Haotian Du(杜皓天) Mingzhu Jiang(江明珠) Lizhen Zeng(曾麗珍) Longhui Zhang(張隆輝)Weilin Xu(徐衛(wèi)林) Xiaowen Zhang(張小文) and Fangrong Hu(胡放榮)

1Guangxi Key Laboratory of Automatic Detecting Technology and Instrument,Guilin University of Electronic Technology,Guilin 541004,China

2Guilin Institute of Information Technology,Guilin 541004,China

Keywords: switchable,terahertz(THz)metamaterial,polarization conversion,vanadium dioxide(VO2)

1. Introduction

Terahertz (THz)[1]technology has become a very important scientific and technological frontier in the world.Polarization[2]is the basic property of the THz wave,because the THz waves are usually linearly polarized[3]along a specific direction. However, in the fields of THz communication,[4]imaging,[5,6]sensing,[7]and detection,[8,9]it is necessary to dynamically control the polarization state of the THz wave.The polarization converter can control the polarization state of electromagnetic (EM) waves by designing anisotropic,[10]and the traditional polarization converter is composed of polarizer[11]and wave plate,[12]which are not conducive to the integration[13]of equipment. Metamaterial[14]is an artificial material consisting of periodic sub-wavelength structures with unique EM properties,such as negative dielectric constant[15]and negative refractive index.[16]In recent years, many THz polarization converters based on metamaterial have been reported. For example,Akoet al.[17]demonstrated a multilayer transmission polarization converter, and its conversion efficiency is improved by using an Fabry–Perot(FP)resonator[18]composed of multilayer metal grating and H-shape resonator.Liuet al.[19]designed a single-layer THz metamaterial with double F-shape voids to realize cross-elliptical polarization conversion. It is noted that, the unit structures of these polarization converters are fixed after been fabricated, and the polarization state cannot be dynamically controlled.[20]

Vanadium dioxide (VO2) is a phase transition material,[21]and its conductivity can be greatly improved under external electrical,[22,23]thermal,[24,25]and optical excitation.[26,27]Therefore, it can be used for dynamic regulation of amplitude,[28]filter,[29]and polarization.[30]In recent years, many polarization converters based on the VO2metamaterial have been demonstrated. Yanet al.[31]designed a metamaterial with broadband absorption and linear-circular polarization conversion. Using the square ring with VO2,broadband absorption can be realized at high temperature and linear-circular polarization conversion can be realized at low temperature and a broadband. Liet al.[32]proposed a metamaterial with dual functions of polarization conversion and filtering. Using VO2strip, linear polarization conversion can be realized at low temperature. And thus, a broadband band stop filter can be realized at high temperature. However, the pattern of VO2in the above works is high cost and requires a variety of processes, such as magnetron sputtering, lithography,etching,coating,etc.

In this paper,a switchable polarization converter based on VO2metamaterial is designed. It consists of metal split-ringresonator(SRR),the first polyimide(PI)spacer,VO2film,the second PI spacer and metal grating. At room temperature,the VO2is in insulating state,and the device realizes cross-linear polarization conversion. When the temperature is higher than 68°C, the VO2is in metallic state, and the device realizes linear-to-circular polarization conversion. The proposed polarization converter can dynamically control the polarization of THz waves by controlling the temperature.

2. Design and simulation method

As shown in Fig. 1, the designed polarization converter consists of five layers and the period inxandydirections is 100 μm. The THz wave normally incidents to the top surface of the device. The SRR on the top surface and the grating on the bottom surface are composed of aluminium,and the middle layer is VO2film separated by two layers of polyimide(PI),In order to obtain the best effect,the geometric parameters of the device are optimized and listed in Table 1.

Table 1. Geometric parameters of the unit cell.

Fig.1. Schematic diagram of the proposed polarization converter(a)for VO2 in insulating state;(b)for VO2 in metallic state. (c)Geometric parameters of the unit cell. VO2 (D)and VO2 (M)represent that VO2 is in insulating state and metallic state respectively.

A commercialized full wave EM calculation soft CST microwave studio 2021 based on finite integration technology is used to simulate and optimize the performance of the device.The linearlyy-polarized THz waves normally incident. The boundary conditions are set in thexandydirections,and open boundaries are set in thezdirection. In simulation,the relative dielectric constant of PI is 3.50,[33]and the conductivity of aluminium is 4.56×107S/m.[34]The Drude model[35]is used to describe the relevant dielectric constant of the VO2in different state,

where,σ0=3×105S/m,ωp(σ0)=1.4×1015rad/s. In simulation,theσof the VO2at room temperature is 3×102S/m,and that for the temperature higher than 68°C is 3×105S/m,respectively.

3. Results and discussion

3.1. Switching between polarization conversion modes

At room temperature, the chemical form of the VO2is monoclinic crystal structure,and its physical property is insulating. Therefore, the THz waves can pass through the VO2film. With the increase of temperature, new chemical bonds are formed between crystals, the chemical form of the VO2changes to tetragonal diamond phase,and its conductivity increases. When the temperature reaches nearly 68°C(340 K),the conductivity of the VO2will suddenly increase[36–38]by nearly 4–5 orders of magnitude in the range of 10°C,and its physical property will become metallic. At this time,the THz waves will be reflected by the VO2film. When the temperature drops from high temperature to room temperature again,the conductivity of the VO2can completely returns to the insulating state.[4]

Here, we studied the influence of the VO2conductivity,and calculated the transmission and reflection of the device under different state of the VO2, and the results are shown in Fig. 2. It is evident from Fig. 2(a) that the transmission decreases with the increase of the conductivity of the VO2,while the reflection increases with it in Fig.2(b).

Fig.2. (a)Transmission;(b)reflection of the device at different conductivities of the VO2.

3.1.1. Transmission polarization conversion

When the VO2is at room temperature, the transmission components oftxxandtxyare presented in Fig.3(a).At the central frequency of 0.66 THz, the transmission oftxyis higher than 60%. The PCR can be calculated by the following formula:

whereS0is the total intensity of the THz waves,S3is the circular polarization of the THz waves.Atxyrepresents the amplitude of the THz waves polarized inxdirection after the THz waves polarized inydirection are transmitted through the sample, andAtyyrepresents the amplitude of the THz waves polarized inydirection after the THz waves polarized inydirection are transmitted through the sample.δis the phase difference between thex-polarized outgoing waves and they-polarized outgoing waves when the incident waves areypolarized waves,δ=φxy-φyy.

Fig.3. (a)Transmission;(b)PCR of the device for VO2 in insulating state.

In addition, the polarization state of the THz waves can be judged byχ,as shown in Table 2.

Table 2. Relationship between χ and polarization state.

The polarization ellipse model in electric field mode is shown in Fig. 4(a). In the electric field ellipse,S0represents the component of THz waves passing through or reflected by the device that are still polarized in theydirection,andS3represents the component of THz waves passing through or reflected by the device that are polarized in thexdirection. The relationship between the valuesS0andS3determines the state of the polarization ellipse. In the triangle composed of semimajor axis,semiminor axis and their end connecting lines,the corresponding angle ofS3isχ. Figure 4(b)shows that theχof the outgoing waves is close to 0 in a broadband of 0.3 THz–1.0 THz. It means that when the VO2is in insulating state,the polarization state of outgoing THz waves remains linear after transmitting through the device.

Fig.4. (a)Polarization ellipse model in electric field mode. (b)The χ of the THz waves transmitted by the device for VO2 in insulating state.

3.1.2. Reflective polarization conversion

When the VO2is in metallic state, the reflective spectra are shown in Figs.5(a) and 5(b). They show that in a broadband of 0.44 THz–0.94 THz,the reflection is higher than 80%,and the PCR is higher than 88%, which can be calculated by formula (7). Moreover, the PCR can reach 100% in a broadband of 0.48 THz–0.55 THz and 0.86 THz–0.9 THz.

Fig.5. (a)Reflection;(b)PCR of the device for VO2 in metallic state.

Fig.6. (a)The δ,(b)schematic diagram of polarization conversion,(c)χ,and(d)polarization state of the THz waves reflected by the device for VO2 in metallic state.

Figure 6(a) shows that near 0.41 THz,rxy ≈ryy, andδ=90°,indicating that the conversion of linear polarization waves to right-handed circular polarization waves is realized.Near 1.0 THz–1.1 THz,rxy ≈ryy, andδ=-90°, indicating that the conversion of linear polarization waves to left-handed circular polarization waves is realized. It can be known that the polarization state of the outgoing THz waves is jointly determined byrxy,ryy,andδ,as shown in Fig.6(b).

For further verification, the polarization state of outing THz waves can be determined by Table 2, as shown in Figs. 6(c) and 6(d). The polarization state atf1andf4are circular polarization state,and atf2andf3are elliptical polarization state.

3.2. Parameter optimization

In order to study the influence of differentαon the performance of the device,the transmission and reflection at four differentαare calculated, whereαexpand along the 45°direction, and the results are shown in Figs. 7(a) and 7(b), respectively. With the increase ofα,the transmission spectrum shows blueshift and the transmittance decreases slightly. And there is also a blueshift in the reflection curve. Therefore,the effect is the best forα=90°.

Fig.7. (a)Transmission and(b)reflection at different α.

Moreover, the different values of the thickness of each layer (t1,t2,t3,t4, andt5) of the device will cause the amplitude change or translation of the THz waves curve. Here,the transmission and reflection for the device with different thickness of PI are calculated, and the results are shown in Figs.8(a)and 8(b). With the increase of thickness of PI at the down layer,the transmission decreases gradually,and it is the best att4=16 μm. With the increase of PI thickness at the upper layer,the reflection curve gradually changes from multiple resonant peaks to broadband,and it is the best att2=59 μm.

Fig.8. (a)Transmission and(b)reflection for the device at different thicknesses of PI.

3.3. Physical mechanism

3.3.1. VO222 is in insulating state

In order to understand the physical mechanism of the device,we calculated the distribution of surface current at different state of the VO2. When the VO2is in insulating state,the surface current distribution at the resonant frequency is calculated and shown in Fig.9(a). When the THz waves vertically incident the SRR at the upper layer of the device,the direction of the electric field is perpendicular to the propagation direction of the EM waves. At the resonance peak,the electric field excites the internal charge of the SRR ring to move along the ring and generates a ring current. The SRR can be equivalent to a magnetic dipole perpendicular to the surface of the metamaterial. And the existence of the opening destroys the original flow circuit of the charge,and the induced current will cause many heterogeneous charges to accumulate at the opening of the SRR ring and generate an electric field. The opening of the SRR is equivalent to an electric dipole,as shown in Fig. 9(b). TheLCresonance forms on the SRR and couples with the incidenty-polarized THz wave. This coupling effect changes the original polarization direction of the THz wave,and the polarization conversion process begins. The resonant frequency is given by

where,Lis the equivalent inductance,Cis the equivalent capacitance of the SRR,respectively.

As shown in Fig. 9(c), the cross-linear polarization conversion can be explained by the FP resonance of the multilayer structure. When the lineary-polarized waves incident to the SRR surface, the polarization components inxandydirections will be generated by theLCresonance. Due to the action of the metal grating, only the polarization component inxdirection can pass through the metal grating, while the polarization component inydirection is reflected to the SRR and generate the polarization components inxandydirections again. Therefore,the device can realize cross-linear polarization conversion in transmission mode.

Fig.9. (a)Surface current distribution;(b)LC resonance principle for VO2 in insulating state. (c)Principle of cross-linear polarization conversion.

3.3.2. VO222 in metallic state

When the VO2is in metallic state, the surface currents distribution at two resonant frequencies of 0.54 THz and 0.88 THz are calculated and presented in Figs.10(a)and 10(b),respectively. Figure 10(a) shows that, the surface currents mainly distribute on the upper left and lower right of the SRR at 0.54 THz. At this time,the electric field is coupled with the SRR to form electric dipole resonance inxandydirections.

When the lineary-polarized waves incident to the SRR surface,as shown in Fig.10(c),the polarization components inxandydirections are excited on the SRR and reflected by the VO2film. The polarization component inxdirection can be first reflected on the front surface of the device,while the polarization component inydirection can pass through the front surface and get to the VO2film. And then,it can be reflected many times between the front surface and the VO2film with rotation of polarization. When the rotation angle of polarization reaches to 90 degrees,it can pass through the front surface again.

Figure 10(b) shows that the surface currents mainly distribute on the right side of the SRR at 0.88 THz. And thus,the electric field of the THz wave couples with the SRR,and then the electric dipole resonance forms in thexdirection.

For the linearlyy-polarized wave incident to the surface of SRR,as shown in Fig.10(d),it can only generate the polarization component inxdirection and is reflected by the VO2film. Therefore, the designed polarization converter can realize reflective broadband polarization conversion.

Fig.10. Current distribution at(a)0.54 THz and(b)0.88 THz;broadband polarization conversion principle at(c)0.54 THz and(d)0.88 THz for VO2 in metallic state.

4. Conclusion

In conclusion, a switchable polarization converter based on the VO2metamaterial is proposed. When the VO2is in insulating state, the incident THz wave producesLCresonance on the SRR,and then the transmitted cross-linear polarization conversion is realized by using the function of the FP cavity.When the VO2is in metallic state,the incident THz wave induces the electric field coupling and the FP cavity resonance between the SRR and the VO2films,realizing reflective broadband polarization conversion. And thus,the linear-to-circular polarization conversion in a broadband is realized. Therefore,under the thermal stimulus, the proposed polarization converter can switch freely between cross-linear polarization conversion and linear-to-circular polarization conversion.

Acknowledgements

Project supported in part by the National Natural Science Foundation of China (Grant Nos. 62065005, 61565004,11774288, and 62003107), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant Nos. 2018GXNSFAA050043, 2020GXNSFDA238019,2019JJB110033, and 2017GXNSFBA198029), the Innovation Project of Guangxi Graduate Education, China (Grant Nos. YCSW2021188, YCBZ2021071, and 2020YCXB04),the Foundation from Guangxi Key Laboratory of Automatic Detecting Technology and Instrument(Grant No.YQ21101);and the Research and Development Project in Hunan Province,China(Grant No.2020SK2111).