Filamentation Instability of Electromagnetic Beams In Nonlinear Media: A Tutorial Review
This paper is a tutorial presentation of spatial growth of a transverse instability, associated with the propagation of an electromagnetic beam, with uniform or Gaussian irradiance along the wavefront. There are two approaches to the study of filamentation in a plasma. The results of the two approaches have been expressed in a form where they can be compared. It has been noted that the growth of the instability in the first approach is equivalent to the self-focusing of a ripple in the second approach. The dependence of the maximum growth rate and the corresponding optimum value of the wave number of the instability on the irradiance of the main beam has also been studied. Further a paraxial like approach has also been adopted to analyze the characteristics of propagation of the ripple, when the dielectric function is determined by the composite (Gaussian and ripple) electric field profile of the beam. The effect of different parameters on the critical curves has been highlighted and the variation of the beam width parameter with the distance of propagation has been obtained for three typical cases viz of steady divergence, oscillatory divergence and self-focusing of the ripple.