1. Introduction

Using metamaterials (MMs) and transformation optics (TO) to manipulate electromagnetic wave (EMW) in a desirable way has been a research highlight due to its great potential influence on both science and engineering. In the past few years, great achievements have been made in this field and various devices have been developed [1–3]. Motived by the great success in EMW, it has been rapidly and successfully extended to other waves such as acoustic waves [4] elastic wave [5] and matter waves [6]. Recently, increasing attention is paid to the manipulation of Laplace fields such as dc magnetic field [7, 8], dc electric field [9–11], thermal field [12–18] and great progress has been made. However, the previously reported researches are usually limited to bulk material system, while the possibilities in film system are unexplored. In fact, the thin film, which is usually a material with the thickness from one nanometer to several millimeters, plays a significant role in a considerably wide range of areas like MEMS, electron semiconductor and optical devices. Employing MMs and TO to control the physical fields like dc electric field and thermal field in the thin film would open new possibilities and bring about many potential applications.

Although sharing similar physics with the bulk material system, controlling the physical fields in thin film using MMs and TO method is quite different in many aspects. The first obvious difference are their sizes, hence the corresponding processing technology would change. Usually, the reported researches achieve the desired parameters (such as thermal or electric conductivity) by making a material inserted into another one. When it comes to bulk material system, it can be readily implemented by machining, even by handwork. However, it is not easy to be scaled to microscale or nanoscale despite the great advances made in micro-nano fabrication technology in recent years. Firstly, it is difficult to insert the material into another one and the size is hard to be controlled precisely. Second, the inevitable and uncontrollable interfacial effect would cause new problems. As a result, more convenient and feasible scheme for manipulation of physical fields in the thin film is highly desired.

Moreover, the previously reported researches are usually limited to a single physical domain. Recently, bifunctional metamaterials and transformation multiphysics are proposed by several groups to manipulate multi-physics field simultaneously, which however are limited to bulk material system [19–22]. It is interesting to manipulate the multi-physics field in film system.

Here, we proposed a practical scheme to manipulate Laplace physical fields in film system, and we further experimentally demonstrated multi-physics cloak and multi-physics concentrator to confirm the feasibility of our proposed methodology.

2. Bilayer composite

The key to manipulating Laplace fields in film system is to find a simple and practicable method to achieve desired conductivities. Figure 1 schematically shows the general strategy of bilayer composite. Fig. 1(a) illustrates a film A with homogeneous and isotropic parameters (material A with electric conductivity ${\sigma }_1$, thermal conductivity ${\kappa }_1$ and thickness $a$). Fig. 1(b) shows that film A is covered with film B with homogeneous and isotropic parameters (material B with electric conductivity ${\sigma }_2$, thermal conductivity ${\kappa }_2$ and thickness $b$). Assume that the films are exposed to air, which can be considered as insulation (electric conductivity ${\sigma }_{\text{0}}=0$ S/M, thermal conductivity ${\kappa }_{\text{0}}=0$ W/mK) approximatively. Here, film A and film B form so-called “bilayer composite”, marked by red frame. To investigate the properties of such a composite, one can consider that the background film and film made of air (with electric conductivity ${\sigma }_0$, thermal conductivity ${\kappa }_0$ and thickness b) form “background bilayer composite”, marked by dash line (see Fig. 1(a)). Take electric property as an example, the effective conductivity of background bilayer composite can be determined by ${\sigma }_{01}=f{\sigma }_0+(1-f){\sigma }_1$, where $f=b/(a+b)$. Similarly, the effective conductivity for bilayer composite can be determined by ${\sigma }_{12}=f{\sigma }_2+(1-f){\sigma }_1$. As a result, the relative conductivity of bilayer composite to background bilayer composite is $(f{\sigma }_2+(1-f){\sigma }_1)/(f{\sigma }_0+(1-f){\sigma }_1)$. Consider ${\sigma }_0=0$, the relative conductivity can be described by $(f{\sigma }_2+(1-f){\sigma }_1)/((1-f){\sigma }_1)$. Consequently, the case for Fig. 1b can be viewed as equivalent to the one for Fig. 1(c), where film C made of material C with conductivity of $(f{\sigma }_2+(1-f){\sigma }_1)/(1-f)$ is inserted into film A. In previous works, one needs to insert another film into the background film to realize required parameters, which would complicate the fabrication. However, by introducing the concept of “bilayer composite”, one only needs to cover the background film with another one, thus greatly simplifying the realization.

 

Fig. 1 The principle of bilayer composite: (a) film A . (b) film A is covered with another film B. (c) Τhe equivalent structure: film C made of material C with conductivity of $(f{\sigma }_2+(1-f){\sigma }_1)/(1-f)$ is inserted into the film A. The principle of electric/ thermal cloak in film system: (d) The current in homogenous medium. (e) An air hole is placed in the central region. (f) The cloak made of bilayer composite is applied. (g) The required relative conductivity of the cloak shell, i.e σ₂/σ₀, as a function of outer and inner radii ratio R₂/R₁. (h) The required relative thermal conductivity of the cloak shell, i.e κ₂/κ₀, as a function of outer and inner radii ratio R₂/R₁.

Download Full Size | PDF

3. Multi-physic cloak

To demonstrate the feasibility of proposed method, we employ it to manipulate dc electric and thermal fields in a 50um thickness film exposed in air. First, we consider a dc electric cloak that can make an object invisible by guiding the current to circumvent it smoothly. The corresponding physical model is schematically shown in Figs. 1(d) to 1(f). The background material is made of homogenous and isotropic medium with electric conductivity${\sigma }_0$. Fig. 1(d) shows that a homogenous current is generated from the high potential to the low one. In Fig. 1(e), an air hole, with electric conductivity ${\sigma }_1=0$ and radius of $R_1$, is placed in the central region. Clearly, the presence of air hole would bring about serious distortion of the current. Fig. 1(f) shows that the current keeps its original path when the air hole is surrounded by a bilayer composite shell, which is a shell (background film with electric conductivity${\sigma }_0$, inner and outer radii $R_{\text{1}}$, $R_2$, thickness of $a$) covered with another shell with electric conductivity ${\sigma }_2$, inner and outer radii $R_{\text{1}}$, $R_2$, thickness of $b$. To make the electric current outside the cloak shell undisturbed, one can employ bilayer cloak model. According to work [11], the electric conductivity for bilayer cloak can be easily obtained by:

As a matter of fact, this method is a general one applicable to thermal field governed by the Laplace equation in film system. Here, the air is considered as thermal insulation, namely κ = 0, to simplify the theoretical analysis (It is found that such approximation has little influence on the performance). We also calculate the relative thermal conductivity of the cloak shell, i.e κ₂/κ₀ as a function of outer and inner radii ratio R₂/R₁ (see Fig. 1(h)), which shows similar properties to the one for electric field. Similarly, three cases were considered: the red line and blue line corresponding to thickness ratio of shell and background medium c/a = 1 (f = 1/2) and c/a = 2 (f = 2/3), respectively, and the black line represents the case for the previous bilayer structure cloak [16]. The alternative materials were also marked by red dash lines. Interestingly, it is found that when the thickness ratio R₂/R₁ is 1.73 (c/a = 1), the relative thermal conductivity of shell κ₂/κ₀ = 1, which means that the shell can also be made of the same material to background medium. Combining with the analysis on electric current field, it can be found that one can obtain a bifunctional cloak that can simultaneously render the object invisible thermally and electrically by covering the background medium with the same material when the thickness ratio R₂/R₁ is 1.73. Compared to the previous work on bifunctional cloak [20], several problems can be avoided such as complex structure and fabrication.

We have designed such a bifunctional device, which has the following geometrical parameters: R₁ = 5mm, R₂ = 8.63mm, f = 1/2. Simulations based on Comsol were conducted to examine the performance of designed dc cloak. Two simulations are performed for comparison: electric current flows in homogeneous material (Fig. 2(a)) and flows in the one with an air hole in the central region (Fig. 2(b)). In the simulations, 1V potential was applied to the each end of samples. As shown in Fig. 2(a), uniform electric current field is generated in the homogeneous material, while obvious perturbation of electric field can be observed when an air hole is made in the central region (Fig. 2(b)). To make the air hole invisible, bilayer composite structure is used, which is shown in Fig. 2(c). The thickness and conductivity of cloak shell are the same as those of the background film. As one can see, excellent performance is obtained for the designed cloak, confirming the theoretically analysis.

 

Fig. 2 (a) Simulated isopotential lines for the homogeneous medium. (b) Simulated isopotential lines for the one with object (air hole). (c) Simulated isopotential lines for the object (air hole) wrapped with cloak. (d) Simulated isotemperature lines for the homogeneous medium. (e) Simulated isotemperature lines for the one with object (air hole). (f) Simulated isotemperature lines for the object (air hole) wrapped with cloak.

Download Full Size | PDF

To obtain the thermal properties, corresponding simulations are also performed. Two cases are considered for comparison: homogeneous background material (Fig. 2(d)) and another one with air hole (Fig. 2(e)). In the simulations, the samples are put into contact with hot source (80° C) and cold source (0° C). All the geometrical and material parameters are the same as the ones used in the electric field simulations. As shown in Fig. 2(d), uniform thermal flux is produced in homogeneous background material, and it is distorted when an object (air hole) is put in the central region (Fig. 2(e)). The result for the designed cloak is shown in Fig. 2(f). As one can see, good thermal cloak performance can also be obtained. In this way, a bifunctional cloak that can simultaneously make an object invisible both thermally and electrically is obtained.

Next, the experiment results are compared. A gradually changing structure is employed to obtain planar electric equipotential lines (which indicate uniform electric current field from left to right) in the observation area (see Fig. 3(a)). By etching the center region of homogeneous material with a 1064nm laser, an object (namely air hole) is created. To cloak the object, the structure is covered with a cloak shell made of nickel by electroplating processing. All the materials parameters and geometrical parameters are the same as those in the above simulations. Experimentally, a dc power supply is used to produce current and a Multimeter (Agilent 34410A, 6, 1/2Digit Multimeter) is used to obtain the potential distribution. To evaluate the cloaking performance, one can measure the normalized potential distribution along the lines x = −9mm and x = 9mm, as depicted in the insets of Fig. 3(b) and 3(c). The corresponding measurement and data processing methods can be seen in previous references [11, 21]. As expected, the isopotential lines in homogeneous background material are straight, while those for the one with an air hole are distorted. However, the ones for the designed cloak remain straight, exhibiting no distortion. The experiment and simulation results show good agreement, which confirms the feasibility of proposed method.

 

Fig. 3 (a) The normalized potential distribution at the left observation line. Simulation and experimental results of potential distribution for the cloak: (b) The normalized potential distribution at the right observation line,(c) The normalized potential distribution at the right observation line.

Download Full Size | PDF

To characterize the thermal property of such a structure, infrared heat camera (Fluke Ti300) is used to measure the temperature profiles. It should be noted that to reduce the heat conduction/convection by air and the high reflection of Nickel for the operating wavelengths of the thermal heat camera, 50 um thickness electrical insulation tape with emissivity higher than 93% is attached to the upper surface of the sample. In the measurement, two sides of the sample are connected to two temperature sources, namely hot water at 80°C and ice-water mixture at 0°C. For comparison, the background material (Nickel) without any structure is also measured. Figure 4 shows the simulated and measured steady temperature profile. As for homogeneous medium without any structure, a uniform thermal gradient is formed from left to right (see Fig. 4(a)). However, when an air hole is placed in the center, the thermal field is seriously disturbed (see Fig. 4(b)). Fig. 4(c) shows the result for the one with designed bilayer composite: the thermal flux flows around the air hole with less distortion as if the hole was also filled with homogeneous materials. Meanwhile, the air hole is protected from the thermal flux and remains its original temperature. As a result, a good air cloak has been obtained. The corresponding measured results are provided in Figs. 4(d)-(f), which are in good agreement with the simulations. Therefore, one can conclude that a bifunctional cloak made of bilayer composite capable of cloaking both electric field and thermal field has been demonstrated experimentally.

 

Fig. 4 (a) Simulated temperature profile for the homogeneous medium. (b) Simulated temperature profile for the one with object (air hole). (c) Simulated temperature profile for the object (air hole) wrapped with cloak. (d) Measured temperature profile for the homogeneous medium. (e) Measured temperature profile for the one with the air hole. (f) Measured temperature profile for the air hole wrapped with cloak.

Download Full Size | PDF

4. Multi-physic concentrator

To demonstrate the robustness of proposed method, a bifunctional concentrator that can concentrate thermal and electric fields in a certain region simultaneously is investigated experimentally. The principle of bifunctional concentrator is depicted in Fig. 5. Figure 5(a) shows that uniform thermal flux and current are established across the homogeneous medium (50 um stainless steel film with thermal conductivity of 15 W/mK and electric conductivity of 1.3e6 S/M). As shown in Fig. 5(b), the thermal flux and current are concentrated into core region, resulting in an increasing of thermal flux and current density due to the employment of bifunctional shell made of bilayer composite. Here, the bifunctional shell is actually a fan-like metamaterial made of 9 bilayer composite wedges and 9 air wedges. The bilayer composite is made of background medium (namely 50 um stainless steel film) covered with copper film (with thermal conductivity of 402 W/mK and electric conductivity of 5.9e7 S/M) with the same thickness (a = b, f = 1/2). According to the analysis above, the calculated relative effective thermal conductivity and electric conductivity to the background medium are 27.8 and 46.38, respectively. According to reference [21], such shell can function as bifunctional concentrator that can concentrate thermal and electric fields simultaneously while keeping the external fields undisturbed.

 

Fig. 5 The principle for bifunctional concentrator in film system. (a) A uniform thermal flux and current are generated in homogeneous medium. (b) The thermal flux and current are concentrated into core region resulting in an increasing of thermal flux or current density due to the employment of bifunctional concentrator. The red arrows represent thermal flux or current.

Download Full Size | PDF

We have designed such bifunctional concentrator, which has geometrical parameters as follows: R₁ = 4mm, R₂ = 9mm, f = 1/2. Firstly, simulations are obtained based on COMOSOL. Figures 6(a) and 6(c) show the thermal and electric fields simulation results for homogeneous background medium. As expected, uniform temperature gradient and electric potential gradient are produced from high temperature (80°C) to low temperature (0°C) and from high potential (1V) to low potential (0V). Figures 6(b) and 6(d) show the corresponding results for bifunctional concentrator: both thermal and electric fields are concentrated into the core region, resulting in an increasing of temperature gradient and electric potential gradient. In addition, the external fields both for thermal field and electric field keep nearly undistorted. Those results indicate that good thermal and electric concentrator performance is obtained. The fabricated bifunctional concentrator can be seen in Fig. 7(a). The measured steady temperature profile is shown in Figs. 7(b) and 7(c). As expected, uniform temperature gradient is produced from left to right (Fig. 7(b)), while one can find that an obvious increasing of temperature gradient in the core region is obtained when the concentrator is used (Fig. 7(c)). In addition, the external thermal field keeps nearly undistorted (Fig. 7(c)). Consequently, one can conclude that good thermal concentrator performance is obtained. One can evaluate the electric concentrator’s performance by measuring the potential distribution along lines $x=\text{10}$ mm, $x=-\text{10}$ mm and $y=0$ mm. The observation lines can be seen in the inserts in Figs. 8(a)-8(c). As can be seen, the potential lines along the lines $x=\text{10}$ mm and $x=-\text{10}$ mm are straight, which means that no distortion for the external field occurs. In addition, the potential gradient in the central region is increased obviously (Fig. 8(c)). The simulation results show good agreement with the experimental ones, evidently confirming the prediction. Thus, we can draw a conclusion that a bifunctional concentrator which can concentrate thermal and electric fields in the same region simultaneously is demonstrated.

 

Fig. 6 Simulation results. (a) Temperature profile for homogeneous background material. (b)Temperature profile for bifunctional concentrator. (c) Electric potential distribution for homogeneous background material. (d) Electric potential distribution for bifunctional concentrator. The white lines represent isotemperature lines or isopotential lines.

Download Full Size | PDF

 

Fig. 7 (a) The photograph of fabricated bifunctional device. Experimental measured temperature profile: (b) homogeneous background medium (c) bifunctional device. The black circles represent the inner and outer radii of concentrator shell.

Download Full Size | PDF

 

Fig. 8 The simulation and experiment results for the different cases at corresponding positions: (a) x = 10mm, (b) x = −10mm and (c) y = 0mm. The red dash lines in inserts represent observed lines.

Download Full Size | PDF

5. Conclusion

In conclusion, a practical scheme for manipulating Laplace fields applicable to film system has been successfully demonstrated. This method provides a novel way to obtain the desired conductivity parameters, which can be easily realized by current micro-nano technology. As for this paper, multi-physic cloak and multi-physic concentrator are realized successfully, confirming the feasibility of our method. It should be noted that film plays an extremely important role in various fields, like IC technology, MEMS and so on. This scheme for manipulation of physical fields in film system is specifically proposed for current micro-nano fabrication technology, therefore it may help find considerable potential applications in various areas.