Reflection of light from a nonlinear interference mirror

An investigation is made of the reflection of light from a nonlinear pile of thick plates. Assuming a small difference between the refractive indices of neighboring plates $\triangle n/n\leqslant1$, an analytic solution is found in the approximation of a continuous number of plates. It is shown that beginning with a certain intensity, the transmission regime becomes multivalued. At a moderate intensity, high reflection changes to transmission. Numerical calculations are made for the case <$\triangle n/n\thicksim1$. It is found that the qualitative behavior of the transmission coefficient as a function of the incident radiation intensity is similar in both cases.