Calculation of Chirped Grating Reflection Spectrum Using Transfer Matrix Method

In this section, we employ the transfer matrix method to calculate the reflection spectrum and time delay of chirped gratings. Below is a complete MATLAB program example that has been tested and runs successfully in MATLAB 5.13 and Windows 2000 environments. The code implementation enables parameter variation including grating length, effective refractive index, refractive index modulation depth, and chirp coefficient to obtain reflection spectra and time delay curves under different conditions. The algorithm works by dividing the grating into discrete sections and applying matrix multiplication to model light propagation through each segment. Key functions include boundary condition handling and phase matching calculations. By removing the comment symbol "%" from the "% apodization" line, you can generate apodized grating reflection spectra and time delay characteristic curves. The computed curves in this case will be significantly smoother than those displayed in Figure 8, demonstrating the effectiveness of apodization techniques in reducing sidelobes and improving spectral characteristics.