Bragg Mirrors for Thermal Waves

Abstract

We present a numerical calculation of the heat transport in a Bragg mirror configuration made of materials that do not obey Fourier’s law of heat conduction. The Bragg mirror is made of materials that are described by the Cattaneo-Vernotte equation. By analyzing the Cattaneo-Vernotte equation’s solutions, we define the thermal wave surface impedance to design highly reflective thermal Bragg mirrors. Even for mirrors with a few layers, very high reflectance is achieved (>90%). The Bragg mirror configuration is also a system that makes evident the wave-like nature of the solution of the Cattaneo-Vernotte equation by showing frequency pass-bands that are absent if the materials obey the usual Fourier’s law.

Causality in non-fourier heat conduction

“…For example, in temperonic crystals [23] a graphene layer is illuminated by a modulated heat source producing a periodic change in the temperature and a band structure. This band-structure is also obtained with a superlattice made of a regular array of materials for both finite periodic (thermal Bragg mirrors) and semi-infinite systems [24,25]. Another case is the use of thermal waves for cloaking employing core-shell spheres.…”

“…When we solve either the CV equation or the DPL equation, there are two choices for the frequency and wavevector: (i) to assume that the frequency takes complex values while the wave vector is real [23,61], in general, this is useful for infinite and semi-infinite systems; (ii) to assume a real frequency and complex wavevector, generally used for finite systems. We adopt the second case since it is a more common approach in wave propagation phenomena, particularly problems involving boundaries [24,43].…”

Complex band structure of thermal wave crystals: The plane-wave method

“…Thermal Wave Crystals (TWCs), which were first proposed by A-Li Chen et al in 2018, have attracted a lot of interest for the existence of band gaps when heat flow is of oscillatory nature [1]. The fact that TWCs exhibit band gaps for their oscillatory behavior motivated the development of numerous studies aimed at exploring their properties and potential applications [2][3][4][5][6]. For instance, the presence of band gaps within a TWC structure has the potential to reduce heat propagation by means of interference [1].…”