Heterodyne detected transient gratings in supercooled molecular liquids - A phenomenological theory

We present an analysis, based on a phenomenological set of Generalised Navier-Stokes equations, of Heterodyne Detected Transient Gratings on supercooled molecular liquids of anisotropic molecules. This set of equations generalises equations proven in Franosch, Latz and Pick [24] for the same type of liquids. It also takes into account the three different sources generated by the laser pumping process pertinent for these experiments. We give analytical expressions for the response functions that can be measured using the different polarisation of the experimental set-up. Specialising to the case of parallel polarisation (where longitudinal phonons are launched), we show that each response function is a sum of the same seven "elementary response functions" (ERFs) whose time and temperature evolutions are individually analysed. We also show that the response functions corresponding to two of the sources can be directly connected to the Laplace Transform of a light scattering signal. The ERFs generated by the heat-absorption process, which is the third source, are of a different nature. They do not have the same time and temperature behaviours and they can provide, inter alia, unique information on the rotation-translation coupling function characteristic of these liquids.