Analytical expression of sampled Bragg gratings with chirp in the sampling period and its application in dispersion management design in a WDM system

An analytical expression for a sampled Bragg grating (SBG) with chirp in the sampling period (CSP) is derived for the first time. It is shown that such a grating can be equivalent to a special SBG with a chirp in the grating period (CGP) which is varied in the stopbands. The corresponding equivalent chirp coefficients are determined, and the design procedure of a SBG with both CSP and CGP is outlined aiming at dispersion management in WDM system device.