Resistance of Short Pulses to Self-Focusing

Self-focusing arises in all materials, gases, liquids, solids or plasmas. Yet, it has been investigated only in the limit where the beam diameter is significantly less than the pulse length (cτ, where τ is the pulse duration). In this case, the beam is predicted to selffocus to moving singularities in the absence of other nonlinear effects. However, there is another extreme which is rarely, if ever, noted where the beam diameter is much larger than the pulse length and the pulse will disperse before any self-focusing can occur. Short pulse self-focusing is more related to the second extreme than the first.