Design of tunable terahertz metamaterial absorber based on strontium titanate

YU Juan, ZHANG Bin-zhen, DUAN Jun-ping

(1. Science and Technology on Electronic Test & Measurement Laboratory,North University of China, Taiyuan 030051, China；2. School of Instrument and Electronics, North University of China, Taiyuan 030051, China)

Abstract： Thermosensitive strontium titanate (SrTiO3) as a ferroelectric crystal with great tunability in microwave and terahertz band shows unparalleled potential value. Utilizing the thermal electromagnetic tunability to achieve the intelligent manipulation, a thermal-tunable metamaterial with terahertz-band absorption based on SrTiO3 crystal was proposed in this paper. The absorbent metamaterial (AM) is formed by Floquet’s linear periodic arranged unit, which is composed of a metallic ground plane and embedded cross SrTiO3 material in rhombic metallic patch, and separated by FR-4 dielectric spacer. The broadband frequency tunability of AM was operated by changing the temperature. The permittivity of SrTiO3 was discussed in detail to illustrate how the reconfigurability with thermal transformation is generated. The numerical results show that the tunable broadband of the absorbent band has reached 90 GHz and the corresponding absorptivity is above 99% when the temperature increases from 280 K to 360 K. The resonance frequency will produce a blue-shift with the increase of the temperature. This paper presents a passive thermal-tunable metamaterial as a potential candidate for sensing, materials detection and frequency selective thermal emitters.

Key words： metamaterial; strontium titanate (SrTiO3); terahertz-band; thermal-tunable absorption

0 Introduction

Metamaterial is a kind of synthetic material that does not exist in nature and is composed of subwavelength metal element structures arranged periodically. Metamaterial can artificially control the electromagnetic (EM) waves irradiated on them, so they have many special properties such as negative refractive index[1-3], invisibility cloaking[4-8], perfect lens imaging[9-12]and great optical absorption[13-14]. It has been widely concerned in microwave EM, materials, optics and so on. The emergence of metamaterial has brought new design ideas in the field of science and technology[15-16]. EM metamaterial as a kind of metamaterial, can be mainly divided into microwave metamaterial[17], terahertz metamaterial[18-21]and light wave metamaterial[22-24]according to their different working wavelengths. Terahertz metamaterial absorber is a very important functional device of terahertz metamaterial[25-29], which has broad application prospects in solar cells, sensing, thermal imaging and bolometer. In 2008, Tao et al. reduced the structure size of microwave absorbent metamaterial (AM) to the micron scale, and constructed the AM with working frequency at terahertz by using the open-loop electric resonator, polyimide dielectric layer and metal stubs[30]. Since then, researchers have devoted to the study of terahertz metamaterial absorbers. Terahertz metamaterial absorbers with dual-band, multi-band, wide-band, polarization insensitivity, wide incidence angle characteristics and tunable frequency, bandwidth and absorption intensity have been successively proposed and implemented by researchers.

The intrinsic properties of AM, such as mode, dimension and materials, are associative with its EM absorbency (absorption peak frequency, bandwidth, intensity). In order to satisfy the actual needs, it is urgently need to design the resonant frequency, absorption intensity, bandwidth and other tunable AM. These AM can both achieve target absorption of specific frequency of EM wave and control the absorption amplitude of the EM field, so as to obtain the switching function of the EM field. In recent years, researchers have proposed a variety of tunable absorbers, which can be divided into three categories: electronically controlled absorber, optically controlled absorber and temperature controlled absorber. At present, electronically controlled absorber and optically controlled absorber commonly use external control methods. For example, Zhang et al.[31]and Xu et al.[32]proposed electronically controlled tunable absorbor based on graphene. Shrekenhamer et al. proposed an perfect electronically controlled liquid crystal tunable absorber[33]. Xu et al. proposed an optically controlled broadband blue-shift tunable terahertz wave absorber based on semiconductor silicon[34]. Compared with electronically controlled absorber and optically controlled absorber, the research on temperature controlled absorber to achieve tunable absorption gets less attention. However, temperature controlled absorber has the characteristics of simple equipment, while optically controlled absorber needs external light source and electronically controlled absorber needs additional electrode. The thermosensitive strontium titanate (SrTiO3) as a ferroelectric crystal with great tunability in microwave and terahertz band exhibits unparalleled potential value in passive components applications[35]and it is available to the AM in passive electronic tunability. In fact, by changing the size of the resonant structure unit, the thickness of the intermediate dielectric layer and the material, it is possible to achieve the tuning of the AM, but this passive tuning method has great limitations in practical application. In order to satisfy the increasingly stringent requirements for metamaterial absorbers in practical applications, it is urgent to design and develop active tunable metamaterial absorbers in frequency, intensity or bandwidth.

In this paper, a thermal-tunable AM formed by a metallic ground plane, FR-4 dielectric layer and SrTiO3material embedded in a rhombic metallic patch is designed. The proposed structure not only provides a compact unit cell but also apparently increases the tuning range which is needed in the practical application. The shift of the resonance frequency is attributed to the temperature-dependent refractive index of the dielectric layer and the real part of the dielectric constant. The proposed absorbers with its superior performance pave a path towards applications with different operating frequencies requirements, such as tunable selective thermal emitters, sensors and bolometers. Tunable terahertz AM can be realized within the effective control of the incident EM wave, which is of great significance in the development and application of terahertz technology.

1 Structure development of AM and thermal tunability of SrTiO3

The unit of the proposed thermal-tunable AM is shown in Fig.1. It shows that a “十” shape of SrTiO3material is filled into rhombic metallic patch on the top layer, a metallic ground plane is on the bottom, and a dielectric layer is in the middle. The FR-4 with relative permittivity ofεr=4.3 and loss tangent of 0.025, is chosen for the dielectric layer. The copper with electric conductivity ofσ=4.56×107S/m is as the top of a rhombic metallic patch and bottom metallic layers, and the thickness is 0.3 μm. The other dimension parameters are fixed asP=65 μm,L=44 μm,a=50 μm,b=6 μm andt=3 μm. All of these geometrical sizes are carefully designed to acquire the optimal effect.

Fig.1 Structure of thermal-tunable AM

SrTiO3crystal is one of the most commonly used ferroelectrics in the early stage. On account of its great tunability in microwave and terahertz band, the crystal can control the bias voltage and external temperature to change the real part of its permittivity. And the current technology can make SrTiO3thin films have superior performance and potential application value in tunable microwave devices. The complex permittivity of dielectric spacing layer of SrTiO3can be given by[35-36]

(1)

The real part and imaginary part of the complex permittivity of the SrTiO3can be separated from Eq.(1) as

It should be noted that the real part and imaginary part of the complex permittivity of SrTiO3are related to the frequency of the incident EM wave and changes with the external temperature. The complex dielectric constant of SrTiO3can be controlled by changing the external temperature, and then the tuning of SrTiO3to the EM response characteristics of incident terahertz wave can be realized.

The dependence of the real part and loss tangent of the SrTiO3complex permittivity on the external temperature and the frequency of the incident terahertz wave was calculated by MATLAB software as shown in Fig.2. It can be seen from Fig.2(a) that the real part (Re(ε)) of the SrTiO3gradually decreases with the increase of the temperatureT. Particularly, at each certain temperature, Re(ε) remains almost unchanged with the increase of the frequency, which means the dispersion of the SrTiO3is very weak. The Re(ε) is extremely sensitive to the change of the temperatureT, which immediately indicates its potential in tunable terahertz metamaterials. In contrast to the change of the Re(ε), the loss tangent of the SrTiO3(tanδ), that is less than 0.05 with the increase of frequency, almost does not change with the temperatureTas shown in Fig.2(b). Duing to the real part of the SrTiO3permittivity changes greatly with temperature and the tangential loss basically does not change with temperature, the absorber realized the tuning of the central absorption frequency.

In addition, the absorption spectra of the thermal-tunable AM are simulated by using the commercial time-domain package CST Microwave Studio. In the simulation, the unit cell periodic boundary condition was employed in bothXandYdirections, and the open boundary condition was employed inZdirection. The absorbance is calculated byA(ω)=1-R(ω)-T(ω) orA(ω)=1-|S11|2-|S21|2, whereR(ω) andT(ω) are the reflectance and transmittance, respectively. The transmittanceT(ω) is close to zero due to the shielding effectiveness of metallic layer, thus the calculation of absorption can be simplified asA(ω)=1-R(ω). TheA(ω) may achieve unity or perfect absorption when theR(ω) is also close to zero.

Fig.2 Dependence of real part (Re(ε)) and loss tangent (tanδ) of SrTiO3 complex permittivity on external temperature T and frequency of incident terahertz wave

2 Results analysis and discussion

Fig.3(a) shows frequency curves about the absorption spectraA(ω), reflectionS11and transmissionS21of the designed AM at temperatureT=300 K. The designed AM has a resonance band at frequency of 1.896 THz with an absorptivity of 99.42%. The absorption bandwidth defined as the full width at half maximum (FWHM) of the AM atT=300 K is 0.18 THz, and the quality factorQof resonance absorption peak is 10.53. When the frequency is in the range of 1.869-1.923 THz, theS11is below 0.3 andS21is close to 0. Thus, the designed AM has no polarization conversion function or polarization conversion is almost zero. In addition,T(ω)=0. So it can be obtained by the formulaA(ω)=1-R(ω)-T(ω) that the absorptivity is greater than or equal to 90% in this frequency range.

Fig.3 EM response of AM for normal incidence EM wave at T=300 K

Fig.3 illustrates that most of the EM waves are absorbed by the model when the EM wave is normally incident (incident on the upper surface of the model vertically). The reason is that at this situation, there is no EM wave is transmitted to the back of the model and no cross-polarization of the EM wave, only a small portion of the EM wave is reflected in the same manner. Whenf=1.896 THz, the peak value of reflection curve and absorption curve is reached. The corresponding reflectionS11is 0.076 and the absorptivityA(ω) is 99.42%. Therefore, the absorber achieves a perfect absorption atf=1.896 THz.

The materials loss analysis as shown in Fig.3(b) exhibits the resonant consistency corresponding with absorbent peak in entire operating band, which indicates the EM wave absorption is caused by the intrinsic material loss. Hence, the superposition of material loss acts on the accepted power of EM energy when the incident wave power is 1 W as shown in Fig.3(c).

The simulated absorption spectra for the EM wave with different angles of polarization and incidence are shown as Fig.4.

Fig.4 Dependence of absorption spectra on polarization angles and incidence angles for proposed AM at T=300 K

As seen from Fig.4(a), the absorption performance of the AM is almost unchanged when the polarization angle of the vertically incident EM wave changes from 0° to 90°. The AM is extremely insensitive to the polarization angle of the incident EM wave, which is mainly due to the orthogonal symmetry of the metal resonant structure. The polarization insensitivity of this kind of AM is the most desired in design. Moreover, simulated absorption performance for the incident EM waves with different incidence angles is shown in Fig.4(b). The resonant frequency, absorptivity and absorption bandwidth corresponding to the absorption frequency band of the AM remain basically unchanged when the incidence angle of the EM wave varies from 0° to 45°. However, when the incidence angle of the EM wave increases to 60°, the absorption of the absorption frequency band decreases obviously and the bandwidth also changes. It is shown that the effective EM resonance can not be produced between the metal resonant structure array, the intermediate medium layer and the metal bottom plate of the AM at this time. The equivalent impedance of the AM can not be well matched with the wave impedance in the free space, which leads to the increase of EM wave reflectivity and the decrease of the absorption. According to simulated results, the AM can still achieve better EM wave absorption in a wide range of incidence angles. Therefore, the AM has the characteristics of wide incidence angle.

The relationship between the absorption characteristics of the relative permittivity and thickness of the dielectric layer is researched. Firstly, the influence of the relative permittivity of the dielectric layer on the microwave absorption characteristics of the AM is investigated. In the process of numerical simulation, all the parameters remain unchanged, only the relative permittivity of the dielectric material changes. The microwave absorption characteristics of polyimide, FR-4 and porcelain are simulated and studied respectively. The relative permittivity of those materials is 3.5, 4.3 and 6, respectively.

Fig.5 shows the variation of the absorption characteristic curve of the metamaterial absorber with the relative permittivity of the dielectric material. The influence of the relative permittivity change of the dielectric material on the absorption characteristics of the AM is mainly reflected in the overall absorption frequency. With the increase of the relative permittivity of the dielectric layer, the absorption frequency of the AM gradually moves to the low frequency band, but the absorption intensity basically remains above 85%.

Fig.5 Variation of absorption of metamaterial absorber with relative permittivity of dielectric material

Then the influence of the thickness of the dielectric layer on the absorption characteristics of the AM is studied. In the process of numerical simulation, the other structural parameters remain unchanged. When the thickness of the dielectric layer is 3, 4, 5 and 6 μm, respectively, the absorption characteristics of metamaterial absorbers are studied by simulation. Fig.6 shows the variation of the absorption characteristic of metamaterial absorbers with the thickness of the dielectric layer.

Fig.6 Variation of absorption characteristic of metamaterial absorbers with thickness of dielectric layer

Fig.6 mainly reflects the following two aspects: one is that the absorption frequency band of the AM gradually produces a red-shift with the gradual increase of the dielectric layer thickness; The other is that the absorption intensity of the AM decreases gradually with the increase of the dielectric layer thickness.

Fig.7(a) shows the simulated absorption spectra of the proposed SrTiO3-based AM on different temperaturesT. The results display that the absorption peak has a blue-shift from 1.869 THz at 280 K to 1.959 THz at 360 K and the total frequency shift is 90 GHz, which indicates that in the process of external temperature changing from 280 K to 360 K, the absorptivity of the AM is almost unchanged (more than 99%) and the incident EM wave can be perfectly absorpted.

From Fig.7(b), it can be obtained that the resonant frequency of the SrTiO3-based AM shifts to 1.869, 1.896, 1.92, 1.941 and 1.959 THz when the temperature is 280, 300, 320, 340 and 360 K, respectively.

Fig.7 Variation of absorption characteristic curve of metamaterial absorbers on different temperatures T

To explain the physical mechanism of the AM, the simulated electric field and surface current density distribution corresponding to resonant absorption peak at different temperatures are plotted. Fig. 8 shows the surface electric field distribution at different temperatures. The electric field is almost distributed at the edge of the rhombic metallic resonant ring whenT=280 K. WhenT=320 K, in addition to the strong resonance at the edge of the rhombic metallic resonant ring, the electric field distribution of the intermediate filled SrTiO3material is enhanced. The rhombic edge has a strong resonance with the internal cross structure atT=360 K.

Through the previous analysis, it indicates that the higher temperature for SrTiO3materials exhibits, the smaller the real part of the corresponding permittivity is. With the carrier concentration in SrTiO3material becoming higher, the properties of SrTiO3material are close to the metal properties. Therefore, the electric field distribution of the position filled with SrTiO3material in the middle of the rhombic metal resonant ring becomes stronger when the temperature increases from 280 K to 360 K. It can get conclusions that the increase of temperature will change the electric field distribution in SrTiO3material and finally leads to the resonant frequency deviation of the AM filled with SrTiO3material in the middle of rhombic metal resonant ring.

Fig.8 Simulated electric field distribution corresponding to resonant absorption peak at different temperatures

According to the absorption mechanism analysis of the AM, it can be seen that the realization of the perfect AM mainly originates from the existence of both electric resonance and magnetic resonance. The metal resonant structure unit on the surface of AM will produce electric resonance under the action of incident EM wave electric field. Due to the strong coupling effect between the top metal resonant structure and the bottom metal plate, there will be a reverse charge distribution between the upper and lower metal layers to form a reverse current, thus forming a magnetic dipole resonance. As shown in Fig.9. the current on the mixed structure of SrTiO3-metal is mainly concentrated on the “十” shape of the SrTiO3material. With the increase of temperature, the current increases gradually around the square metal structure, which hinders the effect of EM resonance and leads to the change of metamaterial central frequency. The magnetic field induced by magnetic resonance is mainly distributed in the intermediate dielectric layer. Under the condition that the structure and size of the metamaterial absorber keep the same, the form of the electric resonance remains unchanged. By changing the thickness of the dielectric layer, the form of the magnetic resonance and the coupling between the electric resonance and the magnetic resonance can be changed, thus changing the absorption characteristics of metamaterial absorbers. When the thickness of the dielectric layer is optimized, the corresponding metamaterial absorber can realize the perfect absorption of the incident EM wave.

Fig.9 Simulated sufface current distribution corresponding to resonant absorption peak at different temperatures

3 Conclusion

In conclusions, a thermal-tunable metamaterial with terahertz-band absorption based on SrTiO3crystal has been designed and demonstrated theoretically. The complex dielectric constant of SrTiO3can be controlled by changing the external temperature, and then the tuning of SrTiO3to the EM response characteristics of incident terahertz wave can be realized. Especially, the absorptivity could reach above 99% when the temperature changes from 280 K to 360 K. Furthermore, the proposed concept is applicable to other types of the absorber structure and the frequency tunable absorbers have potential applications in sensing, materials detection and frequency selective thermal emitters.