Writing the Temperature Grating

The phenomenological description of signal generation in TDFRS is, in principle, straightforward [27,28,33,44,45]. The primary source of excitation is the optical interference grating formed by the two writing beams, which intersect under an angel 6 inside the sample  

The optical axis defines the j-direction. The x-axis points along the direction of the grating vector, whose absolute value is 

due to the plane-parallel geometry of the sample cell, the wavelength of light in air. With a plane-parallel geometry of the sample cell and the optical axis perpendicular to the windows, the refractive index n of the sample does not appear in Eq. (9), since, according to Snell s law, 

The complex notation in Eq. (9) indicates that the grating is characterized by both an amplitude and a phase factor, and I (t) may also be a complex quantity containing both amplitude and phase modulation. For heterodyne detection schemes, both contributions are of importance. In most experiments, but not in all, 180°-phase switching, corresponding to f0-amplitude switching of the interference grating, has been employed. 

Both finite-size effects of the beam diameter and exponential intensity decay due to absorption within the sample have been neglected in Eq. (9). A purely one-dimensional treatment of the problem, as implied in Fig. 7 and as usually employed in the literature, is not always adequate and can only be justified if the experimental boundary conditions are carefully chosen. 

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