Abstract

The room-temperature strong plasmon-exciton coupling is first investigated in a metal-insulator-metal (MIM) waveguide-resonator system with WS2 monolayer. Finite-difference time-domain (FDTD) simulated results exhibit that the Fabry-Pérot (F-P) cavity is realized by the MIM plasmonic waveguide with two separated metal bars. When the F-P resonance is tuned to overlap with the A-exciton absorption peak of WS2 monolayer, the strong plasmon-exciton coupling is obtained at visible wavelengths. As a result, the spectral splitting response confirmed by the coupled-mode theory (CMT) appears in the transmission spectrum. Intriguingly, the switching response is handily witnessed by tuning the orientation of WS2 monolayer along the cavity, and the coupling strength is dynamically tuned by changing the position of the WS2 monolayer. Simultaneously, the anticrossing behavior with the Rabi splitting up to 109 meV is achieved by small changes in the length of the F-P cavity and the refractive index of dielectric in the cavity, respectively. The underlying physics is further revealed by the coupled oscillator model (COM). The proposed strong plasmon-exciton coupling can find utility in highly integrated plasmonic circuits for optical switching.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Two-dimensional layered materials [13], such as graphene [4,5] and transition-metal dichalcogenides (TMDs) [6,7], have attracted a great deal of attention in the past decade due to the remarkable mechanical, optical and electronic properties [8,9] they demonstrate. In the context of optoelectronics, considerable attention has shifted towards the TMDs monolayers because they are natural direct-bandgap semiconductors [10,11]. However, due to the atomic thickness of a few angstroms, the light-matter interactions demonstrated by the TMDs monolayers are limited [12]. The absolute absorption of light in a free-standing monolayer TMDs is only about 10-20% [13], which is insufficient for high-performance optoelectronic devices, such as two-dimensional photodetectors [14], light emitters [15], transistors [16] and valleytronics [17]. Research on enhancement of light-matter interactions in TMDs monolayers thus has become a fundamental issue to address to further take advantage of TMDs in optoelectronic devices [18]. Strong coupling [19] between optical cavities and excitons has received considerable interest recently and has been proposed as a successful way to boost light-matter interactions. In that scenario, the rate of coherent energy exchange between matter and optical excitation is faster than their respective dissipation rates, which results in new hybrid states with part-light and part-matter characteristics [20]. Simultaneously, the coupling strength depends on the inner product of the electric field E of the cavity photons and the exciton transition dipole moment d. Interestingly, the direct-bandgap TMDs monolayers simultaneously own the large exciton transition dipole moment and exciton binding energy [21]. Such properties will contribute to the realization of strong coupling. What’s more, single-crystalline TMDs monolayers exhibit the high optical stability, uniform optical and electronic behaviors across the entire two-dimensional flake. These prominent characteristics undoubtedly benefit the robustness of strong coupling.

So far, various types of optical resonators, including dielectric mirror cavities [22], metallic mirror cavities [23] and plasmonic hole arrays [24], have been proposed to realize strong coupling between photons and excitons in TMDs monolayers. Especially, the metal particles [25] are frequently utilized, because the supported localized surface plasmon polaritons (LSPPs) can overcome the conventional diffraction limit and confine the electric field into deep sub-wavelength nanoscales, thereby leading to the ultra-strong electric field E and the ultra-small mode volume. Owing to these distinct advantages, strong plasmon-exciton coupling has been handily achieved in the system of TMDs monolayers with metallic particles, such as the silver nanodisk array with monolayer MoS2 [26], the silver cube array with monolayer WSe2 [27], the individual silver nanorod with monolayer WS2 [28] or WSe2 [29], and gold bi-pyramids with monolayer WSe2 [30]. With the combination of intense electric fields around metal particles and the large exciton transition dipole moment, as well as the large exciton binding energy in monolayer TMDs, the strong plasmon-exciton coupling with the Rabi splitting exceeding 100 meV has been obtained at ambient conditions [28]. However, in addition to the LSPPs on nanostructured metal particles, propagating surface plasmon polaritons in optical waveguides own strongly confined electric fields at the metal surface. As a potential candidate, the metal-insulator-metal (MIM) [31] plasmonic waveguide is preferred, because it owns the ultra-strong field confinement and is easy to integrate into chips with miniaturization. Thus, introducing the TMDs monolayers into MIM plasmonic waveguide systems may offer a new possibility of realizing strong plasmon-exciton coupling.

Herein, we demonstrate for the first time the observation of the room-temperature strong plasmon-exciton coupling in a MIM plasmonic waveguide-resonator system with WS2 monolayer. The normal F-P resonator and thereby the bass-pass filter are achieved in an individual MIM plasmonic waveguide with two separated metal bars. When the monolayer WS2 with the exciton energy approaching to that of the F-P cavity is introduced, the strong exciton-cavity coupling, thereby the spectral splitting, is observed in the transmission spectrum. In particular, the switching effect is witnessed by tuning the orientation of WS2 monolayer along the cavity. As an evidence of strong coupling, the anticrossing response with the Rabi splitting up to 109 meV appears in color-coded transmission spectra for different lengths and refractive indices of the F-P cavity, respectively. The coupling strength is dynamically tuned by changing the position of the WS2 monolayer. All simulation results are theoretically verified by the CMT and COM. Our finding will play an important role in highly integrated plasmonic circuits for optical switching, and the obtained room-temperature strong light-matter interactions in WS2 monolayer provides an attractive route for the development of practical polaritonic devices.

2. Structure and model

The inset in Fig. 1 shows the proposed hybrid structure. The waveguide-resonator system is constructed by the individual MIM plasmonic waveguide with two separated metal bars. The monolayer WS2 is embedded into the realized cavity between two metal bars. The detailed structural parameters are demonstrated in Fig. 1. The width of the MIM plasmonic waveguide is W. The distance between two identical metal bars with the thickness of d is L. It is well known that the strongly confined surface plasmon polaritons (SPPs) are supported to propagate along the MIM waveguide. When the two separated metal bars are introduced, the incident SPP waves will be partly reflected at the metal-air interface and partly penetrate the first metal bar by near-field coupling. The original plasmonic cavity will be realized between two separated metal bars. The plasmon waves at especial wavelengths coupled into the cavity will bounce back and forth at the inner sides of two metal bars, thereby enabling the standing-wave resonance in the cavity. Namely, the F-P cavity forms between two separated metal bars. As a result, only the incident plasmon wave with the wavelength satisfying the resonance condition of the F-P cavity can resonate between two metal bars and finally pass the MIM plasmonic waveguide by near-field coupling, whereas others are reflected. The band-pass filtering effect without doubt will be achieved by such simple waveguide-resonator system. FDTD simulated results are described by the red curve in Fig. 2(b). As expected, a transmission peak appears at the transmission spectrum of the proposed waveguide-resonator system with W = 50, d = 15 and L = 172 nm. The obtained transmission peak is attributed to the realization of the second-order F-P resonance between two separated metal bars, as confirmed by the magnetic field distribution in Fig. 2(e).

 

Fig. 1. The x-y cross section of the proposed hybrid structure. The inset shows the schematic.

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Fig. 2. (a) The permittivity of WS2 monolayer. (b) Transmission spectra of the individual WS2 monolayer and the isolate waveguide-resonator system, respectively. (c) The simulated transmission of the hybrid structure. (d) The transmission spectrum obtained by using the CMT. The inset demonstrates the schematic of the CMT. (e) and (f) respectively illustrate the magnetic field |Hz| and electric field |Ey| distribution of the individual waveguide-resonator system at the transmission peak of 617 nm. (g) The |Ey|2 profile along the x-axis at the line of y = 0 nm. The s stands for the distance between WS2 monolayer and the center of the cavity. (h) The transmission of the hybrid structure with the embedded WS2 monolayer along the x direction. The inset describes the schematic of the corresponding structure.

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In addition, the splitting of the valence band by spin-orbit coupling leads to two excitonic features denoted by A and B in the monolayer TMDs [32]. As shown in Fig. 2(a), the strong light-matter interactions at the A-exciton emission energy give rise to the peak in the dielectric function of WS2 monolayer. Correspondingly, the transmission dip appears at the A-exciton emission wavelength of 617 nm, as depicted by the blue curve in Fig. 2(b). Especially, the larger energy difference (approaching 400 meV) between A and B exciton transitions in monolayer WS2 is conductive to only focus on the coupling between the external cavity and A excitons. Here, when the WS2 monolayer is embedded into the realized F-P cavity and simultaneously the plasmonic F-P resonance is tuned to overlap with the A exciton transition, the strong exciton-plasmon coupling is allowed. On the other hand, the excitons in monolayer WS2 have a dipole orientation in the plane of the monolayer. The coupling strength is proportional to the inner product of the tangential component of electric field in the cavity and the exciton transition dipole moment. Hence, the larger intensity of electric field Ey in the cavity will benefit the coupling strength, because the WS2 monolayer is placed along the y direction. As shown in Figs. 2(f) and 2(g), the maximum value of the electric field Ey for the second-order F-P resonance appears at the center of the cavity. Therefore, the ideal position of the monolayer WS2 for strong exciton-plasmon coupling is the center of the cavity.

To confirm the above predication, the 2D FDTD method (Lumerical FDTD Solutions) with the perfectly matched layer absorbing boundary conditions is performed for numerically investigating this device. In the implementation, the insulator filled into the waveguide is first assumed to be air (ɛd = 1). The metal is chosen as the silver with the complex permittivity characterized by the Drude model [33]${\varepsilon _m}(\omega )= {\varepsilon _\infty } - {{\omega _p^2} \mathord{\left/ {\vphantom {{\omega_p^2} {({{\omega^2} + i\omega \gamma } )}}} \right.} {({{\omega^2} + i\omega \gamma } )}}.$ Here, ɛ∞ = 3.7 is the dielectric constant at infinite angular frequency; ωp = 9.1 eV is the bulk plasma frequency representing the natural frequency of the oscillations of free conduction electrons; γ = 0.018 eV stands for the damping frequency of the oscillations; and ω is the angular frequency of the incident light. The permittivity of silver obtained from Drude model is nearly same as the experimental data of Johnson & Christy at the visible region. The same optical response thus will be observed. The complex permittivity of WS2 monolayer with the thickness of 0.618 nm is derived from experimental data measured by Li et al [34]. To excite the propagating SPP waves, the transverse-mangetric (TM) polarized plane wave with the electric polarization along the y direction is launched into this waveguide, as shown in Fig. 1. Two power monitors are placed at two ports of the waveguide-resonator system, for detecting the incident power Pin and transmitted power Pout, respectively. The transmission hence is defined to be T = Pout / Pin. In all simulations, the minimum mesh size inside WS2 monolayer is 0.1 nm along the x direction and is 1 nm in the y direction, to precisely calculate the optical response of the monolayer material. The mesh size gradually increases outside the WS2 sheet for saving the computing time. The L = 155 nm is first chosen for enabling the F-P resonant energy to match that of the A-exciton emission at the hybrid structure. FDTD results are illustrated in Fig. 2.

3. Results and discussion

Figure 2(c) shows the transmission of the hybrid structure with the WS2 monolayer placed at the center of the cavity. The comparison of Figs. 2(b) and 2(c) exhibits that the spectral splitting occurs at the wavelength of the A exciton transition after introducing the WS2 monolayer into the waveguide-resonator system. Correspondingly, the previous transmission peak has been replaced by the transmission dip marked by II and two new transmission peaks (labeled by I and III, respectively) appear. This behavior is analogous to the traditional electromagnetically induced transparency response [3538] which permits the use of the three-level theory to better understand the underlying physics. Figure 3(a) shows the diagram of the three-level system [39,40]. The incident SPPs are considered as the ground state |0 > . The F-P resonance between two metal bars is excited directly by near-field coupling with the incident SPP waves and thus is treated as an excited state (bright mode) |1 > . This direct excitation process corresponds to the transition of |0>→|1 > . In addition, only the incident plasmon wave with the wavelength satisfying the resonance condition of the F-P resonator can be coupled into the F-P cavity and resonate between two metal bars, whereas others are directly reflected at the metal-air interface of the first metal bar. Thus, because of the introduced two metal bars, the excitons in monolayer WS2 cannot be directly coupled to the incident SPPs. But the A exciton can be strongly coupled with the awakened F-P cavity when they have the same resonant wavelength. Thus, the A excitons can be treated as the metastable state (dark mode) |2 > . Namely, the coherent transition of |1>↔|2 > is permitted.

 

Fig. 3. (a) The diagram of the classical three-level system. The inset shows the absolute absorption of light in the individual WS2 monolayer and that of WS2 in structure. (b) The electric field Ey distribution at the transmission peaks I, III, and the dip II, respectively. (c) The energy diagram at the strong-coupling region.

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Figure 3(b) describes the electric field Ey distribution at transmission peaks I, III, and the dip II, respectively. For the field distribution at the dip II, there is nearly no field in the F-P cavity. Namely, the F-P resonance is suppressed at the wavelength of 617 nm. Based on the three-level system, the destructive interference between two transition pathways, |0>→|1 > and |0>→|1>→|2>→|1>, occurs at the wavelength of 617 nm. The extreme destructive interference leads to the suppressed F-P resonance at the wavelength of 617 nm in fact. The incident SPP waves thus cannot arrive at the out port indirectly by virtue of the F-P resonance, thereby enabling the transmission dip II. On the contrary, the comparison of the electric field distribution at transmission peaks indicates that the F-P cavity is awakened and owns the opposite phase between peaks I and III. Based on the three-level system, the in- and out-phase coupling between excitons (dark mode) and the F-P cavity (bright mode) should occur at the transmission peak III with the wavelength of 630 nm, and at the transmission peak I with the wavelength of 597 nm, respectively. The coherent coupling leads to the simultaneous excitations of excitons and the F-P resonance. As long as the F-P resonance is excited, the incident SPP power can pass the waveguide indirectly by virtue of the F-P cavity, thereby giving rise to the transmission peaks. Thus, the strong plasmon-exciton coupling with the remarkable spectral splitting is firstly obtained in the MIM plasmonic waveguide-resonator system. As a result, the light-matter interaction in WS2 monolayer will be boosted. The absolute absorption of WS2 monolayer can be calculated by the ration of the absorbed power in the volume V of WS2 monolayer to the incoming power through WS2 surface area S. The equation is described as [41]

$$\alpha = \frac{{\int\!\!\!\int\!\!\!\int_V {w({x,y} )dV} }}{{0.5c{\varepsilon _0}|{E_{inc}}{|^2}S\cos \theta }},$$
where the $w(x,y) = 0.5{\varepsilon _0}\omega {\varepsilon ^{,,}}(x,y)|E(x,y){|^2}$ is the power dissipation density in the structure. The ɛ,,(x, y) is the imaginary part of the relative permittivity of monolayer WS2. The θ is the incident angle. The obtained absolute absorption of the bare WS2 monolayer and that in the hybrid structure is shown in the inset of Fig. 3(a). Obviously, at the hybrid structure, the absolute absorption of light in the monolayer WS2 has been extremely enhanced in the strong coupling regime, compared with the individual WS2 monolayer.

It should be pointed out that even though the realized strong plasmon-exciton coupling in a MIM plasmonic waveguide-resonator system is based on numerical simulations currently, the fabrication of such a structure of the MIM plasmonic waveguide with two vertical metallic bars will be feasible in the future based on the state-of-the-art technology, especially the E-beam lithography, such as reported in these articles [4244]. In addition, according to previous experimental reports [23,28,30], the strong plasmon-exciton coupling on metallic particles with TMDs monolayers is based on the LSPPs around the metal surface and works at room-temperature. Herein, the realized strong plasmon-exciton coupling in a MIM plasmonic waveguide-resonator system with WS2 monolayer is based on the propagating SPPs on the metal surface and thus could work at room temperature in practice.

Additionally, such transmission behavior can be illustrated by the typical CMT [45,46]. As shown in the inset of Fig. 2(d), the amplitudes of the incoming and outgoing SPP waves in the MIM waveguide are depicted by the Sin, and Sout, respectively. The quality factor related to the coupling loss between the waveguide and the F-P resonator is Qw. The quality factor related to the coupling loss between the F-P cavity and A excitons in WS2 monolayer is Qc. When SPP waves with frequency ω is launched into this system, the time-evolution normalized amplitude a of the F-P cavity and amplitude b of the exciton transition can be respectively expressed as

$$\frac{{da}}{{dt}} = \left( {j{\omega_0} - \frac{{{\omega_0}}}{{2{Q_1}}} - \frac{{{\omega_0}}}{{2{Q_w}}}} \right)a + j\sqrt {\frac{{{\omega _0}}}{{2{Q_w}}}} {S_{in}} + j\frac{{{\omega _0}}}{{2{Q_c}}}b,$$
$$\frac{{db}}{{dt}} = j{\omega _0}b - \frac{{{\omega _0}}}{{2{Q_2}}}b + j\frac{{\omega {}_0}}{{2{Q_c}}}a.$$
Here, ω0 is the overlapping resonant frequency of the A excition and the F-P resonator. Q1 and Q2 are quality factors related to the intrinsic losses in the F-P resonator and the excition transition, respectively. Because of the power conservation and the time reversal symmetry, the relationship of the amplitudes of the incoming and outgoing SPP waves in the waveguide-resonator system is described as
$${S_{out}} = j\sqrt {\frac{{{\omega _0}}}{{2{Q_w}}}} a.$$
According to above equations, the transmission Tr of the hybrid system is derived as
$${T_r} = {\left|{\frac{{{S_{out}}}}{{{S_{in}}}}} \right|^2} = {\left|{1 - \frac{1}{{{Q_w}}}\frac{{i2({\omega - {\omega_0}} )+ \frac{1}{{{Q_2}}}}}{{{{\left( {i2({\omega - {\omega_0}} )+ \frac{1}{{2{Q_1}}} + \frac{1}{{2{Q_2}}} + \frac{1}{{2{Q_w}}}} \right)}^2} + {{\left( {\frac{1}{{{Q_c}}}} \right)}^2} - {{\left( {\frac{1}{{2{Q_1}}} - \frac{1}{{2{Q_2}}} + \frac{1}{{2{Q_w}}}} \right)}^2}}}} \right|^2}.$$
The transmission spectrum obtained by the CMT is shown in Fig. 2(d). The excellent match between theoretical calculations and FDTD results is found. The corresponding fitted parameters of Q1, Q2, Qw, and Qc are 15.42, 100.06, 22.50, and 19.67, respectively. The coupling strength g can be calculated by $g = \hbar \frac{{{\omega _0}}}{{2{Q_c}}} = \frac{{\hbar \pi c}}{{{\lambda _0}{Q_c}e}}$. Here, ћ is the Planck’s constant divided by 2π. c is the vacuum velocity of light. -e is the electron charge. The unit of the coupling strength g is converted into eV. The fit parameter of the Qc = 19. 67 is obtained. The overlapping resonant wavelength of the A excition and the F-P resonator is λ0 = 617 nm. Hence, the coupling strength g = 51.1 meV and the Rabi splitting energy of ћΩ = 2 g = 102.2 meV are obtained. Both FDTD simulation and CMT analysis confirm that the strong plasmon-exciton coupling, accompanied by the spectral splitting, is realized in the simple waveguide-resonator system with WS2 monolayer. However, if the monolayer WS2 is embedded into the cavity along the x direction (as shown in the inset in Fig. 2(h)), the dipole orientation of excitons is perpendicular to the dominant electric field component (Ey) in the F-P resonator. The inner product of the electric field and the exciton transition dipole moment is nearly zero, and thus the strong plasmon-exciton coupling is not permitted. Without the effect of excitons, the hybrid structure is returned to exhibit the intrinsic band-pass filtering response, as shown in Fig. 2(h). Therefore, an optical switching effect is handily realized just by tuning the orientation of the introduced WS2 monolayer along the cavity.

As a hard evidence of strong coupling, the typical anticrossing behavior is also realized by a small change in the distance L between two metal bars, as shown in Fig. 4(a). It is mainly because that the resonant wavelength of the F-P cavity depends on the length L, as suggested by Eq. (6).

$$2{\mathop{\textrm Re}\nolimits} (\beta )L + 2\varphi = 2m\pi .$$
Here, the m = 2 stands for the second-order F-P resonance. The φ is the reflected phase shift at the air-metal interface. The β is the propagation number of SPP waves along the MIM waveguide and satisfies the dispersion equation [47,48] below.
$$\left. \begin{array}{l} {k_d}{\varepsilon_m}\tanh \left( {\frac{{{k_d}W}}{2}} \right) + {\varepsilon_d}{k_m} = 0\\ {k_d} = \sqrt {{\beta^2} - {\varepsilon_d}{k_0}^2} ,\textrm{ }{k_m} = \sqrt {{\beta^2} - {\varepsilon_m}{k_0}^2} \end{array} \right\}.$$

 

Fig. 4. (a) Color-coded transmission spectra of the hybrid structure with variable lengths L of the F-P cavity. The green and red solid lines represent the uncoupled excitons and the F-P resonance, respectively. The dots denote the hybrid states calculated by the COM. (b) The fractions of the F-P resonance and excitons for the LEHM and HEHM, respectively.

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The ɛd is the permittivity of the insulator in the waveguide and is assumed to be ɛd = 1 for air. The ${k_0} = 2\pi /\lambda$ is the vacuum wave vector. Based on Eqs. (6) and (7), we find that the resonant wavelength of the F-P cavity tends to exhibit a redshift as the length L increases. However, the exciton emission wavelength in WS2 monolayer is unchanged. As the length L increases, the F-P resonance energy shifts across the A-exciton energy. Accompanied by the strong coupling, the unique anticrossing behavior and two new hybrid states are obtained as a result. This behavior can be qualitatively illustrated by the COM in Hamiltonian representation. The collective response of the excitons is viewed as a “super oscillator” and the whole system is qualitatively modeled as two coupled harmonic oscillators. The satisfied eigenvalue equation is expressed as [19,22]

$$\left( {\begin{array}{cc} {{E_{FP}} - i{\Gamma _{FP}}/2}&g\\ g&{{E_{ex}} - i{\Gamma _{ex}}/2} \end{array}} \right)\left( {\begin{array}{c} \alpha \\ \beta \end{array}} \right) = {E_ \pm }\left( {\begin{array}{c} \alpha \\ \beta \end{array}} \right),$$
where EFP and ΓFP represent the F-P resonant energy and its dissipation rate, respectively. The Eex and Γex correspond to the A-exciton energy and its dissipation rate, respectively. E± stand for the eigenvalues corresponding to the energies of two new hybrid modes. The g is the coupling strength. The α and β denote the eigenvectors and satisfy |α|2 + |β|2 = 1. The mixing fractions of |α|2 and |β|2 denote the weighting coefficients of the F-P resonance and excitons at each hybrid mode. For simplicity, the dissipations are ignored and the energies of two new hybrid modes thus are approximated as
$${E_ \pm } = 0.5({{E_{FP}} + {E_{ex}}} )\pm \sqrt {4{g^2} + \delta } ,$$
where δ = EFP - Eex is the energy detuning between the F-P resonance and A excitons. The Rabi splitting energy of ћΩ = 2 g = 109 meV at δ = 0 is extracted from the Fig. 4(a), as also suggested in Fig. 3(c). Meanwhile, the Fig. 2(b) suggests the ΓFP = 81.4 meV. The Γex = 29 meV is obtained by fitting the complex dielectric function of monolayer WS2 to the multi-Lorentzian model [34]. Compared to the fit result of ћΩ = 102.2 meV obtained from the CMT, the extracted ћΩ = 109 meV at δ = 0 from Fig. 4(a) slight overestimates the true Rabi splitting [49]. However, both results suggest that the criterion for strong coupling (ћΩ > (ΓMRex) / 2) is rigorously satisfied. For the energies of two hybrid states, the excellent matching between FDTD simulations and theoretical results is also observed in Fig. 4(a). The fractions of the F-P resonance and excitons constituents in the low- (LEHM) and high-energy (HEHM) hybrid modes are obtained by the COM. They are shown in Fig. 4(b). As the length increases, the detuning changes from positive to negative. The F-P resonant (excitons) constituent dominates HEHM (LEHM) for small lengths and reverses for large lengths. The strong-coupling induced anticrossing response is confirmed again.

In addition to the change in the length of the F-P cavity, the resonant wavelength of the cavity can be tuned by changing refractive index of the insulator filled into the F-P cavity, according to Eqs. (6) and (7). The similar strong-coupling induced anticrossing behavior thus will be obtained with increasing the refractive index, because of the unchanged A-exciton emission energy in WS2 monolayer. Figure 5(a) demonstrates the color-coded transmission spectra for different refractive indices of the insulator filled into the F-P cavity. The outstanding anticrossing behavior indeed is witnessed. Certainly, it should also be pointed out that in addition to the second-order resonance mode, other resonant modes in the F-P cavity can be used for investigating the strong plasmon-exciton coupling, as long as their resonance wavelengths overlap with that of the A excition in WS2 monolayer. However, each-order resonant mode has different electric field distribution, especially the Ey. At the same time, the electric field intensity around the introduced monolayer WS2 directly affects the light-matter interaction in the monolayer material and thereby the coupling strength between plasmons and excitons. Correspondingly, the strong-coupling transmission spectrum hinges on the position of the monolayer WS2 placed at the cavity. As shown in Fig. 2(g), the electric field Ey of the second-order F-P resonance is symmetric at the cavity. Its maximum value appears at the center of the cavity. As the monolayer WS2 keeps away from the center of the cavity, the intensity of the electric field Ey decrease. Therefore, the coupling strength decreases as the distance s increases and the symmetry of the spectral splitting is gradually broken, as illustrated in Fig. 5(b). In other word, we can handily tune the coupling strength between plasmons and excitons only by changing the position of WS2 monolayer in the hybrid system.

 

Fig. 5. (a) Color-coded transmission spectra for different refractive indices of the insulator filled into the F-P cavity with L = 125 nm. (b) Transmission spectra with different distances s of the WS2 monolayer to the center of the cavity. Other simulated parameters are same as these used in Fig. 2(c).

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4. Conclusions

In summary, we have theoretically and numerically investigated, for the first time, the room-temperature strong coupling between excitons and plasmons in the MIM plasmonic waveguide-resonator system. Due to the destructive interference between exciton transition in WS2 monolayer and the F-P resonance, the remarkable spectral splitting appears in the transmission spectrum at visible wavelengths. Due to the strong plasmon-exciton coupling, the anticrossing behavior with the Rabi splitting up to 109 meV is of interesting to be observed by small changes in the length of the F-P cavity and the refractive index of the insulator in the F-P cavity, respectively. More importantly, the intriguing switching response is handily realized by tuning the orientation of the monolayer WS2 along the cavity, and the coupling strength is dynamically tuned by changing the position of the WS2 monolayer. All simulation results are in excellent agreement in theoretical calculations. Our findings thus offer new possibilities of enhancing light-TMDs interactions, and will play a significant role in optical switches and filters at ambient conditions.

Funding

National Natural Science Foundation of China (11604069, 61805064); Fundamental Research Funds for the Central Universities (JZ2019HGTB0091).

Disclosures

The authors declare no conflicts of interest.

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14. O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2,” Nat. Nanotechnol. 8(7), 497–501 (2013). [CrossRef]  

15. J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, D. H. Cobden, and X. Xu, “Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions,” Nat. Nanotechnol. 9(4), 268–272 (2014). [CrossRef]  

16. V. Podzorov, M. E. Gershenson, C. Kloc, R. Zeis, and E. Bucher, “High-mobility field-effect transistors based on transition metal dichalcogenides,” Appl. Phys. Lett. 84(17), 3301–3303 (2004). [CrossRef]  

17. X. Xu, W. Yao, D. Xiao, and T. F. Heinz, “Spin and pseudospins in layered transition metal dichalcogenides,” Nat. Phys. 10(5), 343–350 (2014). [CrossRef]  

18. X. He, F. Liu, F. Lin, G. Xiao, and W. Shi, “Tunable MoS2 modified hybrid surface plasmon waveguides,” Nanotechnology 30(12), 125201 (2019). [CrossRef]  

19. P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015). [CrossRef]  

20. L. Shi, T. K. Hakala, H. T. Rekola, J. P. Martikainen, R. J. Moerland, and P. Törmä, “Spatial coherence properties of organic molecules coupled to plasmonic surface lattice resonances in the weak and strong coupling regimes,” Phys. Rev. Lett. 112(15), 153002 (2014). [CrossRef]  

21. A. Ramasubramaniam, “Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides,” Phys. Rev. B: Condens. Matter Mater. Phys. 86(11), 115409 (2012). [CrossRef]  

22. X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-c. Lin, Y.-H. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2015). [CrossRef]  

23. M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017). [CrossRef]  

24. L. Zhang, R. Gogna, W. Burg, E. Tutuc, and H. Deng, “Photonic-crystal exciton-polaritons in monolayer semiconductors,” Nat. Commun. 9(1), 713 (2018). [CrossRef]  

25. G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114(15), 157401 (2015). [CrossRef]  

26. W. Liu, B. Lee, C. H. Naylor, H. S. Ee, J. Park, A. C. Johnson, and R. Agarwal, “Strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice,” Nano Lett. 16(2), 1262–1269 (2016). [CrossRef]  

27. J. Sun, H. Hu, D. Zheng, D. Zhang, Q. Deng, S. Zhang, and H. Xu, “Light-Emitting Plexciton: Exploiting Plasmon–Exciton Interaction in the Intermediate Coupling Regime,” ACS Nano 12(10), 10393–10402 (2018). [CrossRef]  

28. J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017). [CrossRef]  

29. D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017). [CrossRef]  

30. M. Stührenberg, B. Munkhbat, D. G. Baranov, J. Cuadra, A. B. Yankovich, T. J. Antosiewicz, E. Olsson, and T. Shegai, “Strong Light-Matter Coupling between Plasmons in Individual Gold Bi-pyramids and Excitons in Mono-and Multilayer WSe2,” Nano Lett. 18(9), 5938–5945 (2018). [CrossRef]  

31. H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016). [CrossRef]  

32. L. F. Mattheiss, “Band structures of transition-metal-dichalcogenide layer compounds,” Phys. Rev. B: Condens. Matter Mater. Phys. 8(8), 3719–3740 (1973). [CrossRef]  

33. J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008). [CrossRef]  

34. Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B: Condens. Matter Mater. Phys. 90(20), 205422 (2014). [CrossRef]  

35. K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef]  

36. X. He, F. Liu, F. Lin, and W. Shi, “Investigation of terahertz all-dielectric metamaterials,” Opt. Express 27(10), 13831–13844 (2019). [CrossRef]  

37. C. Shi, X. He, J. Peng, G. Xiao, F. Liu, F. Lin, and H. Zhang, “Tunable terahertz hybrid graphene-metal patterns metamaterials,” Opt. Laser Technol. 114, 28–34 (2019). [CrossRef]  

38. X. He, F. Lin, F. Liu, and W. Shi, “Tunable high Q-factor terahertz complementary graphene metamaterial,” Nanotechnology 29(48), 485205 (2018). [CrossRef]  

39. H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013). [CrossRef]  

40. H. J. Li, L. L. Wang, B. H. Zhang, and X. Zhai, “Tunable edge-mode-based mid-infrared plasmonically induced transparency in the coupling system of coplanar graphene ribbons,” Appl. Phys. Express 9(1), 012001 (2016). [CrossRef]  

41. H. Lu, X. Gan, D. Mao, Y. Fan, D. Yang, and J. Zhao, “Nearly perfect absorption of light in monolayer molybdenum disulfide supported by multilayer structures,” Opt. Express 25(18), 21630–21636 (2017). [CrossRef]  

42. Y. Wang, C. Sun, Q. Gong, and J. Chen, “Coupled-resonator-induced plasmonic bandgaps,” Opt. Lett. 42(20), 4235–4238 (2017). [CrossRef]  

43. J. Chen, C. Sun, H. Li, and Q. Gong, “Ultra-broadband unidirectional launching of surface plasmon polaritons by a double-slit structure beyond the diffraction limit,” Nanoscale 6(22), 13487–13493 (2014). [CrossRef]  

44. J. Chen, C. Sun, K. Rong, H. Li, and Q. Gong, “Polarization-free directional coupling of surface plasmon polaritons,” Laser Photonics Rev. 9(4), 419–426 (2015). [CrossRef]  

45. H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991). [CrossRef]  

46. H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017). [CrossRef]  

47. B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005). [CrossRef]  

48. T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009). [CrossRef]  

49. M. Pelton, S. D. Storm, and H. Leng, “Strong coupling of emitters to single plasmonic nanoparticles: exciton-induced transparency and Rabi splitting,” Nanoscale 11(31), 14540–14552 (2019). [CrossRef]  

References

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  21. A. Ramasubramaniam, “Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides,” Phys. Rev. B: Condens. Matter Mater. Phys. 86(11), 115409 (2012).
    [Crossref]
  22. X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-c. Lin, Y.-H. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2015).
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  23. M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
    [Crossref]
  24. L. Zhang, R. Gogna, W. Burg, E. Tutuc, and H. Deng, “Photonic-crystal exciton-polaritons in monolayer semiconductors,” Nat. Commun. 9(1), 713 (2018).
    [Crossref]
  25. G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114(15), 157401 (2015).
    [Crossref]
  26. W. Liu, B. Lee, C. H. Naylor, H. S. Ee, J. Park, A. C. Johnson, and R. Agarwal, “Strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice,” Nano Lett. 16(2), 1262–1269 (2016).
    [Crossref]
  27. J. Sun, H. Hu, D. Zheng, D. Zhang, Q. Deng, S. Zhang, and H. Xu, “Light-Emitting Plexciton: Exploiting Plasmon–Exciton Interaction in the Intermediate Coupling Regime,” ACS Nano 12(10), 10393–10402 (2018).
    [Crossref]
  28. J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
    [Crossref]
  29. D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017).
    [Crossref]
  30. M. Stührenberg, B. Munkhbat, D. G. Baranov, J. Cuadra, A. B. Yankovich, T. J. Antosiewicz, E. Olsson, and T. Shegai, “Strong Light-Matter Coupling between Plasmons in Individual Gold Bi-pyramids and Excitons in Mono-and Multilayer WSe2,” Nano Lett. 18(9), 5938–5945 (2018).
    [Crossref]
  31. H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
    [Crossref]
  32. L. F. Mattheiss, “Band structures of transition-metal-dichalcogenide layer compounds,” Phys. Rev. B: Condens. Matter Mater. Phys. 8(8), 3719–3740 (1973).
    [Crossref]
  33. J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16(1), 413–425 (2008).
    [Crossref]
  34. Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B: Condens. Matter Mater. Phys. 90(20), 205422 (2014).
    [Crossref]
  35. K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
    [Crossref]
  36. X. He, F. Liu, F. Lin, and W. Shi, “Investigation of terahertz all-dielectric metamaterials,” Opt. Express 27(10), 13831–13844 (2019).
    [Crossref]
  37. C. Shi, X. He, J. Peng, G. Xiao, F. Liu, F. Lin, and H. Zhang, “Tunable terahertz hybrid graphene-metal patterns metamaterials,” Opt. Laser Technol. 114, 28–34 (2019).
    [Crossref]
  38. X. He, F. Lin, F. Liu, and W. Shi, “Tunable high Q-factor terahertz complementary graphene metamaterial,” Nanotechnology 29(48), 485205 (2018).
    [Crossref]
  39. H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
    [Crossref]
  40. H. J. Li, L. L. Wang, B. H. Zhang, and X. Zhai, “Tunable edge-mode-based mid-infrared plasmonically induced transparency in the coupling system of coplanar graphene ribbons,” Appl. Phys. Express 9(1), 012001 (2016).
    [Crossref]
  41. H. Lu, X. Gan, D. Mao, Y. Fan, D. Yang, and J. Zhao, “Nearly perfect absorption of light in monolayer molybdenum disulfide supported by multilayer structures,” Opt. Express 25(18), 21630–21636 (2017).
    [Crossref]
  42. Y. Wang, C. Sun, Q. Gong, and J. Chen, “Coupled-resonator-induced plasmonic bandgaps,” Opt. Lett. 42(20), 4235–4238 (2017).
    [Crossref]
  43. J. Chen, C. Sun, H. Li, and Q. Gong, “Ultra-broadband unidirectional launching of surface plasmon polaritons by a double-slit structure beyond the diffraction limit,” Nanoscale 6(22), 13487–13493 (2014).
    [Crossref]
  44. J. Chen, C. Sun, K. Rong, H. Li, and Q. Gong, “Polarization-free directional coupling of surface plasmon polaritons,” Laser Photonics Rev. 9(4), 419–426 (2015).
    [Crossref]
  45. H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
    [Crossref]
  46. H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017).
    [Crossref]
  47. B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005).
    [Crossref]
  48. T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009).
    [Crossref]
  49. M. Pelton, S. D. Storm, and H. Leng, “Strong coupling of emitters to single plasmonic nanoparticles: exciton-induced transparency and Rabi splitting,” Nanoscale 11(31), 14540–14552 (2019).
    [Crossref]

2019 (4)

X. He, F. Liu, F. Lin, G. Xiao, and W. Shi, “Tunable MoS2 modified hybrid surface plasmon waveguides,” Nanotechnology 30(12), 125201 (2019).
[Crossref]

X. He, F. Liu, F. Lin, and W. Shi, “Investigation of terahertz all-dielectric metamaterials,” Opt. Express 27(10), 13831–13844 (2019).
[Crossref]

C. Shi, X. He, J. Peng, G. Xiao, F. Liu, F. Lin, and H. Zhang, “Tunable terahertz hybrid graphene-metal patterns metamaterials,” Opt. Laser Technol. 114, 28–34 (2019).
[Crossref]

M. Pelton, S. D. Storm, and H. Leng, “Strong coupling of emitters to single plasmonic nanoparticles: exciton-induced transparency and Rabi splitting,” Nanoscale 11(31), 14540–14552 (2019).
[Crossref]

2018 (4)

X. He, F. Lin, F. Liu, and W. Shi, “Tunable high Q-factor terahertz complementary graphene metamaterial,” Nanotechnology 29(48), 485205 (2018).
[Crossref]

J. Sun, H. Hu, D. Zheng, D. Zhang, Q. Deng, S. Zhang, and H. Xu, “Light-Emitting Plexciton: Exploiting Plasmon–Exciton Interaction in the Intermediate Coupling Regime,” ACS Nano 12(10), 10393–10402 (2018).
[Crossref]

M. Stührenberg, B. Munkhbat, D. G. Baranov, J. Cuadra, A. B. Yankovich, T. J. Antosiewicz, E. Olsson, and T. Shegai, “Strong Light-Matter Coupling between Plasmons in Individual Gold Bi-pyramids and Excitons in Mono-and Multilayer WSe2,” Nano Lett. 18(9), 5938–5945 (2018).
[Crossref]

L. Zhang, R. Gogna, W. Burg, E. Tutuc, and H. Deng, “Photonic-crystal exciton-polaritons in monolayer semiconductors,” Nat. Commun. 9(1), 713 (2018).
[Crossref]

2017 (6)

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
[Crossref]

D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017).
[Crossref]

H. Li, M. Qin, L. Wang, X. Zhai, R. Ren, and J. Hu, “Total absorption of light in monolayer transition-metal dichalcogenides by critical coupling,” Opt. Express 25(25), 31612–31621 (2017).
[Crossref]

H. Lu, X. Gan, D. Mao, Y. Fan, D. Yang, and J. Zhao, “Nearly perfect absorption of light in monolayer molybdenum disulfide supported by multilayer structures,” Opt. Express 25(18), 21630–21636 (2017).
[Crossref]

Y. Wang, C. Sun, Q. Gong, and J. Chen, “Coupled-resonator-induced plasmonic bandgaps,” Opt. Lett. 42(20), 4235–4238 (2017).
[Crossref]

2016 (5)

H. J. Li, L. L. Wang, B. H. Zhang, and X. Zhai, “Tunable edge-mode-based mid-infrared plasmonically induced transparency in the coupling system of coplanar graphene ribbons,” Appl. Phys. Express 9(1), 012001 (2016).
[Crossref]

H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
[Crossref]

W. Liu, B. Lee, C. H. Naylor, H. S. Ee, J. Park, A. C. Johnson, and R. Agarwal, “Strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice,” Nano Lett. 16(2), 1262–1269 (2016).
[Crossref]

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nat. Photonics 10(4), 216–226 (2016).
[Crossref]

C. Janisch, H. Song, C. Zhou, Z. Lin, A. L. Elías, D. Ji, and Z. Liu, “MoS2 monolayers on nanocavities: enhancement in light-matter interaction,” 2D Mater. 3(2), 025017 (2016).
[Crossref]

2015 (5)

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
[Crossref]

H. Zhao, Q. Guo, F. Xia, and H. Wang, “Two-dimensional materials for nanophotonics application,” Nanophotonics 4(1), 128–142 (2015).
[Crossref]

G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114(15), 157401 (2015).
[Crossref]

X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-c. Lin, Y.-H. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2015).
[Crossref]

J. Chen, C. Sun, K. Rong, H. Li, and Q. Gong, “Polarization-free directional coupling of surface plasmon polaritons,” Laser Photonics Rev. 9(4), 419–426 (2015).
[Crossref]

2014 (8)

J. Chen, C. Sun, H. Li, and Q. Gong, “Ultra-broadband unidirectional launching of surface plasmon polaritons by a double-slit structure beyond the diffraction limit,” Nanoscale 6(22), 13487–13493 (2014).
[Crossref]

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B: Condens. Matter Mater. Phys. 90(20), 205422 (2014).
[Crossref]

X. Xu, W. Yao, D. Xiao, and T. F. Heinz, “Spin and pseudospins in layered transition metal dichalcogenides,” Nat. Phys. 10(5), 343–350 (2014).
[Crossref]

J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, D. H. Cobden, and X. Xu, “Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions,” Nat. Nanotechnol. 9(4), 268–272 (2014).
[Crossref]

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref]

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref]

L. Shi, T. K. Hakala, H. T. Rekola, J. P. Martikainen, R. J. Moerland, and P. Törmä, “Spatial coherence properties of organic molecules coupled to plasmonic surface lattice resonances in the weak and strong coupling regimes,” Phys. Rev. Lett. 112(15), 153002 (2014).
[Crossref]

J. T. Liu, T. B. Wang, X. J. Li, and N. H. Liu, “Enhanced absorption of monolayer MoS2 with resonant back reflector,” J. Appl. Phys. 115(19), 193511 (2014).
[Crossref]

2013 (3)

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref]

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499(7459), 419–425 (2013).
[Crossref]

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

2012 (3)

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref]

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
[Crossref]

A. Ramasubramaniam, “Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides,” Phys. Rev. B: Condens. Matter Mater. Phys. 86(11), 115409 (2012).
[Crossref]

2011 (1)

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref]

2010 (2)

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105(13), 136805 (2010).
[Crossref]

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10(4), 1271–1275 (2010).
[Crossref]

2009 (1)

2008 (1)

2007 (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref]

2005 (1)

B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87(1), 013107 (2005).
[Crossref]

2004 (1)

V. Podzorov, M. E. Gershenson, C. Kloc, R. Zeis, and E. Bucher, “High-mobility field-effect transistors based on transition metal dichalcogenides,” Appl. Phys. Lett. 84(17), 3301–3303 (2004).
[Crossref]

1991 (2)

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

1973 (1)

L. F. Mattheiss, “Band structures of transition-metal-dichalcogenide layer compounds,” Phys. Rev. B: Condens. Matter Mater. Phys. 8(8), 3719–3740 (1973).
[Crossref]

Agarwal, R.

W. Liu, B. Lee, C. H. Naylor, H. S. Ee, J. Park, A. C. Johnson, and R. Agarwal, “Strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice,” Nano Lett. 16(2), 1262–1269 (2016).
[Crossref]

Alexeev, E. M.

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref]

Antosiewicz, T. J.

M. Stührenberg, B. Munkhbat, D. G. Baranov, J. Cuadra, A. B. Yankovich, T. J. Antosiewicz, E. Olsson, and T. Shegai, “Strong Light-Matter Coupling between Plasmons in Individual Gold Bi-pyramids and Excitons in Mono-and Multilayer WSe2,” Nano Lett. 18(9), 5938–5945 (2018).
[Crossref]

G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114(15), 157401 (2015).
[Crossref]

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref]

Baranov, D. G.

M. Stührenberg, B. Munkhbat, D. G. Baranov, J. Cuadra, A. B. Yankovich, T. J. Antosiewicz, E. Olsson, and T. Shegai, “Strong Light-Matter Coupling between Plasmons in Individual Gold Bi-pyramids and Excitons in Mono-and Multilayer WSe2,” Nano Lett. 18(9), 5938–5945 (2018).
[Crossref]

Barnes, W. L.

P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78(1), 013901 (2015).
[Crossref]

Baumberg, Jeremy J.

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

Boller, K. J.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

Bucher, E.

V. Podzorov, M. E. Gershenson, C. Kloc, R. Zeis, and E. Bucher, “High-mobility field-effect transistors based on transition metal dichalcogenides,” Appl. Phys. Lett. 84(17), 3301–3303 (2004).
[Crossref]

Burg, W.

L. Zhang, R. Gogna, W. Burg, E. Tutuc, and H. Deng, “Photonic-crystal exciton-polaritons in monolayer semiconductors,” Nat. Commun. 9(1), 713 (2018).
[Crossref]

Carnegie, C.

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

Chang, H.

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref]

Z. Sun and H. Chang, “Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology,” ACS Nano 8(5), 4133–4156 (2014).
[Crossref]

Chen, H.

J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
[Crossref]

Chen, J.

J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
[Crossref]

Y. Wang, C. Sun, Q. Gong, and J. Chen, “Coupled-resonator-induced plasmonic bandgaps,” Opt. Lett. 42(20), 4235–4238 (2017).
[Crossref]

J. Chen, C. Sun, K. Rong, H. Li, and Q. Gong, “Polarization-free directional coupling of surface plasmon polaritons,” Laser Photonics Rev. 9(4), 419–426 (2015).
[Crossref]

J. Chen, C. Sun, H. Li, and Q. Gong, “Ultra-broadband unidirectional launching of surface plasmon polaritons by a double-slit structure beyond the diffraction limit,” Nanoscale 6(22), 13487–13493 (2014).
[Crossref]

Chen, P. Y.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref]

Chen, S.

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Cheng, H.

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Chernikov, A.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B: Condens. Matter Mater. Phys. 90(20), 205422 (2014).
[Crossref]

Chikkaraddy, R.

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

Chim, C. Y.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10(4), 1271–1275 (2010).
[Crossref]

Cobden, D. H.

J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, D. H. Cobden, and X. Xu, “Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions,” Nat. Nanotechnol. 9(4), 268–272 (2014).
[Crossref]

Coleman, J. N.

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
[Crossref]

Cuadra, J.

M. Stührenberg, B. Munkhbat, D. G. Baranov, J. Cuadra, A. B. Yankovich, T. J. Antosiewicz, E. Olsson, and T. Shegai, “Strong Light-Matter Coupling between Plasmons in Individual Gold Bi-pyramids and Excitons in Mono-and Multilayer WSe2,” Nano Lett. 18(9), 5938–5945 (2018).
[Crossref]

de Nijs, B.

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

de Pury, A. Casalis

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

Deacon, W.

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

Deng, H.

L. Zhang, R. Gogna, W. Burg, E. Tutuc, and H. Deng, “Photonic-crystal exciton-polaritons in monolayer semiconductors,” Nat. Commun. 9(1), 713 (2018).
[Crossref]

Deng, Q.

J. Sun, H. Hu, D. Zheng, D. Zhang, Q. Deng, S. Zhang, and H. Xu, “Light-Emitting Plexciton: Exploiting Plasmon–Exciton Interaction in the Intermediate Coupling Regime,” ACS Nano 12(10), 10393–10402 (2018).
[Crossref]

D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017).
[Crossref]

Deng, S.

J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
[Crossref]

Deng, Z.

J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
[Crossref]

Duan, X.

H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
[Crossref]

Ee, H. S.

W. Liu, B. Lee, C. H. Naylor, H. S. Ee, J. Park, A. C. Johnson, and R. Agarwal, “Strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice,” Nano Lett. 16(2), 1262–1269 (2016).
[Crossref]

Elías, A. L.

C. Janisch, H. Song, C. Zhou, Z. Lin, A. L. Elías, D. Ji, and Z. Liu, “MoS2 monolayers on nanocavities: enhancement in light-matter interaction,” 2D Mater. 3(2), 025017 (2016).
[Crossref]

Fan, Y.

Galfsky, T.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-c. Lin, Y.-H. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2015).
[Crossref]

Gan, X.

Geim, A. K.

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499(7459), 419–425 (2013).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref]

Gershenson, M. E.

V. Podzorov, M. E. Gershenson, C. Kloc, R. Zeis, and E. Bucher, “High-mobility field-effect transistors based on transition metal dichalcogenides,” Appl. Phys. Lett. 84(17), 3301–3303 (2004).
[Crossref]

Ghimire, N. J.

J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, D. H. Cobden, and X. Xu, “Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions,” Nat. Nanotechnol. 9(4), 268–272 (2014).
[Crossref]

Gogna, R.

L. Zhang, R. Gogna, W. Burg, E. Tutuc, and H. Deng, “Photonic-crystal exciton-polaritons in monolayer semiconductors,” Nat. Commun. 9(1), 713 (2018).
[Crossref]

Gong, Q.

Y. Wang, C. Sun, Q. Gong, and J. Chen, “Coupled-resonator-induced plasmonic bandgaps,” Opt. Lett. 42(20), 4235–4238 (2017).
[Crossref]

J. Chen, C. Sun, K. Rong, H. Li, and Q. Gong, “Polarization-free directional coupling of surface plasmon polaritons,” Laser Photonics Rev. 9(4), 419–426 (2015).
[Crossref]

J. Chen, C. Sun, H. Li, and Q. Gong, “Ultra-broadband unidirectional launching of surface plasmon polaritons by a double-slit structure beyond the diffraction limit,” Nanoscale 6(22), 13487–13493 (2014).
[Crossref]

Grigorieva, I. V.

A. K. Geim and I. V. Grigorieva, “Van der Waals heterostructures,” Nature 499(7459), 419–425 (2013).
[Crossref]

Große, C.

M.-E. Kleemann, R. Chikkaraddy, E. M. Alexeev, D. Kos, C. Carnegie, W. Deacon, A. Casalis de Pury, C. Große, B. de Nijs, J. Mertens, A. I. Tartakovskii, and Jeremy J. Baumberg, “Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature,” Nat. Commun. 8(1), 1296 (2017).
[Crossref]

Guo, Q.

H. Zhao, Q. Guo, F. Xia, and H. Wang, “Two-dimensional materials for nanophotonics application,” Nanophotonics 4(1), 128–142 (2015).
[Crossref]

Hakala, T. K.

L. Shi, T. K. Hakala, H. T. Rekola, J. P. Martikainen, R. J. Moerland, and P. Törmä, “Spatial coherence properties of organic molecules coupled to plasmonic surface lattice resonances in the weak and strong coupling regimes,” Phys. Rev. Lett. 112(15), 153002 (2014).
[Crossref]

Harris, S. E.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

Haus, H. A.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

He, X.

X. He, F. Liu, F. Lin, and W. Shi, “Investigation of terahertz all-dielectric metamaterials,” Opt. Express 27(10), 13831–13844 (2019).
[Crossref]

C. Shi, X. He, J. Peng, G. Xiao, F. Liu, F. Lin, and H. Zhang, “Tunable terahertz hybrid graphene-metal patterns metamaterials,” Opt. Laser Technol. 114, 28–34 (2019).
[Crossref]

X. He, F. Liu, F. Lin, G. Xiao, and W. Shi, “Tunable MoS2 modified hybrid surface plasmon waveguides,” Nanotechnology 30(12), 125201 (2019).
[Crossref]

X. He, F. Lin, F. Liu, and W. Shi, “Tunable high Q-factor terahertz complementary graphene metamaterial,” Nanotechnology 29(48), 485205 (2018).
[Crossref]

Heinz, T. F.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B: Condens. Matter Mater. Phys. 90(20), 205422 (2014).
[Crossref]

X. Xu, W. Yao, D. Xiao, and T. F. Heinz, “Spin and pseudospins in layered transition metal dichalcogenides,” Nat. Phys. 10(5), 343–350 (2014).
[Crossref]

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105(13), 136805 (2010).
[Crossref]

Hill, H. M.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B: Condens. Matter Mater. Phys. 90(20), 205422 (2014).
[Crossref]

Hone, J.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically thin MoS2: a new direct-gap semiconductor,” Phys. Rev. Lett. 105(13), 136805 (2010).
[Crossref]

Hu, H.

J. Sun, H. Hu, D. Zheng, D. Zhang, Q. Deng, S. Zhang, and H. Xu, “Light-Emitting Plexciton: Exploiting Plasmon–Exciton Interaction in the Intermediate Coupling Regime,” ACS Nano 12(10), 10393–10402 (2018).
[Crossref]

Hu, J.

Huang, W.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Imamoglu, A.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

Janisch, C.

C. Janisch, H. Song, C. Zhou, Z. Lin, A. L. Elías, D. Ji, and Z. Liu, “MoS2 monolayers on nanocavities: enhancement in light-matter interaction,” 2D Mater. 3(2), 025017 (2016).
[Crossref]

Ji, D.

C. Janisch, H. Song, C. Zhou, Z. Lin, A. L. Elías, D. Ji, and Z. Liu, “MoS2 monolayers on nanocavities: enhancement in light-matter interaction,” 2D Mater. 3(2), 025017 (2016).
[Crossref]

Johnson, A. C.

W. Liu, B. Lee, C. H. Naylor, H. S. Ee, J. Park, A. C. Johnson, and R. Agarwal, “Strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattice,” Nano Lett. 16(2), 1262–1269 (2016).
[Crossref]

Jones, A. M.

J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, D. H. Cobden, and X. Xu, “Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions,” Nat. Nanotechnol. 9(4), 268–272 (2014).
[Crossref]

Kalantar-Zadeh, K.

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
[Crossref]

Käll, M.

G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114(15), 157401 (2015).
[Crossref]

Kang, M.

D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017).
[Crossref]

Kayci, M.

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2,” Nat. Nanotechnol. 8(7), 497–501 (2013).
[Crossref]

Kéna-Cohen, S.

X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-c. Lin, Y.-H. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2015).
[Crossref]

Kim, H.

Kim, J.

A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, and F. Wang, “Emerging photoluminescence in monolayer MoS2,” Nano Lett. 10(4), 1271–1275 (2010).
[Crossref]

Kis, A.

O. Lopez-Sanchez, D. Lembke, M. Kayci, A. Radenovic, and A. Kis, “Ultrasensitive photodetectors based on monolayer MoS2,” Nat. Nanotechnol. 8(7), 497–501 (2013).
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H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
[Crossref]

H. J. Li, L. L. Wang, B. H. Zhang, and X. Zhai, “Tunable edge-mode-based mid-infrared plasmonically induced transparency in the coupling system of coplanar graphene ribbons,” Appl. Phys. Express 9(1), 012001 (2016).
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Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
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Watanabe, K.

J. S. Ross, P. Klement, A. M. Jones, N. J. Ghimire, J. Yan, D. G. Mandrus, T. Taniguchi, K. Watanabe, K. Kitamura, W. Yao, D. H. Cobden, and X. Xu, “Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p-n junctions,” Nat. Nanotechnol. 9(4), 268–272 (2014).
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J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
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Wersäll, M.

G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114(15), 157401 (2015).
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X. Liu, T. Galfsky, Z. Sun, F. Xia, E.-c. Lin, Y.-H. Lee, S. Kéna-Cohen, and V. M. Menon, “Strong light–matter coupling in two-dimensional atomic crystals,” Nat. Photonics 9(1), 30–34 (2015).
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H. Zhao, Q. Guo, F. Xia, and H. Wang, “Two-dimensional materials for nanophotonics application,” Nanophotonics 4(1), 128–142 (2015).
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X. Xu, W. Yao, D. Xiao, and T. F. Heinz, “Spin and pseudospins in layered transition metal dichalcogenides,” Nat. Phys. 10(5), 343–350 (2014).
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X. He, F. Liu, F. Lin, G. Xiao, and W. Shi, “Tunable MoS2 modified hybrid surface plasmon waveguides,” Nanotechnology 30(12), 125201 (2019).
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C. Shi, X. He, J. Peng, G. Xiao, F. Liu, F. Lin, and H. Zhang, “Tunable terahertz hybrid graphene-metal patterns metamaterials,” Opt. Laser Technol. 114, 28–34 (2019).
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H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
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J. Sun, H. Hu, D. Zheng, D. Zhang, Q. Deng, S. Zhang, and H. Xu, “Light-Emitting Plexciton: Exploiting Plasmon–Exciton Interaction in the Intermediate Coupling Regime,” ACS Nano 12(10), 10393–10402 (2018).
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D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017).
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J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
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X. Xu, W. Yao, D. Xiao, and T. F. Heinz, “Spin and pseudospins in layered transition metal dichalcogenides,” Nat. Phys. 10(5), 343–350 (2014).
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H. J. Li, L. L. Wang, B. H. Zhang, and X. Zhai, “Tunable edge-mode-based mid-infrared plasmonically induced transparency in the coupling system of coplanar graphene ribbons,” Appl. Phys. Express 9(1), 012001 (2016).
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J. Sun, H. Hu, D. Zheng, D. Zhang, Q. Deng, S. Zhang, and H. Xu, “Light-Emitting Plexciton: Exploiting Plasmon–Exciton Interaction in the Intermediate Coupling Regime,” ACS Nano 12(10), 10393–10402 (2018).
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D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017).
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H. J. Li, L. L. Wang, B. H. Zhang, and X. Zhai, “Tunable edge-mode-based mid-infrared plasmonically induced transparency in the coupling system of coplanar graphene ribbons,” Appl. Phys. Express 9(1), 012001 (2016).
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H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, and J. Tian, “Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips,” Appl. Phys. Lett. 103(20), 203112 (2013).
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H. J. Li, L. L. Wang, and X. Zhai, “Plasmonically induced absorption and transparency based on MIM waveguides with concentric nanorings,” IEEE Photonics Technol. Lett. 28(13), 1454–1457 (2016).
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J. Wen, H. Wang, W. Wang, Z. Deng, C. Zhuang, Y. Zhang, F. Liu, J. She, J. Chen, H. Chen, S. Deng, and N. Xu, “Room-temperature strong light-matter interaction with active control in single plasmonic nanorod coupled with two-dimensional atomic crystals,” Nano Lett. 17(8), 4689–4697 (2017).
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D. Zheng, S. Zhang, Q. Deng, M. Kang, P. Nordlander, and H. Xu, “Manipulating coherent plasmon-exciton interaction in a single silver nanorod on monolayer WSe2,” Nano Lett. 17(6), 3809–3814 (2017).
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H. Zhao, Q. Guo, F. Xia, and H. Wang, “Two-dimensional materials for nanophotonics application,” Nanophotonics 4(1), 128–142 (2015).
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Nanoscale (2)

J. Chen, C. Sun, H. Li, and Q. Gong, “Ultra-broadband unidirectional launching of surface plasmon polaritons by a double-slit structure beyond the diffraction limit,” Nanoscale 6(22), 13487–13493 (2014).
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Figures (5)

Fig. 1.
Fig. 1. The x-y cross section of the proposed hybrid structure. The inset shows the schematic.
Fig. 2.
Fig. 2. (a) The permittivity of WS2 monolayer. (b) Transmission spectra of the individual WS2 monolayer and the isolate waveguide-resonator system, respectively. (c) The simulated transmission of the hybrid structure. (d) The transmission spectrum obtained by using the CMT. The inset demonstrates the schematic of the CMT. (e) and (f) respectively illustrate the magnetic field |Hz| and electric field |Ey| distribution of the individual waveguide-resonator system at the transmission peak of 617 nm. (g) The |Ey|2 profile along the x-axis at the line of y = 0 nm. The s stands for the distance between WS2 monolayer and the center of the cavity. (h) The transmission of the hybrid structure with the embedded WS2 monolayer along the x direction. The inset describes the schematic of the corresponding structure.
Fig. 3.
Fig. 3. (a) The diagram of the classical three-level system. The inset shows the absolute absorption of light in the individual WS2 monolayer and that of WS2 in structure. (b) The electric field Ey distribution at the transmission peaks I, III, and the dip II, respectively. (c) The energy diagram at the strong-coupling region.
Fig. 4.
Fig. 4. (a) Color-coded transmission spectra of the hybrid structure with variable lengths L of the F-P cavity. The green and red solid lines represent the uncoupled excitons and the F-P resonance, respectively. The dots denote the hybrid states calculated by the COM. (b) The fractions of the F-P resonance and excitons for the LEHM and HEHM, respectively.
Fig. 5.
Fig. 5. (a) Color-coded transmission spectra for different refractive indices of the insulator filled into the F-P cavity with L = 125 nm. (b) Transmission spectra with different distances s of the WS2 monolayer to the center of the cavity. Other simulated parameters are same as these used in Fig. 2(c).

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

α = V w ( x , y ) d V 0.5 c ε 0 | E i n c | 2 S cos θ ,
d a d t = ( j ω 0 ω 0 2 Q 1 ω 0 2 Q w ) a + j ω 0 2 Q w S i n + j ω 0 2 Q c b ,
d b d t = j ω 0 b ω 0 2 Q 2 b + j ω 0 2 Q c a .
S o u t = j ω 0 2 Q w a .
T r = | S o u t S i n | 2 = | 1 1 Q w i 2 ( ω ω 0 ) + 1 Q 2 ( i 2 ( ω ω 0 ) + 1 2 Q 1 + 1 2 Q 2 + 1 2 Q w ) 2 + ( 1 Q c ) 2 ( 1 2 Q 1 1 2 Q 2 + 1 2 Q w ) 2 | 2 .
2 R e ( β ) L + 2 φ = 2 m π .
k d ε m tanh ( k d W 2 ) + ε d k m = 0 k d = β 2 ε d k 0 2 ,   k m = β 2 ε m k 0 2 } .
( E F P i Γ F P / 2 g g E e x i Γ e x / 2 ) ( α β ) = E ± ( α β ) ,
E ± = 0.5 ( E F P + E e x ) ± 4 g 2 + δ ,

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