Toward Cavity Quantum Electrodynamics with Hybrid Photon Gap

Toward Cavity Quantum Electrodynamics with Hybrid Photon Gap-Plasmon States Francesco Todisco,†,‡,∥ Marco Esposito,*,†,‡,∥ Simone Panaro,§ Milena De Giorgi,*,† Lorenzo Dominici,† Dario Ballarini,† Antonio I. Fernández-Domínguez,⊥ Vittorianna Tasco,† Massimo Cuscunà,† Adriana Passaseo,† Cristian Ciracì,§ Giuseppe Gigli,‡,† and Daniele Sanvitto† †

CNR NANOTEC Istituto di Nanotecnologia, c/o Campus Ecotekne Via Monteroni Lecce, Lecce 73100, Italy Dipartimento di Matematica e Fisica “Ennio De Giorgi” Strada Provinciale Lecce-Monteroni, Universitá del Salento, Campus Ecotekne, Lecce 73100, Italy § Center for Biomolecular Nanotechnologies@UNILE, Istituto Italiano di Tecnologia, Via Barsanti, Arnesano 73010, Italy ⊥ Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid Calle Francisco Tomás y Valiente, 7 Madrid E-28049, Spain ‡

S Supporting Information *

ABSTRACT: Combining localized surface plasmons (LSPs) and diffractive surface waves (DSWs) in metallic nanoparticle gratings leads to the emergence of collective hybrid plasmonic−photonic modes known as surface lattice resonances (SLRs). These show reduced losses and therefore a higher Q factor with respect to pure LSPs, at the price of larger volumes. Thus, they can constitute a flexible and efficient platform for light−matter interaction. However, it remains an open question if there is, in terms of the Q/V ratio, a sizable gain with respect to the uncoupled LSPs or DSWs. This is a fundamental point to shed light upon if such modes want to be exploited, for instance, for cavity quantum electrodynamic effects. Here, using aluminum nanoparticle square gratings with unit cells consisting of narrow-gap disk dimersa geometry featuring a very small modal volumewe demonstrate that an enhancement of the Q/V ratio with respect to the pure LSP and DSW is obtained for SLRs with a well-defined degree of plasmon hybridization. Simultaneously, we report a 5× increase of the Q/V ratio for the gap-coupled LSP with respect to that of the single nanoparticle. These outcomes are experimentally probed against the Rabi splitting, resulting from the coupling between the SLR and a J-aggregated molecular dye, showing an increase of 80% with respect to the DSW-like SLR sustained by the disk LSP of the dimer. The results of this work open the way toward more efficient applications for the exploitation of excitonic nonlinearities in hybrid plasmonic platforms. KEYWORDS: plasmon, plasmon-exciton-polaritons, surface lattice resonance, aluminum, plasmonic crystals, plexciton the optical field in subdiffraction-limited distances, leading to extremely high EM field enhancement. For this reason, the strong coupling of LSPs with excitons in organic3,4 and inorganic5,6 semiconductor materials has recently gained tremendous interest motivated by the possibility of combining the field concentration with the strong local amplification7,8 featured by LSP modes. Shape, size, and material composition of nanostructures represent the fundamental degree of freedom to mold LSP spectral profiles, including their energy position and radiative and nonradiative losses.9

n the field of cavity quantum electrodynamics (cQED),1 much interest has been devoted to the quest for high finesse resonators with ultrasmall modal volumes that could allow for many fascinating strong light−matter coupling phenomena. In fact, all cQED effects that derive from the full control of the emission of a dipole source via an optical mode, which ultimately can lead to a Mott-insulator transition for strongly interacting photons,2 can only be possible in systems where the electromagnetic (EM) field is highly enhanced while keeping its volume to a minimum. A general parameter that defines such conditions is usually given by the ratio between the mode quality factor and its effective volume (Q/V). Unlike photonic cavities, for which the modal volume is always of the order of λ3, localized surface plasmons (LSPs) sustained by metallic nanostructures can confine evanescently

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© 2016 American Chemical Society

Received: September 30, 2016 Accepted: December 1, 2016 Published: December 1, 2016 11360

DOI: 10.1021/acsnano.6b06611 ACS Nano 2016, 10, 11360−11368

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RESULTS AND DISCUSSION Our samples consist in square arrays of 70 × 70 aluminum ND dimers (100 nm ND diameter, 40 nm height and 20 nm gap) realized on a glass substrate by electron beam lithography, with lattice period a, ranging from 275 to 590 nm. In the past few years, the choice of aluminum rather than standard plasmonic materials, such as silver and gold, is spreading. This is motivated by its attractive properties, including low cost and high frequency plasmon resonances. Moreover, aluminum suffers from fewer interband losses than gold in the visible range, and it is more stable than silver against oxidation at ambient conditions.32 These features can be fundamental in terms of the quality factor of the related LSP resonances. Compared to silver dimer-based arrays considered in previous works,33,34 the narrow geometrical gap in our samples promotes an efficient near-field coupling within the dimer, even maintaining the system in a local, classical theory frame, far from the quantum regime that arise for subnanometer gaps.35 Under these conditions, the ND coupling still results in a strong hybridization of the modes of the two isolated nanoparticles and a consequent high EM field enhancement inside the gap. Moreover, the use of aluminum ensures a low cost solution for UV/vis spectral range applications and a better stability against oxidation32,36 compared to silver,37 thus offering a robust optical platform for the study of light-matter coupling and for high energy applications. From now on, we indicate as x the direction along the long dimer axis and y its perpendicular in-plane direction, as shown in Figure 1. A refractive index matching oil (Olympus, n = 1.515) and a coverslip were used to ensure the optical homogeneity of the environment surrounding the nanostructures. The plasmonic lattices were characterized by far-field transmission spectra on a homemade confocal setup, whose

However, the promise of plasmonics to shrink optical energy below the diffraction limit needs to face the low quality factor inherent to LSP resonances. This originates from metallic interband absorption losses which limit the exploitation of LSP to only certain applications such as nanolasers,10 plasmonic nanocircuits,11 and sensing,12,13 leaving the regime of plasmonic cQED yet to be reached. Although some recent experiments have reported far-field signatures of strong coupling between a LSP and a single emitter in specific systems,14,15 any nonlinearity at the single particle level has so far only been theoretically proposed.16 A good strategy to maximize the plasmonic Q/V ratio could be the hybridization of LSPs with high Q factor optical modes, such as the optical diffractive surface waves (DSWs) supported by periodic arrays of metallic nanostructures.17 In these periodic systems, in fact, it is always possible to find the proper unit cell size (interelement distance) for which the DSWs are at resonance with the LSP of the isolated unit cell. Under these conditions, a normal mode splitting arises and a hybrid mode, the so-called surface lattice resonance (SLR), emerges.18 SLRs are characterized by extremely high quality factors (compared to those typical in LSPs),19,20 therefore improving the performance of isolated nanoparticles through a strong suppression of absorption losses. Recently, strong coupling effects between SLRs and a molecular dipole have been demonstrated in arrays of monolithic disk6,21 and rod22 nanostructures coupled with organic molecules. In these platforms, interesting physical effects have been observed due to plasmon−photon−exciton coupling, like spatial coherence23 and lasing.24−27 Such coupling, which gives origin to a new quasi-particle called plasmon−exciton polariton (PEP), could lead to strong nonlinear effects driven by the excitonic component when combined with high EM field enhancement in ultrasmall modal volumes. However, it is still debatable if the SLR modes have any advantage in terms of Q/V with respect to the LSP of isolated nanoparticles. In this paper, we study the generation of SLRs in narrow-gap aluminum nanodisk (ND) dimer arrays. Because of their ultrasmall LSP volume and high EM field enhancement, capacitive gap dimer nanostructures have been widely studied in literature,28 either with coupled nanodisk,29 bow-tie,15,30 or nanoparticle-on-mirror8,14,31 geometries. These systems are characterized by two orthogonal LSPs: a low-energy gap-mode polarized parallel to the dimer axis and a high-energy singleparticle-mode along the normal direction. Given their energy detuning, these LSPs result in the generation of SLRs with different plasmonic/photonic character, thus offering the possibility to simultaneously explore the physics of the system at different degrees of plasmon−photon hybridization. Through experimental measurements and numerical (finite element) simulations we demonstrate that SLRs can show high quality factors while maintaining moderate low mode volumes when the gap-LSP is excited, yielding a Q/V factor up to 5 times larger than that of single nanoparticle LSPs. This effect can be exploited in boosting the light−matter interaction with excitonic dipoles. Indeed, by strongly coupling a J-aggregated molecular dye to both SLR polarizations, we show an 80% increase of the Rabi splitting for the higher Q/V gap-coupled SLR mode with respect to the ND-coupled SLR, indicating that this system can be considered as a good candidate for efficient light-matter interactions and future cQED applications.

Figure 1. Sketch of the experimental setup. White light from a tungsten lamp is focused on the sample by means of a condenser lens with variable numerical aperture and is detected with a 40× (0.95 NA) objective lens. Transmitted light is collected by lens L1, collimated by lens L2, and focused by lens L3. Adjustable squared slits placed in the L1 focal plane are used to select the lattice area. The lens’ mutual positions are such that, by removing lens L2, the image of the back focal plane of the objective is recreated on the monochromator slits, thus enabling direct Fourier space imaging. In the inset, an SEM image of the dimers is shown (scale bar 500 nm) together with the relative axes. The black lines are a guide for the eye to highlight the square lattice with period a. 11361


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Figure 2. Energy−momentum extinction maps E(ky,kx = 0) for lattice periods of 300 nm (a, d), 405 nm (b, e), and 510 nm (c, f), for polarization directions parallel (a, b, c) and perpendicular (d, e, f) to the dimer gap, as indicated by the red and blue arrows in the sketches. The dispersion of the DSWs (indicated by black lines) were calculated from eq 1 for the indicated (Nx,Ny) indices. The colors render the measured extinction in linear scale from minimum (black) to maximum (white), as shown in the color legend.

polarization parallel (Px) and normal (Py) to the disk dimer axis. For Px polarization, Figure 2a shows the linear dispersion of the (0, ± 1) DSWs as a function of ky, while in Figure 2b,c, higher order modes (±1, ± 1), (0, ± 2), and (±1, ± 2) appear. When the detected polarization is switched to Py, the (0, ± 1) and (0, ± 2) DSWs are almost completely extinguished, and the parabolic degenerate (±1,0) modes emerge, as shown in Figure 2d−f. On the contrary, due to their symmetric properties, the (±1, ± 1), and (±1, ± 2) modes remain clearly visible in the maps. This situation is reversed when the kx component is analyzed by rotating the sample 90° within the xy plane (see the Supporting Information). For the Px polarization, an extinction flat band due to the gap LSP can be observed at 2.4 eV, clearly bending at the (0, ± 1) DSWs energy. While the diffraction dip remains, the DSW bends, merging with the LSP band. This effect is clearly apparent in Figure 2a,b for the (0, ± 1) modes and to a lesser extent also in Figure 2c for the (0, ± 1) and the (±1, ± 1) modes. However, by rotating the detected polarization to Py (Figure 2d−f), the signature of the LSPs, supported by the single NDs, blueshifts at energies higher than 3 eV, resulting in an almost purely photonic SLR (basically coinciding with the unperturbed DSW). A comprehensive picture of the effect of the lattice periodicity on the optical spectra is shown in Figure 3a,b, where the extinction at normal incidence (kx = ky = 0) is plot as 2π a function of the lattice wavevector kL = a for Px and Py polarization, respectively. The spectra were extracted from the far-field maps at the central pixel, corresponding to an incident light angular divergence of less than ±0.1°. When light is polarized along the x-axis (Figure 3a), the gap LSP appears as a broad resonance near 2.4 eV (indicated by a short dash line), while the uncoupled DSWs, characterized by a linear dispersion (long dash lines), are given by

scheme is sketched in Figure 1. The far-field transmission spectra were normalized to the light transmitted through the bare substrate, taken from an area without nanostructures. The optical behavior of the system was resolved both in polarization, by rotating a broadband linear polarizer in the detection optical path, and in the in-plane wavevector component kx and ky, by rotating the sample itself. The dispersion of a generic array, observed in transmission, is defined by the interference between the DSWs, propagating grazing on the surface, and the transmitted light. While the latter results in a dip in the extinction maps (i.e., a transmission peak), the former gives rise to an enhanced extinction line. As a consequence, if no LSPs are present (at a given operating frequency), the extinction spectrum would result in an asymmetrical Fano-like form typical of periodic gratings.38 On the other hand, when the DSW is resonant with the LSPs sustained by the unit cell metallic nanostructure, the strong coherent coupling leads to a mode splitting and the formation of hybrid SLRs which departs from the energy of the diffracted light. The generic expression for the momentum-energy dispersion of the DSWs can be written as

E DSW

2 ⎛ ⎞2 ℏc ⎛ π 2π ⎞ 2 = ⎜kx + Nx ⎟ + ⎜⎜k y + Ny ⎟⎟ n ⎝ ax ⎠ ay ⎠ ⎝

(1)

where n is the refractive index of the homogeneous environment surrounding the array, kx and ky are the k-vector components of the incident light, ax = ay = a is the square lattice period, and Nx, Ny identify the diffraction orders in the xy basis. As the lattice constant, a, increases, the energy of the (Nx,Ny) DSWs available for excitation by the incident light decreases, and higher order modes gradually appear in the extinction maps at a given energy. In order to gain insight into the characteristics of the DSWs in our samples, we plot in Figure 2 the measured extinction farfield maps as a function of ky (at kx = 0) for three different lattice periods (300, 405, 510 nm) for incident light

E DSW (kx = k y = 0) = 11362

ℏc kL Nx 2 + Ny 2 n

(2)


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234 ± 44 meV between LSP and (1,0), (1,1), and (2,0) DSWs, respectively. The coupled dispersion branches are shown in solid lines in Figure 3a. On the contrary, in the Py case no anticrossing is visible in the maps for the considered energy range, and the coupling coefficients cannot be extracted. The properties of this hybrid plasmonic−photonic lattice can be exploited as an efficient optical platform for the study of light−matter interaction with organic excitonic dipoles, with the useful possibility of controlling the plasmonic contribution to the hybrid SLRs by independently exciting the two distinct LSPs of the dimers. For this purpose, a 40 nm thick layer of a cyanine dye (TDBC, 5,5′,6,6′-tetrachloro-1,1′-diethyl-3,3′-di(4sulfobutyl)benzimidazolocarbocyanine) was spin coated on the sample. This dye forms J-aggregates in the solid state, with a sharp J-band at 2.11 eV (see the Supporting Information). The optical transmission is always normalized to the light transmitted through the bare substrate, without spin-coated molecules. Parts a and b of Figure 4 show the far-field extinction maps for a 405 nm lattice period (kL = 0.0155 rad/ nm). To facilitate the comparison, we plot the maps as a

Figure 3. Normalized extinction maps as a function of the lattice wavevector for (a) Px and (b) Py polarization. The long dashed lines indicate the uncoupled DSWs, the short dashed line indicates the localized plasmon mode, and the solid lines plot the fitting of the experimental peaks through the four coupled-oscillator model given by eq 3.

. As the DSWs approach the LSP energy, a clear band anticrossing appears in the map, which proves the formation of the SLR. In particular, for dense arrays (small a, large kL values), the mixed SLRs take on a more plasmonic character while for sparse arrays (large a, small kL) the SLRs assume a predominant photonic behavior. On the other hand, in the case of perpendicular polarization (Py, Figure 3b), the plasmonic mode of the dimer blue-shifts at energies higher than 3 eV and the SLRs recover the dispersion of pure DSWs. In order to explore the hybridization between LSPs and diffractive waves under Px illumination, the experimental extinction peaks position were extracted by fitting a Gaussian profile. The result of this procedure is shown by the black dots in Figure 3a,b. Using a four coupled-oscillator model, characterized by the following Hamiltonian ⎛ E LSP gLSP − (1,0) gLSP − (1,1) gLSP − (2,0) ⎞ ⎜ ⎟ ⎜g ⎟ E ( k ) 0 0 ⎜ LSP − (1,0) (1,0) L ⎟ Ĥ = ⎜ ⎟ 0 E(1,1)(kL) 0 ⎜ gLSP − (1,1) ⎟ ⎜⎜ ⎟ 0 0 E(2,0)(kL)⎟⎠ ⎝ gLSP − (2,0)

(3)

we can extract the interaction strength between the LSPs and the lowest DSWs. The diagonal entries represent the LSP (ELSP) and DSWs (E(Nx,Ny)) energies, while the off-diagonal entries, g, describe their couplings. Neglecting loss and detuning effects, these amount to half the Rabi splitting ΩR between the corresponding modes. The coupling coefficients between DSWs of different order have been set to zero, while the plasmon energy and the coupling coefficients have been used as fitting parameters. Through the diagonalization of the Hamiltonian in eq 3, a LSP energy of 2.44 ± 0.01 eV has been extracted for Px polarization, while the obtained coupling strengths yielded Rabi splittings of 478 ± 14, 324 ± 16, and

Figure 4. Hybrid SLR−exciton system. (a, b) Far-field maps for (a) Px and (b) Py polarization as a function of ky and kx, respectively. (c, d) Normalized extinction maps at normal incidence as a function of lattice wave-vector for both polarizations. The experimental peak positions are fitted with a five coupled oscillators model. The colors render the measured extinction in a nonlinear scale from minimum (black) to maximum (white), as shown in the color legend. In the insets, the near-field distributions of the electric field are shown in log scale, corresponding to the points circled in the map. 11363


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ACS Nano function of ky (kx) for Px (Py) polarization. For Px-polarized light, a strong bending of the modes manifests at high k-vectors (Figure 4a) as a consequence of the strong SLR-exciton coupling. On the other hand, for Py polarization (Figure 4b), the LSP of the single disks are out of resonance with both the exciton absorption and the DSW in that energy range, giving origin to a strongly coupled exciton-DSW. To better visualize and quantitatively analyze the excitonic coupling to each photonic−plasmonic mode, in Figure 4c,d we extract the extinction spectra for normal incidence condition as a function of the lattice wavevector. The extinction peaks (except for that of the uncoupled TDBC molecules) have been fitted by multiple Gaussian peaks and are shown as scatter dots. For Px (Figure 4c), four branches arise as a result of the strong coupling between SLRs and the TDBC exciton. On the contrary, for Py polarization (Figure 4d), only two branches with a typical anticrossing behavior can be distinguished, corresponding to the coupling between the first order SLR (mainly pure DSW-like) and the excitonic transition. Similar to the bare array, the TDBC-interacting system can be described, in the most general case, with a five-coupled oscillator model, characterized by the Hamiltonian ⎛ E LSP gLSP − (1,0) gLSP − (1,1) gLSP − (2,0) ⎜ ⎜g 0 0 E(1,0)(kL) ⎜ LSP − (1,0) ⎜ 0 0 E(1,1)(kL) Ĥ = ⎜ gLSP − (1,1) ⎜ 0 0 E(2,0)(kL) ⎜ gLSP − (2,0) ⎜ ⎜g ⎝ LSP − TDBC g(1,0) − TDBC g(1,1) − TDBC g(2,0) − TDBC

= 30 meV, respectively, ensuring that the conditions for the energy transfer regime are fulfilled. In this case, Rabi splitting occurs when ℏΩR > (γLSP−γexc)/2, which is satisfied in our case, taking γLSP = 300 meV for Px polarization. The splittings obtained are coherent with previous reports, either on silver,37,40 gold,29 and aluminum41 nanostructures and in both isolated and arrays of nanoparticles interacting with molecular dyes. In particular, the difference observed here between the two SLR polarizations reveals the significant effect that the LSP and DSW have on the strong coupling interactions with the molecular dye. This, in fact, results in an 80% increment of the Rabi splitting when both the gap-plasmon and the lattice resonance participate in the excitonic coupling. In order to shed light on the behavior in the near-field regime, we performed numerical simulations of the EM response of the dimer array employing a finite element method based on commercial software (Comsol Multiphysics). Single aluminum dimers (100 nm diameter, 40 nm height, 20 nm gap) with periodic boundary conditions along the xy plane were considered in a homogeneous medium with constant refractive index n = 1.515. Both the bare and the TDBC-coupled cases have been studied, with the latter simulated by embedding the dimer arrays in a 40 nm thick layer of molecules, modeled through a Lorentzian homogeneous permittivity, describing the dye absorption band. The system was illuminated by a plane wave impinging normally with respect to the substrate plane, and the two orthogonal light polarization configurations were considered, Px and Py. A 3 nm thick native oxide layer was considered around the nanoparticles32 with permittivity of both the aluminum and the Al2O3 taken from literature.42 For a direct comparison with the experimental maps, the extinction of the arrays was computed, defined as 1 − T, with T corresponding to the transmittance of the array normalized to unity. A very good agreement between experimental and simulated extinction maps was obtained, as numerical calculations reproduced all of the spectral features faithfully (see the Supporting Information). The modal volumes of the hybrid SLR-exciton system for both incident polarizations, Px and Py, are shown in the insets of Figure 4c,d. For Px polarized light, a strong field localization is observed in the gap region, while for Py polarization the system manifests a more delocalized and less intense field distribution, thus explaining the measured increase in the Rabi splitting. A similar polarization-dependent behavior has been reported for individual gold ND dimers, with the peak splitting disappearing for the transverse plasmonic mode because of a weaker plasmon-exciton coupling.29 Here, on the contrary, strong coupling with different Rabi splittings is observed for the two orthogonal polarizations of the SLR mode, suggesting an active effect of the hybrid mode volume and LSP−DSW fractions to the strong coupling regime. A more quantitative insight into the physics of the coupled system can be gained by evaluating the theoretical modal volume associated with the first-order SLRs as a function of kL. A definition of modal volume Vmod in nonmagnetic loss-less materials can be given in terms of the electric energy density 1 uE = 2 εrε0 |E ⃗|2 , with εr the relative permittivity, as

gLSP − TDBC ⎞ ⎟ g(1,0) − TDBC ⎟ ⎟ ⎟ g(1,1) − TDBC ⎟ ⎟ g(2,0) − TDBC ⎟ ⎟ E TDBC ⎟⎠

(4)

which is similar to eq 3, with the introduction of the exciton oscillator energy in the diagonal and its relative coupling coefficients in the off-diagonal terms. Equation 4 provides us with a simple description of the formation of LSP−DSW− exciton mixed modes resulting from the strong coupling between TDBC excitons and SLRs. The eigenvalues for this Hamiltonian have been used to fit the data in Figure 4c,d, fixing the TDBC energy to 2.11 eV and leaving the remaining terms as free parameters. The resulting plasmon energy, for xpolarized light, is centered at ELSP = 2.39 ± 0.02 eV, slightly red-shifted with respect to the bare case, as a consequence of the increased effective refractive index surrounding the nanostructures due to the presence of the dye. For a clearer comparison between the two polarization states, we limit the analysis of the fitting results to the lowest SLR sustained by the system, leaving additional discussions on the higher order modes for the Supporting Information. The fitting yields Rabi splittings of Ωx(1,0)−TDBC = 296 ± 18 meV, ΩxLSP−TDBC = 284 ± 24 meV, and ΩxLSP−(1,0) = 252 ± 20 meV between the first-order DSW, the LSP, and the exciton. For Py polarization (Figure 4d), the splitting visibility is lower because of the reduced extinction efficiency of the DSW-like SLR. By fitting the observable peaks, we found a Rabi splitting of Ωy(1,0)−TDBC = 164 ± 12 meV. A more complete picture of the system can be gained by considering which coupling regime can better describe our observations. A distinction, in fact, has been introduced in the literature between plasmonic splitting and energy-transfer regime for LSPs interacting with excitonic dipoles, the former emerging for high oscillator strength (f > 2) and broad (γexc > 200 meV) excitonic resonances.39 For our system, the molecular oscillator strength and line width are f = 1 and γexc

Vmod =

∫Ξ uE dV uEmax

(5)

where Ξ formally extends to infinity in the direction orthogonal to the array plane and uEmax is the maximum energy density 11364


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ACS Nano within the same region of interest.43 In structures that are characterized by both radiative and ohmic losses, calculating modal volumes is challenging and still remains an unsettled problem in the literature.44,45 Moreover, eq 5 would diverge when calculated for a diffractive wave. In order to circumvent these problems, but simultaneously maintain a physical and meaningful interpretation of our results in the two analyzed polarizations, we define an effective modal volume, Veff, confined within the 40 nm thick interacting TDBC layer, ranging between the bottom and the top surfaces of the NDs, and whose base area is the entire unit cell of the array. The Q-factor was calculated as ΔE by fitting the experimental E extinction peaks with a Lorentzian profile with ΔE as the full width at half-maximum near the peak center E. Although the extinction peaks would under certain conditions come to have an asymmetric Fano-like line shape, for sake of simplicity we used in all cases a symmetric Lorentzian fitting in order to evaluate how the sharpness of the peaks evolve at different lattice wave-vectors. The obtained values for quality factor and mode volume (shown in Figure S6) are on the order of 10 and 105 nm3, respectively, in the limit of high kL (high gap plasmon character), which is consistent with values usually measured in standard plasmonic nanostructures.46 As the system evolves toward a more photonic behavior, the quality factor raises up to 130 while the mode volume increases. A comprehensive picture of the SLR evolution is shown in Figure 5a, where the Q/V ratios are shown for Px (black) and Py (red) polarization as a function of the lattice wavevector and of the plasmonic fraction of the SLR (see the Supporting Information for details on the polariton fraction calculation). For both analyzed polarizations, Q/V shows a clear maximum, thus indicating that an optimum balance between the LSP mode volume and the DSW Q factor is reached around 10% of the plasmonic fraction in the SLR mode. However, there is a huge difference between the two LSP modes in the SLRs. When the gap plasmon of the dimer is excited (black curve), the Q/V ratio is always larger than that obtained with the single-disk-like mode (red curve) because of the higher EM field concentration inside the dimer gap (i.e., lower mode volume). When the plasmonic fraction of the SLR is higher than 15%, Q/V decreases, indicating that the EM field concentration in space, related to the increasing plasmonic behavior, is not strong enough to balance the decrease of the mode quality factor. Interestingly, we can identify an intermediate region, for plasmonic fractions between 5% and 15%, where the hybrid character of SLR allows for the simultaneous exploitation of the high photonic Q factors and the low plasmonic modal volumes, Veff, resulting in an enhanced Q/V value. These observations clearly explain the extinction differences measured for the coupled system. The TDBC energy crosses the uncoupled DSW dispersion at kL = 0.016 rad/nm, corresponding to 20% plasmonic fraction for x-polarized and 5% for y-polarized SLR (see Figure 5a). At this point, the difference between the two plasmonic modes of the dimer results in a mode volume ratio between Px and Py of Vx/Vy = 5 (see the Supporting Information). In agreement with recent theoretical reports,47 this spatial concentration is therefore responsible for the observed increase of 80% in the Rabi splitting for x-polarized light. The effect of the dimer gap is also shown in Figure 5b−g, where we compare, using the same scale, the near-field

Figure 5. Q/V ratio of the first-order SLR, calculated from numerical modal volumes and experimental Q factors for Px (black curve) and Py (red curve) polarization. The curves are plotted as a function of the lattice k-vector (bottom axis) and of the relative plasmonic fraction of the hybrid mode (top axis). The latter is shown in black for Px and red for Py polarization. The relative near-field distribution (electric field in log scale) evaluated at the energy of the lower SLR mode are also shown, for the lattice wavevectors indicated, as 0.012 rad/nm (b/e), 0.017 rad/nm (c/f), and 0.024 rad/nm (d/g).

distributions of EM field in the unit cell of the array for three different lattice wave-vectors (kL = 0.012 rad/nm, 0.017 rad/nm and 0.024 rad/nm in b/e, c/f, and d/g respectively) and at the two considered polarizations. Here we can appreciate how we move from small lattice wavevectors where the field is highly delocalized (Figure 5b and 5e), to a condition, at higher lattice wavevectors, in which the field is more confined inside the gap for Px polarization (Figure 5c-d) and around the dipolar lobes of the two disks for Py polarization (Figure 5f-g).

CONCLUSIONS In summary, we have shown the active role that surface lattice resonances, emerging from the strong coupling of localized plasmonic and diffractive photonic modes, play on light−matter interaction in a plasmon−exciton polariton lattice composed of aluminum nanodisks dimers and a J-aggregated cyanine dye, demonstrating that an effective gain in terms of Q/V is obtained when mixing DSW and LSP modes around 10% of the plasmon hybridization. Experimentally, this has been proved showing that, with the mixing of plasmonic (low modal volume) and photonic (high Q-factor) modes, an 80% increase in the Rabi splitting is obtained when coupling the hybrid SLR with a molecular dye compared to the coupling with the DSWlike SLR mode sustained by the plasmon of the single nanodisks. These experimental observations are sustained by numerical simulations, showing that the gap hybrid SLR is able 11365


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the environmental point of view, the disks have been considered embedded in a nondispersive dielectric medium with refractive index n = 1.515. The performed simulations can be divided into two groups: the first one involving the “bare” plasmonic system and the second one regarding the arrays of dimers covered by a uniform 40 nm thick layer of TDBC. For what concerns the optical properties of this layer of molecules, we have assumed a Lorentzian dispersion εTDBC(ω) = ε∞ − fω2LT/(ω2 − ω20 + iγω), with ε∞ = 2.5, f = 1, ωLT = 0.4 eV, ω0 = 2.1 eV, and γ = 0.03 eV.37

to support low volume and relatively high Q, resulting in an overall Q/V ratio five times larger than that of the SLR formed by the LSP of single nanostructures. These results can open the way toward a complete engineering of the optical properties of plasmonic lattices and of their mediated light-matter interaction. In particular, the exploitation of low-loss dark plasmonic modes or electric multipolar modes of semiconducting nanostructures could constitute, in the near future, an effective low-mode-volume alternative to photonic crystals and whispering gallery modes for cQED applications.

ASSOCIATED CONTENT S Supporting Information *

METHODS

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b06611. Molecular J-aggregated cyanine dye spectra, far-field extinction maps in the ky = 0 space, numerical simulations, modal volumes and quality factor, polariton fractions calculations, and higher order diffractive modes coupling (PDF)

Sample Fabrication. Two-dimensional 70 × 70 aluminum nanodisks dimers with 100 nm diameter, 40 nm height, and 20 nm gap were realized on a glass substrate by electron beam lithography, with lattice period a, ranging from 275 to 590 nm, with 10 nm step. The substrate was first cleaned in acetone and 2-propanol. Then a 250 nm poly(methyl methacrylate) (PMMA) layer was spin-coated at 6000 rpm and soft-baked at 180 °C for 3 min. A 2 nm thick chrome layer was thermally evaporated onto the PMMA to prevent charge effects in the electron beam writing procedure. The arrays were written by a Raith 150 system at 22 pA beam current and 30 keV. After electron exposure, the Cr layer was completely removed by a ceric ammonium nitrate based wet etching for 20 s and rinsed in water. The exposed resist was development in MIBK:IPA solution in a 1:3 ratio for 3 min and rinsed in 2-propanol for 1 min. After thermal evaporation of 40 nm of aluminum, a lift-off process was performed in an mr-Rem 500 remover solution (Microresist Technology) and rinsed in 2-propanol. For the molecule interacting system, a 1 mg/mL solution of TDBC in methanol was prepared and filtered. Dichloromethane was added to it in a 1:2 volume ratio. The resulting solution was finally spin coated onto the sample at 2000 rpm. Optical Characterization. The sample was characterized by transmission measurements on an homemade confocal setup comprising an optical microscope (Zeiss AxioScope A1) coupled to a spectrometer. Light from a tungsten lamp was focused on the sample by an adjustable numerical aperture condenser (NA from less than 0.1 to 0.95). Transmitted light was collected with a 40× 0.95 NA objective lens. A system of three lenses was used to collect light from the back focal plane of the objective and reconstruct the real space (L1 in Figure 1), collimate (L2), and refocus (L3) the real space image on the slits of a 300 mm spectrometer equipped with a 150 lines/mm grating and a CCD camera. Adjustable square slits were used to select the array area in the L1 focal plane. By this method, both the real and the Fourier space imaging can be obtained, the former by using all the three lenses, the latter by removing the L2 lens. Mode Fitting. The maxima in the normal incidence extinction spectra were extracted by multiple Lorentzian fittings. The dispersions obtained this way were fitted by using a nonlinear model function, mimicking the solution for the eigenvalue problem of eqs 3 and 5. In the case of x-polarized light, all of the oscillators were included into the model. For y-polarized light instead, only the DSWs and the exciton were taken into account. This is justified by the large LSP detuning, which leads to mode splittings observable at energies above 3 eV, out of the spectrum investigated here. Numerical Simulations. Electromagnetic simulations have been carried out using a commercial software, based on Finite Element code (COMSOL Multiphysics). Considering the array systems investigated, all parametric studies have been performed by simulating an elemental unit cell with an Al disk dimer and employing periodic boundary conditions in the array directions. For the optical properties of the plasmonic metal involved, we considered a Lorentz−Drude formula for the permittivity dispersion of aluminum.48 Moreover, from the literature, the Al disks have been considered covered by a uniform 3 nm thick layer of native Al2O3 (refractive index n = 1.765). Due to fabrication constraints, the top edges of the disks have been rounded by a curvature radius of 20 nm, while to avoid numerical artifacts, a radius of curvature of 2 nm has been used for the bottom edges. From

AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Francesco Todisco: 0000-0002-0188-6048 Milena De Giorgi: 0000-0002-4522-7933 Massimo Cuscunà: 0000-0002-4934-3376 Cristian Ciracì: 0000-0003-3349-8389 Author Contributions ∥

F.T. and M.E. contributed equally to this work.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We thank P. Cazzato and I. Tarantini for technical support. This work was supported by the ERC Project POLAFLOW (Grant No. 308136) and the national project “Molecular nAnotechnologies for eAlth and environmenT” (MAAT, PON02_00563_3316357 and CUP B31C12001230005). A.I.F.-D. acknowledges funding from the Spanish MINECO under Contract FIS2015-64951-R (CLAQUE). REFERENCES (1) Haroche, S.; Kleppner, D. Cavity Quantum Electrodynamics. Phys. Today 1989, 42, 24−30. (2) Greiner, M.; Mandel, O.; Esslinger, T.; Hänsch, T. W.; Bloch, I. Quantum Phase Transition from a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms. Nature 2002, 415, 39−44. (3) Sugawara, Y.; Kelf, T. A.; Baumberg, J. J.; Abdelsalam, M. E.; Bartlett, P. N. Strong Coupling between Localized Plasmons and Organic Excitons in Metal Nanovoids. Phys. Rev. Lett. 2006, 97, 266808. (4) Bellessa, J.; Symonds, C.; Vynck, K.; Lemaitre, A.; Brioude, A.; Beaur, L.; Plenet, J. C.; Viste, P.; Felbacq, D.; Cambril, E.; Valvin, P. Giant Rabi Splitting between Localized Mixed Plasmon-Exciton States in a Two-Dimensional Array of Nanosize Metallic Disks in an Organic Semiconductor. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 33303. (5) Gomez, D. E.; Vernon, K. C.; Mulvaney, P.; Davis, T. J. Surface Plasmon Mediated Strong Exciton−Photon Coupling in Semiconductor Nanocrystals. Nano Lett. 2010, 10, 274−278. 11366


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