Wave propagation and tunneling through periodic structures

The phenomenon of tunneling manifests itself in nearly every field of physics. The ability to distinguish a wave tunneling through a barrier from one propagating is important for a number of applications. Here we explore the properties of the wave traveling through the band gap created by a lattice, either as a consequence of tunneling through the barrier or due to the presence of a pass band inside the gap. To observe the pass band for studying tunneling and propagating waves simultaneously, a localized lattice defect was introduced. The differences between the two phenomena are highlighted via waves' dispersion characteristics.