Nonlinear thermal responses in geometrically anisotropic metamaterials

Nonlinear metamaterials have great potential in heat management, which has aroused intensive research interest in both theory and application, especially for their response to surroundings. However, most existing works focus on geometrically isotropic (circular) structures, limiting the potential versatile functionalities. On the other hand, anisotropy in architecture promisingly offers an additional degree of freedom in modulating directional heat transfer. Here, we investigate nonlinear composition effects in geometrically anisotropic (confocal elliptical) thermal medium under the framework of effective medium approximation, and deduce a series of general formulas for quantitatively predicting nonlinearity enhancement. Enhancement coefficients are analytically derived by the Taylor expansion method in different nonlinearity cases. In particular, we find that some coupling conditions can greatly promote the nonlinear modulation coefficients, introducing stronger enhancement beyond isotropic construction. Our theoretical predictions are verified by finite-element simulation, and feasible experimental suggestions are also given. For extending these results to practical scenes, two intelligent thermal metadevices are designed in proof of concept and demonstrated by numerical simulation. Our works provide a unified theory for anisotropic nonlinear thermal metamaterial design and may benefit flexible applications in self-adaptive thermal management, such as switchable cloaks, concentrators, or macroscopic thermal diodes.