Electromagnetic wave propagation in almost periodic media

A solution obtained directly from Maxwell's equations is presented for propagation in almost periodic media. Techniques to evaluate this solution are developed. These techniques involve a generalization to almost periodic media of the Brillouin diagram of periodic media. The method of invariant imbedding is applied to the coupled mode equations which determine the Brillouin diagram for the purpose of transforming them to coupled Riccati equations. These coupled Riccati equations, when subjected to a single boundary condition, determine the solutions to both the periodic and almost periodic boundary value problems. These evaluation techniques are used to place in evidence similarities and differences of wave propagation in periodic and almost periodic media. Although the periodic and almost periodic theories agree in many cases of interest, there exist cases in which distinct differences appear. In cases of multitone perturbations, the almost periodic theory yields both simpler and more reasonable results than the periodic theory.