Plotting Dispersion Curves for Photonic Crystal Fibers

The plotting of dispersion curves for photonic crystal fibers (PCFs) serves as a fundamental method for investigating their optical properties. Dispersion curves characterize the wavelength-dependent phase velocity differences of light propagating through the fiber, directly influencing transmission performance parameters such as bandwidth and signal distortion.

This program employs numerical simulation techniques to compute the dispersion properties of PCFs. The core algorithm is rooted in waveguide theory, specifically accounting for how the periodic microstructure of PCFs affects light propagation. Through finite-element or plane-wave expansion methods, the code calculates the effective refractive index across varying wavelengths, subsequently deriving dispersion parameters using numerical differentiation.

Key implementation steps include: First, constructing the geometric model of the PCF by defining air-hole arrangements, pitch parameters, and diameter ratios through coordinate matrices. Second, solving electromagnetic field distributions using eigenmode solvers with boundary conditions matching the crystal symmetry. Finally, post-processing functions extract effective index data from eigenvalue solutions, compute group velocity dispersion via D(λ) = -(λ/c)·d²n/dλ², and generate plots using visualization libraries.

The dispersion curve typically plots wavelength (X-axis) against dispersion value in ps/(nm·km) (Y-axis). Curve analysis reveals critical performance indicators including zero-dispersion wavelength locations, dispersion slopes, and anomalous/normal dispersion regimes. These parameters are essential for optimizing PCF designs for applications in nonlinear optics, telecommunications, and sensing systems.