Theory of group delay ripple generated by chirped fiber gratings

The theory of the group delay ripple generated by apodized chirped fiber gratings is developed using the analogy between noisy gratings and superstructure Bragg gratings. It predicts the fundamental cutoff of the high frequency spatial noise of grating parameters in excellent agreement with the experimental data. We find simple general relationship between the high-frequency ripple in the grating period and the group delay ripple. In particular, we show that the amplitude of a single-frequency group delay ripple component changes with grating period chirp, C, as 3/ 2 C and is proportional to the grating index modulation, while its phase shift and period changes as 1 C .