Spatial Coherence Properties of Organic Molecules Coupled to Plasmonic Surface Lattice Resonances in the Weak and Strong Coupling Regimes

We study spatial coherence properties of a system composed of periodic silver nanoparticle arrays covered with a fluorescent organic molecule (DiD) film. The evolution of spatial coherence of this composite structure from the weak to the strong coupling regime is investigated by systematically varying the coupling strength between the localized DiD excitons and the collective, delocalized modes of the nanoparticle array known as surface lattice resonances. A gradual evolution of coherence from the weak to the strong coupling regime is observed, with the strong coupling features clearly visible in interference fringes. A high degree of spatial coherence is demonstrated in the strong coupling regime, even when the mode is very excitonlike (80%), in contrast to the purely localized nature of molecular excitons. We show that coherence appears in proportion to the weight of the plasmonic component of the mode throughout the weak-to-strong coupling crossover, providing evidence for the hybrid nature of the normal modes.

Figure 1

(a) A SEM of a typical sample. The scale bar is $1\mu \mathrm{m}$ (200 nm for the inset). (b) The measurement setup. Angle resolved transmission spectra for each array were measured by placing the back focal plane of the sample at the entrance slit of the spectrometer. For spatial coherence measurements, a double slit was placed at the first intermediate image plane of the system.

Figure 2

The dispersions of three different nanoparticle arrays with inreasing DiD concentration. (a)–(e) Array 1, $(d_x)\times (d_y)=50\mathrm{nm}\times 220\mathrm{nm}$, $p_x=500\mathrm{nm}$. (f)–(j) Array 2, $(d_x)\times (d_y)=50\mathrm{nm}\times 355\mathrm{nm}$, $p_x=500\mathrm{nm}$. (k)–(o) Array 3, $(d_x)\times (d_y)=50\mathrm{nm}\times 167\mathrm{nm}$, $p_x=380\mathrm{nm}$. The first column corresponds to a case without DiD molecules, while the second, third, fourth, and fifth columns have 20, 200, 400, and 800 mM concentrations of DiD, respectively. White areas correspond to maximum extinction. The blue horizontal lines depict the absorption maximum of the DiD film. The yellow lines correspond to peak positions obtained from fitting a Gaussian curve to the line cuts of dispersions while keeping $k$ constant, and the red lines are obtained from the coupled oscillator model. (p) The SLR-exciton coupling strength as a function of square root of concentration. The blue plus signs, red crosses, and green circles correspond to arrays 1, 2, and 3, respectively. (q)–(s) The relative SLR-exciton weights of arrays 1–3, respectively. The solid (dashed) line corresponds to exciton (SLR) percentage and black, orange, and purple to concentrations of 200, 400, and 800 mM, respectively.

Figure 3

(a)–(d) The spatial coherence images for array 2 with concentrations 0, 20, 400, and 800 mM, respectively. Here white areas correspond to transmission maximum. The yellow lines (gray) have the same meaning as in Fig. 2. (e) A sample having a random distribution of nanoparticles with 800 mM DiD concentration. Two transmission minima are seen at 1.85 eV (yellow or gray line) and 2.25 eV, corresponding to DiD absorption and the single particle plasmon resonance, respectively.

Figure 4

(a) A close-up of the spatial coherence image (800 mM concentration). (b) The interference image obtained from the coupled oscillator model. (c) The $\mathrm{\Delta }k$ obtained from the experiments (red empty circles) and from the coupled oscillator model (blue crosses). Dashed and solid lines correspond to the SLR and exciton weights of the mode, respectively. (d) The spatial coherence length obtained from the experiments (red solid circles) and from the coupled oscillator model (blue empty circles). The dashed line is the effective interslit distance at the sample plane.