# Hyperspectral Molecular Orientation Mapping in Metamaterials
## 3 Results and Discussion  
### 3.1 4-pol. Chemical Mapping: Image Shifts and Baseline Correction  
Figure 1a shows an absorbance map of MIM areas with diameters \(d\) ranging from 500 nm (pattern #1) to 1600 nm (#24) with increment \(\Delta d=50\) nm. The triangular lattice period was \(\Lambda=1.5d\) with a single pixel on the sample being \(25\times 25\) um\({}^{2}\). Figure 1b shows the corresponding integrated spectra from area #21 at four polarisations. At the magnification used, the side length of each area was approximately 10 pixels (pattern area \(\sim\)250 \(\times\) 250 um\({}^{2}\)). The integrated absorbance over the sample area, showed strong differences in the MIM regions with different diameters recognisable by the blue-yellow (weak-strong) absorbance map; quantitative analysis at specific wavelengths is presented further in the text. Absorbance amplitude at specific absorption bands were polarisation dependent (b), which provides a direct motivation to apply the four polarisation method. The strongest absorbance band for C=O stretch at 1810 cm\({}^{-1}\) was chosen for the orientation analysis (Figure 2a). Orientation angle \(\theta_{O}\) for the best fit of the absorbance at the four \(\theta\) angles by \(A(\theta)\propto Amp\times\cos(2\theta-2\theta_{O})\) is shown in Figure 2b. The length of arrows is proportional to the amplitude of the absorbance (the strongest absorbance). It is apparent that the strongest orientation changes were observed at the very edges of the MIM regions where absorbance changed over 2-3 pixels (\(\sim\)50 um). This indicates the importance of alignment of the images taken at different orientations of the polarisation grid. Slight lateral shifts occur when polariser is rotated, primarily due to noninfinity corrected optics in the spectrometer (beam had a slight convergence at the mesh-grid polariser plane). Next, chemical mapping was carried at a larger magnification (a smaller field of view) with pixel size of \(6.25\times 6.25\) um\({}^{2}\). Since there were small lateral shifts between images taken at four different orientations \(\theta\), we applied lateral xy-plane compensation shifts as illustrated in Figure 3a. The central cross sections of the absorbance map along x and y-axes were used for alignment compensation of the overlay Figure 3c. The judgement of best compensation was carried out by maximising the area of overlap (below the cross section curve) at four polarisation angles. Once lateral compensation of image overlay was made (Figure 3), the integrated absorbance was baseline corrected. For this, a central region of the pattern where absorbance is maximum was selected (two edge pixels were not included in calculating the average  
Figure 2: Orientation mapping. (**a**) FTIR Absorbance \(Abs=-\lg(T)\) map of metal-insulator-metal (MIM) metasurfaces at the 1810 cm\({}^{-1}\) polyimide band (see Figure 1b). (**b**) Orientation angle \(\theta_{O}\) extracted from a fit to the absorbance at four polarisation angles by \(Amplitude\times\cos^{2}(\theta-\theta_{O})\). The length of arrow is proportional to \(Amp\) of absorbance and the orientation of absorbing dipoles is \(\theta_{O}\); 0° is x-axis (horizontal). absorbance spectrum). The average spectra are shown before and after baseline correction in Figure 4. First, the region where absorbance does not change (out from the absorbance bands at 3250 cm\({}^{-1}\)was set as the minimum and was intensity shifted for all four spectra to match. In this particular example (Figure 3), it was corresponding to the zero absorbance \(A=0\). Spectra measured at all four polarisations was set to the the same minimum to correct for the baseline. After the lateral compensation and baseline correction, the four polarisation fit was carried out for every single pixel in the hyperspectral data set. The amplitude of absorbance  
Figure 4: Baseline correction for the integrated absorbance; integration was carried out over the most uniform part of MIM region excluding the edge regions where strongest absorbance changes occurred.