GRAPHICAL AND WKB ANALYSIS OF NONUNIFORM BRAGG GRATINGS

A deeper insight into the relationship between the shape of a slowly v arying nonuniform Bragg grating and its reflectance spectrum is obtain ed through a qualitative graphical analysis of the local photonic band gaps in the grating and a quantitative WKB (or phase-integral) approx imation of the grating fields. Three different gratings-a linearly chi rped grating, a moire grating, and a Gaussian tapered grating-are anal yzed in detail to illustrate the power of the technique. The results a re in excellent agreement with the exact numerical results obtained vi a coupled-mode analysis.