1. Introduction

Subwavelength electromagnetic metamaterials [1] have interesting optical properties, such as negative [1–4], ultra high [5], and zero [6,7] indices of refraction, not found in natural materials. Their development has been rapid in recent years. Their properties are controlled by adjusting the artificial microstructure design to impedance match with free space. They have both an effective electric permittivity and an effective magnetic permeability. Modulating the electrical [8] and magnetic [9] responses to incident waves, metamaterials can possess properties such as invisible cloaking [10,11], perfect lensing [12,13], and new variants of antennas [14,15]. The interest here is in so-called “metamaterial perfect absorbers” (MPAs) [16–20].

The first MPAs based on metallic microstructures, using split ring resonators backed by metallic wires and working at microwave frequencies, were demonstrated in 2008 [16]. Since then, an increasing number of MPAs have been demonstrated both in numerical simulations and experiments, spanning frequencies from the microwave [16,21] to the optical realm [19,22], and various applications have arisen, such as thermal imagers [23], emitters [24], and sensors [25]. Nevertheless, MPAs based on metallic microstructures are spatially anisotropic absorbers [26]. As an alternative, dielectric particle based on Mie resonances can overcome this deficiency [27]. Recently, Liu et al. [28] prepared an isotropic Mie resonance-based MPA composed of an array of dielectric cubes and a metallic ground plane and obtained an absorptivity of 98%. However, as its physical nature is a resonance, the peak absorption frequencies are inevitably limited, greatly constraining potential applications. Some approaches to countering this narrow bandwidth problem have been presented including mechanically tunable MPAs [29], in which the spacing between two cubes is adjusted, and magnetically tunable MPAs [30], whose ferromagnetic resonance frequency can be changed by an applied magnetic field. Other physical systems allowing a degree of bandwidth control are liquid crystals [31], phase change materials [32], and graphene [33]. Here, we describe a new tunable and compact MPA. Certain ceramics have permittivities which are both large and temperature sensitive. By varying the thermal loading of the ceramic absorbers, their working frequencies can be adjusted. This allows a substantially miniaturized tunable MPA than that with external tuning agents like magnets.

Herein, we present calculations and experimental results from a miniaturized tunable MPA based on Mie resonances. A high permittivity dielectric cube was adhered to a specially shaped 2 μm thick copper film sputtered on a quartz plate. A magnetic resonance results in near unity absorption in the X-band (8-12 GHz). Simulations and experiments show that by changing a DC current in the copper from zero to 1.5 A, the working frequency increases from 11.74 to 11.85 GHz while the peak of absorption is maintaining over 99%. This demonstrates both efficient miniaturization and a possible tuning methodology that can extend to other active optical devices. More importantly, dielectric permittivity gradients can be constructed to broaden the absorption bandwidth and potentially expand the range of applications such as metasurfaces and cloaking structures.

2. Experimental section

2.1 Ceramic preparation

Samples of ceramic CaTiO₃-1wt% ZrO₂ were prepared by solid-state reaction. The raw materials were commercial powders of CaCO₃, TiO₂, and ZrO₂. These powders were mixed with special stoichiometric quantities and ball-milled for 24 h in deionized water using a polyamide bottle and zirconia balls. Next, the milled slurry was dried in a 150 °C oven to evaporate the water, then sintered at 1150 °C for 2 h in an Al₂O₃ crucible using a Nabertherm furnace (LTH 08/17, Nabertherm, Germany). The obtained powder was ball-milled again and subsequently pressed into disks with a diameter of 50 mm and a thickness of 15 mm under a pressure of 2 MPa. After cold isotactic pressing in a pressure of 200 MPa, the powder compacts were sintered at 1350 °C for 2 h. The obtained ceramics have high permittivity (ε = 119.1) and low dielectric loss (tanδ = 0.007) at room temperature.

2.2 Numerical simulations and experiment measurements

Numerical simulations for this Mie resonance-based MPA were made by the commercial finite-difference time-domain package CST Microwave Studio^TM and Comsol Multiphysics 5.2a. The permittivity ε and dielectric loss tanδ of the dielectric cube was set as 119.1 and 0.007 in CST. The boundary conditions were set as electric (Et = 0) along x direction and magnetic (Ht = 0) along y direction in the simulations. The microwave reflectance and transmittance S-parameters were measured by an Agilent N5230A PNA-L network analyzer and an aligned WR-90 X-band rectangular waveguide (cross section 22.86 × 10.16 mm). The copper film was obtained by Magnetron Sputtering System. In the actual measurements, the copper film covered the waveguide aperture (see Fig. 7 in Appendixes), mitigating microwave leakage. A regulated direct current power supply connected the two ends of the metal substrate for heating. The waveguide end face had a thin insulator to prevent heating current from flowing into the waveguide metal.

3. Results and discussion

Figure 1(a) shows a schematic of the dielectric resonator, a 2 mm cube of CaTiO₃-1 wt% ZrO₂ ceramic. It has high permittivity (ε = 119.1) and low dielectric loss (tanδ = 0.007). In Fig. 1(b), the shape of the copper film has been specially designed for these experiments. The film is approximately 2 μm thick, sputtered on a quartz plate. The resonator is adhered to the film using a 0.15 mm thickness of cyanoacrylate glue. Photographs of the cubes and the assembled MPA are shown in Figs. 1(c) and 1(d).

 

Fig. 1 (a) Schematic diagram of the CaTiO₃-1wt% ZrO₂ ceramic cube, whose size is 2 mm × 2 mm × 2 mm. (b) Schematic of the 2 μm thick specially shaped copper film sputtered on a quartz plate. (c,d) Photographs of (c) the dielectric cubes and (d) the whole MPA.

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In the CST software package, the MPA was modeled as in Fig. 2(a), showing the dielectric cube and metal plane. The microwaves are incident along the negative z (blue) direction, with the electric field polarized along x (red) and the magnetic field along y (green). The absorption $A\left(\omega \right)=1-R\left(\omega \right)-T\left(\omega \right)$, where in terms of the two-port S-matrix elements reflectance $R\left(\omega \right)={\left|S_{11}\left(\omega \right)\right|}^2$, and transmittance $T\left(\omega \right)={\left|S_{21}\left(\omega \right)\right|}^2$. It is impossible for electromagnetic waves to penetrate through the metallic layer, so the absorption can be obtained from the reflectance:

 

Fig. 2 (a) Schematic diagram of the Mie resonance-based MPA unit cell for calculations. (b) Simulated distribution of the electric field orientation. Displacement currents are indicative of a magnetic dipole. (c,d) Simulated and experimental absorption data with a series of heating currents from zero to 1.5 A

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$A\left(\omega \right)=1-R\left(\omega \right)=1-S_{11}{\left(\omega \right)}^2.$ (1)

Figure 2(b) shows that the orientation of the displacement currents inside and nearby the cube are characteristic of a magnetic dipole. This means the cube couples intensely to the incident magnetic field, leading to absorption at the magnetic resonance frequency. The simulated A(ω) spectrum near resonance is shown in Fig. 2(c), and experimental measurements are given in Fig. 2(d). An obvious absorption feature appears at 11.74 GHz with a peak magnitude of 99.9% at zero DC current. As current is increased to 1.5 A, a blue shift occurs to 11.85 GHz with 99.4% absorption. The experimental data match the calculated peak frequencies well except slightly rough. Oscillations in the experimental curves appears and there are likely several reasons: firstly, the appearance of the ceramic cube is slightly irregular due to the limitations of cutting techniques and there is an imperfect adhesion between the cube and the copper film. In addition, the electromagnetic wave is not vertical to the sample absolutely as the limited experimental conditions. The temperature-induced change in permittivity at different currents can be deduced directly. It is worth noting that higher current or dielectric permittivity ceramics could be used to acquired stronger tunability [34].

To investigate the intrinsic mechanism that generates tunability, we tested the microwave transmission of an isolated single cube at different temperatures. The cube was suspended in the waveguide by a small piece of foam insensitive to microwave. We put the heater band evenly around the rectangular waveguides, and the temperature controller is used to real-time detect the temperature of the whole. The microwave transmittance S-parameters were measured by the equipment mentioned above. Figure 3(a) is a modeling schematic of one dielectric cube. In Fig. 3(b), the calculated displacement currents wrap around the cube as in Fig. 2(b). A magnetic dipole oscillates inside, indicative of a magnetic Mie resonance. Figures 3(c) and 3(d) shows the calculated and measured transmittance S-parameters of the isolated cube at different temperatures. The Mie resonance frequency primarily depends on the permittivity and size of the dielectric. The permittivity of CaTiO₃-1wt% ZrO₂ decreases from approximately 119 to below 117 with a temperature increase from 18 to 45 °C, shifting the resonant frequency higher. At 18 °C, the measured resonance peak is near 11.68 GHz in Fig. 3(d), increasing to 11.80 GHz at 45 °C. There is good correspondence between the sets of calculated and measured frequencies.

 

Fig. 3 (a) Schematic diagram of the unit cell of an isolated dielectric cube. (b) Simulated distribution of the electric field. (c,d) Simulated and experimental transmittance (S₂₁) at a series of temperatures from 18 to 45 °C

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For further verification, a multimeter is used to measure the temperature of the ceramic cube in the MPA at different currents (see Fig. 5 in Appendixes). The permittivity versus temperature is calculated. The relationships between current, temperature, and permittivity are shown Fig. 4(a). The dashed black curve shows the cube temperature rising from 18 to 40 °C as the current increases from zero to 1.5 A. The solid red curve shows the permittivity decreasing from 119.1 to 117.1. From this temperature calibration, we can derive two ways of the permittivity versus temperature, from the MPA resonance curves measuring reflectance, and from the isolated cube spectra measuring transmittance. These data are plotted together as red and black curves in Fig. 4(b). The good overlap confirms the frequency tunability results from temperature control of the dielectric cube.

 

Fig. 4 (a) The relationship between current, temperature, and permittivity. (b) The permittivity variation derived from reflection and transmission tests. (c) Current density magnitudes and vectors in the copper film, simulated by Comsol 5.2a. (d) In simulation, the peak of absorption broadens as the permittivity gradient heighten from zero (means no gradient) to 0.8 between adjacent cubes along y axis.

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There are some methods to enhance the tunability: Firstly, the copper film can be changed to other metallic film such as Nickel, as an alternative, which has a skin depth of less than 90 nm at 12 GHz, but has a resistivity higher than that of copper. It means that a higher temperature is able to achieved in the same current, causing a larger variation of permittivity consequently. Secondly, ceramics which have larger variation in permittivity-temperature property could be used to replace that we have used. They have stronger permittivity variations as the temperature changes, generating higher tunability.

The special shape of the MPA copper film is chosen to evenly distribute the current density across the center to get an isothermal region. This is supported by a current density simulation using Comsol 5.2a in Fig. 4(c). The current flow vectors point uniformly in one direction across the middle of the metallic film. We note there are current density gradients and hence temperature gradients are generated at both ends of the metal film. It is therefore possible to make a permittivity gradient with alternate foil shapes. As is shown in Fig. 4(d), the peak of absorption broaden and the absorptivity slight declines as the permittivity gradient heighten from zero (means no gradient) to 0.8 between adjacent cubes along y axis. The position of absorption compared with Fig. 2(d) changes due to coupling effects resulting from the spacing of the cubes shrinking (see Fig. 6 in Appendixes). So dielectric permittivity gradients can be constructed to broaden the absorption bandwidth. Potentially this could expand the range of applications such as cloaking and metasurfaces.

4. Conclusion

In conclusion, we fabricated an electrically controlled Mie resonance MPA. A ceramic dielectric resonator is placed atop a specially shaped copper film sputtered on a quartz plate. Passing DC current through the film serves to heat the dielectric, changing its permittivity and shifting its operating frequency. The resonance peak frequency increases from 11.74 GHz to 11.85 GHz on increasing the current from zero to 1.5 A, corresponding to a temperature shift from 18 to 40 °C. The absorption is over 99% consistently. This MPA design opens a path to further miniaturization and tunability variation for applications. More importantly, dielectric permittivity gradients can be constructed to broaden the absorption bandwidth. This has potential for expand the range of applications such as metasurfaces and cloaking structures.

Appendixes:

 

Fig. 5 Photograph of the setup used to calibrate temperature in the MPA as a function of current flow in the copper film.

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Fig. 6 Absorbing properties of different space models in simulation. Due to coupling effects resulting from the spacing of the cubes shrinking the peak of the absorption changes from about 11.7 GHz to 15.5 GHz.

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Fig. 7 The details of the experiments. The microwave reflectance and transmittance S-parameters were measured by an Agilent N5230A PNA-L network analyzer and an aligned WR-90 X-band rectangular waveguide. A regulated direct current power supply connected the two ends of the metal substrate for heating. The waveguide end face had a thin insulator to prevent heating current from flowing into the waveguide metal.

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Funding

National Natural Science Foundation of China (NSFC) (11274198, 51532004, 51575297); Science and Technology Plan of Shenzhen City (JCYJ20160301154309393).

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