# Hyperspectral Molecular Orientation Mapping in Metamaterials
## 3 Results and Discussion
### Anisotropy, Orientation Maps and Absorbance Line-Shapes  
From the 4-pol. fit the orientation of absorbers \(\Theta_{0}\) can be extracted. For the larger disk diameters \(d\), the plasmonic resonance and field enhancement in the polyimide 60-nm-thick film occurs at the longer wavelengths (smaller wavenumbers) with rich spectral features (Figure 1b). Figure 7 shows orientation maps \(\Theta_{0}\) in colour for the regions #22 and 21 at several absorbance bands. Apart from the edge effects (edges are different on left-right sides as compared with the top-bottom for the triangular lattice pattern), there were apparent orientation patterns for the 2735 cm\({}^{-1}\) C-H alkyl band and surprisingly for the O-H (water) band at 3850 cm\({}^{-1}\). There was approximately 90\({}^{\circ}\) orientation difference between the two. Since polyimide is water permeable material [32], there should be preferential adsorbed water orientation inside polyimide film. As described previously in Section 2, polyimides have anisotropy with preferential molecular alignment in the plane of film and perpendicular to it. More detailed measurements of the absorption at the C-H alkyl bands were investigated where anisotropy was present. The large planar PMDA segment of polyimide has a C-H predominantly aligned in the direction perpendicular to the molecular chain (vertical in the chemical structure shown in Figure 7). Figure 8a shows 4-pol. data plotted for the all segments #1-22 after the position shift and baseline correction were made as previously described. There was a distinct pattern of the absorbance peaks blue-shifted (higher energy/wavenumber) for the 0\({}^{\circ}\) (horizontal) orientation while the largest red-shift was for the 90\({}^{\circ}\) (vertical) orientation in back-reflected signal. This tendency was consistent over the entire O-H and C-H bands 3700-2700 cm\({}^{-1}\) window and extending to the low energy 1000 cm\({}^{-1}\) spectral range here isotropic absorbance was detected (see Figure 7). This polarisation response can be explained by the plasmonic pattern which has larger separation between Au-disks in horizontal direction as compared with vertical, \(\Lambda_{H}>\Lambda_{V}\). As we showed for the rectangular pattern with different periods in horizontal and vertical directions [33], the absorbance along the larger period of nanodisks was blue-shifted and vice versa or visible to near-IR spectral range. The same scaling was observed in the case of MIM patterns for IR wavelengths (Figure 8a). The orientation of absorbing dipoles \(\Theta_{0}\) determined from the 4-pol. method at a particular wavenumber was found to be dependent on the polarisation and wavelength at which it was measured (Figure 8b). This is a consequence of two contributions: (1) the cross-coupling between plasmonic bands of different separation between nanoparticles (discussed above) and (2) phase changes around the absorption band. Apart of the purely plasmonic nature of nanodisks (1), these small \(\sim 15\) cm\({}^{-1}\) spectral shifts for the two perpendicular polarisations can be additionally affected by the very nature of the phase changes (2) around the absorption band of polyimide discussed next. Figure 6: Sub-wavelength mapping of MIM metasurface. Absorbance maps at selected wavelengths in the region #2 and #1 overlaid with orientation angle \(\theta_{O}\) map (spectra are shown in Figure 5). One pixel is \(6.25\times 6.25\) μm\({}^{2}\) on the sample. Each pixel contains approximately 6–8 periods of the MIM structure: #1 has \(d=0.5\) μm and period of \(\Lambda=1.5d=0.75\) μm, while the wavelength is \(7.14\) μm at the 1400 cm\({}^{-1}\). Figure 8: Spectral absorption lineshape dependence on the polarisation (for compensated shifted and baseline corrected spectra). (**a**) Cumulative spectra from all #1-22 regions at four polarisations; the inset shows the absorption map. The quality factors of the resonance bands is \(Q\equiv\omega_{0}/\Delta\omega=1/(2\gamma)\approx 11\).