Semi-Analytical Modeling of Distributed Phase-Shifts Applied on Chirped Fiber Bragg Gratings

Tunable notch filters with multiple transmission lines have been proposed and demonstrated by temporarily inducing phase-shifts in chirped fiber Bragg gratings through the application of stress or thermal perturbations. These filters find application in many fields including microwave photonics or optical communications. So far, study of this type of filter has been mostly experimental with occasional numerical modeling based on coupled-mode theory. This paper presents a theoretical analysis using the WKB approximation that highlightens the presence of resonators and quantitatively describes both the phase-shift accumulated in the propagation region and the reflection strength of the surrounding grating regions. The model provides an approximated function of the transmission peak amplitude that gives good insight into its dependence on the grating parameters and perturbation profile. This analysis predicts the filter bandwidth, tuning capability and minimum spectral separation between two transmission lines leading to straightforward design and optimization of the filter parameters.