MATLAB FDTD Source Code for Calculating Photonic Crystal Transmission

Research on photonic crystal transmission characteristics typically employs the Finite-Difference Time-Domain (FDTD) method, a numerical approach that discretizes Maxwell's equations to solve electromagnetic field distributions. Implementing an FDTD program in MATLAB for calculating photonic crystal transmission spectra requires consideration of the following core computational logic: Grid Discretization and Parameter Configuration Mapping the photonic crystal structure to Yee grids requires defining the permittivity distribution (such as periodically arranged cylinders or holes). The implementation must set spatial steps (Δx, Δy) and temporal step (Δt) satisfying the CFL stability condition. In code, this typically involves creating 2D arrays for epsilon values and calculating time steps based on grid resolution. Field Component Update Iteration The algorithm alternately updates electric field (Ez) and magnetic field (Hx, Hy) components. Electric field updates must account for the permittivity distribution through material-dependent coefficients, while magnetic field updates rely solely on free-space parameters. The implementation uses staggered grid updating with central difference schemes. Boundaries typically employ Perfectly Matched Layer (PML) absorption to minimize reflections, implemented through additional loss terms in the update equations. Excitation Source and Transmission Monitoring A Gaussian pulse or sine-modulated wave is added as an excitation source at the input port. The code places field detectors at the opposite side of the structure to record transmitted fields. Fourier transform converts time-domain signals to frequency-domain transmission spectra, implemented using FFT operations with proper windowing. Post-processing Analysis The program compares input and output energy spectra to calculate transmission coefficients for specific frequency bands. Photonic band gaps manifest as frequency ranges with sharp transmission drops. The MATLAB implementation typically includes spectral normalization and band gap identification algorithms. Extension Considerations: The code can be enhanced with parallel computing (using parfor loops) to accelerate large-scale structure simulations, or combined with parameter scanning scripts to automatically optimize lattice parameters for desired band gap characteristics.