Topological Protection in Disordered Photonic Multilayers and Transmission Lines

The Su-Schrieffer-Heeger (SSH) model is the simplest example of a lattice with non-trivial topology. It supports mid-gap topologically protected states, whose energies are unaffected by disorder. We show that photonic multilayer structures provide an exact implementation of an SSH lattice, provided each layer has the same propagation thickness. From this, it follows that the cavity mode in a conventional semiconductor microcavity is a protected SSH mid-gap state. We demonstrate this experimentally using controlled disorder in a mathematically equivalent system, a radio frequency transmission line made from sections of coaxial cable with high and low impedances. We also show theoretically that transmission lines connected to form networks map onto topologically interesting lattices in in higher dimensions.