Resonant interaction of molecular vibrations and surface plasmon polaritons: The weak coupling regime

Adjusting the free-electron concentration, the surface plasmon frequency of the semiconductor ZnOGa is tuned into resonance with the molecular vibrations of the $n$-alkane tetracontane. Closed molecular films deposited on the semiconductor's surface in the monolayer regime generate distinct signatures in total-attenuated-reflection spectra at the frequencies of the symmetric and asymmetric stretching vibrations of the ${\mathrm{CH}}_2$ group. Their line shape undergoes profound changes from absorptive to dispersive and even antiresonance behavior when moving along the surface-plasmon dispersion by the angle of incidence. We demonstrate that this line-shape diversity results from a phase-sensitive perturbation of the surface-plasmon-polariton generation at the molecule-metal interface.

Figure 1

(a) SPP dispersion of the sole air-ZnOGa interface and positions of the symmetric and asymmetric ${\mathrm{CH}}_2$ vibrational resonances of C40. The dispersion is derived from $[1+{\epsilon }_p\left(\omega \right)]c^2{k}_{\parallel }^2={\omega }^2{\epsilon }_p\left(\omega \right)$ with $\hslash {\omega }_p=0.94\mathrm{eV}$ and $\hslash {\gamma }_p=63\mathrm{meV}$ [16]. The resultant surface plasmon frequency is $\hslash {\omega }_{sp}=\hslash {\omega }_p/\sqrt{1+{\epsilon }_{bp}}=0.43\mathrm{eV}$. Dotted: photon line. Inset: Transmission spectra of C40 on sapphire recorded for reference. The dashed vertical lines in the main panel represent the two transmission minima. (b) Atomic force image of the C40 layer with almost upright-standing molecules on the ZnOGa surface. (c) Schematics of the ATR measurements with the Si hemisphere. The in-plane wavevector of the dispersion in (a) is set by the angle of incidence $\alpha$ through $k_{\parallel }=\sqrt{{\epsilon }_{Si}}(\omega /c)sin\alpha$. For more details of the setup, see Ref. [15].

Figure 2

ATR spectra of the C40-ZnOGa specimen described in the text. (a) TM polarization for different angles of incidence (denoted at the curves). (b) Example for agreement between experimental (full curve) and calculated (dotted curve) spectra in TM polarization. (c) Comparison of TE and TM polarization at maximum molecular signal $\left(\alpha ={22}^{\circ }\right)$. For parameters used in the transfer matrix computations, see caption of Fig. 1 (ZnOGa) and text. In (a) and (c), spectra are vertically shifted to increase visibility of the molecular features.

Figure 3

ATR spectra in vicinity of the vibrational resonances. The baseline (zero signal) is related to the background signal obtained by (i) extrapolating the spectra from sufficiently far distances continuously through the resonance region for the experimental data and (ii) by switching off the resonance contribution $\left({\epsilon }_m={\epsilon }_{bm}\right)$ in the calculations. The arrows mark the position of the broad ATR minimum of the SPP feature.

Figure 4

ATR line shape of the molecular signal in the weak-coupling regime. All frequencies are measured in units of ${\omega }_{sp}^{*}$. (a) Resonance case: Inverted absorptive line shape. Full curve: Exact slab reflectivity ${\left|r\right|}^2$. Dashed curve: Account of the molecular resonance only in $r_2$. For other detunings, the agreement is similarly perfect. Left inset: Overview spectrum. Right inset: $|r_2{|}^2$ in vicinity of the molecular transition. (b) Depth of the reflectivity minimum in $|r_0{|}^2$ as function of the SPP frequency. Inset: Configuration analyzed. (c) Phases of $r_0$ and $\delta r_0$ versus frequency $\omega$ at the ${\omega }^{*}$ marked by arrows in (b). Parameters: ${\omega }_L^2-{\omega }_T^2={10}^{-4},2{\gamma }_m={10}^{-3}$ [for (a) only], ${\gamma }_p=0.1$ [and ${\gamma }_p=0.05,0.01$ in (b)], all in units of the half-space surface-plasmon frequency ${\omega }_p/\sqrt{{\epsilon }_{bp}+{\epsilon }_{bm}},d=0.05(2\pi c/{\omega }_{sp})$.

Figure 5

Plasmonic environment: Contour plot in the $\omega {\omega }^{*}$-plane of (a) the phase term $sin\left(\delta \varphi \right)$ and (b) the amplitude $2|r_0\delta r_0|$ term in Eq. (4). Parameters as described in the legend of Fig. 4. The inserted curves depict symbolically the line shape of the molecular transition at representative locations.