Abstract
A theory of wave propagation in periodic structures with smoothly varying parameters is developed. Consideration is provided for the case when both periodicity and modulation are in one dimension. The theory is based on the Wannier-function expansion. As an example, it is shown that electromagnetic waves can propagate along effective waveguides, which are interpreted in terms of defect modes. Related effects such as anomalous scattering, self-channeling (gap solitons) in nonlinear periodic media), and miniband spectra are discussed.
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