Two-dimensional cylindrical thermal cloak designed by implicit transformation method

Abstract

As a new-type technology of heat management, thermal metamaterials have attracted more and more attentions recently and thermal cloak is a typical case. Thermal conductivity of thermal cloak designed by coordinate transformation method is usually featured by inhomogeneity, anisotropy and local singularity. Explicit transformation method, which is commonly used to design thermal cloak with the coordinate transformation known in advance, has insufficient flexibility, making it hard to proactively reduce the difficulty of device fabrication. In this work, we designed the thermal conductivity of two-dimensional (2D) cylindrical thermal cloak using the implicit transformation method without knowledge of the coordinate transformation in advance. With two classes of generation functions taken into consideration, this study adopted full-wave simulations to analyze the thermal cloaking performances of designed thermal cloaks. Material distributions and simulation results showed that the implicit transformation method has high flexibility. The form of coordinate transformation not only influences the homogeneity and anisotropy but also directly influences the thermal cloaking performance. An improved layered structure for 2D cylindrical thermal cloak was put forward based on the generation function g ( r ) = r 15 , which reduces the number of the kinds of constituent materials while guaranteeing good thermal cloaking performance. This work provides a beneficial guidance for reducing the fabrication difficulty of thermal cloak.