Self-waveguiding effect

Low-dimensional crystals such as epitaxial needles and solution-grown platelets of TPCOs act as a microscale gain medium. The self-cavity and self-waveguiding effects of these crystals result in ASE in the wavelength region of the fluorescence band where the self-absorption loss is minimized. Furthermore, the uniaxial orientation of the TPCO molecules in these low-dimensional crystals promotes the stimulated emission process and enhances the polarized ASE. 

The nonlinear part of the susceptibility was introduced into the quasi-linear finite-difference scheme via iterations, so that at any longitudinal point, the magnitude of E calculated at the previous longitudinal point was used as a zero approximation. This approach is better than the split-step method since it allows one to jointly simulate both the mode field diffraction on irregular sections of the waveguide and the self-action effect by introducing the nonlinear permittivity into the implicit finite-difference scheme which describes the propagation of the total field. 

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). 

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. 

Such a behavior of the total field is observed provided that the beam power is smaller than a definite value P which depends on the waveguide width (for a = 1.8pm, P 8). The spatial dynamics of a light beam with P > Pi is more complicated because nonlinear self-effects in radiation field increase so that the formation of soliton-like light beams propagating in the waveguide cladding is observed. 

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