Calculating Effective Refractive Index of Core Modes in Long-Period Fiber Gratings

In the fields of fiber optic communications and sensing, long-period fiber gratings (LPGs) are widely utilized due to their unique mode coupling characteristics. Understanding the effective refractive index of core modes is essential for analyzing grating performance and designing novel photonic devices. This MATLAB program employs numerical methods to calculate the effective refractive index of core modes. The implementation begins by establishing electromagnetic field equations based on optical fiber geometric parameters (core diameter, cladding diameter) and material properties (refractive index profile). The code utilizes mode-solving algorithms such as finite difference method or finite element method for discretization, transforming continuous partial differential equations into matrix eigenvalue problems. During the solution process, the program handles boundary condition matching to ensure electromagnetic field continuity at the core-cladding interface. The resulting eigenvalues correspond to effective refractive indices of different modes, while eigenvectors characterize the field distribution patterns of each mode. Key functions likely include mesh generation routines, boundary condition applicators, and sparse matrix eigenvalue solvers like eigs() for efficient computation. Compared to analytical solutions, this numerical approach is more suitable for complex refractive index profiles in fiber structures. The computational results can be used for subsequent analysis of critical parameters including mode coupling and resonance wavelengths. When developing similar programs, special attention should be paid to mesh discretization accuracy and proper boundary condition implementation, as these significantly impact computational efficiency and result accuracy. The code structure typically involves parameter initialization, matrix assembly, eigenvalue solution, and post-processing modules for result visualization.