FBG filter with minimal dispersion

An optimal filter for super-fast fiber-optic communication lines should cause minimal phase distortions. The simplest case of Bragg grating with a symmetric profile is considered. A distortion functional is presented, which is the mean square group delay over the Bragg reflection band at a fixed integral reflectivity. The functional is minimized analytically in the simplest limiting case. Numerical calculations confirm that the optimal reflection spectrum is realizable.