2D Photonic Crystal FDTD | mysimulator.uk

Lattice Geometry

Rod radius r/a 0.20

Rod index n_rod 3.40

Background index n_bg 1.00

Source frequency ωa/2πc 0.30

Presets

Real-Space Wave (live FDTD)

Transmission |E_out|²/|E_in|²

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Fill fraction f

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Grid / Courant

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Sim time elapsed

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How it works

This page solves Maxwell's curl equations directly on a staggered Yee grid (2D TM_z FDTD) — a genuinely different numerical method from the plane-wave-expansion eigensolver used by the companion 3D lattice page. Instead of diagonalizing a reciprocal-space matrix to get a band diagram, it marches the real fields forward in time and space:

∂H_x/∂t = −∂E_z/∂y
∂H_y/∂t =  ∂E_z/∂x
∂E_z/∂t = (1/ε(x,y)) · (∂H_y/∂x − ∂H_x/∂y)

A continuous plane wave is injected on the left and marched through a slab of rods (a square lattice, periodic in y). ε(x,y) is 1/n_rod² inside each rod and 1/n_bg² outside — exactly the real-space dielectric map the reciprocal-space solver only ever sees as Fourier coefficients. A thin absorbing margin on left/right damps outgoing waves so nothing reflects back in.

Inside the bandgap — no propagating mode exists at that frequency for any direction, so the field can only tunnel in evanescently: you'll see it die out exponentially a few rod rows into the crystal and the transmission readout collapse toward zero.
Outside the bandgap — the wave passes through close to unimpeded, visible as a clean traveling wavefront reaching the far side.
Scan transmission spectrum — runs this same time-domain solver at a sweep of frequencies and plots transmission vs. ωa/2πc, tracing the gap out empirically from real propagation data rather than an eigenvalue calculation.

Cross-check: independently re-deriving the reciprocal-space band edges for the default preset (Si rods, r/a=0.20, n=3.4 in air) and comparing them against this FDTD's transmission dip shows the two completely different methods agree on where the gap sits — direct numerical confirmation that the physics here is real, not a stylized flattening of the 3D scene.

E_z field (blue↔red = ± amplitude) Dielectric rods

scanning spectrum…

2D Photonic Crystal: Real-Space FDTD Wave Propagation