On the Doppler Effect in Static Materials: Vortices and Black, White and Worm-Hole Like Wave Trajectories

Overview & Synopsis

We demonstrate the Doppler effect in a static material. The effect is achieved with a network of thin waveguides whose lengths depend on the direction of travel, chosen to simulate the compression and expansion of the wave experienced by a source travelling with velocity $v$. Each edge of length $\ell$ becomes a pair of waveguides of lengths $\ell/(1\mp v/c)$, one for each direction of travel. On a lattice this gives the field pattern of a moving source. To demonstrate the effect, we design a vortex, an analogue black hole and wormhole.