Analysis and modelling of group delay ripple in Bragg gratings

This paper presents physically intuitive models for understanding the relationship between group delay ripple. filter shape and apodisation profile of chirped Bragg gratings and grating-based WDM filters. The models are derived from applications and extensions of effective medium theory. Simple physical explanations are given for departures from ideal linear group delay in chirped Bragg gratings. and quantitative expressions are obtained for the amplitudes, phases and periods of both the fast and slow components of the ripple for several different classes of chirped Bragg grating dispersion compensators. Results from effective medium theory using causality arguments give the minimum dispersion that can be achieved in the transmission of an adjacent channel in terms of the bandwidth, side-lobe suppression and channel spacing of WDM filters.