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.

We analyze the time-harmonic heating of a non-Fourier medium by spherical nanoparticles via the photothermal effect. The nanoparticle is embedded in a medium with thermal properties similar to those reported for organic tissue that does not obey Fourier’s law of heat conduction but rather the Cattaneo–Vernotte equation. By assuming the nanoparticle is illuminated with an intensity-modulated laser, we show that the temperature profile outside the nanoparticle oscillates and, at specific separations, can have a temperature 16% lower than predicted using Fourier’s law of heat conduction.

We present a study of the causal response of non-Fourier heat conduction by introducing a dispersive generalized thermal susceptibility and show it obeys Kramers-Kronig relations. In particular, we discuss the Cattaneo-Vernotte and the dual-phase lag models. The constitutive equations are written as a linear response theory and determine the conditions for which the dual-phase lag model does not satisfy Kramers-Kronig relations. An alternative model is presented to describe non-Fourier transport using the similarity with the causal response of viscoelastic materials to avoid this unphysical issue.

In this paper we solve the Cattaneo-Vernotte Equation for a periodic heterostructure made of alternate layers of different materials. The solutions describe thermal waves traveling in a periodic system, and it allows us to introduce the concept of thermal crystals. We show that the dispersion relation shows the characteristics of a band-structure, however the corresponding Bloch wave vector is always complex corresponding to pseudo-bands, unlike what happens in photonic or acoustic crystals. In this context, we also discuss the use of the Floquet-Bloch theorem for thermal waves. The case of finite layered structures is also analyzed showing the possibility of changing the temperature and heat flux by introducing defects opening the possibility of thermal management through the pseudo-band structure.

Ultrafast heating processes do not follow Fourier's heat conduction law, but rather the proposed Cattaneo-Vernotte equation (CVe) which has wave-like solutions that have some important differences from other wave phenomenon. In a periodic system made of materials with different thermal conductivities, solutions of the CVe lead to a band-like structure in the dispersion relation. In this work, we show that highly reflective Bragg mirrors for thermal waves can be designed. Even for a mirrors with a few layers a very high reflectance is achieved (>90%). The mirrors are made of materials with large thermal response times, where thermal waves have been measured. A second alternative consists of adding a thin metallic film which also leads to an efficient thermal Bragg mirror. Finally, the role of defects in opening new thermal-stop bands is demonstrated.