Simulating Photonic Crystal Fiber Dispersion Using FDFD Method

Using the Frequency Domain Finite Difference (FDFD) method to simulate dispersion characteristics of Photonic Crystal Fibers (PCF) represents an efficient and accurate numerical approach. The core electromagnetic field solving is handled by FDFD.m as the main program, while dispersion.m is specifically designed to extract dispersion curves from the computational results.

Functionality of FDFD.m FDFD.m solves Maxwell's equations using the frequency-domain finite difference method, discretizing the cross-sectional structure of photonic crystal fibers to compute mode field distributions and effective refractive indices at specific wavelengths. Key implementation steps include mesh generation, dielectric parameter assignment, boundary condition configuration, and eigenvalue problem solving. Given PCF's complex periodic air-hole structure, FDFD must accurately handle spatial variations in dielectric constants through careful matrix formulation and eigenmode analysis algorithms.

Capabilities of dispersion.m This program calculates Group Velocity Dispersion (GVD) through numerical differentiation based on FDFD.m output data (such as effective refractive indices at different wavelengths). The computational workflow involves: - Fitting curves of effective refractive index versus wavelength variations - Computing dispersion parameters using second-derivative relationships - Potential extension analysis for higher-order dispersion terms through polynomial fitting techniques

Critical Implementation Details - Mesh resolution must be sufficiently high to capture field discontinuities at air-hole boundaries, typically requiring sub-wavelength grid spacing - Boundary conditions commonly employ Perfectly Matched Layers (PML) to minimize reflection errors through complex coordinate stretching - Wavelength sampling interval selection in dispersion calculations requires careful consideration to avoid numerical noise, often implemented with adaptive step-size algorithms

Application Extensions This methodology can be further optimized for analyzing nonlinear effects or specialized designs (such as highly nonlinear PCFs or dispersion-compensating fibers). By adjusting PCF structural parameters (hole pitch, duty cycle, etc.), the program can rapidly evaluate dispersion characteristics under different geometric configurations, providing theoretical foundations for fiber design through parameter sweep simulations.