Strong Coupling between Molecular Excited States and Surface Plasmon Modes of a Slit Array in a Thin Metal Film

We demonstrate strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film. The coupling manifests itself as an anticrossing behavior of the two newly formed polaritons. As the coupling strength grows, a new mode emerges, which is attributed to long-range molecular interactions mediated by the plasmonic field. The new, molecular-like mode repels the polariton states, and leads to an opening of energy gaps both below and above the asymptotic free molecule energy.

Figure 1

Simulated absorption spectrum (dash line) of a 10 nm molecular layer and transmission spectrum (solid line) of bare Ag slit array with thickness of 100 nm. The molecular transition frequency is 2.62 eV, with transition dipole moment of 25.5 Debye, radiationless lifetime of 1 ps, and molecular density of $3\times {10}^{25}{\mathrm{m}}^{-3}$. The slit array periodicity is 410 nm with slit width of 160 nm. The inset schematically depicts the hybrid system: molecular layer is deposited directly on the Ag slit array.

Figure 2

(a) Transmission spectra for the series of Ag slit arrays covered by a 10 nm thin film of molecular layer with a density of ${10}^{24}{\mathrm{m}}^{-3}$. The molecular parameters, are as for Fig. 1, but with radiationless lifetime of 300 fs. By changing the slit array periodicity, the SPP modes are tuned to be off and on resonance with respect to the molecular subsystem. (b) Positions of the peaks in panel (a) are plotted as functions of the slit array period. The solid curves superimposed on the numerically derived eigenmodes result from diagonalizing the Hamiltonian of the system [Eq. (1)].

Figure 3

Transmission spectra for the Ag slit array with periodicity of 410 nm, covered by a thin film of molecular layer with molecular parameters are as for Fig. 1. When the molecular density is high (a) or the transition dipole moment value is large (b), an additional mode (splitting) is observed. Insets: RS values as function of (a) the square root of molecular densities and (b) as a function of molecular dipole moment values. The curves are displaced for clarity.

Figure 4

(a) Transmission spectra for the series of Ag slit arrays covered by a 10 nm thin film of molecular layer with a density of $3\times {10}^{25}{\mathrm{m}}^{-3}$. The molecular parameters are as for Fig. 1. An additional mode is clearly seen at about 2.64 eV. (b) Anticrossing behavior of the hybrid system with RS value of 0.15 eV. The peak position of the additional mode barely changes with detuning of the SPP mode. The solid curves superimposed on the numerically derived eigenmodes result from diagonalizing the Hamiltonian of the system [Eq. (1)]. The orange (gray) zone indicates an opening of an energy gap between the molecular state and the upper polariton.

Figure 5

Set of transmission spectra for the Ag slit array with slit width of 160 nm and periodicity of 410 nm covered by a spacer with varied thickness of $d=0–300\mathrm{nm}$ and a thin molecular film with the same parameters as for Fig. 1. At $d=0–100\mathrm{nm}$ three peaks are observed, whereas at $d=300\mathrm{nm}$ the three peaks merge and almost no splitting is observed.

Figure 6

Simulated transmission spectra for Ag slit array covered by molecules with physical parameters as in Fig. 1. When all interactions are taken into account (middle curve) at a molecular density of $3\times {10}^{25}{\mathrm{m}}^{-3}$, a third peak close to the molecular transition is observed. When plasmon-induced dipole-dipole interactions are excluded the RS value is smaller and the third peak disappears (bottom). At the even higher molecular density of ${10}^{27}{\mathrm{m}}^{-3}$, the third peak is not observed.