Complex band structure of two-dimensional thermal wave crystals

We investigate the complex band structure of temperature oscillations in a two-dimensional thermal wave crystal. We use the Cattaneo-Vernotte heat model to describe the thermal properties. We apply the plane wave method to calculate the complex band structure of a square lattice composed of an infinite array of square bars. We find that a complete band gap exists across the first Brillouin zone, where temperature oscillations are forbidden. This has potential applications in thermal management, thermal cloaking, and other areas.