Critical power for self-focusing

Fig. 5.2. Start of filamentation in BaF2 at different values of incident laser power expressed in multiples of Pcr, the critical power for self-focusing. Vertical arrows indicate the filament start position in each case...

The origin of the n2 measured using the 10 ns pulses could be electronic or molecular rotation. These can be distinguished by measuring the ratio of the critical power for self-focusing for linear and circular polarised light. The observed ratio of 2.1 is consistent with a molecular rotation (11-13.161 and relates to the anisotropic polarisability of the molecule. The rotational relaxation time, calculated from the Debye formula (H), is about 0.5-2 ns, consistent with these results. 

When the intensity of the incident beam is low, the nonlinear effects are negligible, and the transmitted intensity (measured by a detector) is linear with the input intensity (see Fig. 10). After the intensity reaches a critical power, P, self-focusing occurs. A more focused beam induces other nonlinear effects which levels-off the transmitted power (see Figure 11). Therefore, for powers greater than P, the transmitted intensity does not depend linearly on the input intensity. 

For incident powers above the critical power, the self-focusing overcomes diffraction and a beam of radius a focuses at a distance given by... 

For incident powers below the critical power, the self-focusing cannot overcome the spreading due to diffraction and the beam does not focus, although it spreads more slowly than it would in the absence of the nonlinear index. Values of the nonlinear index and the critical powers for some materials are given in Table XIV. 

There are two different x measurement techniques that are based on self-actimi (i) optical power limiter and (ii) the z scan. In the case of the optical power limiter the laser beam is focused in the sample with high 2- For low input powers the transmitted beam is focused through a pinhole on the detector. As the power increases the self-focusing starts so that the focused beam is no longer focused through the pinhole and the power after pinhole decreases. Beyond a certain critical input power Pc, transmitted power levels off due to many other NLO processes. The critical power Pc is directly related to 2 through the relation (for spatial Gaussian beam) [116]... 

In order for a beam to self-focus, the self-focusing force must overcome the tendency of the beam to increase in size due to diffraction. This requirement leads to the existence of a critical power defined by... 

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