2D Photonic Crystal: Real-Space FDTD Wave Propagation

A photonic bandgap blocks certain light frequencies from propagating through a periodic dielectric structure no matter the direction of travel — but *why* that happens is easiest to see by actually watching a wave hit the crystal. This simulator runs a full 2D finite-difference time-domain (FDTD) solver for Maxwell's equations directly in real space: a TM-polarized plane wave is injected on one side of a slab of dielectric rods and marched forward step by step on a staggered Yee grid, with the true dielectric map (not a Fourier approximation) determining how each grid cell responds. Tune the rod radius and the index contrast between rods and background, then dial the source frequency across the gap to watch the field either sail through the lattice or die out evanescently a few rows in — and use the spectrum scan to trace the transmission dip directly from real time-domain propagation data, independently of any eigenvalue calculation.