Optical FBG filter with minimum group delay for WDM systems

The causality principle is taken into account to couple amplitude and phase of the reflection coefficient in a symmetric grating for the optimization purpose. The distortion functional for group delay minimization is proposed. The minimization of mean square group delay within the Bragg reflection band is carried out at fixed integral reflectivity. The optimal reflection coefficient with minimum phase distortion is found analytically. The described approach is shown to give the close to rectangular FBG filter with low group delay variation over the reflection band.