Strong coupling of monolayer $\mathrm{W}{\mathrm{S}}_2$ excitons and surface plasmon polaritons in a planar $\mathrm{Ag}/\mathrm{W}{\mathrm{S}}_2$ hybrid structure

Monolayer (1L) transition-metal dichalcogenides (TMDCs) are of strong interest in nanophotonics due to their narrow-band intense excitonic transitions persisting up to room temperature. When brought into resonance with surface plasmon polariton (SPP) excitations of a conductive medium, opportunities arise for studying and engineering strong light-matter coupling. Here, we consider a very simple geometry, namely a planar stack composed of a thin silver film, an ${\mathrm{Al}}_2{\mathrm{O}}_3$ spacer, and a monolayer of $\mathrm{W}{\mathrm{S}}_2$. We perform total internal reflection ellipsometry, which combines spectroscopic ellipsometry with the Kretschmann-Raether-type surface plasmon resonance configuration. The combined amplitude and phase response of the reflected light at varied angles of incidence proves that despite the atomic thinness of $1\text{L-}\mathrm{W}{\mathrm{S}}_2$, the strong-coupling (SC) regime between $A$ excitons and SPPs propagating in the thin Ag film is reached. The phasor representation of $\rho =r_p/r_s$, where $r_p$ and $r_s$ are the Fresnel refection coefficients in $p$- and $s$-polarization, respectively, corroborates SC as $\rho$ undergoes a topology change indicated by the occurrence of a double point at the crossover from the weak- to the strong-coupling regime. Our findings are validated by both analytical transfer-matrix method calculations and numerical Maxwell simulations. The findings open up new perspectives for applications in plasmonic modulators and sensors benefitting from the tunability of the optical properties of $1\text{L-}\mathrm{TMDCs}$ by electric fields, electrostatic doping, light, and the chemical environment.

Figure 1

(a) Sample layout and TIRE geometry to study the coupling between SPPs of an Ag film and $1\text{L-}\mathrm{W}{\mathrm{S}}_2$ excitons. An Ag (50.8 nm)/ ${\mathrm{Al}}_2{\mathrm{O}}_3$ (2 nm)/$1\text{L-}\mathrm{W}{\mathrm{S}}_2$ stack is attached to a BK7 glass prism. Ellipsometry measurements are performed at a variable angle of incidence $\theta$. (b) Ellipsometric parameters $\mathrm{\Psi }$ (blue) and $\mathrm{\Delta }$ (red) recorded at an angle of incidence $\theta =43.{55}^{\circ }$. The symbols represent the experimental data. The solid lines are fits to the data as described in the main text. (c) Real ($n$) (green) and imaginary part ($\kappa$) (blue) of the dielectric function of $1\text{L-}\mathrm{W}{\mathrm{S}}_2$ extracted from the ellipsometry measurement in (a). (d) Representation of the phasor $\rho \left(E_{\mathrm{ph}}\right)$ in the complex plane at an angle of incidence $\theta =43.{55}^{\circ }$ where the Ag SPP is in resonance with $1\text{L-}\mathrm{W}{\mathrm{S}}_2 X_A$. The photon energy $E_{\mathrm{ph}}$ covers a range from 1.46 to 3.54 eV and runs along the black arrow. The orange arrows in (b) and (d) indicate a photon energy of 2.022 eV. (e) Representation of the phasor $\rho \left(E_{\mathrm{ph}}\right)$ in the complex plane at an angle $\theta ={50}^{\circ }$ where the Ag SPP is in resonance with $1\text{L-}\mathrm{W}{\mathrm{S}}_2 X_C$. The photon energy $E_{\mathrm{ph}}$ covers again a range from 1.46 to 3.54 eV. The orange arrow indicates a photon energy of 2.84 eV.

Figure 2

Density plots of the $|r_p/r_s|$ spectra of the ${\mathrm{Ag}/\mathrm{Al}}_2{\mathrm{O}}_3/1\text{L-}\mathrm{W}{\mathrm{S}}_2$ stack embedded between BK7 glass and air vs the angle $\theta$ obtained from ellipsometry measurements (a) and TMM simulations (b). For better contrast, the second derivative $\frac{{\partial }^2}{\partial E^2}\left|r_p/r_s\right|$ of the spectra is plotted. The TMM simulations are performed with the dielectric functions of Ag and $1\text{L-}\mathrm{W}{\mathrm{S}}_2$ derived from the fit of ellipsometry measurements depicted in Fig. 1. (c) Dispersion relation $E$ vs $k_{\parallel }$ of the coupled $1\text{L-}\mathrm{W}{\mathrm{S}}_2 X_A\text{−}\mathrm{Ag}$ SPP resonances. The symbols represent the energetic positions of the minima in the $|r_p/r_s|$ spectra. The solid line is a fit to the data using the coupled oscillator model as described in the main text. The inset shows that the ${|r_p/r_s|}^2$ spectrum of the coupled $X_A\text{−}\mathrm{SPP}$ resonances is composed of two peaks with very similar FWHM. The fit of the spectrum was performed with two pseudo Voigt profiles.

Figure 3

TMM simulations of an $\mathrm{Ag}\left(50\mathrm{nm}\right)/{\mathrm{Al}}_2{\mathrm{O}}_3\left(2\mathrm{nm}\right)/\mathrm{Lorentz}$ oscillator (0.72 nm) stack embedded between BK7 glass and air. As in the experiment, the light is incident from the BK7 glass. The ellipsometric parameters $\tan \mathrm{\Psi }=|r_p/r_s|$ (a) and $\mathrm{\Delta }$ (b) as well as the parametric plot of $\rho \left(E_{\mathrm{ph}}\right)$ in the complex plane (c) are calculated as functions of the strengths $\beta$ of the oscillators given in (b) (different shades of blue). The definition of $\beta$ is given in (c). For comparison, the red dashed curve in (c) depicts $\rho \left(E_{\mathrm{ph}}\right)$ of the uncoupled SPP obtained by setting $\beta =0.$