Photonic Crystal Bandgap Engineering

A photonic bandgap is a range of light frequencies that simply cannot propagate through a periodic dielectric structure, no matter the direction — the electromagnetic analogue of the electronic bandgap that makes semiconductors work. This simulator solves the real 2D plane-wave-expansion eigenproblem for TM-polarized light in a square lattice of dielectric rods, diagonalizing the exact matrix at every point along the Γ–X–M–Γ path of the Brillouin zone to trace out the first bands. Tune the rod radius and the index contrast between the rods and the background medium to watch the gap between bands 1 and 2 open, widen, and close, with the actual 3D rod lattice and live gap-ratio readouts updating alongside the band diagram — the same design space engineers explore when building photonic-crystal fibers and on-chip waveguide filters.