Strong light-matter coupling in ${\mathrm{MoS}}_2$

Polariton-based devices require materials where light-matter coupling under ambient conditions exceeds losses, but our current selection of such materials is limited. Here we measured the dispersion of polaritons formed by the $A$ and $B$ excitons in thin ${\mathrm{MoS}}_2$ slabs by imaging their optical near fields. We combined fully tunable laser excitation in the visible with a scattering near-field optical microscope to excite polaritons and image their optical near fields. We obtained the properties of bulk ${\mathrm{MoS}}_2$ from fits to the slab dispersion. The in-plane excitons are in the strong regime of light-matter coupling with a coupling strength ($40-100\mathrm{meV}$) that exceeds their losses by at least a factor of two. The coupling becomes comparable to the exciton binding energy, which is known as very strong coupling. ${\mathrm{MoS}}_2$ and other transition metal dichalcogenides are excellent materials for future polariton devices.

Figure 1

Dispersion of the (a) ${\mathrm{TE}}_0$ and (b) ${\mathrm{TM}}_0$ modes in a thin slab of a layered material with an exciton resonance. The slab thickness is shown in the legend in (b). The full line is the photon dispersion in air, the dashed line is the dispersion of the substrate with ${\varepsilon }_s=2.25$, and the dotted line is the dispersion for a dielectric constant (a) ${\varepsilon }_b=20$ and (b) ${\varepsilon }_o=9$. The exciton was modeled as being polarized within the plane with ${\omega }_{ex}=2\mathrm{eV}$, ${\gamma }_{ex}=50\mathrm{meV}$, and $g_{ex}=100\mathrm{meV}$.

Figure 2

Near-field imaging. (a) Sketch of the metallic tip that excites an exciton polariton in a flake of ${\mathrm{MoS}}_2$ (green) when illuminated by a laser with wavelength ${\lambda }_{pt}$. The polariton scatters at the edge of the sample and is emitted partly into free space. Light gets scattered also by the tip directly, which will interfere with the edge-emitted photons. (b) On-top view of light emission in the $\theta =0^{\circ }$ configuration. $\theta$ is the angle between the optical axis of the mirror and the sample edge, see supplemental material for details [36]. The electric fields $E_s$ produced at the tip and $E_m$ produced at the edge interfere in the detection system (indicated as the red line representing the collecting mirror). Yellow dot: tip, green line: ${\mathrm{MoS}}_2$ edge. The inset at the bottom shows the in-plane corrdinate system. (c) Near-field amplitude on an ${\mathrm{MoS}}_2$ flake with $d=68\mathrm{nm}$ excited at ${\lambda }_{pt}=578\mathrm{nm}$. Clearly visible are the interference patterns from the superposition of $E_s$ and $E_m$. (d) Topography image recorded simultanesouly with (c).

Figure 3

Experimental dielectric function of thin ${\mathrm{MoS}}_2$ slabs. Dots: Dispersion of the ${\mathrm{TM}}_0$ mode measured with the s-SNOM at a flake with (a) $d=68\mathrm{nm}$, (b) 58 nm (blue), and 82 nm (purple). (a) The line is a fit to the experimental data with Eq. (2). (b) The lines are plots of the predicted ${\mathrm{TM}}_0$ dispersion using the fit parameters of (a); see Table 1.

Figure 4

Imaginary and real parts of the polariton wave vector in the $d=68\mathrm{nm}{\mathrm{MoS}}_2$ flake. The data points were obtained from the near-field images; see Supplemental Fig. S1. The line is a fit obtained from the data in Fig. 3; see text.

Figure 5

Index of refraction in ${\mathrm{MoS}}_2$. The full line shows the polaritonic contribution to the index of refraction as determined from the slab measurements. The dashed red line is for ellipsometry measurements (Ref. [12]) and the dashed blue line is from optical reflectance (Ref. [11]).