Temperature Filtering Characteristics Analysis of Fiber Chirped Bragg Grating Filters Using Transfer Matrix Method

This article presents a computational approach using the Transfer Matrix Method (TMM) to analyze the temperature-dependent filtering characteristics of fiber chirped Bragg grating (FBG) filters. Chirped FBG filters serve as critical optical components in fiber optic communication systems, providing wavelength-selective filtering functionality. These devices enable optical signal filtering that responds to temperature variations, allowing precise control over light signal propagation. The implementation involves discretizing the grating structure into multiple uniform segments, where each segment's transfer matrix accounts for local grating period, refractive index modulation, and thermo-optic effects. Key computational steps include formulating 2×2 matrices for forward and backward propagating waves, incorporating temperature-dependent refractive index changes through the thermo-optic coefficient, and cascading segment matrices using matrix multiplication to obtain the overall device response. Through this methodology, we can systematically calculate filtering properties - including reflection spectra, bandwidth, and center wavelength shifts - across varying temperature conditions. This analysis facilitates deeper understanding of thermal sensitivity mechanisms and enables performance optimization for enhanced stability in practical fiber optic communication systems. The code implementation typically involves iterative matrix operations with temperature as an input parameter, allowing engineers to simulate real-world operating scenarios and improve device design robustness.