Self focusing

Materials are also classified according to a particular phenomenon being considered. AppHcations exploiting off-resonance optical nonlinearities include electrooptic modulation, frequency generation, optical parametric oscillation, and optical self-focusing. AppHcations exploiting resonant optical nonlinearities include sensor protection and optical limiting, optical memory appHcations, etc. Because different appHcations have different transparency requirements, distinction between resonant and off-resonance phenomena are thus appHcation specific and somewhat arbitrary. 

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...

Fig. 6.2. Mechanism of filamentation. (a) Kerr effect (self-focusing) (b) defocusing by the plasma...

Saddle point method, 68 Self-focusing, 83, 84, 86 Self-injection, 150... 

In the problem of pulse diffraction on waveguide junctions, the quasistatic approximation is feasible if the diffraction length of the light beam is much shorter than the characteristic length of the pulse variation owing to the mentioned above MD, FTNR and SS effects which influence the pulse envelope. Then the results obtained for stationary light beam can be used in the analysis of the non-stationary beam self-focusing. 

As a result of self-focusing, power propagating within the core f iz) inereases behind the region of unsteady-state regime (Fig. 10). Meanwhile the total power of the light beam calculated within the computational window decreases due to emitting of radiation field outside the window. 

The transmittance of the structure A depending on the input power P was evaluated via calculation of Tfz) (Fig.l3) and T2 z) (Fig.l4). It is seen that self-focusing of the light beam in the core of nonlinear waveguide increases with input power, but rate of the increase diminishes so that for the powers P > 7 (a = 1.8 pm) and P > 4 (a = 3.0 pm) the dependence is weak. Negative slope of the curve in this range results from the mentioned above soliton-like... 

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. 

G. Fibich, W. Ren, X-P. Wang, Numerical simulations of self-focusing of ultrafast laser pulses , Phys. Rev. E 67, 056603 (2003). 

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