayton, Victoria, 3168, Australia, and § Bio21 Institute and School of Chemistry, The University of Melbourne, Parkville, Victoria, 3010, Australia ABSTRACT We present an experimental demonstration of strong coupling between a surface plasmon propagating on a planar silver thin film and the lowest excited state of CdSe nanocrystals. Attenuated total reflection measurements demonstrate the formation of plasmon-exciton mixed states, characterized by a Rabi splitting of ∼112 meV at room temperature. Such a coherent interaction has the potential for the development of nonlinear plasmonic devices, and furthermore, this system is akin to those studied in cavity quantum electrodynamics, thus offering the possibility to study the regime of strong light-matter coupling in semiconductor nanocrystals under easily accessible experimental conditions. KEYWORDS surface plasmon polaritons, semiconductor nanocrystals, strong coupling, Rabi splitting, excitons
D
localized to subwavelength scales and have frequencies comparable to those of light in free space, features that are attractive for the miniaturization of photonic elements. A key aspect for the development of plasmonic devices is the interaction of SP with optically active materials such as QDs. The SP-exciton interaction has been shown to result in enhancements of the excitation rate of the QDs8 and of their fluorescence intensity,6,9-13 an effect even observable at the single QD level.14,15 This effect has been utilized to enhance the performance of organic LEDs.16 When an SP mode is resonant with the exciton transition of an ensemble of QDs, two interaction regimes can be distinguished. These originate from competition between the rates of exciton-SP coupling and the dephasing rates of either type of excitation. In the weak coupling regime, damping of either resonance dominates over coupling and the interaction only modifies the radiative decay rate of the exciton state (Purcell effect) and its angular pattern of radiation. Theoretically, this regime can be described by perturbation theory through Fermi’s golden rule. However, in the strong coupling regime, the states of the SP-exciton system are coherent superpositions of both types of excitations and are expected to have significantly different optical properties. For instance, in the case of a single exciton transition, these mixed states are characterized by a doublet of SP-exciton “polaritons”, which should be readily observable in transmittance and reflectivity measurements. Although this SP-exciton coupling regime has been reported for silicon nanocrystals,17 molecular systems,18-20 J aggregates,21-25 and quantum well structures,26-28 direct experimental evidence of coherent coupling of excitons in colloidal semiconductor QDs with SPs has not been documented.
ue to the quantum size effect, the optical properties of semiconductor nanocrystals, also referred to as quantum dots (QDs), are different from those of their bulk counterparts, leading to interesting phenomena such as size-dependent photoluminescence and Coulomb blockades, effects that arise from the existence of discrete energy levels in these structures.1 To date, most of the proposed applications of these materials exploit their unique optical properties, in particular, their tunable photoluminescence (PL). In QDs, PL stems from radiative exciton annihilation (i.e., electronshole recombination), an irreversible process that occurs in competition with nonradiative decay mechanisms that deteriorate the performance of the QDs. One approach to overcome these detrimental processes consists of coupling the QDs to optical microcavities.2 The boundary conditions imposed by these microcavities (neglecting leaky modes) only allow a finite number of optical modes. This implies that only a set number of exciton transitions can take place, and this results in photon emission only if the energy of these transitions matches one of the allowed photonic modes of the cavity, leading, as a consequence, to enhancement or suppression of radiative decay pathways.3-5 These effects can also take place when these materials are placed near metallic interfaces. In this case, the exciton can transfer its energy into radiative and nonradiative surface plasmon polariton (SP) modes of the metal.6 SP modes are coherent charge oscillations that take place at metal/dielectric interfaces.7 These surface waves are * To whom correspondence should be addressed,
[email protected]. Received for review: 10/16/2009 Published on Web: 12/15/2009 © 2010 American Chemical Society
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DOI: 10.1021/nl903455z | Nano Lett. 2010, 10, 274-278
FIGURE 2. Reflectivity spectra (shown as 1 - Rp to improve its visualization) plotted as a function of the angle of incidence external to the prism θext (external to the prism, measured with respect to the normal of the base of the prism, see Figure 1). The white lines are the positions of the reflectivity minima. There is a clear discontinuity at θext ∼40° and at a wavelength of ∼570 nm.
FIGURE 1. Normal incidence absorption spectrum of a CdSe film, ∼25 nm in thickness spin coated onto a glass slide (thickness measured with a surface profilometer). From the position of the first exciton transition, the estimated diameter of these QDs is ∼3.4 nm. The inset shows a diagram of the ATR experiments.
wavelengths by varying the angle of incidence, providing a means to probe the SP-exciton interaction by bringing the SP excitations in and out of resonance with the excitonic ones. All the measurements were carried out at room temperature and at wavelengths well below the bulk plasma frequency of Ag pωP ) 3.78 eV (328 nm).7 The measured reflectivity of p-polarized white light for a typical Ag/CdSe film is shown in Figure 2, where it can be observed that at any given angle of incidence (AOI), the Rp spectrum (a vertical slice of the figure) exhibits two minima, whose relative contribution and position in wavelength change as the AOI is increased. Initially, at AOIs below 37°, the Rp curves are dominated by one dip, but at around 40° the two reflectivity minima have equal contributions and are separated in wavelength as shown in Figure 3. As the AOI is increased beyond this point, the contribution from the lowerwavelength dip increases and the net result is the appearance of an avoided crossing of two branches at a wavelength of ∼570 nm, which corresponds to the first absorption feature of the CdSe film, as shown in Figure 1. Such avoided crossings were theoretically predicted by Pockrand et al.31 and arise from a reversible energy exchange that takes place between the SP mode at the Ag/CdSe interface and the exciton transitions in the CdSe QDs. Importantly, one observation to be made in connection to Figure 2 and Figure 3 is that the reflectivity spectra consist of only two features. This implies that although there are several exciton transitions in each CdSe QD in the film (see Figure 1), the SPs only couple to one. From the position of the avoided crossing in Figure 3, it is evident that this exciton level is the lowest excited state of the QDs, namely, the 1S3/2(h)1Se exciton state.32,33 This result is partly due to the fact that in CdSe QDs, this exciton state carries most of the oscillator strength, but additionally, ultrafast spectroscopic measurements have revealed that higher exciton states in CdSe QDs exhibit fast nonradiative relaxation to the 1S3/2(h)1Se exciton state, which may compete with the implicit Rabi oscillations associated with strong SP-exciton coupling.34
In this Letter, we present an experimental demonstration of such coherent energy coupling between SPs on a thin Ag film and excitons confined in CdSe semiconductor QDs. This coupling is evident in the energy dispersion of the coupled system as an anticrossing of two “polariton-like” branches, as derived from reflectivity measurements. The CdSe QDs were synthesized following standard literature procedures.29 These were washed (two times, with methanol/acetone/chloroform mixtures, approximately 1:4:1 in composition) and subsequently treated with pyridine at 30 °C overnight. The pyridine-treated QDs were then passivated with butylamine, redispersed in chlorobenzene, and filtered (0.22 µm), resulting in dispersions with approximate concentrations of ∼4 × 10-4 M. Small portions of this stock solution were then directly spin-coated on top of 53.3 nm thick films of Ag, which were thermally evaporated onto glass coverslips. (This represents the average thickness that was measured by first obtaining an estimate using surface profilometry which was later used as an initial guess for a fit of the normal incidence transmission spectrum of the film, using the dielectric data of ref 30.) An optical absorption spectrum of a representative CdSe film on bare glass is shown in Figure 1. The angle-dependent, attenuated total reflection (ATR) reflectivity measurements were performed in the Kretschmann-Raether7 configuration (sketched in the inset of Figure 1), wherein p-polarized light is incident at the base of a right angle glass (SF10) prism, onto which the Ag/ CdSe coated coverslip was attached using an index matching oil. SPs are excited in the system only when the projection kx of the wave vector of the incident photons matches that of surface polaritons at the Ag/CdSe interface. The magnitude of kx is given by (2π/λ)np sin(θint), where λ is the (vacuum) wavelength of the light, nP the refractive index of the prism, and θint the angle of incidence measured at the base of the prism. Since kx depends on both the wavelength and angle of incidence of the light, the resonance condition for the excitation of SPs can be achieved at different © 2010 American Chemical Society
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QDs. By assuming that the CdSe layer consists of closely packed spheres, the maximum fraction of volume occupied by these spheres would be φ ) π/6. Furthermore, by considering that the surrounding medium consists exclusively of butylamine (nD20 ) 1.401), the Maxwell-Garnett model yields a refractive index for CdSe QDs (at 850 nm) of 2.47, which is close to the value reported for the bulk crystal (∼2.5).37 Furthermore, with these assumptions, the predicted extinction coefficient for the CdSe QDs is R(570 nm) ∼ 6.8 × 104 cm-1, which is in reasonable agreement with recently published data.38 Obviously, to obtain more accurate estimates, one would have to determine the volume fraction of CdSe QDs in the layer as well as the refractive index of the medium surrounding these particles. The coupling of the excitons in the QDs with the SPs is mediated via a dipole interaction, which exists between the electric field produced in the CdSe by the SP and the electric dipole moment of the exciton transition. Most of the physics of this interaction can be accurately described by considering a system of two coupled oscillators.5,39,40 Ignoring damping effects in either oscillator, the allowed energy eigenvalues of the coupled system are given by
FIGURE 3. Experimental (dots) reflectivity curves of p-polarized white light measured at 38, 40, 40.5, 41, and 45°. The lines are fits to the data as described in the text, where the adjustable parameters were the background dielectric permittivity εb ) 3.5721, and the oscillator strength f ) 0.04 (see eq 1). The spectra have been vertically offset, relative to the one corresponding to 40.5°, for visual clarity.
EU,L(θ) )
To model the optical properties of the Ag/CdSe films, we employed a homogeneous stratified model35 consisting of a semi-infinite layer of glass [nSF10(λ) ) 1.728 + 0.01342 µm2/λ2], a layer of Ag (53.3 nm thick, optical constants from Johnson and Christy30) a CdSe layer and a semi-infinite layer of air (n ) 1). Given that we observed coupling to one exciton transition only, the effective dielectric permittivity of the CdSe layer was modeled with a single Lorentz oscillator
ε(ω) ) εb +
2
ωo
f - ω2 - iΓω
{( ) pΩR 2
2
+
1 (E (θ) - EX)2 4 SP
}
1/2
(2)
where ESP(θ) is the energy of the uncoupled SP mode (found by setting f ) 0 in eq 1), which changes with the angle of incidence as we have discussed before. EX is the dispersionless exciton transition energy (2.175 eV, 570 nm), and pΩR is the vacuum Rabi splitting, which for the present case was found to be 112 meV (the energy splitting observed at resonance when ESP(θ) ) EX). As shown in Figure 4, this simple model reproduces the measured energy position of the reflectivity dips as a function of the AOI (external to the prism), providing evidence of the strong interaction between the SP and exciton resonances in the Ag/CdSe film. The magnitude of the Rabi splitting is expected to increase with the number N of QDs in the sample as N1/2.5,39,40 To test this relationship, we deposited thin films of CdSe QDs of different absorbance (proportional to the number of QDs) at the position of the 1S3/2(h)1Se exciton transition, and summarize the results in the inset of Figure 4, where it can be observed that the magnitude of the Rabi splitting increases linearly with the square root of the absorbance. Similar strong interactions can be obtained with QDs of different sizes. In Figure 5, we summarize the results obtained for CdSe QDs of ∼4.3 nm in diameter, where it can be noticed that the experimental dispersion curve is also characterized by an anticrossing of two branches at the energy of the exciton state. This dispersion curve was also accurately described by the coupled-oscillators model of eq 2.
(1)
where εb is the background dielectric permittivity (adjustable parameter), pωo is the energy of the exciton transition (2.175 eV or 570 nm, from the absorption spectrum), pΓ the width (broadening) of the exciton transition (0.1 eV, from a fit to a single Lorentzian line shape to the first feature of the absorption spectrum of Figure 1), and f its oscillator strength (adjustable parameter). By a least-squares optimization of the adjustable parameters, we obtained the red lines of Figure 3, which reproduce the experimental data reasonably well and correspond to εb1/2 ) 1.89 and f ) 0.04. It is important to note that, with this model, the obtained permittivity does not correspond to that of the CdSe QDs, rather, it is an effective permittivity. However, by using an effective medium model, such as the one of MaxwellGarnett,36 it is possible to estimate the permittivity of CdSe © 2010 American Chemical Society
ESP(θ) + EX ( 2
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typically resulting in Rabi splittings of the order of a few hundred microelectron volts.5 For individual colloidal CdSe nanorods41 coupled to microsphere resonators, this splitting was found to be between 30 and 40 µeV at 15 K. In the experiments just described, the number of QDs that interact with the SPs is much larger than 1, consequently leading to larger Rabi splittings. Furthermore, in the present case the light-matter coupling is mediated by SPs, collective surface-charge motion that produce large local fields per photon and the SP-exciton coupling occurs via absorption of the electromagnetic field by the exciton transition, a process that has a higher oscillator strength than the one associated with PL.42 The demonstration of room temperature strong coupling involving SPs and colloidal QDs has important practical consequences, partly from the versatility of colloidal QDs (high photostability and ease of fabrication and manipulation) but also because it provides a fundamental framework for the optimization of all-optical nonlinear devices,43 thresholdless laser operation,44 single-photon optical transistors,45 and spasers (surface plasmon amplification by stimulated emission),46 applications that rely on optimizing nanoscale light-matter interactions.
FIGURE 4. Experimental dispersion curve. The points originate from the minima in the (experimental) reflectivity curves shown in Figure 3 and are plotted against the external angle of incidence. The horizontal line is the energy of the exciton in CdSe QDs. The green line is the energy of the uncoupled SP, obtained by setting f ) 0 in the model of the CdSe layer of eq 1. The orange lines are the polariton branches obtained from eq 2 with pΩR ) 112 meV. The inset is a plot of the upper-lower polariton branch splitting vs the square root of the absorbance of the exciton feature in CdSe films of different thicknesses. The line is a guide to the eye.
Acknowledgment. We would like to express our gratitude to J. Jasieniak for fruitful discussions and valuable advice, to T. L. Nguyen for assistance with CdSe synthesis, and to B. Sexton for his help with the physical vapor deposition of the Ag films. Supporting Information Available. Plots of experimental dispersion curves. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1) (2) (3) (4) (5) (6)
FIGURE 5. (A) Reflectivity spectra measured for a Ag/CdSe film with nanocrystals of ∼4.3 nm in diameter. The angles of incidence are indicated in the figure. For this CdSe film, the parameters obtained for the Lorentz model of eq 1 are: pΓ ) 0.187 eV, εb1/2 ) 1.89 and f ) 0.07. (B) Normal incidence absorption spectrum of a film of the CdSe nanocrystals. The vertical line indicates the 1S3/2(h)1Se exciton transition. (C) Experimental dispersion curve (dots). The energy position of the reflectivity minima is on the vertical axis and the external angle of incidence on the horizontal one. The green line is the energy of the uncoupled SP, the red line corresponds to the position of the 1S3/2(h)1Se exciton transition, and the orange lines are obtained from a fit to eq 2 with pΩR ∼ 102 meV.
(7) (8) (9) (10) (11)
In the past, experiments aimed at demonstrating strong light-matter interactions with semiconductor QDs have been carried out by resonantly coupling the photoluminescence of single QDs to a single mode of a high-Q microcavity, © 2010 American Chemical Society
(12) (13)
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