Phase-matching condition

Using now the phase matching condition, it can be seen that besides the quasi shear wave (qSV) which is obtained as usual, a second quasi shear wave (qSV(2)) results from the upper quasi shear wave part. Since the direction of the group velocity vector points downwards this wave is able to propagate and can be seen in the snapshot (see Fig. 10) if a is properly adjusted, i.e. is pointing upwards as in Fig. 2. 

Hirose et al. [26] proposed a homodyne scheme to achieve the background-free detection of the fourth-order field. With pump irradiation in a transient grating configuration, the fourth-order field propagates in a direction different from that of the second-order field because of different phase match conditions. The fourth-order field is homodyned to make ffourth(td. 2 D) and spatially filtered from the second-order response hecond td, 2 D). 

From the coupled mode theory, it is possible to retrieve a modified phase matching condition, which is more accurate than (3.1)26 ... 

The resonance wavelength (2rcs) of a LPFG can be roughly estimated by the following phase matching condition ... 

Figure 4. The graph shows the SHG output as a function of distance through a nonlinear crystal for various phase matching conditions.

It can be shown that, under phase-matching conditions, is related to An and Ax by the expression (Nagy et al. 2005) ... 

The phase matching condition is Afc L ir, which means that for the generation of CARS the coherence length defined by 7r/ Afc has to exceed the effective interaction length L. The latter is determined by the axial dimension of the nonlinear sample. Thus, the actual extent of Afc acts as a size filter for the scatterer of dimensions for which an efficient CARS signal is generated. When the slab thickness is smaller than the pump wavelength, i.e., L 0, the... 

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