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Tunable third-harmonic generation from polaritons in the ultrastrong coupling regime Fabio Barachati, Janos Simon, Yulia Getmanenko, Stephen Barlow, Seth R. Marder, and Stéphane Kéna-Cohen ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b00305 • Publication Date (Web): 11 Aug 2017 Downloaded from http://pubs.acs.org on August 14, 2017
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Tunable third-harmonic generation from polaritons in the ultrastrong coupling regime Fábio Barachati,
∗,†
Janos Simon,
Seth R. Marder,
†Department
∗,‡
∗,‡
Yulia A. Getmanenko,
∗,‡
and Stéphane Kéna-Cohen
Stephen Barlow,
∗, ‡
∗, †
of Engineering Physics, École Polytechnique de Montréal, Montréal H3C 3A7, QC, Canada
‡School
of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, GA 30332-0400, USA
E-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected];
[email protected] Abstract Strong inter-particle interactions between polaritons have traditionally stemmed from their exciton component. In this work, we impart a strong third-order nonlinearity to a polaritonic mode by embedding a nonlinear polymethine dye within a high-Q all-metal microcavity. We demonstrate nonlinear microcavities operating in the ultrastrong coupling regime with a normalized coupling ratio of 62%, the highest reported to date. When pumping the lower polariton branch, we observe tunable third-harmonic generation spanning the entire visible spectrum, with internal conversion enhancements more than three orders of magnitude larger than in bare lms. Transfer matrix calculations indicate that the observed enhancements are consistent with the enhanced pump electric eld. 1
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Keywords Third-harmonic generation, ultrastrong coupling, exciton-polaritons, microcavities, organic semiconductors, cavity QED Semiconductor microcavities are natural platforms for the study of light-matter interaction due to their ability to con ne cavity photons and semiconductor excitons to the same region of space. 1 If their interaction is strong enough, hybrid light-matter states are formed, called upper (UP) and lower (LP) polaritons. 2,3 They are separated in energy by the vacuum Rabi splitting (ΩR ), which is related to the coupling strength. Much of the interest in the strong light-matter coupling regime stems from the broad range of nonlinear phenomena that can be observed using polaritons, such as parametric scattering, ampli cation, bistability, soliton formation and super uidity. 1,4,5 Most of these phenomena have, however, been restricted to inorganic microcavities at low-temperatures. There, the intrinsic nonlinearity responsible for pairwise scattering, similar to an optical χ(3) , is strong due to the delocalized nature of Wannier-Mott excitons. The large binding energy of organic Frenkel excitons can in principle allow for such phenomena to be observed at room-temperature, but the exciton-exciton nonlinearities inherent to Frenkel excitons tend to be much weaker than in inorganics. To date, only a handful of nonlinear processes have been observed using organic polaritons. 611 In the limit where the exciton-photon coupling is increased to a signi cant fraction of the uncoupled exciton energy ( ΩR ∼ EEX ), the system enters the so-called ultrastrong coupling regime (USC). In this regime, the presence of non-negligible antiresonant lightmatter coupling terms leads to modi cations of both excited and ground state properties, a subject which is currently under intense investigation. 1214 Demonstrations of USC in organic microcavities 1517 have triggered many interesting studies about its eects on observable material properties, 1820 with many open questions remaining. In this paper, we demonstrate organic microcavities operating in the USC regime with a Rabi splitting corresponding to a record 62% of the uncoupled exciton energy. We impart a 2
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strong third-order nonlinearity to the resulting polaritons by using a nonlinear polymethine dye as the cavity material and show that the resulting large magnitude of the third-order susceptibility χ(3) contributes to enhancing polariton-polariton interactions via their photonic component. The enhanced polariton-polariton nonlinearity is used to demonstrate tunable thirdharmonic generation (THG) spanning the entire visible spectrum upon resonant excitation of the LP mode. When compared to bare lms, the fabricated microcavities show conversion e ciency enhancements of over two orders of magnitude and even larger internal enhancements. Two advantages of polariton states in the USC regime are that they are characterized by narrow, homogeneously broadened lineshapes and a nearly angle-independent dispersion relation. 16 This allows us to obtain high quality factors (Q) over a broad spectral range and achieve e cient frequency conversion using focused excitation from a high numerical aperture (NA) microscope objective. This structure may also form a versatile platform for the study of other nonlinear phenomena in the USC regime.
Results and Discussion The microcavities are composed of a lm of a bis(selenopyrylium)-terminated heptamethine dye (see Fig. 1). Dyes of this type exhibit extremely large magnitudes of the molecular thirdorder polarizability in solution. 21 The dye used in this study is one of many developed in which bulky substituents on both the chalcogenopyrylium end groups and on the polymethine chain, along with a large counterion, are used to disrupt intermolecular interactions such that the solution linear and nonlinear properties are largely preserved in high chromophore-density lms. 22 To characterize the linear optical properties of the polymethine dye, neat lms were prepared by spin-coating from 5-20 mg/ml dichloromethane solutions. The refractive index obtained using ellipsometry is shown in Fig. 1. The imaginary component shows a strong exciton absorption maximum at 1067 nm ( EEX = 1.162 eV) and a vibronic shoulder. Note
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in particular the low losses in the near-infrared part of the spectrum. 3.0
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Figure 1: Real (blue) and imaginary (red) refractive index of neat polymethine. The imaginary part has a peak value of 1.06 at 1067 nm. Round (triangular) markers indicate the pump (THG) wavelengths where power dependence measurements were performed. The inset shows (top) the chemical structure of the polymethine dye and counterion and (bottom) a schematic of the THG experiment, where a microscope objective is used to focus the pump beam onto the microcavity and to collect the third-harmonic signal from the excitation side. Planar microcavities were fabricated by embedding a neat polymethine layer between silver mirrors. To improve the wetting and optical properties of the back mirror, cleaned quartz substrates were rst functionalized with a monolayer of (3-mercaptopropyl)-trimethoxysilane. 23 Then, a 75 nm-thick silver mirror was grown by thermal evaporation at a base pressure of
∼10−7 mBar. After spin-coating the polymethine lm, the structure was capped with a 35 nm top mirror. All of the measurements were performed at room temperature. Figure 2 (a) shows the measured angle-resolved TM-polarized re ectivity from a 350 nm thick microcavity, which corresponds to nearly zero detuning between the exciton and photon energies at normal incidence. The dashed lines correspond to a least-squares t to the full Hop eld Hamiltonian (see Methods), 16 yielding a Rabi splitting of ΩR = 0.707 eV. A slightly larger value of ΩR = 0.719 eV is obtained for the TE-polarized re ectivity spectrum and the remaining t parameters are summarized in Table 2. These values correspond to 60-62% of the uncoupled exciton energy, slightly exceeding the largest normalized coupling ratio ( ΩR /EEX ) reported to date of 60% in organic micro4
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Figure 2: (a) Angle-dependent TM-polarized re ectivity spectrum of a 350 nm-thick microcavity. The dashed lines show the least-squares t to the full Hop eld Hamiltonian, yielding a Rabi splitting of ΩR = 0.707 eV and a cavity energy at normal incidence of EC = 1.098 eV. The detuning is ∆ = EC − EEX = −64 meV. (b) Measured (red) and calculated (black) TM-polarized 20o re ectivity spectra for regions of dierent thickness present on the same sample, as well as the experimental LP quality factors. The dip below 600 nm is the UP that originates from coupling to the second-order cavity mode. cavities. 17 The large ratio observed is a consequence of the high oscillator strength (f) of the dye and the large number density of molecules (N) resulting from the use of a neat lm, both evidenced by the strong absorption band shown in Fig. 1. From a simple Lorentz oscillator t to the real part of the refractive index in the transparency region, we obtain
N f = 5.59 × 1020 cm−3 for this material. In addition, the use of metallic mirrors instead of dielectric ones leads to a reduced photonic mode volume. These two factors contribute to the increased ΩR . Meanwhile, the near-infrared transition energy leads to a smaller EEX than in previous reports. Note that for larger cavity thicknesses, the coupling ratio can exceed 90% in this structure. We nd that the experimental LP quality factors can exceed 100, which is considerably higher than typical values (below 30) obtained for all-metal microcavities. 15,24,25 This is a consequence of the material's low linear losses and the high re ectivity of silver in the near-infrared part of the spectrum. This is helpful for increasing the e ciency of nonlinear processes or, in some cases, lowering their thresholds. 26,27 Despite the inhomogeneously 5
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broadened absorption of the dye, the LP re ectivity spectra showed Lorentzian lineshapes characteristic of homogeneous broadening, a consequence of the large Rabi splitting compared to the inhomogeneous linewidth. 28 The LP resonance position can be readily tuned via changes in angle of incidence or sample thickness. Our use of high concentration solutions and of a high vapor pressure solvent naturally leads to large-scale thickness gradients (hundreds of microns) over the sample surface. This allows for multiple cavity thicknesses to be probed using a single sample. These can be easily identi ed experimentally due to changes in the surface color caused by the changing position of the UP branch. Figure 2 (b) shows a collection of measured (red) and calculated (black) TM-polarized 20o re ectivity spectra taken at dierent locations. The corresponding sample thicknesses are indicated below the traces. Third-harmonic generation was rst studied by exciting the sample with a broad IR pump spanning 1250-1950 nm. The bottom inset of Fig. 1 shows a schematic of the microcavity and the THG measurement con guration, where a microscope objective is used to focus the pump beam and to collect the third-harmonic signal from the excitation side (see Methods). Figure 3 (a) shows a calculated microcavity re ectivity map, where the spectral positions of the polariton modes are obtained for increasing values of cavity thickness. The rst four polaritonic modes indicated by LP1/UP1 and LP2/UP2 correspond to strong coupling to the rst- and second-order cavity modes, respectively. The broad pump is spectrally ltered by the thickness-dependent LP resonance position, as shown in the top box in Fig. 3 (a). The resonant component is coupled into the microcavity and interacts with the high χ(3) material to generate the third-harmonic signal. The THG wavelengths corresponding to the rst LP branch are shown as a dashed line in the bottom of Fig. 3 (a). Figure 3 (b) shows a series of normalized THG spectra taken by laterally translating the sample and illustrates the tunability of the THG process at normal incidence. Note that the third-harmonic is not resonant with higher order modes and only light that can leak out due to the nite transmission of the mirrors is observed. Nevertheless, the generated harmonic signals were
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Figure 3: (a) Calculated microcavity re ectivity spectra at normal incidence for increasing values of polymethine thickness. The four polaritonic modes indicated by LP1/UP1 and LP2/UP2 arise due to the strong coupling of the exciton transition to the rst- and secondorder cavity modes, respectively. The top box indicates the range of LP spectral positions covered by the broad infrared pump (1250-1950 nm). The corresponding third-harmonic wavelengths are indicated by a dashed line. (b) Experimental normalized THG spectra obtained by laterally translating the same microcavity sample. easily visible with the naked eye through the microscope optics. To investigate the THG power dependence as a function of wavelength, the broad IR pump was spectrally ltered using 12 nm bandpass lters, which is slightly narrower than the mean LP linewidth of 14 nm obtained from Fig. 2 (b). The pump and corresponding THG wavelengths are indicated in Fig. 1 by round and triangular markers, respectively. Figure 4 shows the results obtained for the fabricated microcavities (curves 1-3). We observe a doubling of the conversion e ciency when changing from 1320 nm to 1650 nm excitation. This corresponds to an increased THG e ciency for polaritonic modes that are more photonic in nature, as highlighted in Fig. 5 (a). When pumping at 1320 nm, which corresponds to modes with a strong exciton component, we observed a fast irreversible decay of the THG signal due to sample damage a clear signature of the mode matter content. Note, in contrast, that the linear absorption of the bare lm is negligible at this wavelength. For longer wavelengths, no decrease in THG powers was observed for up to an hour of measurement. The values at the end of each curve correspond to the peak power conversion e ciencies, 7
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1 - Cavity (410 nm): 1650 nm 2 - Cavity (376 nm): 1550 nm 3 - Cavity (285 nm): 1320 nm 4 - Film (70 nm): 1650 nm 5 - Film (368 nm): 1650 nm
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Figure 4: Measured third-harmonic powers (squares) as a function of pump power. Red, black and blue data sets correspond to microcavities pumped at 1650 nm, 1550 nm and 1320 nm, respectively. Bare polymethine lms of 70 nm and 368 nm were investigated at 1650 nm and the results are shown in purple and green, respectively. The solid lines indicate a cubic power t to each data set. The values at the end of each curve correspond to their peak conversion e ciencies, de ned as P3ω /Pω . The top (bottom) gray boxes indicate the range of calculated THG powers on the excitation side for the microcavity (bare lms) shown in Fig. 5. The pump spot had a FWHM of 1.5 µm. de ned as P3ω /Pω . In all cases, the THG wavelength was not resonant with the higher order upper polariton modes and was not e ciently extracted from the microcavity. Nonetheless, the experimental conversion e ciencies for the microcavities were comparable to those of other systems that required patterning or considerably thicker lms. 2931 For comparison, THG from bare polymethine lms of dierent thicknesses are shown in Fig. 4 (curves 4-5). The 368 nm-thick lm (curve 5) is of comparable thickness to the microcavities and allows for an accurate estimate of the conversion enhancements. Table 1 shows the t coe cients C obtained by tting each data set with a cubic power dependence of the form P3ω = C × Pω 3 . The last column shows the conversion enhancements with respect to the 368 nm-thick lm. At the wavelength of highest conversion e ciency (1650 nm), the fabricated microcavities show raw (external) THG enhancement factors of 108±1.7 compared to the bare lm. As shown in Fig. 5 (a), the internal e ciency at this wavelength is approximately 50 times higher than this value due to the low fraction of THG that is out-coupled from the cavity. 8
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Table 1: Experimental cubic t coe cients for data sets 1-5 shown in Fig. 4 and the THG conversion enhancement with respect to the 368 nm-thick bare lm. # 1 2 3 4 5
C (254.2 ± 2.1) × 10−4 (142.9 ± 2.7) × 10−4 (119.7 ± 2.7) × 10−4 (195.8 ± 7.4) × 10−7 (235.4 ± 3.2) × 10−6
THG Enhancement 108.0 ± 1.7 60.7 ± 1.4 50.6 ± 1.3
Simulations To correlate our results with the LP exciton and photon fractions at normal incidence, Fig. 5 (a) shows the polariton modal content calculated using the full Hop eld Hamiltonian from experimental (circles) and simulated (squares) angle-resolved re ectivity spectra. Note that in the USC regime, the contribution from the squared electromagnetic vector potential leads to a blueshift of the bare cavity photon energy and that the modal content of both components is no longer equal at zero detuning, which corresponds to 1432 nm in Fig. 5 (a). 12 We nd that the LP branch varies from 73% to 52% exciton content over the range of thicknesses used in Fig. 4 (indicated by colored arrows). To determine the origin of the enhancement, THG was investigated using a modi ed transfer matrix approach, which includes nonlinear source terms. 3234 In this way, the combined eects of multiple re ections and absorption at both the fundamental and thirdharmonic wavelengths are automatically taken into account, as well as the resonant pump enhancement and non-resonant THG extraction factors. Figure 5 (b) shows a map of the calculated THG powers for the fabricated microcavities as a function of cavity thickness and pump wavelength for an average input power of 1 mW. As expected, the THG map resembles the re ectivity map shown in the boxed region of Fig. 3 (a) because THG is only generated when the pump is resonant with the LP branch. The colored arrows indicate the experimental conditions of cavity/ lm thickness and pump wavelength for the measurements in Fig. 4. The top gray box in Fig. 4 shows the range
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Figure 5: (a) Calculated exciton (red) and photon (blue) fractions for the rst LP branch from experimental (circles) and simulated (squares) re ectivity data. The solid black curves show the calculated THG irradiances inside the cavity (top) and outside on the excitation side (bottom). (b) Calculated third-harmonic powers radiated towards the excitation side as a function of microcavity thickness and pump wavelength for an average input power of 1 mW. THG is obtained when the pump is resonant with the LP mode, maintaining the same shape as in the boxed region in Fig. 3. Inset: same calculation for a thin lm on quartz pumped at 1650 nm. For the calculations, χ(3) = −5.1 × 10−11 esu (−7.12 × 10−19 m2 /V2 ), THG and pump spots with a FWHM of 1.5 µm were used. The colored arrows in a,b indicate the experimental conditions for the measurements in Fig. 4. of calculated THG powers emitted towards the excitation side for the microcavities. The quantitative agreement with the experimental values is remarkable, considering that the only parameter not known with certainty is the third-order susceptibility χ(3) (3ω; ω, ω, ω), which was kept dispersionless and equal to the value χ(3) (ω; −ω, ω, ω) measured using the z-scan technique. 22 A similar calculation for the bare lms pumped at 1650 nm is shown in the inset of Fig. 5 (b) and was found to be less accurate for the 368 nm-thick lm, with the experimental value closer to the transmitted THG power (not shown) instead of the one measured on the excitation side. The bottom gray box in Fig. 4 shows the range of calculated THG powers for the bare lms. We believe that the discrepancy stems from the large angular spread of wavevectors in the focussed pump beam, which is not taken into account in our calculations. For microcavities, wavevectors away from the resonance condition are naturally ltered out
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by the LP dispersion. The agreement for the thinner lm and microcavities con rm that the value of χ(3) used in the calculations is a reasonable estimate for the real one. Therefore, even when neglecting possible resonant enhancements of χ(3) due to the weak absorption bands in the visible part of the spectrum, the observed enhancements in THG from polaritons are consistent with the cavity enhancement of the pump electric eld and the bulk third-order nonlinearity, as opposed to a drastic modi cation of the material's nonlinear properties. 35 At the same time, in the equivalent polaritonic picture, the THG enhancement stems from the three resonantly pumped polaritons with increased nonlinear interactions. Still, compared to bare lms, microcavities oer the advantage that they require smaller thicknesses to generate the same harmonic power. This is a consequence of the pump electric eld enhancement, the reduced absorption of the generated signal and the absence of a phase-matching requirement, with the conversion e ciency depending instead on mode overlap, which can be tuned by microcavity design or by the use of polaritonic modes. 34,36 Fig. 5 (a) also shows the calculated peak THG irradiances inside the cavity as compared to the THG emitted on the excitation side. Both curves signi cantly decrease towards shorter wavelengths because of the absorption band peaked at 1067 nm. The internal THG rst increases towards longer wavelengths as losses in the mirrors are reduced for thicker cavities. The decreasing transmission of the front silver mirror towards longer wavelengths eventually leads to a decrease in both the internal and external components, the latter already visible in Fig. 5 (a). For this range of wavelengths, the internal THG enhancements are up to 56 times higher than the ones observed from the excitation side. Further calculations show that small modi cations of the structure to improve out-coupling, such as reducing the top mirror thickness or achieving a doubly-resonant condition of the THG wavelength with an UP branch can further increase the THG e ciency by more than an order of magnitude.
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Conclusions We have fabricated organic microcavities containing a nonlinear dye operating in the USC regime and possessing a normalized coupling ratio of 62%, slightly exceeding the highest value ever reported. 17 The combination of the material's low losses and the use of high re ectivity silver mirrors led to LP quality factors much higher than conventional all-metal microcavities. The polariton nonlineariy was exploited to demonstrate e cient and tunable third-harmonic generation when the cavity was excited resonantly with the LP branch. Although the THG was not resonantly extracted from the microcavities, conversion enhancement factors of up to two orders of magnitude were obtained in comparison to bare lms. Transfer matrix calculations indicate that the observed enhancement can be explained by the pump eld enhancement alone, suggesting that the material's third-order susceptibility is not strongly modi ed even in the case of ultrastrong light-matter coupling. This demonstration of nonlinear polariton microcavities operating in the USC regime can allow for the observation of room-temperature nonlinear eects so far restricted to low-temperature inorganic systems, in addition to to new phenomena unique to the USC regime.
Methods Linear optical characterization.
A variable-angle ellipsometer (J. A. Woollam Co., RC2
D+NIR) was used to obtain the thicknesses and optical constants of the neat polymethine lms, the silver mirrors and the quartz substrate. Angle-resolved re ectivity measurements were performed using the same instrument with the help of focusing probes.
Fitting of the re ectivity data.
The experimental Rabi splitting and mixing coe -
cients were extracted from the angle-resolved re ectivity data by performing a least-squares t to the eigenvalue equation
Hˆq~v j,q = ωj,q~v j,q . 12
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Hˆq is the full Hop eld Hamiltonian given by
2D V Eph (q) + 2D V V E V 0 EX Hˆq = , −2D −V −Eph (q) − 2D −V −V 0 −V −EEX
(2)
where q = (ω/c) sin θ is the in-plane wavevector, θ is the angle of incidence, V = ΩR /2 is the interaction energy and D = V 2 /EEX is the energy contribution of the squared electromagnetic vector potential. 12,16 The eigenvectors ~v j,q = (wj,q , xj,q , yj,q , zj,q )T are obtained from the polariton annihilation operators
pj,q = wj,q aq + xj,q bq + yj,q a†−q + zj,q b†−q ,
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where j ∈ {LP, U P } and a, b are photon and exciton annihilation operators, respectively. They provide the Hop eld coe cients for the photon ( |wj,q |2 ) and exciton (|xj,q |2 ) fractions as well as the anomalous coe cients ( |yj,q |2 , |zj,q |2 ) which only become comparable to the rst ones when ΩR ∼ EEX . The eigenvalues ωj,q = {±ωLP,q , ±ωU P,q } correspond to the polariton energies to be matched with the re ectivity minima. The t parameters were the interaction energy V , the normal-incidence cavity energy EC and the cavity's eective refractive index nef f , the last two being related by
s Eph (q) =
h ¯ cq nef f
2 + EC2 .
(4)
The t parameters obtained for the TE- and TM-polarized spectra are summarized in Table 2. We note that the dierent eective refractive indices obtained for TE and TM polarizations are not a consequence of anisotropy in the organic lm, but of the polarizationdependent penetration depth of the electric eld into the metallic mirrors. 16
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Table 2: Full Hop eld Hamiltonian t parameters obtained for the re ectivity data of a 350 nm cavity. Pol. TE TM
ΩR (eV) nef f 0.719 ± 0.004 1.57 ± 0.04 0.707 ± 0.002 1.83 ± 0.04
Nonlinear optical characterization.
EC (eV) 1.09 ± 0.01 1.10 ± 0.01
Third-harmonic measurements were performed
from the excitation side using an Olympus IX-81 inverted microscope. The samples were mounted facing an Olympus LUCPlanFl 40 × 0.6 NA objective with the correction collar set to zero. A supercontinuum laser (Fianium FemtoPower 1060, 40 MHz) was used as the infrared light source. The pulse duration was measured with a streak camera (Hamamatsu C10910) and found to be 48 ps. A dierent set of excitation (EX), beam splitter (BS) and detection (DET) lters was used for each fundamental wavelength. All lters were purchased from Thorlabs unless indicated otherwise. 1320 nm: (EX) LP1250, BP1320-12, SP1500 (Edmund Optics), 1 cm quartz cuvette with toluene; (BS) BSW29R; (DET) SP950, BP430-20 (Chroma), 1 cm quartz cuvette with water. 1550 nm: (EX) LP1250, LP1500, BP1550-12, 1 cm quartz cuvette with toluene; (BS) BSW29R; (DET) SP1500. 1650 nm: (EX) LP1250, LP1500, BP1650-12; (BS) FF538-FDi01 (Semrock); (DET) 1 cm cuvette with toluene. The transmission of all detection lters was measured and used to calibrate the measured powers. The third-harmonic powers were measured with a cooled CCD camera (Princeton Instruments, PIXIS 400B eXcelon). The calibration procedure was performed with a 532 nm laser (supercontinuum followed by BP532-3, SP700, SP1500, 1 cm cuvette with toluene). The laser was focused on a 75-nm thick silver mirror and the re ected light was measured at the side-port of the microscope with a power meter (Thorlabs, S120VC/PM100D). Neutraldensity lters with measured transmission values at 532 nm were inserted in the excitation path so that the powers at the side-port of the microscope could be adjusted in the range of
10−13 − 10−10 W. For each power value, a series of images was acquired with the CCD camera and the 14
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corresponding integrated counts on two adjacent 30 ×30 pixel regions were obtained, the rst one including the laser spot and the second one only background light. The procedure was repeated for dierent integration times and the detector response was obtained by tting the background-corrected counts over the known input power to a fourth-degree polynomial in integration time. The CCD quantum e ciency is taken to remain constant in the range of THG wavelengths from 440 nm to 550 nm. The collection e ciency of the objective from the excitation side based on the detection solid angle was estimated to be η = 1 − cos sin−1 (N A) = 0.2. This value only aects absolute powers, but not the enhancement factors.
Acknowledgement The authors thank Johannes Feist and Simone de Liberato for helpful comments on this manuscript. FB and SKC acknowledge support from the Natural Sciences and Engineering Research Council of Canada Discovery Grant Program, the Canada Research Chair in Hybrid and Molecular Photonics and the FQRNT PBEEE scholarship program. Work at GT was supported by the Air Force O ce of Scienti c Research through the COMAS MURI program (agreement no. FA9550-10-1-0558).
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