THEORIALight as a wave · the wave tank

Behind the tank

What is calculated, and what is drawn.

The tank solves Maxwell’s equations live, on a grid of 200 × 200 cells, each 25 nm across (the visible part is 152 cells, 3.8 µm). It is the Yee finite-difference time-domain method in two dimensions: the electric field points out of the screen and the magnetic field lies in it. Nothing about waves is put in by hand: ripples, interference, diffraction, reflection, refraction and focusing all come out of the equations.

∂B/∂t = −∇ × E, ε ∂E/∂t = ∇ × B (c = 1)

Colours

The shading is the brightness: the field squared, averaged over a few cycles, which is what a camera or your eye would record. The thin ink lines mark where the electric field is at a crest at this instant (pointing most strongly out of the screen); they move at the speed of light, slowed right down. Only the generator swatch uses the real colour of the light.

Materials

Glass has permittivity ε = n², so light in it moves at c/n and its wavelength shrinks by n, while its frequency stays the same. Metal is a perfect conductor: the field inside it is zero, so light reflects. The edges of the tank absorb outgoing waves, as if the tank went on for ever.

Oscilloscope

Probes A and B record the field at their positions every step. The time axis is in femtoseconds (10⁻¹⁵ s): light at 600 THz oscillates every 1.67 fs.

Keys

Space pause · R restart · V crest lines on/off · 1–8 experiments.

Drawn for clarity: the slowed-down playback (real light would cross the tank in 13 fs). The tank is a two-dimensional slice, so waves from a point source fade as 1/√r rather than 1/r, and a slit is really a long slot. The grid limits detail to about a twentieth of a wavelength.

Further reading: Feynman Lectures, Volume II, chapter 21 · Hecht, Optics

Theoria · Light as a wave 0.5 · The wave tank