基于二氧化釩寬、窄帶可切換的雙功能超材料吸收器研究

封覃銀，裘國華 ，嚴(yán)德賢 ，李吉寧，李向軍

（1.中國計量大學(xué) 信息工程學(xué)院 浙江省電磁波信息技術(shù)與計量檢測重點(diǎn)實(shí)驗(yàn)室，杭州 310018；2.天津大學(xué) 精密儀器與光電子工程學(xué)院，天津 300072）

1 Introduction

Terahertz wave (THz wave) mainly refers to electromagnetic wave with frequency between 0.1 THz and 10 THz, which is located between microwave and infrared light wave[1].In recent years,with the rapid development of terahertz detection technology and time-domain spectroscopy technology, terahertz wave detection, modulation and other related technologies have attracted more and more attention[2].Metamaterials are a new type of artificially designed electromagnetic composites that have attracted great interest in many potential applications, such as terahertz absorbers[3-4], polarization converters[5], sensors[6].In recent years, many researchers have proposed a variety of the terahertzbased metamaterial absorber models, and studied their single frequency band[7], multi-frequency band[8-10]and wide frequency band[11-12]characteristics.As a functional device that can achieve high absorptivity of incident electromagnetic wave[13-14],metamaterial absorber has promising application prospects[18-19]in many fields such as infrared detection[15], modern communication, electromagnetic stealth[16], thermal radiation, and sensing[17].The early terahertz absorber has a single resonance mode and narrow absorption spectrum bandwidth.Most designed metamaterial absorption devices can only achieve a single function at the working frequency or cannot tune the absorption performance according to the application requirements.Various shortcomings limit its practical application.

With the emergence of functional materials(phase change materials) such as graphene[20-21], liquid crystals (LC)[22], and vanadium dioxide (VO2)[23],it is possible to change the properties of materials simply by applying excitations such as electricity[24-25], magnetism, light[26], and temperature[27].Combining these functional materials with metamaterial structures allows multiple functions to be implemented in a single metamaterial device, thus driving the rapid development of terahertz metamaterial absorbers.VO2, as an excellent phase change material, has optical and electrical properties that change significantly during the phase change, and the conductivity can change by 4-5 orders of magnitude[23], making it ideal for tunable multifunctional metamaterial device.Liu[23]et al.proposed a VO2-based ultra-wideband absorber that can achieve modulation of 5% to 80% absorption in the wideband range of 1.2 to 3.2 THz.Song[28]et al.proposed the design of a VO2-based terahertz wideband tunable absorber, by which the amplitude of the wide-band absorption band can be adjusted from 5% to 96% when the VO2conductivity changes from 10 S/m to 2000 S/m.Zhang[29]et al.proposed a terahertz bi-functional absorber with wide-band and narrow-band absorption characteristics based on a graphene/spacer-VO2/spacer-metal structure.The operating bandwidth and intensity of narrow-band absorption and wide-band absorption can be dynamically tuned by changing the Fermi level of graphene.Huang[30]et al.proposed a tunable wideband terahertz absorber, by which the absorption can be dynamically tuned from 4% to 100% by varying the conductivity of VO2, achieving nearperfect amplitude modulation.

Based on the phase change characteristics of VO2, a bi-functional metamaterial absorber with switchable wide-band and narrow-band absorption is proposed in this paper, and the wide-band and narrow-band absorption characteristics of this absorber can be tuned by changing the conductivity of VO2.When VO2is in the metallic state, the structure is a wide-band absorber consisting of the top layer formed by the metal split ring resonator and VO2disc, the upper polyimide (PI) dielectric layer,and the VO2film.When VO2is in an insulating state, the structure is mainly a narrow-band absorber consisting of the top layer formed by the metal split ring resonator and VO2disc, the upper PI dielectric layer, the VO2film, the lower PI dielectric layer, and the metal substrate.Due to the high symmetry of the designed cell structure, the absorber also has the characteristics of insensitivity in polarization and incidence angles over a wide-range,which greatly reduces the limitations of the absorber in the practical application process.The wide- and narrow-band switchable bi-functional absorber proposed in this paper can provide new research ideas for multifunctional tunable devices in terahertz and other frequency bands.

2 Structure and methodology

The cell structure of the terahertz metamaterial absorber[28-32]is shown in Figure 1 (Color online),which shows the three-dimensional structure, top view and side view of the periodic cell of the absorber, respectively.The cell structure from top to bottom is a top pattern consisting of a metal split ring resonator and VO2disc, an upper PI dielectric layer, a VO2thin film, a lower PI dielectric layer,and a metal substrate, and the device structure is symmetric about thexandyaxes.The resonant structure of the absorber is composed of a metal split ring resonator and a VO2disc placed in the center.The calculated optimal geometrical parameters are the period of the structural cellPx=Py=80 μm, the ring opening angleα=30°, the outer radius of the split ringR1=64 μm, the width of the ringW=2 μm, the radius of the VO2discR2=47 μm, the relative permittivity of the upper PI dielectric layerε=2.0, the loss angle tangent tanδ=0.02[33], and the thicknessZ3=18 μm, the thickness of the VO2filmZ=1.5 μm, and the thickness of the lower PI dielectricZ1=45 μm.And the metal substrate of the ground plane is a gold material with a thickness ofZ=1 μm and a conductivity ofσ(gold)=4.09×107S/m[33].

Fig.1 The absorber (a) 3D schematic; (b) top view; (c) side view圖1 (a)吸收器三維示意圖;(b)頂部視圖;(c)側(cè)視圖

In this paper, the absorption characteristics of the designed switchable metamaterial absorber are numerically simulated by CST software.Terahertz waves are incident on the absorber along -zdirection perpendicular to the absorber surface, and the electric field of the incident wave is polarized alongxdirection and the magnetic field is polarized alongydirection.The periodic boundary conditions are used inxandydirections, and the open boundary condition is used in thezdirection.The Drude mod-is used to describe the optical properties of VO2in the terahertz frequency range, where ε∞=12 is the high-frequency relative permittivity,ωp(σ) is the plasma frequency with respect to the conductivity,σis the conductivity of VO2, γ = 5.75 × 1013rad/s is the collision frequency,and bothωp(σ) andσare proportional to the free carrier density.The relationship between the plasma frequency and conductivity of VO2can be approximated as, whereσ= 3×105S/m,rad/s.By applying the excitation of external electric field, optical field, or temperature field, the phase transition process of VO2can occur in a short time.The variation range of conductivity before and after the phase change of VO2is about 200 S/m～2×105S/m.By changing the conductivity of VO2, the wide-band and narrow-band absorption functions of the absorber can be switched.When VO2is in the metallic (or insulating)state, its conductivity is 2×105S/m (or 200 S/m)[30],and these two conditions are used to simulate the phase change process of VO2in the paper.In the practice, the phase change process of VO2can be achieved by changing the temperature.Under thermally excited conditions, the phase transition temperature of VO2is approximately 68 ℃.At room temperature, VO2is in the insulating state;when the temperature is heated from low to high temperature (over 68 ℃), the molecular structure of VO2changes and VO2converts from the insulating state to the metallic state; the process is reversible and VO2converts from the metallic state to the insulating state when the temperature decreases from the phase change temperature (68 ℃).

3 Results and discussion

The designed metamaterial bi-functional absorber is simulated by using the commercial electromagnetic analysis software CST Microwave Studio.The reflection coefficient (S11) and transmission coefficient (S21) of this absorber are obtained through simulation, then the electromagnetic absorption rate (A) of this structure can be calculated from the following equation:

whereR=|S11|2andT=|S21|2are the reflectance and transmittance obtained from the frequency-dependentS-parameters, and the reflectionR⊥of the crosspolarized wave is also discussed here.In the studied terahertz frequency range, the transmission (T) of the overall metamaterial structure is always 0 due to the presence of metal plates or metallic VO2films at the bottom in both states, and the thickness of the metal plates or VO2films is much larger than the skin depth of the electromagnetic waves, thus suppressing the transmission.The reflection and absorption spectra of VO2with different conductivities are shown in Fig.2(a) and Fig.2(b).When the conductivity changes from 200 S/m to 2×105S/m,the corresponding absorption changes from narrowband absorption to wide-band absorption, achieving a perfect switch between wide and narrow-band absorption functions.

Fig.2 (a) Reflection spectrum; (b) absorption spectrum; (c) real part of and (d) imaginary part of the relative impedance with different conductivities of VO2圖2 二氧化釩不同電導(dǎo)率時的(a)反射光譜;(b)吸收光譜;(c)相對阻抗的實(shí)部和(d)虛部

When terahertz wave is incident perpendicular to the device surface, we introduce impedance matching theory to elucidate the intrinsic mechanism for the absorber's changes.Both the real and imaginary parts of the relative impedance of the absorber can be derived from theS-parameter inversion method.The absorption rate and relative impedance can be expressed as[34-35]:

where Z0and Z are the effective impedances of the free space and the absorber, respectively.AndZr=Z/Z0is the relative impedance between the absorber and the free space.The absorption of the wide-band absorber reaches the maximum when the impedance of the absorber matches the impedance of the free space, i.e., the relative impedance of the structureZr=1.The variation of the real and imaginary parts of the relative impedance for different VO2conductivities is shown in Fig.2 (c) and (d).Obviously, with the continuous increase of the conductivity, the real part gradually approaches to 1 while the imaginary part gradually approaches to 0 in the range of 1.34～2.25 THz, which means that the effective impedance of the absorber and the free space gradually match each other.When VO2is in the metallic state, i.e.,σ(VO2) = 2×105S/m, the designed structure obtains the highest absorption rate and the widest absorption bandwidth at the same time.

3.1 Metamaterials can be used as wide-band absorbers when VO2 is in the metallic state

When VO2is in metallic state, the designed switchable metamaterial can be used as a wide-band absorber, which consists of a metal split ring resonator on top embedded in a VO2disc, an upper PI medium, and a VO2film.When the VO2is in the metallic state, the bottom metallic phase VO2acts as the reflection layer, which can prevent the occurrence of transmission.The structural parameters are shown in Fig.1, and the absorber model is simulated by the finite element method, applying the cell boundary conditions to thexandyboundary conditions and the open boundary inzdirection, with the terahertz wave incident along -zdirection.The reflection and absorption spectra, as well as the real and imaginary parts of the relative impedance of the wide-band absorber are given in Figure 3 (Color online) when the conductivity of VO2is 2×105S/m(metallic state), whereA(ω) denotes the absorption spectrum,R(ω) denotes the reflection spectrum, and Re(Zr) and Im(Zr) represent the real and imaginary parts of the relative impedance of the wide-band absorber, respectively.Two different absorption peaks can be observed at 1.53 THz and 2.12 THz, and the designed structure can absorb more than 90% of the energy in the frequency range from 1.34 to 2.25 THz with a bandwidth ratio (fmax-fmin)/[(fmax-fmin)/2][37]of 50%.And the absorption in the frequency range from 1.10 to 3.18 THz is greater than 50%, and the corresponding bandwidth ratio is 97%.As shown in Fig.1(a), the introduction of the top VO2disc changes the effective impedance of the structure,and the incident electromagnetic waves are better matched with the free space, which also enhances the overall absorption performance of the structure.Therefore, in the wide frequency range of 1.53～2.12 THz, the designed wide-band absorber achieves impedance matching with the free space and obtains a better absorption and wider bandwidth.

Fig.3 Reflection and absorption spectra, real part and imaginary part of relative impedance when the conductivity of vanadium dioxide is 2×105 S/m圖3 二氧化釩電導(dǎo)率為2×105 S/m時反射和吸收光譜、相對阻抗的實(shí)部、虛部

In general, the geometric parameters of the structure have an influence on its resonant frequency and absorption rate.Also, errors can be introduced in the structural dimensional parameters during the device processing.Therefore, the structural parameters of the device were investigated.The variation of the terahertz absorption spectrum of the device with the geometric parameters (α,Z3,R2) was studied under the condition that the other parameters were kept constant as initial settings, and the results are shown in the following figures.From Fig.4(a), it can be seen that the absorption bandwidth increases with the increase of the opening angleα.The center frequency of 1.84 THz shows a slight blue-shift trend with the increase ofα.The resonance peak at the frequency of 1.53 THz remains basically unchanged, and the resonance peak at the frequency of 2.12 THz shows a blue-shift trend, therefore, the absorption bandwidth increases and the absorption rate decreases with the increase of the opening angleα.In Fig.4(b), the intensity of the absorption peak first decreases slightly with the increase ofZ3and reaches the optimum absorption at 18μm, and then the absorption decreases with the increase ofZ3.In Fig.4(c), the absorption bandwidth changes less with the increase of the radiusR2of VO2disc, and the absorption rate decreases slightly, and the best absorption rate is obtained at 47 μm, and the absorption curve shows a blue-shift trend when the radius increases from 44 μm to 47 μm.In summary, it can be seen that the effect of the change in the opening angle on the absorption bandwidth is more significant than that of the dielectric layer thickness and the radius of the VO2disc.

Fig.4 The influence of the structural parameters of the absorber cell: (a) the opening angle α; (b) the thickness of the upper PI medium Z3 and (c) the radius of the VO2 disk R2, on the terahertz absorptivity at the conductivity of 2×105 S/m圖4 當(dāng)電導(dǎo)率為2×105 S/m時，吸收器單元結(jié)構(gòu)參數(shù)對太赫茲吸收率的影響。(a)開口角度α；(b)上層PI介質(zhì)厚度z3；(c) VO2圓盤半徑R2

To further understand the operating mechanism of the wide-band absorber in detail, we have studied the electric field distribution at the two resonant frequencies of the wide-band absorber,1.53 THz and 2.12 THz, as shown in Figure 5.Figure 5 gives the electric field distribution of the absorber at 1.53 THz and 2.12 THz when the incident terahertz wave is transverse electric (TE) polarized, from which it can be seen that the electric fields at the two frequency points are mainly distributed at the two ends of the opening of the metal split ring resonator, the VO2disc near the opening of the metal ring and alongy-direction; and the electric field intensity at the frequency of 2.21 THz is more concentrated compared with the induced electric field intensity at the frequency of 1.53 THz.In addition, the electric field intensity is gradually weakened along the inner edge of the VO2disc parallel tox-axis and near the opening of the metal ring, which may be caused by the weak dipole resonance of the VO2disc in parallel tox-axis near the opening of the metal ring.Due to the structural symmetry, the results of the electric field distribution of the wideband absorber at the above two frequency points exhibit an overall 90° rotation when the incident wave is TM-polarized.

Fig.5 Electric field intensity distribution at the two absorption peak frequencies of 1.53 THz and 2.12 THz under TE mode圖5 1.53 THz、2.12 THz在TE極化下兩個吸收峰頻率處的電場強(qiáng)度分布

For the needs of absorbers in practical applications, polarization angle insensitivity and incidence angle insensitivity are two very important characteristics.Figure 6(a) (Color online) shows the variation of the absorption performance of the metamaterial absorber with the incident terahertz wave frequency and the incident angle in the TE mode.According to the calculated results, the designed absorber still exhibits a stable absorption rate and a wide operating bandwidth in the large incident angle range of 0°～60°, leading to a high incident angle tolerance.When the incidence angle is larger than 60°,the main absorption peak becomes narrower as the incidence angle increases.Therefore, the absorber can still provide good absorption characteristics even at larger incidence angles.In addition, for TM polarization, the absorption performance remains stable up to 8° as shown in Fig.6(b) (Color online).When the incidence angle is larger than 8°, the absorption bandwidth becomes narrower and some higher order modes appear.A similar dependence of the absorption spectrum on the incidence angle was observed in the previously reported VO2-based absorber[36].Therefore, the absorption performance of TE polarization is superior to that of TM polarization.The effect of the polarization characteristics of the incident terahertz wave on the absorption performance was also investigated.Figure 6(c) (Color online) shows the absorption rate vs.frequency as the polarization angle varies from 0° to 90° when a terahertz wave is incident vertically on the absorber surface.It can be seen from Fig.6(c) that the absorption curves of this wide-band absorber are highly overlapping, i.e., the absorption rate of the absorber is completely independent of the polarization under normal incidence conditions, which is highly related to the symmetry of the absorber cell structure inxandydirections, and the large incidence angle and polarization insensitivity characteristics show high potential for applications in energy harvesting and optical sensing.

Fig.6 (a) The absorption of the wide-band absorber with TE polarization at different incident angles; (b) the absorption of the wide-band absorber with TM polarization at different incident angles; (c) the absorption spectrum of the wide-band absorber with different polarization angles; at the conductivity of 2×105 S/m圖6 當(dāng)電導(dǎo)率為2×105 S/m時(a)不同入射角度時，TE極化的寬帶吸收器的吸收率；(b)不同入射角度時，TM極化的寬帶吸收器的吸收率；(c)不同極化角時寬帶吸收器的吸收光譜圖

3.2 Metamaterials can be used as narrow-band absorbers when VO2 is in the insulated state

When VO2is in the insulating state, the structure of a multi-band absorber consists of a metal split ring resonator on top embedded in a VO2disc,an upper PI dielectric, a VO2film, a lower PI dielectric, and a metal substrate.The simulation study is performed by using the numerical simulation method of electromagnetic field, and the three-peak absorption spectrum of the multiband absorber can be achieved.Figure 7 shows the reflection and absorption spectra as well as the real and imaginary parts of the relative impedance of the narrow-band absorber at a VO2conductivity of 200 S/m.Three absorption peaks exist in the frequency range from 2.4 THz to 4 THz with the resonance frequencies of 2.54 THz, 2.93 THz, and 3.34 THz, the corresponding absorption of 96%, 99.9%, and 99.3%, and the corresponding Full Width at Half Maximum(FWHM)[37]of 93.6 GHz, 206.7 GHz, and 39 GHz,respectively, achieving overall perfect multiband absorption.It can also be seen from Fig.7 that the real part of the impedance gradually approaches to 1 and the imaginary part gradually approaches to 0 near the multiband absorption peak.The designed multiband narrow-band absorbers achieve the impedance matching between the narrow-band absorber and the free space near the resonant frequencies of 2.54 THz, 2.93 THz, and 3.34 THz.

Under the condition that other parameters remain unchanged as initial settings, the effect of the geometric parameters (α,Z1,W) on the absorption rate was studied, and the calculated results are shown in Figure 8.In Fig.8(a), the absorption intensity increases significantly with the increase of the opening angle (α), which has a significant effect on the absorption rate at the resonance frequency of 2.54 THz; the absorption rate decreases gradually with the increase of the opening angle at the resonance frequency of 2.93 THz, while the absorption intensity remains unchanged at the resonance frequency of 3.34 THz.In Fig.8(b), the thickness of the lower PI medium (Z1) increases from 44 μm to 48 μm in steps of 1 μm, which has a significant effect on the absorption peaks at 2.93 THz and 3.34 THz, and the absorption rate decreases.The strongest absorption intensity is achieved whenZ1is 45 μm, after which the overall absorption intensity decreases slightly with the increase ofZ1.In Fig.8(c), the intensity of the absorption peak first increases with the width of the metal split-ring (W),and the absorption peak in the middle frequence band is more affected, and the strongest absorption peak is obtained atW=2 μm, after which the overall absorption intensity decreases with the increase ofW.In summary, it can be seen that the effect of the opening angle is more significant than that of the dielectric layer thickness and the width of the metal split-ring on the absorption bandwith.

Fig.7 Reflection and absorption spectra, real part and imaginary part of relative impedance when the conductivity of vanadium dioxide is 200 S/m圖7 二氧化釩電導(dǎo)率為200 S/m時反射和吸收光譜、相對阻抗的實(shí)部、虛部

Fig.8 The influence of the structural parameters of the absorber cell: (a) the opening angle; (b) the thickness of the lower PI medium Z1 and (c) the width of the metal split ring resonator W, on the terahertz absorption at the conductivity of 200 S/m.圖8 當(dāng)σ為200 S/m時，吸收器單元結(jié)構(gòu)參數(shù)對太赫茲吸收率的影響；(a)開口角度(b)下層PI介質(zhì)厚度Z1；(c)金屬開口諧振環(huán)的寬度W而變化

In addition, the electric field intensity distribution at the three absorption peak frequencies of 2.54,2.93 and 3.34 THz under TE mode is shown in Fig.(9).At 2.54 THz, the electric field distribution is highly concentrated along the two openingends of the metal split ring resonator; at 2.93 THz,some energy is uniformly distributed in the center region of the absorber cell; at 3.34 THz, the electric field intensity is strong on both sides of the opening of the metal split ring resonator and within the center region of the absorber cell structure.Due to the symmetry of the structure, the results of the electric field distribution of the narrow-band absorber at the above three frequency points exhibit an overall 90° rotation when the incident wave is TMpolarized.

Fig.9 Electric field intensity distributions at the three absorption peak frequencies of 2.54 THz, 2.93 THz and 3.34 THz under TE mode圖9 2.54 THz、2.93 THz和3.34 THzTE極化時三個吸收峰頻率的電場強(qiáng)度分布

Next, the absorption characteristics of this multiband metamaterial absorber at different polarization angles were also investigated.Fig.10 depicts the variation of the absorption and frequency when the polarization angle is increased from 0° to 90° in steps of 5°.The results show that the absorption performance of the proposed multiband metamaterial absorber in TE mode does not change with the variation of the incident terahertz wave polarization angle when the terahertz wave is incident vertically on the absorber surface, and its absorption curves are highly coincident.The insensitivity to the polarization angle is related to the symmetry of the absorber cell structure inxandydirections.The intrinsic reason for the symmetry of the designed structure ensures the polarization insensitivity at normal incidence, which is very helpful in many applications.

The structures described in this paper can be processed by molecular beam epitaxy.In 2016, Bianet al.[38]used molecular beam epitaxy to grow VO2films on single-crystal sapphire substrates that can be precisely controlled in thickness.In 2017,Sun Hongjunet al.[39]used molecular beam epitaxy to grow a high-quality stoichiometric VO2films on single-crystal sapphire substrates, and achieved precise control of the film thickness through this technique.For this structure, molecular beam epitaxy can be used to deposit thin VO2films on PI substrates, and then introduce the disc structure to the top of the VO2film.Then, metal microstructures are prepared on PI by the conventional lithography and metallization processes to form metallic split ring resonators.The design method proposed in this study provides a new way to study multifunctional components based on continuous VO2films with completely different functions integrated into one structure.

Fig.10 Absorption spectra of narrow-band absorbers with different polarization angles at the conductivity of 200 S/m圖10 當(dāng)電導(dǎo)率為200 S/m，不同極化角時窄帶吸收器的吸收光譜圖

The terahertz wide-band absorber designed in this paper can be mainly applied to stealth and functional measurements.By absorbing terahertz waves and reducing the energy returned to the detector thus achieving stealth, which can be applied to radar detection, modern warfare weapons and other occasions.The wide-band absorber can be also applied to the field of terahertz wave energy collection and measurement, and the absorber can convert the absorbed energy into electrical energy thus realizing energy measurement.

4 Conclusion

In this paper, a switchable bi-functional metamaterial absorber with wide and narrow bands characteristics is designed, which consists of a top layer pattern composed of a metal split ring resonator and a VO2disc, an upper PI dielectric layer, a VO2thin film, a lower PI dielectric layer and a bottom metal substrate, and can be excited by external electromagnetic fields, optical fields and temperature fields to cause the VO2to undergo an insulating state-metallic state reversible phase transition process, so that the switching between different functions can be realized.The switchable structure is numerically simulated in the frequency range of 0～4 THz by the finite element method.The results show that the structure can achieve the function of a high-performance terahertz wideband absorber with the absorption of 98% in the wide-band frequency range of 1.55 THz to 2.21 THz when VO2is in the metallic state.When VO2is converted from the metallic state to the insulating state, this structure can realize the multi-band narrow-band absorber.The designed metamaterial absorber can achieve narrow-band absorption above 95% at the resonant frequencies of 2.54 THz,2.93 THz, and 3.34 THz.In addition, the effects of geometric parameters on the absorption performance are discussed.The absorber device also shows good absorption performance at large incidence angles due to the polarization insensitivity caused by the symmetric structure.The proposed metamaterial absorber with simple structure, switchable function and perfect absorption can be applied to terahertz optical switches, electromagnetic stealth,modulation, thermal emitters and electromagnetic energy harvesting.

——中文對照版——

1 引 言

太赫茲波（THz波），主要指頻率在0.1 THz到10 THz之間的電磁波，位于微波與紅外光波之間[1]。近年來，隨著太赫茲探測技術(shù)以及時域光譜技術(shù)的快速發(fā)展，太赫茲波的檢測和調(diào)制等相關(guān)技術(shù)受到了越來越多的關(guān)注[2]。超材料是一種新型人工設(shè)計的電磁復(fù)合材料，在太赫茲吸收器[3-4]、極化轉(zhuǎn)換器[5]、傳感器[6]等諸多潛在應(yīng)用引起了科學(xué)界的極大興趣。近年來，許多研究者已提出了多種基于太赫茲的超材料吸收器模型，并研究了它們的單頻帶[7]、多頻帶[8-10]和寬頻帶[11-12]特性。超材料吸收器作為一種對入射的電磁波能實(shí)現(xiàn)高吸收率的功能器件[13-14]，其在紅外探測[15]、現(xiàn)代通信、電磁隱身[16]、熱輻射、傳感[17]等諸多領(lǐng)域具有廣闊的應(yīng)用前景[18-19]。早期的太赫茲吸收器共振模式單一，吸收譜的帶寬較窄，大多數(shù)設(shè)計的超材料吸收器件在工作頻率下僅能實(shí)現(xiàn)單一的功能或是無法根據(jù)應(yīng)用需求進(jìn)行吸收性能的調(diào)諧，種種缺點(diǎn)都限制了它的實(shí)際應(yīng)用。

隨著石墨烯[20-21]、液晶(LC)[22]、二氧化釩（VO2）[23]等功能材料(相變材料)的出現(xiàn)，只需要施加電[24-25]、磁、光[26]以及溫度[27]等激勵就能夠改變材料的特性。將這些功能材料與超材料結(jié)構(gòu)相結(jié)合，就可以在單個超材料器件中實(shí)現(xiàn)多個功能，從而推動了太赫茲超材料吸收器的迅速發(fā)展。VO2作為一種優(yōu)良的相變材料，其光學(xué)和電特性在相變過程中可發(fā)生顯著變化，電導(dǎo)率可以發(fā)生4～5個數(shù)量級[23]的改變，因而非常適合用于可調(diào)性多功能超材料器件的設(shè)計。Liu[23]等人提出了一種基于VO2超寬帶吸收器，可以在1.2～3.2 THz的寬帶范圍內(nèi)實(shí)現(xiàn)5%～80%吸收率的調(diào)制。Song[28]等人提出了一種基于VO2的太赫茲寬帶可調(diào)吸收器的設(shè)計，當(dāng)VO2電導(dǎo)率從10 S/m變化至2 000 S/m時，寬頻吸收帶的幅值可從5%調(diào)整至96%。Zhang[29]等人提出了一種基于石墨烯間隔/VO2間隔/金屬結(jié)構(gòu)的具有寬帶和窄帶吸收特性的太赫茲雙功能吸收器，通過改變石墨烯的費(fèi)米能級，可以動態(tài)地調(diào)整窄帶吸收和寬帶吸收的工作帶寬和強(qiáng)度。Huang[30]等人提出了一種可調(diào)諧的寬帶太赫茲吸收器，通過改變VO2的電導(dǎo)率，可以實(shí)現(xiàn)吸收率從4%到100%的動態(tài)調(diào)諧，實(shí)現(xiàn)了近似完美的振幅調(diào)制。

本文基于VO2的相變特性，提出了一種寬、窄帶吸收可切換的雙功能超材料吸收器，可以通過改變VO2材料的電導(dǎo)率，實(shí)現(xiàn)該吸收器的寬、窄帶吸收特性調(diào)控。當(dāng)VO2處于金屬狀態(tài)時，該結(jié)構(gòu)為金屬開口諧振環(huán)和VO2圓盤形成的頂層、上層聚酰亞胺 (PI)介質(zhì)層、VO2膜組成的寬帶吸收器。當(dāng)VO2處于絕緣狀態(tài)時，結(jié)構(gòu)主要為金屬開口諧振環(huán)和VO2圓盤形成的頂層、上層PI介質(zhì)層、VO2膜、下層PI介質(zhì)層、金屬襯底組成的窄帶吸收器。由于所設(shè)計的單元結(jié)構(gòu)具有高度對稱性，該吸收器還具有極化不敏感和寬入射角度范圍內(nèi)不敏感的特性，大大降低了吸收器在實(shí)際應(yīng)用過程中的局限。本文的寬、窄帶可切換的雙功能吸收器可為太赫茲和其他頻段的多功能可調(diào)器件提供新的研究思路。

2 結(jié)構(gòu)與方法

太赫茲波（THz波），超材料吸收器[28-32]的單元結(jié)構(gòu)如圖1（彩圖見期刊電子版）所示，圖1(a)～1(c)分別展示了吸收器的周期性單元三維立體結(jié)構(gòu)、俯視圖和側(cè)視圖。該單元結(jié)構(gòu)從上到下依次是金屬開口諧振環(huán)和VO2圓盤構(gòu)成的頂層圖案、上層PI介質(zhì)層、VO2薄膜、下層PI介質(zhì)層、金屬襯底，器件結(jié)構(gòu)關(guān)于x和y軸對稱。吸收器的諧振結(jié)構(gòu)是由金屬開口諧振環(huán)和中心放置一塊VO2圓盤組成。經(jīng)計算得到最優(yōu)的幾何參數(shù)，其中結(jié)構(gòu)單元的周期Px=Py=80 μm，圓環(huán)開口角度α=30°，開口圓環(huán)外半徑R1=64 μm，圓環(huán)寬度W=2 μm，VO2圓盤半徑R2=47 μm，上層PI介質(zhì)的相對介電常數(shù)為ε=2.0，損耗角正切值為tanδ=0.02[33]，厚度為Z3=18 μm。VO2薄膜的厚度Z=1.5 μm，下層PI介質(zhì)厚度Z1=45 μm，接地面的金屬襯底為金材料，其厚度為Z=1 μm，電導(dǎo)率為σ(gold)=4.09×107S/m[33]。

本文使用CST軟件對設(shè)計的可切換超材料吸收器的吸收特性進(jìn)行數(shù)值仿真研究。太赫茲波垂直表面沿-z方向入射到吸收器上，入射波的電場沿x方向極化，磁場沿y方向極化；x和y方向設(shè)置為單元周期邊界，z方向?yàn)殚_放邊界條件。采用Drude模型來描述太赫茲頻率范圍VO2的光學(xué)性質(zhì)，其中ε∞=12為高頻相對介電常數(shù)，ωp(σ)為與電導(dǎo)率有關(guān)的等離子體頻率，σ為VO2的電導(dǎo)率，γ=5.75×1013rad/s為碰撞頻率，且ωp(σ)和σ都與自由載流子密度成正比。VO2的等離子體頻率與電導(dǎo)率關(guān)系可以近似地表示為：, 其中σ=3×105S/m,=1.4×1015rad/s。通過施加外部電場、光場、溫度場的激勵可使VO2在較短時間內(nèi)發(fā)生相變過程。改變VO2的電導(dǎo)率可切換吸收器的寬帶和窄帶吸收功能。VO2相變前后電導(dǎo)率的變化范圍大約為200 S/m～2×105S/m，通過改變VO2的電導(dǎo)率可切換吸收器的寬帶和窄帶吸收功能。當(dāng)VO2處于金屬（或絕緣）狀態(tài)時，其電導(dǎo)率為2×105S/m（或200 S/m）[30]，文中利用這兩個條件來模擬VO2的相變過程。在應(yīng)用中，VO2的相變過程可以通過改變溫度來實(shí)現(xiàn)。在熱激勵條件下，VO2材料的相變溫度大概為68 ℃。當(dāng)溫度為室溫時，VO2處于絕緣態(tài)；當(dāng)溫度從低溫加熱到高溫時（超過68 ℃），VO2材料的分子結(jié)構(gòu)發(fā)生變化，VO2從絕緣態(tài)變?yōu)榻饘賾B(tài)；該過程是一可逆過程，當(dāng)溫度從相變溫度（68 ℃）以上降低到相變溫度以下時，VO2從金屬態(tài)轉(zhuǎn)換為絕緣態(tài)。

3 結(jié)果與討論

使用商用電磁分析軟件CST Microwave Studio對所設(shè)計的超材料雙功能吸收器進(jìn)行仿真，得到該吸收器的反射系數(shù)（S11）和透射系數(shù)（S21），則該結(jié)構(gòu)的電磁吸收率(A)可以由以下公式計算：

其中，R=|S11|2和T=|S21|2是從與頻率相關(guān)的S參數(shù)獲得的反射率和透射率，這里還需討論交叉極化波的反射R⊥。在所研究的太赫茲頻率范圍內(nèi)，由于兩種狀態(tài)下底部都有金屬板或者金屬態(tài)的VO2薄膜存在，且金屬板或VO2薄膜的厚度遠(yuǎn)遠(yuǎn)大于電磁波的趨膚深度，因而抑制了透射部分，超材料整體結(jié)構(gòu)的透射(T)始終為0。VO2電導(dǎo)率不同時的反射和吸收光譜如圖2(a)和圖2(b)所示。當(dāng)電導(dǎo)率從200 S/m變?yōu)?×105S/m時，相應(yīng)的吸收從窄帶吸收轉(zhuǎn)變成為寬帶吸收，實(shí)現(xiàn)了完美寬、窄帶吸收功能的切換。

當(dāng)太赫茲垂直于器件表面入射時，引入了阻抗匹配理論來闡明吸收器發(fā)生變化的內(nèi)在機(jī)理。吸收器的相對阻抗的實(shí)部虛部均可由S參數(shù)反演法導(dǎo)出。吸收率和相對阻抗可表示成[34-35]：

其中，Z0和Z分別是自由空間和吸收器的有效阻抗。而Zr=Z/Z0則是吸收器與自由空間之間的相對阻抗，當(dāng)吸收器的阻抗與自由空間的阻抗相匹配時，即結(jié)構(gòu)的相對阻抗Zr=1時，寬帶吸收器的吸收率達(dá)到最大值。如圖2(c)和2(d)顯示了不同VO2電導(dǎo)率時相對阻抗的實(shí)部和虛部的變化情況。顯然，隨著電導(dǎo)率不斷地增加，在1.34～2.25 THz范圍內(nèi)，實(shí)部逐漸接近于1的同時虛部逐漸接近于0，這意味著吸收器的有效阻抗和自由空間的有效阻抗之間逐漸匹配。當(dāng)VO2處于金屬態(tài)時，即σ(VO2)＝2×105S/m時，所設(shè)計結(jié)構(gòu)同時獲得了最高的吸收率和最寬的吸收帶寬。

3.1 金屬態(tài)時超材料可作為寬帶吸收器

當(dāng)VO2處于金屬態(tài)時，設(shè)計的可切換超表面可以用作寬帶吸收器，其由頂部金屬開口諧振環(huán)嵌入一塊VO2圓盤、上層PI介質(zhì)、VO2薄膜組成.當(dāng)VO2處于金屬態(tài)時，底部金屬相VO2作為反射層，可以阻止透射的發(fā)生。結(jié)構(gòu)參數(shù)如圖1所示，采用有限元方法對吸收器模型進(jìn)行模擬，將單元格邊界條件應(yīng)用于x和y邊界條件，并在z方向開放邊界，入射太赫茲沿著-z方向入射。圖3（彩圖見期刊電子版）給出了VO2電導(dǎo)率為2×105S/m(金屬態(tài))時寬帶吸收器的反射、吸收光譜以及相對阻抗的實(shí)部、虛部。其中A(ω)表示吸收光譜，R(ω)表示反射光譜，Re(Zr)和Im(Zr)分別代表了寬帶吸收器相對阻抗的實(shí)部和虛部。在1.53 THz和2.12 THz可以觀察到2個不同的吸收峰，在1.34～2.25 THz頻率范圍內(nèi)，所設(shè)計的結(jié)構(gòu)可吸收90%以上的能量，帶寬比(fmax-fmin)/[(fmax-fmin)/2][37]為50%，在1.10～3.18 THz頻率范圍內(nèi)的吸收率大于50%，相應(yīng)的帶寬比為97%。其中如圖1(a)所示，頂層VO2圓盤的引入改變了結(jié)構(gòu)的有效阻抗，入射的電磁波與自由空間更加匹配，這也增強(qiáng)了結(jié)構(gòu)整體的吸收性能。因此在1.53～2.12 THz的寬頻范圍內(nèi)，所設(shè)計的寬帶吸收器與自由空間實(shí)現(xiàn)了阻抗匹配，獲得了較優(yōu)的吸收和較寬的帶寬。

一般來說，結(jié)構(gòu)的幾何參數(shù)對其共振頻率和吸收率有一定的影響。同時，在器件加工過程中，也會在結(jié)構(gòu)尺寸參數(shù)上引入誤差。因此，本文對器件的結(jié)構(gòu)參數(shù)進(jìn)行了研究。在其他參數(shù)作為初始設(shè)置保持不變的情況下，研究了器件的太赫茲吸收譜隨幾何參數(shù)（α、Z3、R2）的變化規(guī)律，研究結(jié)果如圖4（彩圖見期刊電子版）所示。由圖4(a)可以看出，吸收帶寬隨著開口角度α的增加而增大，中心頻率1.84 THz隨著α的增大呈輕微藍(lán)移趨勢，頻率為1.53 THz處的諧振峰基本保持不變，頻率為2.12 THz處的諧振峰呈藍(lán)移趨勢，由此得知，隨開口角度α的增加，吸收帶寬增大，吸收率降低。在圖4(b)中，吸收峰強(qiáng)度首先隨著Z3的增加而略微減少，在18 μm達(dá)到最佳吸收率，而后吸收率隨著Z3的增加而減小。在圖4(c)中，隨著VO2圓盤半徑R2的增加吸收帶寬變化較小，吸收率略有下降，在47 μm處獲得最佳的吸收率，并且當(dāng)半徑從44 μm增加到47 μm時，吸收曲線呈藍(lán)移趨勢。綜上所述，與介質(zhì)層厚度和VO2圓盤半徑的影響相比，開口角度的變化對吸收帶寬的影響效果更為顯著。

為了進(jìn)一步詳細(xì)了解寬帶吸收器的工作機(jī)理，研究了該寬帶吸收器兩個共振頻率1.53 THz和2.12 THz處的電場分布，如圖5所示。圖5給出了入射太赫茲波為TE極化時吸收器在1.53 THz和2.12 THz處的電場分布。從圖中可以看出，兩個頻率點(diǎn)處的電場主要分布在金屬開口諧振環(huán)的開口兩端、VO2圓盤靠近金屬圓環(huán)開口處且沿著y軸方向；且相較于1.53 THz頻率處的感應(yīng)電場強(qiáng)度，2.21 THz頻率處的電場強(qiáng)度更為聚集；此外，電場強(qiáng)度沿著VO2圓盤在與x軸平行且靠近金屬圓環(huán)開口的內(nèi)邊緣逐漸減弱，這可能是由于VO2圓盤在與x軸平行靠近金屬圓環(huán)開口的弱偶極子共振引起的。由于結(jié)構(gòu)設(shè)計的對稱性，入射波為TM極化時寬帶吸收器在上述兩個頻率點(diǎn)處的電場分布整體展現(xiàn)出90°的旋轉(zhuǎn)。

針對吸收器在實(shí)際應(yīng)用中的需求，極化角度不敏感和入射角度不敏感性是非常重要的兩大特性。圖6(a)（彩圖見期刊電子版）給出了在橫電（TE）模式下，超材料吸收器吸收性能隨入射太赫茲波頻率以及入射角度的變化規(guī)律。根據(jù)計算結(jié)果，所設(shè)計的吸收器在0°～60°大入射角范圍內(nèi)仍展現(xiàn)出穩(wěn)定的吸收率和較寬的工作帶寬，具有較高的入射角容忍能力。當(dāng)入射角大于60°時，其主吸收峰隨著入射角的增大而變窄。因此，該吸收器即使在較大的入射角下，仍然能夠提供較好的吸收特性。此外，對于TM極化，如圖6(b)（彩圖見期刊電子版）所示，吸收性能保持在8°以內(nèi)的穩(wěn)定。當(dāng)入射角大于8°時，吸收帶寬變窄，出現(xiàn)了一些高階模態(tài)。在先前報道的基于VO2的吸收器[36]中也觀察到吸收光譜對入射角的類似依賴性。因此，TE極化的吸收性能優(yōu)于TM極化。同時還研究了入射太赫茲波的極化特性對吸收性能的影響。圖6(c)（彩圖見期刊電子版）給出了當(dāng)太赫茲波垂直入射到吸收器表面時，極化角從0°變化到90°時的吸收率和頻率的關(guān)系。從圖6(b)可以看出，該寬帶吸收器的吸收曲線是高度重合的，即在正常入射條件下，吸收器的吸收率與極化是完全無關(guān)的，這與吸收器單元結(jié)構(gòu)在x和y方向上的對稱性有著很大關(guān)系，大入射角度和極化不敏感特性在能量采集和光學(xué)傳感中展現(xiàn)出較高的應(yīng)用潛力。

3.2 絕緣態(tài)時超材料可作為窄帶吸收器

當(dāng)VO2為絕緣態(tài)時，該結(jié)構(gòu)由頂部金屬開口諧振環(huán)嵌入一塊VO2圓盤、上層PI介質(zhì)、VO2薄膜、下層PI介質(zhì)、金屬襯底組合構(gòu)成多頻帶吸收器。采用電磁場數(shù)值模擬方法進(jìn)行模擬研究，可得多頻帶吸收器的三峰吸收譜，圖7展示了VO2電導(dǎo)率為200 S/m時窄帶吸收器的反射、吸收光譜圖以及相對阻抗的實(shí)部、虛部?？梢?，在2.4 THz～4 THz頻率范圍內(nèi)存在3個吸收峰，其共振頻率分別為2.54 THz、2.93 THz和3.34 THz，對應(yīng)的吸收率分別為96%、99.9%和99.3%，對應(yīng)半高寬(FWHM)[37]分別為93.6 GHz、206.7 GHz和39 GHz, 整體實(shí)現(xiàn)了多頻帶的完美吸收。從圖6中還可看出，在多頻吸收峰附近，阻抗實(shí)部逐漸接近于1，虛部逐漸接近0。在2.54 THz、2.93 THz、3.34 THz共振頻率附近所設(shè)計的多頻窄帶吸收器都實(shí)現(xiàn)了窄帶吸收器與自由空間之間的阻抗匹配。

固定其他參數(shù)的初始設(shè)置不變，研究幾何參數(shù)（α、z1、W）對吸收率產(chǎn)生的影響，計算結(jié)果如圖8（彩圖見期刊電子版）所示。圖8(a)中，隨著開口角度(α)的增大吸收強(qiáng)度明顯增加，對共振頻率2.54 THz處的吸收率影響較為顯著；在共振頻率2.93 THz處，吸收率隨著開口角度的增大而逐漸減小, 而在3.34 THz共振頻率處吸收強(qiáng)度保持不變。在圖8(b)中，下層PI介質(zhì)厚度(z1)從44 μm以1 μm為步長變化增加至48 μm，對于2.93 THz和3.34 THz處的吸收峰變化影響較大，吸收率有所降低。z1在45 μm處達(dá)到最佳吸收曲線，之后隨z1的增加整體吸收強(qiáng)度略有減小。在圖8(c)中，隨著金屬開口環(huán)寬度(W)的增加，中間頻帶的吸收峰所受到的影響較大，在2 μm處獲得最佳的吸收曲線，之后隨著W的增加整體吸收強(qiáng)度反而減小。綜上可看出，與介質(zhì)層厚度和金屬開口環(huán)寬度的影響相比，開口角度的影響效果更為顯著。

此外，本文還研究了2.54 THz、2.93 THz和3.34 THz 3個吸收峰頻率處的電場強(qiáng)度分布，如圖（9）所示，給出了TE極化太赫茲波入射時3個吸收峰頻率處的電場分布。在2.54 THz處，電場分布沿著金屬開口諧振環(huán)的開口兩端高度集中；在2.93 THz處，有部分能量均勻分布在吸收單元中心區(qū)域；在3.34 THz處，金屬開口諧振環(huán)的開口兩側(cè)、吸收器單元結(jié)構(gòu)中心區(qū)域范圍內(nèi)的電場強(qiáng)度很強(qiáng)。由于結(jié)構(gòu)設(shè)計的對稱性，入射波為TM極化時，窄帶吸收器在上述3個頻率點(diǎn)處的電場分布的結(jié)果整體展現(xiàn)了90°的旋轉(zhuǎn)。

接下來，還研究了該多頻帶超材料吸收器在不同極化角度下的吸收特性。圖10描述了極化角從0°以5°的步長增加到90°時吸收率與頻率的變化規(guī)律。結(jié)果表明，TE模式下，當(dāng)太赫茲波垂直入射到吸收器表面，本文中所提出的多頻帶超材料吸收器的吸收性能不隨入射太赫茲波極化角度的變化而改變，其吸收曲線是高度重合的。極化角度的不敏感性與吸收器單元結(jié)構(gòu)在x和y方向上的對稱性有關(guān)。所設(shè)計結(jié)構(gòu)的對稱性這一內(nèi)在原因確保了在正常入射下的極化不敏感性，這在許多應(yīng)用中非常有幫助。

本文結(jié)構(gòu)可以采用分子束外延法進(jìn)行加工。2016年，Bian等人[38]利用分子束外延技術(shù)在單晶藍(lán)寶石基底上生長可以精確控制厚度的VO2薄膜。2017年，孫洪君等人[39]采用分子束外延技術(shù)在單晶藍(lán)寶石襯底上生長了高質(zhì)量化學(xué)計量比VO2薄膜，通過該技術(shù)實(shí)現(xiàn)了薄膜厚度的精確控制。就本結(jié)構(gòu)而言，可采用分子束外延在PI襯底上沉積薄VO2薄膜，再將圓盤結(jié)構(gòu)引入到VO2薄膜的頂部。然后，在傳統(tǒng)的光刻和金屬化工藝的基礎(chǔ)上，在PI上制備金微結(jié)構(gòu)，形成金屬CSRRS。本研究提出的設(shè)計方法為以連續(xù)VO2薄膜為基礎(chǔ)，將完全不同的功能集成到一個結(jié)構(gòu)中的多功能元器件的研究提供了新的途徑。

本文所設(shè)計的太赫茲寬帶吸收器主要可以應(yīng)用于隱身和功能測量等方面。通過吸收太赫茲波，降低返回探測器的能量從而實(shí)現(xiàn)隱身，可以應(yīng)用在雷達(dá)探測、現(xiàn)代戰(zhàn)爭武器等場合。同時，寬帶吸收器可以應(yīng)用于太赫茲波能量收集、測試計量領(lǐng)域，吸收器可以將吸收的能量轉(zhuǎn)換為電能量從而實(shí)現(xiàn)能量測量。

4 結(jié) 論

本文設(shè)計了一種具有寬、窄頻帶特性的可切換雙功能超材料吸收器，該吸收器由金屬開口諧振環(huán)和VO2圓盤構(gòu)成的頂層圖案、上層PI介質(zhì)層、VO2薄膜、下層PI介質(zhì)層和底部金屬襯底構(gòu)成，通過外部電磁場、光場以及溫度場等激勵，可以使VO2發(fā)生絕緣態(tài)-金屬態(tài)可逆相變過程，從而可以實(shí)現(xiàn)不同功能之間的轉(zhuǎn)換。采用有限元方法對該可切換結(jié)構(gòu)在0～4 THz頻段進(jìn)行數(shù)值模擬，結(jié)果表明：當(dāng)VO2處于金屬態(tài)時，此結(jié)構(gòu)可以實(shí)現(xiàn)高性能太赫茲寬帶吸收器功能，在1.55 THz～2.21 THz的頻率范圍內(nèi)可實(shí)現(xiàn)98%的寬帶吸收。當(dāng)VO2從金屬態(tài)轉(zhuǎn)換為絕緣態(tài)時，此結(jié)構(gòu)可以實(shí)現(xiàn)多頻帶窄帶吸收器功能，所設(shè)計的超材料吸收器的共振頻率為2.54 THz、2.93 THz、3.34 THz時，窄帶吸收率在95%以上。此外，還討論了幾何參數(shù)對吸收率性能的影響。該吸收器件由于對稱結(jié)構(gòu)產(chǎn)生了極化不敏感性能，在大入射角時也表現(xiàn)出良好的吸收性能。本文提出的超材料吸收器具有結(jié)構(gòu)簡單、可切換功能和完美吸收等特性，可應(yīng)用于太赫茲光電開關(guān)、電磁隱身、調(diào)制、熱發(fā)射器和電磁能量采集等場合。