Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR

SECOND ORDER HARMONIC SURFACE WAVES GENERATED BY ONE FUNDAMENTAL WAVE

No abstract availabl

Effective area of the LP01 mode in non-linear optical fibres

Recent investigations on the nonlinear dispersion law and the nonlinear wavenumber shift of the LP01 mode in step-index optical waveguides are extended to determining the effective area of the mode. The obtained result differs from that conventionally used and defines more precisely the characteristics of the nonlinear effects of self-phase modulation and soliton formation

Experiments on the nonlinear evolution of surface waves in an open plasma waveguide

The nonlinear behaviour of surface waves propagating along a plasma column is investigated. The experiments include (i) measurements of the nonlinear dispersion of the waves and (ii) observation of the evolution of the shape of the wave envelope and of the wave spectrum when the waves are excited with an amplitude-modulated signal. Comparison with theory shows that (i) the measured nonlinear wavelength shift corresponds to increasing wave phase velocity with increasing wave amplitude, (ii) the observed narrowing of the wave envelope can be associated with the formation of periodic nonlinear waves described by dn Jacobi elliptic function solutions of the nonlinear Schrodinger equation and (iii) the observed strong changes of the wave spectrum are mainly related to a nonlinear effect of phase modulation

Pulsed waveguided discharges

Microwave discharges in argon gas produced in pulse regime operation with surface waves being carrier waves are studied in a pressure range between 0.1 and 10 Torr. The changes of the shape of the pulses of the total light emission, as an indication for the plasma density, and of the electric field power are registrated along the discharge length. Experimental results on properties of the ionization front (ionization front velocity, rise time of the pulses) and on separation of a solitary-like ionizing wave from the leading edge of the pulses are presented. Their relation to effects of strong ionization nonlinearity responsible for the discharge production in general, is discussed. Development of modulation instability on the stationary part of the pulses is experimentally demonstrated and modelled in terms of the concept of the nonlinear Schrödinger equation. The tendency of the evolution observed to bright soliton formation is associated with effects of weak ionizatioii nonlinearity of a cubic type superimposed on the mechanism of strong ionization nonlinearity.On présente une étude de décharges microondes créées par ondes de surface dans l'argon en régime pulsé. La pression du gaz se situe entre 0.1 et 10 Torr. On enregistre le long de la décharge les changements de la forme des impulsions de lumière qui donne des indications sur la densité du plasma et la puissance du champ électrique. On présente des résultats expérimentaux sur les propriétés du front d'ionisation (vitesse du front d'ionisation, temps de montée des impulsions) ainsi que sur l'écart onde d'ionisation type soliton du front avant de l'impulsion. On discute le rapport entre les effets de forte non-linéarité d'ionisation en général responsables de la production de la décharge. On présente l'évolution d'une instabilité de modulation des parties stationnaires des impulsions mesurée expérimentalement et on la modélise selon l'approche de l'équation non linéaire de Schrödinger. On a constaté la tendance à la formation d'ondes soliton brillantes que l'on associe aux effets de faible non-linéarité d'ionisation du troisième ordre, superposée an mécanisme de forte non-linéarité d'ionisation