We synthesize and systematically characterize a novel type of magnetically tunable metamaterial absorber (MA) by integrating ferrite as a substrate or superstrate into a conventional passive MA. The nearly perfect absorption and tunability of this device is studied both numerically and experimentally within X-band (8–12 GHz) in a rectangular waveguide setup. Our measurements clearly show that the resonant frequency of the MA can be shifted across a wide frequency band by continuous adjustment of a magnetic field acting on the ferrite. Moreover, the effects of substrate/superstrate’s thickness on the MA’s tunability are discussed. The insight gained from the generic analysis enabled us to design an optimized tunable MA with relative frequency tuning range as larger as 11.5% while keeping the absorptivity higher than 98.5%. Our results pave a path towards applications with tunable devices, such as selective thermal emitters, sensors, and bolometers.
© 2014 Optical Society of America
Metamaterials , whose properties are engineered by configuring their subwavelength inclusions, have attracted considerable attention owing to their unique electromagnetic and optical properties, including negative refraction , reversals of Doppler shift and Cherenkov radiation [3,4], enhancement of evanescent wave , and super-resolution imaging [6,7]. As a result, metamaterials have been extensively studied for applications such as superlenses , invisibility cloaks , as well as microwave/terahertz components [10, 11]. Besides these applications, electromagnetic absorbers based on metamaterial designs, known as metamaterial absorbers (MAs) , have received significant research interests because of the flexible design, sub-wavelength thickness, and nearly perfect absorption. Most importantly, MAs can be realized at almost any frequency by properly selecting the unit cell dimensions. Inspite of having a narrow operating bandwidth, the existence of such a huge operating spectral range enables the use of MAs in applications such as thermal emitting , energy harvesting , and sensing . Various configurations have been developed for MAs [16–20] and corresponding theory and numerical analysis can be found in many references (e.g. [21–24]).
The unique properties of metamaterials can be attributed to associated resonances in the subwavelength unit cells, and thus metamaterials typically have narrow operating bandwidths. Although researchers have tried different methods to increase the operating bandwidths of metamaterials [25–29], flexible control of the operating frequencies is still an intractable issue in metamaterials. Recent researches show that the resonant frequencies of metamaterials can be dynamically adjusted via integrating tunable media (e.g., varactor diodes , liquid crystals , graphene , or phase-change materials ) into traditional passive metamaterials. Most interestingly, in some specific instances, researchers have proposed to utilize oxide films  or film-coupled colloidal nano-antennas  as a substrate or superstrate to control the absorbing frequencies. Recently, we also made a contribution to this field by designing a mechanic-moveable MA with dielectric cover . However, most of the configurations reported in literatures have limited tuning range because their near perfect absorptivities drop down quickly (e.g., [31–36]). Therefore, working on a new type of tunable MAs with wide tuning range while maintain the nearly perfect absorptivity is very important and helpful for the MAs community.
Recently, we theoretically demonstrated that a properly geometrically configurated ferrite based metamaterial  can possess high absorptivity with the added possibility to magnetically tune the absorption band. However, the chosen ferrite must possess a large resonance bandwidth to sustain a strong magnetic loss across a wider bandwidth. At the same time the dimensional parameters of such a MA should be carefully designed for near uniform absorptions. In this paper, we further demonstrate that by integrating a ferrite (the resonance bandwidth characteristic is not crucial any more) as the substrate or superstrate into a conventional planar MA, magnetic biased frequency-tunable absorption can also be achieved. We first briefly analyze the effective permeability of ferrite under different strength of magnetic fields. Then, we demonstrate the absorbing properties and tunable characteristics of the MAs through numerical simulations and experimental measurements. We further discuss the effects of substrate/superstrate’s thickness on the MA’s absorptivity and resonant frequency. The proposed tunable MA paves a path toward to applications with different operating frequencies requirements, such as tunable selective thermal emitters, sensors, and bolometers.
We start by briefly reviewing the electromagnetic properties of ferrite. The relative permittivity of ferrite used in this paper is 13.8 with loss tangent of 0.0002. Assuming that a DC magnetic field with amplitude H0 applies along the z-axis, for a z-polarized electromagnetic wave propagating in the x-axis, the effective permeability μeff of ferrite can be represented by the following expression [37, 38],Fig. 1, when the biasing magnetic field increases from 1.1 kOe to 1.9 kOe, the permeability curve shows a clear blueshift with shift rate of approximately 20 MHz/Oe. At the frequency band of interest (X-band, 8–12 GHz), we see that the effective permeability decreases from positive to negative when the magnetic field increases. This property can be used for dynamical tunability. Different from the previous work  where the ferrite’s tunable permeability within its intrinsic narrow resonant band is employed for synthesizing magnetically controllable metamaterials, the frequency band we interested is outside the intrinsic resonant band. Therefore, the required ferrite is not limited by its narrow resonant bandwidth and can be generally substituted by other types of ferrites.
The unit cell of the considered MAs is schematically shown in Fig. 2(a). Similar to , we use an array of metallic electric-LC (ELC) resonators backed up with a metallic mirror to realize a conventional passive MA. The metallic ELC array is etched on one side of an FR4 printed circuit board and a full-sized metallic ground plane is covered on the other side. The metal used in this paper is copper with conductivity of 5.8 × 107 S/m, and the FR4 can be characterized by its relative permittivity of 4.0 and loss tangent of 0.02. For the purpose of achieving tunable characteristics, we propose two strategies by integrating ferrite into the passive MA. In the first case (MA1), the ferrite layer is inserted between the FR4 layer and the ground plane [see the left plot of Fig. 2(b)]. Both the ferrite and the FR4 layers service together as a substrate. In the second case (MA2), the ferrite layer is employed as a superstrate [see the right plot of Fig. 2(b)] and another FR4 spacer is placed between the ferrite and the passive MA to avoid the interactions between the ferrite and metallic resonators. The performances of these MAs are analysed and measured in an X-band rectangular waveguide system as shown in Fig. 2(c).
Considering electromagnetic wave propagating at the interface between air and a MA in a rectangular waveguide system, the material properties of which are characterized by permittivities εair and εMA and permeabilities μair and μMA, respectively. The simplified Fresnel equations with regard to reflection of normal incident electromagnetic wave in such a system can be rewritten as ,39],
We employ numerical simulations based on finite integration technique for the optimization of the ELC resonator’s geometrical parameters. Due to our experimental restriction, the thicknesses of the metallic patterns, the FR4 layers, and the ferrite layers are fixed to be 0.034 mm, 0.5 mm, and 1 mm, respectively. In order to achieve nearly uniform absorptions, the geometrical parameters for MA1 are chosen to be a = 2.94 mm, b = 1 mm, w = g = 0.2 mm, and d = 4.5 mm. For the case of MA2, the use of an additional FR4 layer would result in the red-shift of the resonance to be outside of X band. To avoid this, we slightly reduce the length of the ELC resonator to be a = 2.82 mm and remain the other geometrical parameters the same as those of MA1. The magnetic fields are preset to be 1.55 kOe and 1.6 kOe in simulations for MA1 and MA2, respectively. The experimental MA samples are fabricated by printed circuit board techniques and measured in an X-band rectangular waveguide using Agilent N5230A vector network analyzer. In particular, the FR4 layer with ELC resonators and ferrite layer are put into the waveguide sequentially for MA1; the ferrite layer, FR4 spacer and passive MA are staked one over the other within MA2. Over these two structures, a metallic plate is tightly fitted to cover the waveguide port to prevent leakage of electromagnetic energy. A tunable z-directed DC magnetic field generator is positioned on the samples. Finally, the rectangular waveguide filled with MA samples is connected to the coaxial cable of Agilent N5230A vector network analyzer by a waveguide-to-coaxial converter (similar detailed setup can be found in ).
In Figs. 3(a) and 3(b), we show the reflectivity R(ω) and absorptivity A(ω) of these two MAs. It is seen that each MA shows a clear absorption peak with a nearly uniform absorptivity. We see that, for both cases, the measured peak frequencies are a bit higher than the simulated ones. The reason for those shifts is that the ferrite layers are difficult to be placed seamlessly to the FR4 layers inside a waveguide. However, this does not affect the tunability of the ferrite based MAs. The absorptivity spectra of the MAs can be dynamically controlled by adjusting the magnetic field. In Fig. 4, we see that when increase the magnetic field gradually, the absorption peaks blueshift for both MAs. Particularly, for MA1 free of magnetic field [see Figs. 4(a) and 4(b)], an absorption peak appears at 10.75 GHz with peak absorptivity of 85.5% in the simulated setup (11.0 GHz and peak absorptivity of 44% in experiment). When we gradually increase the magnetic field from 1.15 kOe to 1.95 kOe, the resonant frequency moves from 10.99 GHz to 11.29 GHz (11.17 GHz to 11.45 GHz in measurement). Meanwhile, the absorptivity first increases from 97.8% to nearly 100% and then drops down to 93.3% (increases from 85% to nearly 100% and then descends to 80% in measurement). Similar frequency shift and absorptivity change can also be found in Figs. 4(c) and 4(d) for MA2 (details can be in the caption of Fig. 4). It is easy to find out that the frequency shift rates of these MA1 and MA2 are about 0.36 MHz/Oe and 0.18 MHz/Oe, respectively.
When we closely look at the measured results and corresponding simulations at the same magnitudes of magnetic fields, we see that the resonant frequencies for both MAs have higher measured values compared with corresponding calculations. Moreover, compared with the two MA configurations, the shift rate of MA1 is twice of that of MA2. This is because the resonance-induced localized electromagnetic fields mainly concentrate in the substrates rather in the superstrates, and the electromagnetic performances of the MAs are more sensitive on the substrates.
In the above analysis, both the thicknesses of ferrite and FR4 layers are fixed at 1 mm and 0.5 mm, respectively. In this section, we further discuss the effects of the thicknesses of the ferrite and the FR4 layers on the electromagnetic performance of the tunable MAs. For this purpose, we fix the thickness of one layer (either ferrite or FR4) and change the other layer’s thickness to investigate the tunable absorptions of the two MA configurations. For MA1, the ferrite (FR4) layer is fixed to be 1 mm (0.5 mm) and the FR4 (ferrite) layer is tuned from 0.1 mm to 0.7 mm (0.6 mm to 1.4 mm). The corresponding numerical results are plotted in Figs. 5(a) and 5(b). For MA2, the ferrite (FR4) layer is fixed to be 1 mm (0.5 mm) and the FR4 (ferrite) layer is tuned from 0.3 mm to 0.6 mm (0.8 mm to 1.1 mm), and the results are shown at Figs. 5(c) and 5(d). Note that for MA2, we only change the thickness of one FR4 layer which acts as a superstrate and the other FR4 layer between the ELC resonators and metallic ground plane remains unchanged.
Some interesting phenomena can be found in Fig. 5. Firstly, the resonant frequencies of the MAs blueshift when increase the magnetic field. This is in accordance to the result in Fig. 1 where the ferrite’s permeability decreases as the increase of the magnetic field. Secondly, for a larger thickness of the FR4 or ferrite layer, a stronger magnetic field is required to ensure a nearly uniform absorptivity (marked as stars in Fig. 5) and the magnetic field range for a high absorptivity (larger than 98.5%) is reduced (see the thicker part at each curve). This is because when the thickness of the substrate or the superstrate increases, the impedance of the MA deviates from that of the background medium. Fortunately, we can increase the magnetic field to reduce the ferrite’s effective permeability (see Fig. 1). By doing so, the impedance matching can be re-gained at a certain magnetic field. However, when the magnetic field increases, the effective permeability of ferrite is more sensitive to the change of the magnetic field. As a result, the magnetic field tuning range for high absorptivities is reduced owing to the impedance mismatching. Moreover, the shift rate of the resonant frequency is nearly linear when the magnetic field is relatively weak, and becomes strongly nonlinear when the magnetic field further increases, especially for the second MA configuration [see Figs. 5(c) and 5(d)]. This is due to the fact that when the magnetic field is relatively low, the intrinsic resonance of ferrite is far below X-band (see Fig. 1), thus the effective permeability of ferrite in the X-band is almost linear to the magnetic field. When the magnetic field increases to a certain value, the intrinsic resonance of ferrite shifts closer to X-band, resulting in a strongly nonlinear response.
On the other hand, some unfavorable properties can also be found when increase the thickness of the FR4 or ferrite layer. In particular, for thicker FR4 layers, the initial peak absorptivity frequencies (without magnetic field) increase and meanwhile the frequency shift rates, denoted as the gradient for each curve in Figs. 5(a) and 5(c), decrease for both MAs. This is because when increase the thickness of the FR4 layer, the ferrite layer with large permittivity would be away from the ELC resonators and therefore contributes less on the resonance. Contrarily, inverse trends are found when increase the thicknesses of the ferrite layers as shown in Figs. 5(b) and 5(d). Compared between the two MAs, we see that MA1 has a higher flexibility in choosing the thicknesses of the FR4 and ferrite layers for keeping high absorptivities and its frequency shift range is also larger than that of MA2.
From the above discussions we see that for a thinner FR4 layer, the resonant frequency of the MA becomes more sensitive to the magnetic field, but unfortunately the high absorptivity band is reduced as well. Therefore, it is important to find an equilibrium condition such that the frequency shift range is relatively large whilst having a uniform absorptivity in the tuning range. Fortunately, extensive computer simulations show such a region indeed exists. Taking MA2 as an example, we choose the FR4 layer between the ELC resonators and ground plane to be 0.65-mm thick, the other FR4 layer to be 0.1-mm thick, and the other geometrical parameters are remained the same as the one we considered in the previous section. Under this condition, the ferrite layer is close enough to the ELC resonators and can give more contributions on MA’s tunability, and meanwhile the other enlarged FR4 layer can offset the impedance mismatching between the MA and surrounding medium (this can be obtained from simulations which is not shown here that the absorptivity will be reduced when the thickness of the FR4 layer between the ELC resonators and ground plane is smaller or larger than the optimized value 0.65 mm). In Fig. 6 we show that when the magnetic field increases from 0 Oe to 1.9 kOe, the resonant frequency of the MA can be shifted from 8.6 GHz to 9.65 GHz and the absorptivity at each resonance keeps higher than 98.5%. The fractional shift range, defined as (fh − fl)/fc where the subscripts denote the higher, lower, and center frequencies for the frequency shift range, is as large as 11.5%. This is a very wide frequency tuning range which is more than 3 times larger than those reported in previous work [31, 32, 34].
We have systematically analyzed two ferrite based tunable metamaterial absorbers (MAs) by integrating ferrite as a substrate or superstrate into a conventional passive MA. The nearly perfect absorption and tunability of the ferrite based MAs were investigated numerically and experimentally in X-band frequency region for a rectangular waveguide system. We show that for both MAs considered in our study, the resonant frequency can be shifted across a wide frequency band by adjusting magnetic field. We further discussed the impact of the thicknesses of the ferrite and the FR4 layers on the tunability of the MAs. Finally, a very wideband tunable MA was numerically presented which shows an 11.5% tuning range with absorptivity higher than 98.5%. The proposed tunable MAs may find useful in various applications, such as selective thermal emitters, biomedical sensors, and bolometers.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61371047 and 61307128) and by Research Fund for the Doctoral Program of Higher Education of China (Grant Nos. 20110185110014 and 20131101120027). Y. Huang gratefully acknowledges the Scholarship Award for Excellent Doctoral Student granted by Ministry of Education of China (Grant No. A03003023901006) and the Excellent Doctoral Student Training Program support by University of Electronic Science and Technology of China. W. Zhu and M. Premaratne also gratefully acknowledge the Australian Research Council, through its Discovery Grant scheme under Grants DP11010071 and DP140100883.
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