Observation of ultra-large Rabi splitting in the plasmon-exciton polaritons at room temperature

1 Introduction

Plasmon-exciton coupling is an important phenomenon in nanophotonics where light interacts with matter. Thanks to localized surface plasmon resonances, light can be confined in the nanoscale level, which leads to a substantial increase of the electromagnetic field, thus uncovering the remarkable strong light–matter interactions. Through the strong coupling, the plasmon polaritons can be formalized, which are the driven collective oscillation of electrons by light, providing the foundation for various applications ranging from coloration, opt-communication, and photocatalysis to biological sensing [1–5]. Owing to the two-dimensional (2D) feature of the excitations, plasmon polaritons supported by 2D metallic metasurfaces are of particular interest. Tight mode confinement and remarkable electrostatic tunability of plasmonic metasurfaces lead to new platforms for the investigation of light–matter interactions.

Recently, the TMDCs have received considerable attention owing to their promising applications in optoelectronics and electronics [6–9]. Thus, they are widely explored as candidates for integration with solids. In addition, monolayer TMDCs possess extraordinary oscillator strength and considerable excitonic binding energy (0.3–0.5 eV) [10, 11], which result from the significant Coulomb interaction and reduced dielectric screening in atomically thin structures. Therefore, integrating the monolayers in an optical resonator can expect to intrigue the intense energy exchange between the electromagnetic field of the light and the excitons [12–16].

Combining the two-dimensional van der Waals crystals with the plasmons in the metal can now be achieved with the plasmonic nanocavities with a gap width down to a subwavelength scale. However, the reported strong coupling of the 2D-based plasmon-exciton system has exploited the nanocavities formed through randomly spraying the single nanowires or nanoparticles over the monolayers [17–22]. Hence it is unable to systematically control and tune the coupling. Moreover, the usual vertical nano-resonator is hard to couple with the 2D materials since the electromagnetic field and the dipole moment is not aligned in the same manner. Therefore, large Rabi-splitting cannot be achieved in such nanostructures and would hinder the efficient energy transferring between the plasmons and excitons, thus lowering the performance of the devices.

In this work, we demonstrate a 2D hybrid coupling system showing an ultra-large Rabi splitting up to 200 meV. It is realized by plasmonic arrays and a monolayer WS₂. The pillars can significantly confine the electromagnetic field in the 2D plane with the same orientation of the dipole moment of the TMDCs monolayers. In addition, the employment of the monolayer WS₂ with a high refractive index can further encapsulate the electromagnetic field in the xy-plane. By modifying the diameters (D) and the periods (Γ), the energy splitting and the number of excitons involved in the coupling can be finely changed. Finally, the splitting feature is presented by performing the photoluminescence measurements, which unambiguously show the hybridization of the modes for the light and the matter interaction. The sufficient modification of the exciton properties with plasmons can raise the exploration of applications such as the development of optoelectronic devices, optical switching, and sensing [23–25].

The fabricated plasmonic metasurface is characterized by SEM in Figure 1(a), which shows that the structure is composed of regular cylindrical arrays. The metasurface is designed with the top Al disks array, whose diameter varies from 90 nm to 130 nm, and the thickness is 20 nm. The middle layer is composed of polymeric pillars with a refractive index of about 1.5, and the diameter varies from 90 nm to 130 nm, the same as the disk array, whose height is 35 nm. The thickness of the bottom Al film is 20 nm as well (see the detailed fabrication procedure in Methods). The whole structure is established on a SiO₂ (glass) substrate. Monolayer WS₂ and thin film h-BN are mechanically exfoliated from the bulk onto PDMS and transferred to silicon and metasurface using a standard dry transfer process [26, 27]. The hybrid system is illustrated in Figure 1(b). The transferred WS₂ is then identified by photo imaging and PL measurements at room temperature. The distribution of the simulated electric field at the resonance wavelength (∼650 nm for D = 100 nm) in the xy-plane is shown in Figure 1(c) (the electric field in the xz-plane can be referred to the Supplementary material in Note 5). We can find that the electric field is symmetrically distributed on both sides of the cylinder, the same as in a dipolar manner. Thus, when the monolayer is placed on the top edge of cylinders, excitons in two-dimensional materials are likely to interact with electric dipoles excited by the plasmonic nanostructures. It is worth noting that, unlike the plasmonic cavities formed by particle-WS₂-metals [28–31], the plasmonic metasurface used here with an open architecture has unique advantages for experimental detection and potential applications in the display industry. Figure 1(d) presents the simulated (finite-difference time-domain (FDTD) full wave simulation) electric field distribution of Al nano-disk with WS₂ monolayer, we can see that by applying WS₂ on the surface, the electric field at the top interface of the metasurface-WS₂ hybrid structure can be significantly enhanced. It is worth mentioning that the applied hybrid plasmonic metasurface with Al holes array under the Al disks ensures the optical field is mainly localized in the top layer which to the maximum extent overlaps with the transferred WS₂ monolayer.

Figure 1:

Optical image and E-field distribution of the hybrid system. (a) Larger magnification of SEM images of the bare plasmonic metasurface with a typical diameter D ∼ 100 nm and a period Γ ∼ 200 nm. (b) Lower magnification SEM image of the plasmonic metasurface with a transferred monolayer WS₂ capped with a thin film hBN on top. The typical size of the monolayer is about 20 μm × 20 μm. The yellow square indicates the zoomed-in area. (c) The calculated 2D electric-field intensity distribution for the bare plasmonic metasurface in top–down view xy-plane. The diameter of the single nano-pillar is 100 nm. (d) The calculated 3D electric-field distribution for the plasmonic metasurface with monolayer WS₂ for the same pillar size shows a typical dipolar field distribution at the rim of the disk.

To resonantly couple to the monolayer WS₂, we designed the nanostructure with the plasmon modes covering the exciton energy of the WS₂ monolayer, which is at 610 nm. We use the FDTD method to calculate the optical properties of the metasurface. As shown in Figure 2(a), the dip in the simulated reflectivity spectra with cylinders of different (increasing) size redshifts. Before investigating the hybrid system, we primarily characterized the plasmonic metasurface in Figure 2(b), which shows the measured reflectivity spectra. We can find that the simulation results are in good agreement with the experimental ones. Note that the experimental spectra are broader than the spectra in the simulation because of the defects introduced during preparation, which may cause extra damping in the hybrid system. From Figure 2(b), the reflectivity spectrum exhibits a dip close to 580 nm with broadband when the diameter is about 90 nm. There is a dip near 600 nm when the diameter of the disk array is about 100 nm. The plasmonic resonances are sensitive to the geometrical aspect ratio, which can be attributed to the change in the average electron density [32]. In our work, by varying the diameter of the cylinders, the surface plasmon resonance can be tuned, which allows the plasmon mode to match with the ex_A of the WS₂ monolayer.

Figure 2:

The simulated reflectivity spectra versus the experimental reflectivity spectra. (a) The simulated reflectivity spectra for the bare plasmonic metasurface with various diameters from 90 nm up to 130 nm. The plasmon mode blue shifts with the increased size. (b) The corresponding experimental reflectivity spectra. The intensity noise above 750 nm can be observed because of the incapability of the white source in that regime.

In addition, considerable coupling strength and low damping loss are those two indispensable aspects for realizing efficient coupling. In a strong coupling plasmon-exciton system, the existence of a splitting in frequency implies the coherent exchange of energy between the SPP field [33] and the oscillators (emitters). The strong coupling regime can be defined as the splitting being large enough compared to the linewidths of the coupled states. The optical mode splitting with the energy separation between the normal modes can be also called the Rabi splitting [34], originally derived from fully quantum theory. The mode-splitting is [35]

where d is the dipole moment of a two-level system, ω ₀ is the frequency at the resonance, N is the number of emitters [36] and V is the mode volume within a plasmonic cavity. To enhance the coupling strength g(∝Ω_R), one of the methods is to decrease the mode volume V. Excited plasmon polaritons of plasmonic metasurfaces can effectively confine the electromagnetic field in the subwavelength scale below the diffraction limit. Thus, it can provide a compact and stable environment for strong coupling at room temperature. When the rate of coherent energy transfer between an excitonic transition and plasmons is faster than their average dissipation rate, the system can undergo a strong coupling regime, forming so-called plexcitons. The interaction between excitons and the plasmon modes can be continuously tuned to reach different coupling strengths by adjusting the dimensions of the nanostructure, for example, nanoparticle size, gap thickness, and shape.

Figure 3(a) presents the sketched structure of the plasmonic metasurface combined with a WS₂ monolayer, where the plasmonic substrate is formed by a 20 nm-thick Al film sputtered onto the substrate with dielectric pillars. The top structure is similar to the bottom, especially its shape is cylindrical and it is arranged periodically according to a period of 200 nm. Figure 3(b) shows a typical optical image of the hybrid structures under a 100× microscope objective, in which the red dots enclosed are WS₂ monolayer and the yellow dots enclosed are h-BN thin film. Here, by adjusting the diameter in lithography, we can achieve feasible tuning of plasmonic resonances supported in the system. Figure 3(c) illustrates the measured differential reflectivity. It should be noted that the demonstrated samples here are with plasmonic resonances which are located near the critical crossing point of the Rabi-type mode splitting. It is implemented micro-zone by an aperture to a 2 μm spot. The differential reflectivity is calculated as Δ R R = I bg − I sample I bg , where I _bg is the reflectance intensity of the background area with bare structure, and I _sample is the reflectance intensity of the WS₂ monolayer on the metasurface. The two separate valleys in the white light-illuminated reflectivity spectra indicate the plasmon and exciton in the hybrid system are strongly coupled.

Figure 3:

The reflectivity spectra in the coupled hybrid system with different sample sizes. (a) Schematic diagram of the sample structure where on the top layer is the monolayer WS₂ and beneath it is the metasurface. (b) Optical microscope image of the sample. WS₂ monolayer and hBN film are illustrated with the red dotted and yellow dotted lines respectively (the monolayer WS₂ is capped with a thin film hBN). (c) The diameter dependence differential reflection spectra. It shows two well-defined plasmon-polariton states at both sides of the ex_A energy. The vertical red line represents the WS₂ ex_A energy, and the blue dotted curves trace the dispersion of plasmon-polariton modes. (d) FDTD-simulated reflection spectra for the samples. (e) The splitting energy (see the Supplementary material Note 1 for more details) versus the effective exciton number N. The structure sizes are for D = 90 nm, D = 100 nm, and D = 110 nm.

Noted that, when the sample diameter is set to be 100 nm (close to the critical splitting point), the energy difference between the upper and lower energy branches is about 200 meV, which shows a remarkable Rabi-type mode splitting and indicates the strong interaction between the in-plane excitons and plasmons. By using the equation ℏ Ω R = 2 g 2 − 1 / 4 ( ℏ γ ex − ℏ γ pl ) 2 (Ω_R is the Rabi splitting, g is the coupling strength), and the experimental halfwidths for plasmon mode ℏγ _pl = 176 meV and the exciton ℏγ _ex = 34 meV (see the Supplementary material Note 2 for more details), we can derive the coupling strength g ∼ 123 meV. This result satisfies the inequality g > ℏ γ ex − ℏ γ pl / 2, a necessary condition for the formation of strongly coupled plexciton states [37]. Figure 3(d) presents the according simulation, which shows coupled mode interference [38]. An obvious mode splitting is presented on both sides of the exciton position (610 nm, denoted with a pink vertical bar in Figure 3(c)), further confirming the strong coupling behavior. For localized dipole plasmon resonances in disks, the effective wavevector k for the dipole mode is simply given by k ∼ 2/D, where D is the diameter of the disks. It should be noted that, for small wavevector k, the coupled plasmon–exciton dispersion has a negligible deviation from the simple k dispersion [39]. In Figure 3(e), we plot the splitting energy as a function of the effective number N for three conditions (D = 90 nm, 100 nm, and 110 nm). Note 1 in the Supporting Information shows the details of the function, (see Supporting Information). We simulated the mode volume (V) and the factor number F using a numerical method, FDTD. The Rabi splitting ( Ω R is obtained in measurement (in Figure 3(c)). In the same effective number N, it clearly shows that the splitting energies of 90 nm and 100 nm samples are similar, both stronger than in the case of 110 nm. It indicates that the N values can be changed by modulating the diameters of the structures. It should be mentioned that although we design the disks array, which is arranged in a periodic architecture, we mainly utilize the localized plasmon mode to investigate its coupling with ex_A of WS₂. We obtain the strong coupling dispersion by varying the diameters of the disks. As the mode we used originated from individual disk, not from the lattice mode involving all the disks, we calculated the mode volume within a unit cell of a disk for the localized plasmonic mode [30, 40, 41]. Hereby, our work provides a new approach for the strong coupling of plasmonic structures with TMDCs and promises to achieve the strong coupling of a few excitons to the plasmon.

The measured splitting in the reflectivity is a bit larger than that in the simulated spectra. This can be attributed to the simplicity of the simulation model exploited to predict the reflectivity spectra. In particular, the modeled reflectivity spectra correspond to the energy that is coupled from the emitter into the plasmon and subsequently radiated from the plasmon into free space with an ideal case where WS₂ is rigidly suspended on top of the Al disks; the measured spectra may also include contributions from light at the side walls of the Al disks covered by the WS₂ monolayer.

To further confirm the strong coupling in the hybrid system, we carried out photoluminescence measurements. The samples were pumped by a continuous wave laser (532 nm). The pump beam was focused by a reflecting microscope objective (0.5 numerical aperture, N.A.) to a spot size of 1 μm on the sample. The emission was collected by the same microscope objective and analyzed with a spectrometer equipped with a charged couple device (CCD). Figure 4(a) shows the measured PL spectroscopy collected under the same experimental conditions on the different samples at room temperature. Comparing the WS₂ monolayer on Si with the one on the metasurface, a slight red shift of the PL emission peak can be observed, due to the stress introduced during the transfer process [42]. With the increasing diameter, the peak of PL increases as well. When the diameter of a sample reaches 110 nm, the PL enhances 53-fold compared to the PL of the sample on the Si wafer [43]. The enhancement of spontaneous emission rates in an optical resonant cavity, known as the Purcell effect, can be estimated by the Purcell factor. For a certain cavity, the Purcell factor F p ∝ Q V , where Q and V are the quality factor and mode volume of the plasmonic cavity, respectively [44]. The way to increase the Purcell factor is again to reduce the mode volume [45]. Therefore, the electric field confinement becomes more obvious for the PL enhancement while the diameter becomes bigger under certain conditions. And it opens up new routes for future applications that can be used for sensitive measurements. Here the result is also in line with the simulation results.

Figure 4:

PL spectra in the coupled hybrid system with different sizes. (a) The measured PL spectra for the samples with D = 90 nm, D = 100 nm, and D = 110 nm. The grey line is the PL for the WS₂ monolayer on a SiO₂/Si substrate as a contrast. (b) PL enhancement spectra for the three different diameters divided by that of the control sample. It shows two well-defined plasmon-polariton states at both sides of the ex_A energy (red line).

Figure 4(b) demonstrates the PL enhancement ratio by dividing the values of the different samples by the values on the Si wafer. As in Figure 4(b), we can find that the PL spectra show two different prominent peaks (ω ₊ and ω ₋) resulting from the strong interaction between plasmon and emitters [46], which match with the reflectivity spectra. The dips in the spectra are almost in the same position, which is the narrow-band exciton of WS₂. It is obviously shown that the up branch (higher energy) displays a stronger signal than the lower branch (lower energy). When the diameter of the cylinder array is set to 100 nm, the plasmon-excitonic PL mode-splitting is up to 112 meV. It should be mentioned that the observed splitting in the PL enhancement spectrum is smaller than the splitting (200 meV) in the reflectivity spectra. The difference of spectral Rabi splitting in different measured spectra is mostly because they contain different contributions from the plasmon or exciton channel [47] and the plasmon channel usually has much larger splitting than the exciton channel because of its larger dipole moment [48]. PL behaviors originate from bounced channels with the complicated interplay among plasmons, phonons, and excitons, resulting in a degraded mode splitting strength. As the diameter increases, the lower branch of PL becomes clear and shows a blue shift. It further indicates that our designed structure obtaining the field localization is critical to minimizing mode volume and achieving strong coupling.

In summary, we have demonstrated a strong plasmon-exciton coupling between the plasmonic metasurface and the WS₂ monolayer. Strong plasmon-exciton coupling is studied by the differential reflectivity measurements, PL measurements and FDTD simulations. We present a giant tunable Rabi splitting and a small number of involved coupling excitons by changing the diameter of the nano-arrays. Combining the distinct properties of localized surface plasmon resonances and the unique properties of 2D semiconductors such as their exceptional exciton binding energies and atomic thickness, the possibility of revealing the plasmon-exciton condensation is an interesting feature offered by such an “open cavity”.

2 Methods