Graphical and WKB analysis of nonuniform Bragg gratings

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Abstract
A deeper insight into the relationship between the shape of a slowly varying nonuniform Bragg grating and its reflectance spectrum is obtained through a qualitative graphical analysis of the local photonic band gaps in the grating and a quantitative WKB (or phase-integral) approximation of the grating fields. Three different gratings—a linearly chirped grating, a moiré grating, and a Gaussian tapered grating—are analyzed in detail to illustrate the power of the technique. The results are in excellent agreement with the exact numerical results obtained via coupled-mode analysis.