Green's function analysis of electromagnetic waves in two-layered periodic structures with fluctuations in thickness

A general method for the construction of the Green's function for finite one-dimensional inhomogeneous layers is developed. Using the results of this method the exact analytical Green's function for periodic dielectric structures is found. As an example of its application, the influence of fluctuations of the widths of the basic layers on the reflection and transmission of electromagnetic waves propagating through the structure is investigated. The results are applied to the design of optical switching systems with periodic dielectric structures as the operating medium. The same Green's function can be used to solve a wide variety of other problems.