Abstract

We investigate the existence and properties of defect-induced localized modes in one-dimensional thermal wave crystals governed by the Cattaneo–Vernotte (CV) hyperbolic heat equation. When a single defect layer is introduced into a periodic bilayer of biological tissues, translational symmetry is broken, and a localized thermal excitation emerges within the band gap, characterized by a discrete frequency at which the imaginary part of the Bloch wave vector exhibits a sharp minimum, indicating maximal penetration depth and energy confinement at the defect layer. Using the transfer matrix method, we show that the resonance frequency of this defect mode is determined by the properties of the defect material and its thickness, and is essentially independent of the number of mirror periods surrounding it. The spatial confinement of the mode, by contrast, is governed by the number of mirror periods: increasing this number dramatically sharpens the localization, in direct analogy with a high-quality-factor optical microcavity. We further demonstrate that the defect-mode frequency is continuously tunable across the entire band gap by varying the defect-layer thickness, for three biologically relevant candidate materials. These results establish the CV thermal wave crystal as a platform for engineering localized thermal excitations at the microscale, using materials and layer thicknesses that are experimentally accessible today, and provide a theoretical framework that may motivate future experimental studies on narrowband thermal filtering and biological-tissue characterization.

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