Nonlocal Effect and Transverse Dependence

The preceding discussion is based on the assumption that the incident laser is a plane wave. If the laser is a focused Gaussian beam, with a beam size o comparable to or smaller than the film thickness, transverse correlation effects will arise. Molecules situated outside the laser beam will exert torques on molecules inside the beam conversely, molecules inside the beam could also exert torques on those on the outside. The result is that the transverse dependence of the reorientation profile is not the same function as the transverse profile of the incident laser beam (e g., Gaussian). Put in another way, one may recognize that Equation (8.53) is basically a diffusion equation, where the elastic term plays the role of the diffusive mechanism. As a result of this diffusive effect, as in marty other physical processes, the spatial profile of the response is not the same as the excitation profile. 

As shown in the detailed calculations given in the woik of Khoo et al.  

For P = 0, there is a threshold intensity for finite reorientation to occur. The threshold intensity depends on both the thickness of the film and the beam size coq- For coq. the threshold intensity increases dramatically (compared with the value for a plane wave). There is no threshold intensity for field-induced reorientation in the p A 0 case. 

The transverse dependence of the reorientation becomes important in the studies of self-phase modulation, self-focusing and self-guiding processes, and spatial soh-tons in liquid crystalline media (see Chapter 12). 

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