  We study a critically coupled system (Opt. Lett., \textbf{32}, 1483 (2007))
with a Kerr-nonlinear spacer layer. Nonlinearity is shown to inhibit
null-scattering in a critically coupled system at low powers. However, a system
detuned from critical coupling can exhibit near-complete suppression of
scattering by means of nonlinearity-induced changes in refractive index. Our
studies reveal clearly an important aspect of critical coupling as a delicate
balance in both the amplitude and the phase relations, while a nonlinear
resonance in dispersive bistability concerns only the phase.

Optics