## 2 Peculiarities of ATR Measurements
### Polarisation Analysis with Atr  
Polarisation analysis in ATR measurements can be explored by using in-plane anisotropy of the sample and along the direction of the evanescent field. All 3D orientations can be sampled for changes in the refractive index and absorption. The real and imaginary parts of the refractive index play their part in defining the polarisation at the output of ATR and are discussed in this section. The popular four-polarisation (4-Pol) method [23] allows determination of the orientation of the absorbing molecular dipoles in the IR fingerprinting spectral range. It can be used to observe a complex molecular arrangement using microscopy and, when combined with high brightness synchrotron radiation, opens the possibility to observe the change in molecular ordering during phase transitions and crystallisation in real time. Monitoring phase transitions at the spectral window for vibrational-rotation energies at <33 cm\({}^{-1}\) (<1 THz) can provide insights into nanoscale mechanics and material re-organisation, and are not usually accessible at low-brilliance (non-synchrotron) sources. For example, Debye rotation, network stretching, and rocking and wagging librations of water molecules all are active at the low-THz spectral band [24]. Recently, the 4-Pol method was implemented to reveal molecular ordering in paracetamol (type-\(I\)) micro-crystals, which are better soluble in water [25]. The principle of measuring absorbance at four sample orientations (or beam polarisation) using linearly polarised light is applicable to any spectral range. Patterns of sub-wavelength, \(\lambda/50\), features can be revealed by measuring angular dependence of absorbance/transmittance [26]. The separation of transmittance changes due to birefringence, \(\Delta n\), and dichroism, \(\Delta\alpha\), in polariscopy (with an aligned polariser and analyser) can be realised, due to the difference in angular dependence of those two contributions, using the 4-Pol technique [27]. Our conjecture here is that the 4-Pol method of orientational probing of absorbance could be also adopted for ATR with one light E-field oriented in the plane of the prism surface (s-pol.) and another perpendicular to it (the evanescent field of incident p-pol.). Developing the 4-Pol method for ATR is our next motivation for experiments on the THz beamline at the Australian Synchrotron. The conjecture is based on basic principles of the polarisation analysis and is applicable to any wavelengths in the ATR measurements. To select the required orientation of linear polarisation, a polarised mesh-grid is used. Polarisation is defined in the plane of incidence as \(E_{s}\) and \(E_{p}\), which are \(\perp\) and \(\parallel\) to the plane (or TE and TM modes), respectively. By rotating the mesh-grip polariser by an angle, \(\varphi\), the linearly polarised power (energy, intensity), \(I\), in the plane of incidence, is defined by \(I\propto E_{s}^{2}\cos^{2}\varphi+E_{p}^{2}\sin^{2}\varphi\) components; \(\varphi=0^{\circ}\) corresponds to the pure \(E_{s}\) light [28]. Depending on the angle \(\varphi\), a different ratio of the \(E_{z}\) and \(E_{y}\) near-field (Figure 5) are created in the sample. Those two components are absorbed differently, depending on the anisotropy of the sample, i.e., alignment of absorbers. The phase and amplitude changes upon ATR reflection (Appendix A) show that one would expect an elliptically polarised light emerging from the ATR prism (even without sample, see inset in Figure A1b and Figure 5). The beam after the prism can be analysed with a linear analyser, which is set to determine \(E_{s}\) and \(E_{p}\) polarisations.