Abstract
The correlation length for sidewall roughness in planar waveguides is comparable to the period of Bragg gratings written in such structures and thus might influence the performance and the spectral properties of such gratings. Using a coupled-mode formalism, we calculate the effect of roughness or inhomogeneity for an arbitrary grating and present specific results for uniform and phase-shifted gratings. The broad spectral characteristics of most gratings are insensitive to roughness. However, narrow spectral features (such as transmission resonances) that rely on interference effects are affected by the presence of roughness.
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