Self-focusing effect

In the structure A, the transverse profile of the initial pulse varies behind the junction due to the self-focusing effect. In the nonlinear waveguide of the structure, a fraction of an initial pulse power is emitted from the guiding region (Fig. 19). 

Behind the junction, power of the field propagating within the core increases due to the self-focusing effect, while the pulse duration at the waveguide axis decreases. In the quasi-static approximation, this effect does not depend on the initial pulse duration. Total losses vary with power at the pulse peak similar to the case of stationary wave propagation in the structure A, i.e. they increase with the power (Fig.21, compare with Fig.l 1). 

It is seen that longitudinal dependences of the variation in the pulse duration plotted for 2 of the same modulus but different signs are approximately symmetrical with respect to the curve obtained in the quasistatic approximation. Hence, at normal GVD, the pulse duration is shorter than the initial one as a result of the self-focusing effect until, owing to GVD, this duration continuously increases to its initial value (denoted by asterisks) and then exceeds it. The size of the region within which the pulse compression is observed at decreases with increasing 2 - In turn,... 

The relative decrease Atq of the pulse duration depends approximately linearly on when 2 < 0 (Fig.31). For 2 > 0, at high powers (e.g. ppeak > 2 in Fig.31), the relative increase of the pulse duration is also almost linear. In this case, such propagation is possible when the pulse duration virtually does not depend on the power of the initial beam. This might result from a balance between the self-focusing effect which decreases the pulse duration (dashed line in Fig.31) and the normal GVD effect which broadens the pulse. 

Brish and coworkers considered the following mechanisms for initiation (1) The impact pressure of light. Calculation showed, however, that this only amounted to 10" bar and could be disregarded. (2) Electrical breakdown. The breakdown strength of compressed lead azide is 10 V/cm. Since at the critical intensity for initiation the laser light produces an average electric field of 0.7 X 10 V/cm, and self-focusing effects could increase this a further 3-5 times, this is clearly a possible mechanism. (3) Photochemical decomposition... 

Study of the interplay between liquid crystal reorientation time scales and transient self-focusing effects [5]. 

Such coherent nonlinear effects may also induce gain losses by the self-focusing effect, destroying the desired mode properties of the optical cavity. A power threshold has been estimated by Yariv (1967)... 

In these studies, however, either physically unrealistic assumptions (such as assuming that the laser transverse beam profile is a rect function) are made or the treatments are too qualitative (they apply to only one particular geometry). In some nonlinear optical processes, e.g., transverse self-phase modulations, self-focusing effects, and bistability, - a more exact description of the transverse spatial dependences of both the laser beam and the nematic reorientation are required. 

As is shown in Fig. 5, the experimentally observed threshold field dependence on wo/d also follows the theoretical prediction. For E46, a 100-Axm sample has a Freedericksz transition field intensity of 200 W/cm (using the values = 0.3, K lO" , d = 0.01 cm, and n no 1.5). For large values of Wo/d (for example, wo/d > 5), the observed threshold field approaches this value. However, as the incident laser beam size decreases to a value comparable with the thickness d or less, the threshold optical intensities increase dramatically. At wq d, the threshold intensity increases by almost an order of magnitude. In general, the experimentally observed relative increase of the threshold field is slightly larger than the theoretical value, probably because of a systematic difference between the experimental observation of the onset of reorientation (by the appearance of the self-focusing effect on the exit Ar+ laser beam) and also... 

In [151] it was shown theoretically that imder intense optical radiation with a Gaussian profile, a retro-self-focusing effect and a pinholing effect occur in CLCs. These effects have been observed in an experiment using a CLC dielectric resonator. The CLC dielectric resonator consists of an HR... 

An effective penetration depth sometimes becomes shorter than a I due to a self-focusing effect (Tanaka and Hisakuni, 2000 Tanaka, 2003). 

In addition, the ultimate shape of the flake is also mysterious. Thick [ 4 pm] and thin [ 1 pm] AS2S3 flakes tend to become as screws [Tanaka, 2008] and spiral filaments [Fig. 3.13], respectively, for which gyration directions are difficult to experimentally determine. The gyration may be related to photoinduced gyrotropy [Lyubin and Klebanov, 2003], but its mechanism has been left unexplained [DiVincenzo, 1988]. The filamentation may be affected by Kerr self-focusing effects [Polynkin et al., 2011] under photoinduced fluidity. These speculations also remain to be studied. 

For a single-mode laser beam with a Gaussian transverse intensity distribution, the index of refraction at the centre of the beam will then be larger than at its periphery, provided n2(co) is positive. Thereby the medium will act as a positive lens, tending to bring the incident beam to a focus at the centre on the beam. However, only if the intensity of the laser beam is sufficiently large will this self-focusing effect be able to counteract the beam spread due to ordinary diffraction. 

In the work by Lee et al.," a theory and some qualitative experimental confirmation are presented on the optical retro-self-focusing effect associated with optically induced pitch dilation. The laser used has a Gaussian radial intensity distribution, which induces a radially varying pitch dilation effect, in analogy to the radially varying director axis reorientation induced by a Gaussian beam (cf Section 8.3.3). 

For self-limiting application dealing with a pulsed laser, a dynamical theoiy is needed. While a dynamical theoiy is extremely complicated (almost insoluble) for self-focusing effects in long media, such a theoiy is relatively easier to constract for thin nonlinear media. 

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