Transverse modulational instability
= Transverse modulational instability
{title2=$g^2=\frac{q^2}{2k}(2\gamma I_0-\frac{q^2}{2k})$}
A broad focusing beam can amplify transverse <intensity> perturbations. Linearizing $iA_z+\nabla_\perp^2A/(2k)+\gamma|A|^2A=0$ about its uniform solution gives the displayed growth rate for transverse wave number $q$. For $\gamma>0$, a finite band grows; noise can develop into filaments. A finite beam and saturating response change the ideal plane-background prediction.