MATLAB Simulation Algorithm for Long-Period Grating Transmission Spectrum Based on Coupling Theory

In this article, we provide a detailed explanation of the MATLAB simulation algorithm for long-period grating transmission spectra, which is fundamentally based on grating coupling theory. Long-period gratings serve as crucial optical components used in manufacturing grating couplers, optical filters, and waveguide devices. The design and fabrication of these devices require precise simulation and computational analysis, and our algorithm assists engineers and researchers in better understanding and designing such components. By applying coupling theory principles, we establish a mathematical model to characterize the transmission spectrum of long-period gratings and implement simulations using MATLAB software. The core algorithm involves solving coupled-mode differential equations through numerical methods like Runge-Kutta or transfer matrix approaches, with key MATLAB functions including ode45 for differential equation solving and matrix operations for grating parameter calculations. This model enables accurate prediction of grating performance metrics such as resonance wavelengths and attenuation peaks, facilitating optimized design iterations. Consequently, this simulation algorithm holds significant importance for both research and practical fabrication of long-period gratings.