Limits of chirped pulse compression with an unchirped Bragg grating filter

It has been suggested that the large value of group velocity dispersion (GVD) found in a Bragg grating filter written in an optical waveguide could be used for pulse compression. Three expressions are derived relating the compression ratio to the value of GVD and to the bandwidth over which GVD is nearly constant. It is shown that the maximum compression ratio that can be achieved with an unchirped grating is severely limited by the small bandwidth of the high dispersion regions in the transmission spectrum of the filter.