Minimization of dispersion for symmetric FBG optical filters

Sharp edges of the reflection spectrum of fiber Bragg gratings originate the group delay. As follows from the dispersion relations, the delay of the symmetric grating grows up with the second derivative of the reflectivity with respect to the frequency. The distortion functional is proposed for filter optimization. It is the mean square delay at fixed integral reflectivity. An analytic solution for filters with minimum distortion is obtained in the limit of weak grating.