Model problem of Bragg fiber design

A new analytical approach to direct and inverse problems of wave propagation in periodic media is developed. By regarding the advancing wave phase as a new independent variable we construct a continuum of exact solutions of the 1D wave equation for arbitrary index profiles. This parametric solution is applied to the study of evanescent Bloch waves in forbidden zones. An explicit formula for the decay decrement is derived, giving an exact quantitative description of the parametric resonance in periodic media. The results are used for constructing optimal smooth models of multilayer dielectric mirrors and Bragg waveguide periodic claddings.