# Hyperspectral Molecular Orientation Mapping in Metamaterials
## 3 Results and Discussion
### Anisotropy, Orientation Maps and Absorbance Line-Shapes
(**b**) The single polarisation 0\({}^{\circ}\)-horizontal (red) and 90\({}^{\circ}\)-vertical (blue) absorbance maps at the maximum of the corresponding absorbance (see, (**a**)). Line-markers show the orientation measured from 4-pol. angles overlaid on the absorbance map at the particular wavenumber. The inset shows phase change \(\varphi\) at the resonance \(\omega_{0}\) of harmonic oscillator at different damping \(\gamma=0.05\) (weak) and 0.5. The E- and H-field orientations for reflection from a surface with refractive index \(n>1\) and \(n<1\) are shown; subscripts “in” and “re” stands for the incident and reflected, \(k\) is the wavevector. Figure 7: Orientation angle \(\theta_{0}\) obtained from the 4-pol best fit at different absorption bands (see wavenumbers) for the #22, 21 regions (see Figure 1). The top-inset shows chemical formula of PDDA-ODA polyimide. The phase change around the absorption band of material with complex refractive index (\(\tilde{n}=n+i\kappa\)) have the phase change due to real part (a phase delay) and due to change of phase at the resonance. For the considered here case, polyimide and gold optical properties are important. The phase change of the reflected field \(E_{re}\) (in air) from the surface with refractive index \(n\) is defined by \(E_{re}=-\frac{n-1}{n+1}E_{in}\), where \(E_{in}\) is the incident E-field; the \"-\" sign means the opposite phase or the \(\pi\)-shift. When \(n>1\), there is a \(\pi\)-shift between the incident and reflected E-fields of light (see the inset in Figure 8b). Since the real part of refractive index of gold \(n<1\) for the visible-IR spectral range, there is no phase change between \(E_{re}\) and \(E_{in}\). For polyimide with \(n\approx 1.5\), there is \(\pi\)-shift upon reflection. Metamaterial reflectors are designed to harness vectorial nature of reflection [34]. Since the optical absorbance measurements of MIM structures were carried out in reflection, the phase changes in 60-nm-thick polyimide were enhanced due to double thickness (optical path) and the E-field enhancement which was 10-100 for intensity \(E^{2}\). This contributed to a stronger absorption. At the absorbing dipole resonance at a cyclic frequency \(\omega_{0}\), there is a phase change from 0 to \(\pi\) as frequency \(\omega\) is increasing. From the mechanical oscillator analogy, the phase change is \(\varphi=-\arctan\frac{2\gamma\omega\omega_{0}}{\omega_{0}^{2}-\omega^{2}}\) for \(\omega<\omega_{0}\) and \(\varphi=-\pi+\arctan\frac{2\gamma\omega\omega_{0}}{\omega^{2}-\omega_{0}^{2}}\) for \(\omega>\omega_{0}\) modulo \(2\pi\), where \(\gamma\) is a dimensionless damping factor defining the quality \(Q=\frac{\omega_{0}}{\Delta\omega}=\frac{1}{2\gamma}\) of the resonance; the equation of mechanical motion is defined as \(md^{2}x/d^{2}t+2m\gamma\omega_{0}dx/dt+m\omega_{0}^{2}x=F_{0}\sin(\omega t)\) for inertial mass \(m\), \(F_{0}\) is the force amplitude acting at cyclic frequency \(\omega\), \(\omega_{0}\) is the resonance frequency and \(x,t\) are the space and time coordinates, respectively. The inset in Figure 8b shows the phase change \(\varphi\) at the resonance. In the MIM structure, reflection from the top-Au disks and bottom-Au film will have a change of phase due to absorption in the polyimide (I-part in MIM); there is no phase change due to reflection from Au. For the aligned absorbers in polyimide, the red-shifted absorbance wing will have a less reduced intensity as compared with the blue-shifted absorbance wing where phase is lagging by \(\pi\). Hence, absorbance anisotropy due to molecular alignment is affected by the phase change and asymmetry in the absorption peak. This phase change around the absorbing line can be also coupled with birefringence to cause polarisation change of the back-reflected light.