Modeling and Performance Analysis of Bragg Grating in Z-Domain

Z-domain model of fiber Bragg grating is developed, and its performance analysis is presented in this letter. The developed mathematical model is used for the evaluation of reflection and transmission response. Spectral characteristics in terms of bandwidth, peak transmittance, and side lobes formation is determined for a model of length 0.84 mm and is found to be in very close agreement with previously published fabrication result. A similar structure with different parameters is considered. The transmission response provides a wide full width half maximum (FWHM) bandwidth of 9.52 nm and a peak transmission of 0.067. The proposed model is extended to determine the transmission response for a very small incidence angle variation. Performance parameters, such as FWHM, stopband width, and optical density, are analyzed. Transmission response of the proposed model for different length combinations is evaluated.