Instability in an illuminated nonlinear waveguide: a phase-conjugation effect

We consider a laser beam incident normally upon a waveguide with a Kerr nonlinearity. Although the laser is uniform in the plane of the waveguide, we show that the waveguide fields can be unstable to growth, forming coherent periodic structures. The initial, exponential time dependence is determined, and we find a steady-state solution. Finally, we note that the mechanism necessary for this instability is that responsible for phase conjugation by means of degenerate four-wave mixing.