Invisibility Cloak Goes Three-Dimensional for Heat

Authors: Hongyi Xu¹, Xihang Shi¹, Fei Gao¹, Handong Sun^1,2, Baile Zhang^1,2

Affiliation:
¹Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore.
²Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore.

While the topic of invisibility has long been investigated in optics-related topics, it is for the first time that invisibility cloaking is realized for heat in a three-dimensional (3D) thermal space, according to a recent research result[1] published by our group at Nanyang Technological University, Singapore.

Thermal invisibility was initially inspired by the concept of Transformation Optics [2, 3], a method that can control light propagation with a coordinate transformation in a 3D optical space, which in general requires optical metamaterials with exotic constitutive parameters (e.g. extremely large or extremely small anisotropic permittivity and permeability). Despite the inspiring elegance of 3D optical invisibility cloaking theory, its experimental realizations have been mainly limited to two dimensions (2D), because of the widely acknowledged tremendous difficulties in constructing optical metamaterials with stringent parameters in 3D.

Similarly, the recent development of thermal invisibility cloaking based on transformation thermodynamics were firstly demonstrated in 2D [4, 5]. The method, similar to transformation optics, requires thermal metamaterials with anisotropy and inhomogeneity, being difficult in 3D.

Researchers in Nanyang Technological University successfully bypassed the problem by taking advantage of the difference between heat (a diffusion phenomenon) and light (a wave phenomenon), and experimentally demonstrated the world’s first ultra-thin 3D thermal cloak that shields an air bubble in a stainless steel from external conductive heat flux [1]. The technology can protect a 3D object from heat flux without distorting the external temperature distribution by simply using an ultra-thin layer of thermal metamaterial made of copper with carefully designed thickness.

The implementation process of thermal cloak is illustrated in Fig.1. A hemi-spherical hole with radius of 0.51 cm was drilled by electrical discharge machining in a half stainless steel block with dimension of 2×2×1 cm. A thin disk of copper was punched into the hemi-spherical hole by a molding rod (Fig 1a), to form a copper shell (Fig. 1b) with homogeneous thickness of 100 μm. Two identical half blocks were further combined together to form a complete 3D thermal cloak (Fig. 1c), with dimension of 0.5/0.51 cm for the inner/outer radius of the copper spherical layer, and 2×2×2 cm for the complete stainless steel block.

Figure 1. Illustration of the Fabrication of a 3D thermal cloak. a, Molding process of half of the 3D thermal cloak: (a) Thin copper disk is punched into the hemispherical hole in the stainless steel block. (b) Illustration and snapshot of half of the thermal cloak after molding. (c) Illustration and snapshot of the full cloak by combining two half blocks. The red/blue plate represents high/low temperature at the bottom/top surface [1].

In the experimental characterization, a hot plate (red color, Fig. 1c) and an ice tank (blue color, Fig. 1c) were closely attached to the bottom and top surface of the thermal cloak. When heat diffused from bottom to top, the temperature at the cross-section surface was captured by a thermal camera. The dynamic process of heat transfer from the beginning to the moment near thermal equilibrium was recorded in a movie clip:
 

The temperature distributions at the beginning time and at the moment near thermal equilibrium are shown in Fig. 2. In Fig. 2a and 2d (cases of background), the temperature distribution is homogeneous across the entire surface, indicating that heat diffuses through the stainless steel smoothly. In Fig. 2b and 2e (cases without thermal cloak), the distribution of temperature is distorted (being ‘bent’ towards the air bubble) and a relatively cool region is left behind the air bubble, indicating that part of heat flux has been blocked by the air bubble. In Fig. 2c and Fig. 2f (cases with thermal cloak), the temperature distribution outside the air bubble is restored to norm, as if the air bubble did not exist, indicating the cloaking effect for heat flux.

Figure 2. Characterization of conductive thermal cloaking for transient homogeneous thermal flux. (a-c) Temperature distributions for the moment of 0.5 min at the beginning of heat transfer. (d-f) Temperature distributions for the moment of 4.5 min close to thermal equilibrium. (a&d) Temperature distributions in the pure background without any air bubble or cloak. (b&e) Temperature distributions when an air bubble without the cloak is present. (c&f) Temperature distributions when the air bubble is cloaked by the ultra-thin cloak. In b-c and e-f, the dotted circles indicate the position of the air bubble, while the dotted circles in a and d are merely for comparison [1].

This thermal invisibility cloak is the first demonstration in 3D that heat flux can be effectively controlled by thermal metamaterials. Application wise, effective control of heat is an important subject in modern semiconductor industries, where the exponential increase of package density is generating more and more heat in a unit space. The heat generated jeopardized the performance and lifetime of semiconductor devices, accounting for over 50 percent of electronic failures [6]. With effective heat control technologies based on thermal metamaterials, it is possible to develop efficient heat dissipation solutions to thermal problems in semiconductor industries.

References: 
[1] Hongyi Xu, Xihang Shi, Fei Gao, Handong Sun, Baile Zhang, "Ultrathin Three-Dimensional Thermal Cloak", Physical Review Letters, 112, 054301 (2014). Abstract.
[2] Ulf Leonhardt, "Optical Conformal Mapping", Science, 312, 1777-1780 (2006). Abstract.
[3] J. B. Pendry, D. Schurig, D. R. Smith, "Controlling Electromagnetic Fields", Science, 312, 1780-1782 (2006). Abstract.
[4] Supradeep Narayana, Yuki Sato, "Heat Flux Manipulation with Engineered Thermal Materials", Physical Review Letters, 108, 214303 (2012). Abstract.
[5] Robert Schittny, Muamer Kadic, Sebastien Guenneau, Martin Wegener, "Experiments on Transformation Thermodynamics: Molding the Flow of Heat", Physical Review Letters, 110, 195901 (2013). Abstract.
[6] Shanmuga Sundaram Anandan, and Velraj Ramalingam, "Thermal Management of Electronics: A Review of Literature," Thermal Science, 12, 5-26 (2008). Full Article.