Strong light-matter coupling is crucial for the modern physics, including semiconductor optoelectronics, plasmonics, ultrafast optics, and quantum electrodynamics, etc. When the coherent exchange rate of energy between light and matter is higher than the decay rate, it reaches the strong coupling regime, where two hybrid modes with different energies instead of original independent eigenstates are formed, known as the vacuum Rabi splitting¹. The strong coupling can result in the formation of half-light, half-matter bosonic quasiparticles called polaritons, which provides a number of possibilities in fascinating advances such as the low-threshold lasing², Bose-Einstein condensation^3-5, chemical reactivity tuning^6-8, and optical spin switching⁹, etc., and has been widely demonstrated in solid-states, like GaAs quantum dots¹⁰, GaN and ZnO wide-bandgap semiconductors^{11, 12}, and organic polymer materials¹³. However, either the small binding energy of excitons or the strong localization effect of disordered potentials¹⁴, makes traditional semiconductors hardly realize strong-coupled polaritonic eigenstates at ambient conditions.

Two-dimensional transition metal dichalcogenides (TMDs) have generated broad interests owing to their unique optical and electronic properties^{15, 16}. Sharp exciton resonances and large exciton binding energies make them excellent candidates for both fundamental and application studies¹⁷. The monolayer of TMDs gives rise to strongly confined excitons with Bohr radii of ~1 nm and large oscillator strength¹⁸. Embedding TMD monolayers in an optical microcavity can realize the strong light-matter coupling and generate polaritonic eigenstates, which creates opportunities for engineering the exciton-polariton interaction^19-21. Though TMD-based polaritons inherit the strong nonlinear interaction and low effective mass properties from the constituent exciton and photon components, most of strong-coupling eigenstates with small Rabi splitting energy were observed in a cryogenic condition and required sophisticated measurement techniques, which impedes the development of practical polaritonic devices.

Surface plasmons (SPs), collective electron oscillations of the metallic nanostructure, can tightly confine the incident light into nanoscale²², which results in a strongly enhanced local field with ultrasmall mode volume and hence provides an advantaged platform for strong coupling investigations^23-28. In the past decades, many attentions have been paid to plasmon-TMD-exciton systems for studying light-matter interactions, such as plasmon-induced resonance energy transfer^{29, 30}, tunable photoluminance by plasmon^31-37 and Fano resonance^38-40. The strong plasmon-TMD-exciton coupling also has been investigated^41-48. However, due to the intrinsic loss of the metal, the quality factor and cooperativity of plasmonic nanocavities are lower than those of conventional optical cavities, and therefore the reliable plasmon-exciton strong coupling has seldom been reported at room temperature. Despite of the Ohmic loss, the strong electric field enhancement and extremely small resonance mode volume⁴⁹ indeed make the plasmonic nanostructure an ideal candidate for the strong light-matter coupling investigation.

Here, we report for the first time the observation of strong coupled plasmon-exciton polaritonic hybrid states by embedding Ag-WS₂ heterostructure in an optical microcavity under ambient conditions. We demonstrate the hybrid states of optical cavity and plasmonic nanostructure can be further coupled with the exciton of WS₂ monolayers, and generate a new kind of quasiparticle with part-plasmon, part-exciton and part-light. The resulted plasmon-exciton polaritonic states can push the Rabi splitting up to 300 meV at the strong coupling regime under the room temperature. Experimental measurements are confirmed by simulations and calculations that based on a three-oscillator model. We believe that the proposed configuration can achieve strong light-matter coupling with a large Rabi-splitting for various flexible device applications based on ultrathin materials in the future.

The schematic of Ag-WS₂ heterostructure is depicted in Fig. 1(a). WS₂ monolayers were first transferred to the prepared substrate that consists of a 100 nm Ag mirror and a 30 nm MgF₂ spacer. Then Ag nanodisks were fabricated on the WS₂ monolayer by using E-beam lithography (EBL) and the following lift-off process. Figure 1(b) shows the scanning electron microscopy (SEM) image of Ag nanodisks with a diameter of 90 nm and thickness of 30 nm on top of WS₂ monolayers. Ag was chosen because of its strong plasmon resonance and the relatively low dissipation in the visible range. Photoluminescence (PL) and Raman spectra were measured (See Fig. S1 in the Supplementary Information), which confirms that the WS₂ used in the experiment is indeed a monolayer. In Fig. 1(c), we can see the Ag plasmon resonance can be tuned to 610 nm with the designed Ag-MgF₂ substrate, and overlaps with the A-exciton absorption peak of WS₂ monolayers to realize the plasmon-exciton coupling.

To systematically investigate the exciton-plasmon interaction of this Ag-WS₂ heterostructure, a series of Ag nanodisks with different diameters were fabricated on the WS₂ monolayers. Reflectivity spectra of bare Ag nanodisks are shown in Fig. S2. The plasmon resonance of Ag nanodisks can be gradually red-shifted from 540 to 700 nm with the diameter increasing, which is in good agreement with finite-difference time-domain (FDTD) simulation results (See Fig. S3 in the Supplementary Information). Figure 1(d) shows reflectivity spectra of Ag-WS₂ heterostructures with the Ag disk diameter changed from 85 to 95 nm. The coupling strength in Ag-WS₂ heterostructure is determined by the resonance overlap between the plasmon and excitons. For the nanodisk with diameter of 90 nm, the plasmon resonance is close to the WS₂ exciton energy, an obvious Rabi splitting can be observed, and two prominent resonance modes are identified as the lower (LPB) and upper plexciton branch (UPB). The Rabi splitting (Ω) between the UPB and LPB on resonance was measured as 85 meV. By comparing this value with the full width at half maximum (FWHM) of the plasmon (γ_pl≈320 meV) and exciton (γ_X≈50 meV) modes, the obtained splitting energy (Ω≈85 meV) is unsatisfied with the strong coupling criterion¹, where Ω < (γ_pl+γ_X)/2, implying that this plasmon-exciton hybridization is still in the weak coupling regime. The size-dependent dispersion of the Ag-WS₂ heterostructure was also calculated by using FDTD solutions. A similar Rabi splitting was observed with the plasmon resonance of the Ag nanodisk getting closer to the exciton of WS₂ monolayers at 610 nm, which is consistent well with experimental measurements. (See Fig. S4 in the Supplementary Information).

In order to enhance the plasmon-exciton coupling, and eventually facilitate entering the strong coupling regime, an optical microcavity was manufactured. As shown in Fig. 2(a), by further depositing a 155 nm thickness MgF₂ layer and a 20 nm top Ag film onto the fabricated Ag-WS₂ heterostructure, we successfully obtained an optical microcavity with the Ag-WS₂ heterostructure embedded in MgF₂ spacer. Figure 2(b) is the reflection mapping of our cavity sample, and its different layered structures are clearly color distinguished. From the cross section of SEM, the top Ag film, MgF₂ spacer, bottom Ag layer, and embedded Ag nanodisks can be detailed characterized, as shown in Fig. 2(c).

The optical microcavity was carefully designed to couple well with excitons and plasmons. And the reflectivity spectrum of an empty microcavity was first measured (Fig. S5(a) (solid line) in the Supplementary Information), where a sharp reflection dip centered at 650 nm was achieved, which is resulted from the excitation of the 1st-order of optical cavity mode⁵⁰. This cavity mode was confirmed with the FDTD simulation (Fig. S5(b) (dotted line) in the Supplementary Information), where the electric field intensity distribution (E/E_in)² on the xoz plane manifests a huge cavity resonance (Fig. S5(b) in the Supplementary Information).

In order to explore the physics origin of strong light-matter coupling, the same optical microcavity with embedded Ag nanodisks (without the WS₂ monolayers) was also investigated. The direct plasmon-photon coupling in this Ag-cavity structure leads to two hybridized modes with a maximum bandwidth of 200 meV as shown in Fig. 2(d). The plasmon-photon coupling strength can be effectively tuned with different sized Ag nanodisks. In comparison with the pure plasmon mode of Ag nanodisk, the Ag-cavity structure shows a higher electric field enhancement and a narrower resonance bandwidth⁵¹, which provides a better option for the further strong coupling study.

Figure 2(e) gives reflectivity spectra of optical microcavity with the Ag-WS₂ heterostructure embedded in the MgF₂ layer. Three different hybridized modes, as the upper branch, middle branch, and lower branch were generated. By increasing the size of Ag nanodisk, the upper branch gradually approaches the A-exciton of the WS₂ monolayers, the middle branch shifts away from the A-exciton and gradually approaches the microcavity mode, while the lower branch shifts away from the A-exciton mode. Black solid lines in Fig. 2(e) trace the dispersion of three branches, and anticrossing trends are found for the Ag disk size changed from 90 to 110 nm, which indicates the strong coupling happened in this Ag-WS₂ heterostructure that associated with the optical microcavity. To highlight these three branches, the spectrum for 110 nm and 95 nm in Fig. 2(e) are expanded and shown in Figs. 2(f) and 2(g), respectively. When the diameter of Ag nanodisk is 110 nm, the weak coupling was observed, only two hybrid modes can be distinguished. However, for diameter of 95 nm, three pronounced hybridized modes generated by the strong coupling effect corresponding to the upper, middle, and lower branches, which can be clearly observed as shown in Fig. 2(g).

In order to clearly see the mode revolution from the week coupling to strong coupling, FDTD simulations were performed on the same optical microcavity with the bare Ag nanodisk and Ag-WS₂ heterostructure, respectively. The hybridization of the Ag plasmon and cavity mode can be easily distinguished in Fig. 3(a) when the disk size changed from 60 to 130 nm. All resonance dips of measured reflectivity spectra (Fig. 2(d)) correspond to the generated hybrid modes in Fig. 3(a), and the spectral resonance shifting reflects the size-dependent dispersion of each hybrid mode. When the Ag nanodisk changed to the Ag-WS₂ heterostructure, the size-dependent dispersion mapping shows upper, middle and lower branches, which has a good agreement with measured resonances (Fig. 2(e)) as shown in Fig. 3(b), where the original hybridized states in Fig. 3(a) are coupled with the A-exciton of WS₂ monolayers, and achieve a strong Rabi splitting around 610 nm. In comparison with the Ag nanodisk without microcavity, the electric field of the Ag nanodisk at resonance wavelength 610 nm is enhanced almost 4 times when the microcavity is implemented, as shown in Fig. 3(c), which creates a feasible condition for the plasmon-exciton strong coupling. By extracting the simulated reflectivity for disks with size of 95 nm and 110 nm, as denoted by dashed lines in Fig. 3(b), one can see the output spectra (Fig. 3(d)) present an excellent agreement with the measured reflectivity as Figs. 2(f) and 2(g). Due to the fabrication error of microcavity and the difference of dielectric function between experiment and simulation, the observed splitting energy between cavity and plasmon is smaller than simulation results, which results in a redshift in simulated low branch compared to the experimental one.

The observed strong coupling of the Ag-WS₂ heterostructure with optical microcavity can be further described and analyzed by using coupled oscillator model. Fig. 4(a) is the schematic of plasmon-exciton-cavity three-coupled oscillator model. In the experiment, because the optical microcavity mode is designed far away from the A-exciton of WS₂ monolayers, only plasmon-exciton and plasmon-cavity oscillators are connected, and there is no direct coupling between the exciton and cavity photon to generate traditional polaritons.

The Hamiltonian of this three-coupled system can be presented by a matrix as Eq. (1).

where γ_pl, γ_X and γ_MC are the linewidths of plasmon, exciton, and microcavity modes, U_pl, U_X, and U_MC are the resonance energies of each mode, while g_X and g_MC represent plasmon-exciton and plasmon-microcavity interaction constants. In three-oscillator model, the eigenstates of Hamiltonian correspond to the three hybrid branches, the eigenvalues of Hamiltonian correspond to the Hopfield coefficients, and the modular square of Hopfield coefficient represents the proportion of uncoupled states in hybrid state. The diagonalization of these Hamiltonians yields three eigenstates and Hopfield coefficients which present the contribution of plasmons, excitons and microcavity modes to each of the state⁵². With the eigenfrequencies of upper, middle, and lower branches that obtained from experimental reflectivity spectra, the Rabi splitting of anticrossing curves can be fitted with the three-coupled oscillator model. By adjusting the parameters g_MC and g_X, and then solving the Hamiltonian, the obtained eigenstates of Hamiltonian can be fitted well with the experimental results.

Figure 4(b) depicts resulting dispersion curves of the Ag-WS₂ heterostructure that was embedded in the optical microcavity. Three resonance bands, corresponding to the upper, middle, and lower hybrid states are observed. The extracted values from the fitting give g_MC≈90 meV and g_X≈60 meV. The splitting between each of two branches depends on both plasmon-exciton (g_X) and plasmon-microcavity (g_MC) coupling strengths, as well as the resonant frequency and linewidths of all contributing parts. Thus, the existed analytical expression cannot obtain simple analytical expressions of the eigenfrequencies in this three-coupled oscillator. In order to evaluate the Rabi splitting of the system and find the trigger condition of strong coupling, the weight of each contribution should be estimated.

As discussed above, the wave function of each hybrid branch is an admixture contribution from the plasmon, cavity and exciton, as $\left| \psi \right\rangle = {\alpha _{{\rm{pl}}}}\left| {{\rm{plasmon}}} \right\rangle + {\alpha _{{\rm{MC}}}}\left| {{\rm{cavity}}} \right\rangle + {\alpha _{\rm{X}}}\left| {{\rm{exciton}}} \right\rangle $. In order to quantify this hybridization, Hopfield coefficients for three branches were calculated as shown in Fig. 4(c), where we can see that each branch consisted of part-plasmon, part-exciton, and part-cavity modes. For the middle branch, a strong hybridization between A-exciton and plasmon is induced by the coupling of cavity mode. A state with comparable weight of plasmon, cavity and A-exciton (|α_pl|²=0.24, |α_MC|²=|α_X|²= 0.38) is obtained at the nanodisk diameter of 99 nm, where all three oscillators intensely participate in the plasmon-exciton-cavity interaction. Therefore, the Ag nanodisk with diameter of 99 nm is considered as the best structure to realize the strongest interaction among these three oscillators, where the corresponding Rabi splitting value Ω≈300 meV is obtained.

On the other side, the linewidths of each hybrid branch also consist of the contributed plasmon, exciton, and cavity modes, and can be written as γ_i=α_plγ_pl+α_MCγ_MC+α_Xγ_X (i=upper, middle, lower). By putting the linewidths (γ_pl, γ_MC and γ_X) into above formula, the relationship of Ag nanodisk size with the linewidths of three hybrid states can be calculated as shown in Fig. 4(d). In the strongest coupling regime as the Ag nanodisk diameter of 99 nm, the linewidths of upper, middle, and lower branches are γ_Upper= 150 meV, γ_Middle= 150 meV, and γ_Lower= 220 meV. Compared to the strong coupling criterion in two coupled oscillator model, the requirement for strong coupling of three coupled oscillators that according to the contribution of each component (plasmon, exciton, and cavity modes), can be written as Ω > W_plγ_pl+W_MCγ_MC+W_Xγ_X (see the detailed derivation in Supplementary Information), where W_pl, W_MC, and W_X are the weight of each component in strong plasmon-exciton-cavity coupling, while γ_pl, γ_MC and γ_X are the linewidths of plasmon, exciton, and microcavity modes. After calculating above parameters (Supplementary Information), the obtained minimal splitting between upper and lower branches of 300 meV, satisfies the proposed criterion condition, which demonstrates that the strong plasmon-exciton polaritonic hybrid state is successfully generated by combining the Ag-WS₂ heterostructure with the optical microcavity.

In summary, we have successfully shown that a large Rabi splitting can be realized under ambient conditions with a high-quality optical microcavity that participated in the plasmon-exciton coupling. The generated plasmon-exciton polaritonic hybrid states can achieve a corresponding Rabi splitting as 300 meV. By calculating the linewidths and Hopfield coefficient of hybridized modes using harmonic oscillator model, the criteria of the strong coupling for three oscillators was proposed for the first time, and the corresponding large Rabi splitting was achieved in the strong coupling regime of the Ag-WS₂ heterostructure that was embedded in the optical microscopy. The proposed three-oscillator configuration provides an effective way to develop the strong coupling effect for the practical applications of plexciton polaritonic device at room temperature based on low dimensional materials.

Growth of WS₂ monolayers: Low-pressure chemical vapor deposition (LPCVD) method was employed to grow WS₂ monolayers on the sapphire substrate (c-plane of α-Al₂O₃). Sulfur and tungsten trioxide powders were used as the S and W sources, respectively. A mixture flow of Ar (60 sccm) and H₂ (10 sccm) was used as the carrier gas. During the CVD growth processes, the sulfur powder was placed on the upstream zone and heated to 100 ℃. Tungsten trioxide powder and substrate were placed on the middle zone of the tube furnace and heated to 887 ℃ with 35 min, and then maintained 60 min for the deposition of the WS₂ monolayers. The pressure of the tube furnace was pumped to ~80 Pa. After the growth of WS₂, the temperatures were naturally cooled down to room temperature.

Sample fabrication: The substrate was prepared by depositing 100 nm Ag and 30 nm MgF₂ successively, which could obviously enhance the optical absorption of WS₂ monolayers (Fig. S6, Supplementary Information). The as-grown WS₂ monolayers were transferred onto the prepared Ag-MgF₂ substrate by a PMMA-assisted method. Then, the designed Ag nanodisks were directly fabricated on WS₂ monolayers by E-beam lithography, and there is no spacer between the Ag nanodisk array and the WS₂ monolayer. The periods of the Ag nanodisk arrays were set at 230 nm, which makes the surface plasmonic lattice resonances far away from the A-exciton resonance wavelength. Positive resist (MircoChem PMMA A2 950) was spin-coated on the prepared substrate at 3000 rpm for 51 s and then heated on a hot plate for 5 min. The designed structure was drawn by nanometer pattern generation system (NPGS) and exposed by scanning electron microscope (FEI Quanta 450 FEG). A 30 nm Ag film was evaporated by E-beam evaporation system (DE Technology Inc, DE400DH) then lifted off after soaking in acetone for 2 h. Finally, by depositing 155 nm MgF₂ and 20 nm Ag, the Ag-WS₂ heterostructure with the optical microcavity was achieved.

Simulations and optical measurements: The commercial FDTD solution was used to simulate the optical characterization of strong coupling system. Ag nanodisks with diameter increased from 60 to 130 nm were used to acquire the anti-crossing line shape and the thickness of Ag (up), MgF₂ and Ag (bottom) for microcavity analysis was chosen as 20 nm, 185 nm and 100 nm. The refractive index for MgF₂ was set as a constant for 1.38. The minimum mesh size for the WS₂ monolayers was 0.05 nm and the optical constants for WS₂ monolayers were taken from literature and were used without further modification⁵³. A non-polarized plane wave with wavelength from 400 to 900 nm was applied as an input source. In the simulation of Fig. 3(c), the monitor of FDTD solutions is located at the interface between the Ag nanodisk and the WS₂ monolayer. In the experiment, the reflectivity spectral mapping was obtained by a commercial microscopic imaging system (HIS V3, CytoViva Co.), and the objective lens is 50× magnifications. The reflectivity spectra of the Ag-WS₂ heterostructure with and without microcavity were extracted from the mapping images. The whole experiment was operated at room temperature.

This work is supported by the National Key Research and Development Program of China (Grant No. 2017YFA0205700), National Basic Research Program of China (Grant No. 2015CB932403, 2017YFA0206000), National Natural Science Foundation of China (Grant Nos. 11674012, 61521004, 21790364, 61422501, and 11374023), Beijing Natural Science Foundation (Z180011, and L140007), and Foundation for the Author of National Excellent Doctoral Dissertation of PR China (Grant No. 201420), National Program for Support of Top-notch Young Professionals (Grant No. W02070003).

The authors declare no competing financial interests.