FANG Xiao-min，JIANG Xiao-wei，WU Hua

（1.Faculty of Information Engineering, Quzhou College of Technology, Quzhou 324100, China；2.College of Physics and Electronic Information, Gannan Normal University, Ganzhou 341000, China）

Abstract: In order to reduce the manufacturing cost of the narrow-bandwidth Metamaterial Absorber (MA)and broaden its application field, a dual-wavelength dielectric narrow-bandwidth MA, composed of Au substrate, SiO2 dielectric layer and Si dielectric asymmetric grating, is designed based on the finite-difference time-domain method using dielectric materials.It is found by simulation that the proposed narrow-bandwidth MA has ultra-high absorption efficiency at λ1 = 1.20852 μm and λ2 = 1.23821 μm, and the FWHM is only 0.735 nm and 0.077 nm, respectively.The main principle that MA achieves the narrow-bandwidth absorption at λ1 is mainly due to the formation of Fabry-Pérot (FP) cavity resonance in the SiO2 layer, while the narrow-bandwidth absorption of MA at λ2 is mainly due to the guided mode resonance effect of the incident light in the asymmetric grating.The theoretical calculations show that the absorption characteristics can be affected more significantly by changing the structural parameters of the MA.

Key words: metamaterial absorber; dual-wavelength; narrow-bandwidth; Fabry-Pérot cavity resonance;guided mode resonance

1 Introduction

Perfect absorption of electromagnetic waves is required in many applications, such as solar cells,thermal emitters, radiation cooling, communication[1-4].However, the absorbers made of natural materials can lead to impedance mismatch due to the lack of magnetic response, and therefore they cannot completely suppress light reflection, thus reducing the light absorption capacity of the absorber[5].Therefore, metamaterial-based absorbers have been proposed, and because the Metamaterial Absorber (MA) has high absorption efficiency for electromagnetic wave, and has the advantages of compact size and settable operating wavelength, it is gradually gaining attention and becoming one of the research hotspots[6].

With further in-depth research, different types of MA have been gradually designed and fabricated,such as wide-bandwidth MA, narrow-bandwidth MA, terahertz MA, and tunable MA[7-9].The reason why narrow-bandwidth MAs have received attention is that narrow-bandwidth MAs are more efficient in detection and thermal emitters compared to wide-bandwidth MAs[10-11], and only narrow-bandwidth in optical modulation, optical detection, and tailoring of thermal radiation MA can meet the requirements[12-13].Different structures of narrowbandwidth MA have been proposed, such as narrowbandwidth MA based on Split Ring Resonator(SRR) arrays, metal/dielectric periodic gratings, and metal/dielectric slits (narrow slits).In 2014, Min Qiu et al.(KTH Royal Institute of Technology) proposed etching metal grating on a silver (Ag) metal substrate, and based on the surface plasmon excitonic resonance formed by Ag grating and air medium they successfully enabled MA with narrow-bandwidth absorption at wavelength 1400 nm, and its linewidth (Full Width Half Maximum, FWHM) can reach 0.4 nm[14]; in 2018, FENG A et al.(the Chinese University of Hong Kong) proposed a narrow-bandwidth MA consisting of asymmetric metal grating and metal substrate, and a SiO2transition layer was added between the grating and the substrate, and the narrow-bandwidth MA was found to achieve ultranarrow absorption in the optical communication band with a FWHM of 0.28 nm[15]; In 2019, KANG S et al.(Southeast University) proposed to etch a cross-shaped nanoarray composed of gold (Au) on a silicon dioxide substrate, while growing a thin layer of Au on the other side of the silicon dioxide to suppress transmission, and the MA was tested and found to achieve narrow-bandwidth absorption in the terahertz band[16].

From the above, it can be found that the materials used in the micro-nano structures in these narrow-bandwidth MAs are metallic materials, but metallic materials have ohmic losses and there are processing problems for fine metallic materials at high frequencies, both of which will affect the application promotion of MAs in the future to some extent.For this reason, some research groups have proposed to design and fabricate narrow-bandwidth MAs using dielectric materials.In 2019, Zhibin Ren et al.(Harbin Institute of Technology) designed and prepared MAs with narrow-bandwidth absorption in the infrared band using silicon nitride and indium tin oxide materials, which were tested to have a FWHM of up to 2.6 nm[17]; in 2020, Yan Zhao et al.(Anhui University) proposed a dielectric grating composed of silicon material etched directly on a metal substrate, and the FWHM of this narrow-bandwidth MA was calculated by simulation up to 0.38 nm[18].

Although the design and preparation of narrowbandwidth MAs using dielectric materials can reduce fabrication costs and improve absorption efficiency, and the absorption bandwidth can be maintained at the sub-nanometer level, it can be seen that few MAs that achieve multi-wavelength narrowbandwidth (sub-nanometer level) absorption are currently available.This can limit the application of narrow-bandwidth MAs in some applications, such as in spectral detection and gas detection, where multi-wavelength narrow-bandwidth MAs are more efficient in improving their efficiency[19-20].To this end, a dual-wavelength narrow-bandwidth dielectric MA consisting of an asymmetric dielectric grating, a dielectric transition layer, and a metal substrate is proposed in this paper, and the MA is designed and analyzed using the Finite Difference Time Domain (FDTD) method.The differential form of Maxwell's equations can be numerically solved in the time domain through FDTD, in which the differential quotient can be substituted for the differential in the equation.In the solution, the electric and magnetic fields are alternately distributed,and the electric and magnetic fields in the simulation region are solved over time.Through simulation calculations, it is found that the FWHM of the dual-wavelength narrow-bandwidth MA is as low as 0.077 nm and the quality factor (figure of merit,FOM) is up to 1524/RIU, and it can also be found that the narrowest absorption bandwidth of the narrow-bandwidth MA designed in this paper decreased by an order of magnitude compared to the reference [14-18].This study can provide high-quality dual-wavelength narrow-bandwidth dielectric MAs for biosensors, thermal emitters, light modulators, etc.

2 Device structure

A dual-wavelength narrow-bandwidth dielectric MA, as shown in Figure 1, consists of an Au substrate, a silicon dioxide (SiO2) dielectric layer,and an asymmetric grating formed by silicon (Si)material from the bottom up.The main function of the Au substrate is to suppress light transmission, so its thickness must be greater than the skinning depth of the incident electromagnetic wave, and the thickness of Au is set to 0.2 μm in this paper.It can be seen from Figure 1 that there are two gratings with the same heighthbut different widths,W1andW2,in a period, and the distance between the gratings in the same period isg, and the thickness of SiO2ist.In the future practical device preparation, the preparation process of the dual-wavelength narrowbandwidth dielectric MA in this paper is compatible with the current micro-nano processing process.First, SiO2and Si thin layers are grown successively on the Au substrate by magnetron sputtering,followed by spin-coating electron beam resist on the Si thin layer, forming asymmetric grating patterns on the resist after electron beam exposure and development, and then debonding and transferring the patterns to the Si thin layer using inductively coupled plasma etching to finally prepare the dualwavelength narrow-bandwidth dielectric MA[21].

Fig.1 Dual-wavelength narrow-bandwidth dielectric MA structure diagram圖1 雙波長窄帶寬介質(zhì)MA結(jié)構(gòu)圖

The dielectric constant of Au is represented by the Drude model as shown in Equation (1), whereωp,γandωare the plasma frequency, damping coefficient and incident light angle frequency, respectively.To ensure the correctness of the simulation calculation results,ωpandγare obtained from the experimental data, and according to the reference [22],ωp=1.32×1016rad/s,γ=1.2×1014rad/s.The refractive indices of SiO2and Si arenSiO2=1.45 andnSi=3.45, respectively.

3 Results and discussion

3.1 Realization of dual-wavelength narrowbandwidth and high absorption

Firstly, a two-dimensional physical model of a single period of the dual-wavelength narrow-bandwidth dielectric MA is established using FDTD, and then periodic boundary conditions are added in thex-direction, perfect matching layer boundary conditions are added in thez-direction, and they-direction is set to grating infinite length by default.Finally, a light source is added directly above the dual-wavelength narrow-bandwidth dielectric MA,the light source polarization is set to TE polarization, the incident angle is set to 0°, and the MA is surrounded by air with refractive indexn=1.

Figure 2 shows the absorption spectrum of the dual-wavelength narrow-bandwidth dielectric MA,whereP=1.05 μm,t=1.2 μm,h=0.78 μm,W1=0.2 μm,W2=0.3 μm andg=0.2 μm.The above grating parameters were obtained based on FDTD optimization.It can be seen from the figure that the MA has ultrahigh absorption efficiency at wavelengthsλ1=1.2085 μm andλ2=1.2382 μm, respectively, and the absorption linewidths FWHM are 0.735 nm and 0.077 nm, respectively.By comparing with references [14-15, 17], the linewidth of the dualwavelength narrow-bandwidth dielectric MA at wavelengthλ2is significantly decreased and narrowbandwidth absorption is achieved.All parameters mentioned above were kept constant for subsequent calculations if not otherwise stated.

Fig.2 Absorption spectroscopy of dual-wavelength narrow-bandwidth dielectric MA圖2 雙波長窄帶寬介質(zhì)MA吸收光譜

MA can achieve ultra-narrow bandwidth high absorption at wavelengthsλ1=1.2085 μm andλ2=1.2382 μm because the effective impedance of MA at these two wavelengths just matches the free-space impedance and thus the reflection of MA at wavelengthsλ1andλ2can be effectively suppressed[23].Because the absorption efficiencyAof MA can be expressed asA=1-T-R, because the thickness of Au substrate is greater than the skinning depth of light, soT=0, and when the reflection of MA at wavelengthsλ1andλ2is suppressed, the absorption efficiency of MA at these two wavelengths can be close to 1.The effective impedanceZof MA can be expressed by Equation (2), whereS11andS21are the scattering matrix coefficients of reflection and transmission under vertical irradiation of TE polarized light, respectively, andR=(S11)2,T=(S21)2, and sinceT=0,S21=0.Figure 3 shows the effective impedance of MA calculated by Equation (2).

From Figure 3(a), it can be seen that the real part of impedanceZrealis close to 1 at wavelengthsλ1andλ2, while from Figure 3(b) it can be found that the imaginary part of impedanceZimagis close to 0 at wavelengthsλ1andλ2.

Fig.3 Effective impedance of dielectric MA.(a) Real part of impedance; (b) imaginary part of impedance圖3 介質(zhì)MA的有效阻抗。（a）阻抗實部；（b）阻抗虛部

In order to explore the intrinsic physical mechanisms of MA achieving dual-wavelength narrowbandwidth absorption, the electric field distribution of MA at wavelengthsλ1andλ2respectively, is calculated in this paper, as shown in Figure 4 (Color online).From Figure 4(a), it can be seen that the narrow-bandwidth dielectric MA has high narrowbandwidth absorption at wavelengthλ1because most of the light is confined in the SiO2dielectric layer, and a small portion of the light is confined in the asymmetric grating.It can be seen that the incident light forms a Fabry-Pérot (FP) cavity resonance in the SiO2dielectric layer.Figure 4(b) shows the electric field distribution of the narrow bandwidth dielectric MA at wavelengthλ2.Unlike the electric field distribution at wavelengthλ1, the light is no longer confined in the SiO2dielectric layer, but in the grating.Based on the electric field distribution,it can be judged that this is due to the formation of a guided mode resonance in the grating by the incident light[24], which also leads to a narrower bandwidth of the MA at wavelengthλ2.

Fig.4 Electric field distribution of dual-wavelength narrow-bandwidth dielectric MA at different wavelengths.(a) λ1; (b) λ2圖4 雙波長窄帶寬介質(zhì)MA在不同波長處的電場分布。（a）λ1；（b）λ2

3.2 Effect of structural parameters on absorption characteristics of MA

In order to investigate the effect of MA structure parameters on the absorption characteristics of dual-wavelength narrow-bandwidth dielectric, the effect of MA structure parameters on its absorption characteristics is simulated and calculated in this paper.Figure 5 (Color online) shows the effect of different SiO2dielectric layer thicknesston MA absorption characteristics.From Figure 5(a), it can be seen that the absorption wavelengthλ1of MA is redshifted astincreases, however, the change inthas a very weak effect on the absorption wavelengthλ2.From Figure 5(b), it can be seen whentincreases from 1.2 μm to 1.215 μm, the absorption wavelengthλ1is red-shifted from 1.2085 μm to 1.2115 μm, an increase of 3 nm.The change inthas a significant effect on the MA absorption wavelengthλ1, which is due to the FP cavity resonance formed by the light in the SiO2dielectric layer as seen in Figure 4(a).The relationship between FP cavity resonance wavelength and SiO2layer thicknesstis shown in Equation (3)[25],

whereneqis the equivalent refractive index of FP cavity,Φis the sum of the phases of the upper and lower interfaces of the FP cavity, andNis an integer,λFPis the resonant wavelength of the FP cavity.According to Equation (3), it is known that an increase intincreases the FP cavity resonance wavelengthλFPwhich leads to a red shift in the absorption wavelengthλ1of MA.

Fig.5 Effect of t on the absorption characteristics of the dual-wavelength narrow-bandwidth dielectric MA.(a) Absorption spectra; (b) absorption wavelength圖5 t對雙波長窄帶寬介質(zhì)MA吸收特性的影響。（a）吸收光譜；（b）吸收波長

However, the reason why the increase inthas a weaker effect on the absorption wavelengthλ2of MA is that the narrow-bandwidth and high-absorption of MA at wavelengthλ2are caused by guided mode resonance, which can be seen from Figure 4(b).According to Ref.[26], the guided mode resonance wavelength is mainly related to the grating parameters and the incident angle.However, the absorption efficiency of MA at the absorption wavelengthλ2will gradually decrease astincreases,which can be explained by Figure 6 (Color online).Figure 6 is the electric field distribution of MA at wavelengthλ2whent=1.205 μm.Comparing Figure 6 with Figure 4(b), it can be found that the electric field focused in the grating in Figure 6 is significantly lower than Figure 4(b).Therefore, the absorption rate of MA will decrease aftertbecomes larger.

Fig.6 Electric field distribution of MA at wavelength λ2 when t = 1.205 μm圖6 t=1.205 μm時MA在波長λ2處的電場分布

Figure 7 (Color online) shows the effect of grating widthW1on the absorption characteristics of dual-wavelength narrow-bandwidth dielectric MA.It can be seen from Figure 7(a) that the absorption wavelengthsλ1andλ2of MA both have red shifted asW1becomes larger, respectively.It can be seen from Figure 7(b) that whenW1increases from 0.2 μm to 0.202 μm, the absorption wavelengthλ2of MA is red-shifted by nearly 7 nm, while the absorption wavelengthλ1of MA is red-shifted by 1.46 nm.

Fig.7 Effect of W1 on the absorption characteristics of the dual-wavelength narrow-bandwidth dielectric MA.(a) Absorption spectra; (b) absorption wavelength圖7 W1對雙波長窄帶寬介質(zhì)MA吸收特性的影響。（a）吸收光譜；（b）吸收波長

The change ofW1can have an impact on the absorption wavelengthλ1because it can be known that the change of the grating width will lead to a change in the equivalent refractive index of the asymmetric grating, and the equivalent refractive index of the FP cavityneqis effectd by the equivalent refractive index of the asymmetric gratingnw.Moreover, it has been shown in Ref.[27] that the increase of the grating width will lead to the increase of the equivalent refractive index of the FP cavityneq.From Equation (3), it is known that an increase inneqwill increase the FP cavity resonance wavelengthλFP.And the increase ofλFPwill lead to the red-shift of the absorption wavelengthλ1of MA.Figure 8 showsneqvarying withW1and it is calculated by FDTD.From Figure 8, it can be found that whenW1increases from 0.2 μm to 0.202 μm,neqincreases from 1.510 to 1.512.

Fig.8 Effect of W1 on neq圖8 W1對neq的影響

The grating, SiO2layer, and air form an optical waveguide, and according to the grating guidedmode resonance theory, it is known that the grating equivalent refractive index change will affect the guided-mode resonance wavelength[26], as shown in Equation (4).

whereλgis the guided-mode resonance wavelength andmis the diffraction order of the grating.According to the equivalent medium theory, an increase inW1will increase the grating equivalent refractive indexnw, and from Eq.(4), an increase innwwill redshift the guided-mode resonance wavelengthλgand thus the MA absorption wavelengthλ2will red-shift.The effect ofW2on MA absorption characteristics is not shown in this paper, because the effect of the change inW2on MA absorption characteristics is similar to that ofW1on MA, and the intrinsic physical mechanism of the effect is essentially the same.

The electric field distribution in Figure 4(b)shows that a part of the electric field is distributed among the slits of the dielectric grating, so it can be seen that the change of the surrounding gas will have an effect on the absorption wavelengthλ2of MA.Therefore, the narrow bandwidth dielectric MA proposed in this paper can be applied in the fields of gas or biological detection.In order to evaluate the performance of the narrow-bandwidth dielectric MA in gas detection, two parameters,sensitivity and quality factor, are defined, and the specific expressions are shown in equations (5) and(6).WhereSis the sensitivity of narrow-bandwidth MA,△nand△λare the amount of change in refractive index and the amount of change in absorption wavelength of the surrounding gas, respectively[18].

From Figure 9 (a) (Color online), it can be seen that the absorption wavelengthsλ1andλ2of MA are redshifted asnincreases.This is because a largernleads to a larger refractive indexnlof the grating's low refractive index material, which in turn leads to a larger equivalent refractive index of the grating for different wavelengths.And from the previous description, the grating refractive index will lead to a larger equivalent refractive indexneqof FP cavity,so according to Equation (3), the increase ofnwill lead to a red shift of MA absorption wavelengthλ1.Unlike the mechanism that causes the red shift of MA absorption wavelengthλ1,λ2is red-shifted asnbecomes larger, because the grating equivalent refractive indexnwincreases, which means that it increases the refractive index of the central layer of the optical waveguide, and this must lead to the red shift of the grating guided mode resonance wavelength according to the guided mode resonance theory and Equation (4)[27].

Fig.9 Effect of n on the absorption characteristics of the dual-wavelength narrow-bandwidth dielectric MA.(a) Absorption spectra; (b) absorption wavelength圖9 n對雙波長窄帶寬介質(zhì)MA吸收特性的影響。（a）吸收光譜；（b）吸收波長

From Figure 9(b), whennincreases from 1 to 1.03, the absorption wavelengthλ2increases from 1.2382 μm to 1.2417 μm, which is red-shifted by 3.5 nm, and according to Eqs.(5) and (6),S=117.3 nm/RIU and FOM = 1524/RIU.It can be found that the FOM in this paper is significantly improved compared to the references [14-15, 18].

Finally, the effect of the asymmetric grating periodPon the absorption characteristics of the dielectric MA was analyzed, and the specific results are shown in Figure 10 (Color online).From Figure 10, it can be found that the absorption wavelengthsλ1andλ2of MA are red-shifted with the increase ofP.WhenPincreases from 1.05 μm to 1.1 μm, the wavelengthλ1increases from 1.2085 μm to 1.2249 μm, while the wavelengthλ2increases from 1.2382 μm to 1.2525 μm.From Equation (4) we can know the reason why the wavelengthλ2increases with the increase ofP[24].When the period increases, if the guided mode resonance is to be maintained, the resonance wavelength must be shifted to the long wavelength direction.

AsPincreases, the phaseΦof the FP cavity decreases significantly because the effect of the change ofPonneqis not as significant as the phaseΦ.Therefore, according to Equation (3), it is known that the FP cavity resonance wavelengthλFPincreases with the increase ofP, which leads to the red-shift of the absorption wavelengthλ1of MA.The trend of the effect ofPon the phaseΦis calculated by FDTD and is shown in Figure 11, from which it can be seen thatΦdecreases from 4.64 rad to 0.22 rad whenPincreases from 1.05 μm to 1.1 μm.

Fig.10 Effect of P on the absorption characteristics of the dual-wavelength narrow-bandwidth dielectric MA圖10 P對雙波長窄帶寬介質(zhì)MA吸收特性的影響

Fig.11 Effect of P on Φ圖11 P對Φ的影響

4 Conclusion

In order to broaden the application field of narrow-bandwidth MA, a medium MA is designed in this paper that can achieve dual-wavelength narrowbandwidth absorption in the infrared band based on the finite-difference time-domain method.Through simulation analysis, the narrow bandwidth dielectric MA in this paper has ultra-high absorption efficiency at wavelengthλ1= 1.2085 μm andλ2= 1.238 2 μm, and the FWHM is only 0.735 nm and 0.077 nm, respectively.Because of the different mechanisms of MA forming narrow-bandwidth and high absorption onλ1andλ2, the study found thatλ1is very sensitive to the change of the thicknesstof the SiO2transition layer, whileλ2is very sensitive to the change of the dielectric grating widthW1.With the increase oftandW1, the absorption wavelengthsλ1andλ2of MA will red-shift respectively.When the grating periodPincreases, the absorption wavelengthsλ1andλ2of MA will shift to the long wavelength direction at the same time.From the electric field distribution of MA atλ2, a large part of its electric field is distributed in the gap between the gratings, so the change of air refractive index has a significant effect onλ2.This allows it to be used in the field of detection.It is calculated that the FOM of the narrow-bandwidth dielectric MA in this paper can reach 1524/RIU.

——中文對照版——

1 引言

在許多應(yīng)用中都有需要對電磁波實現(xiàn)完美吸收，如太陽能電池、熱發(fā)射器、輻射冷卻、通信等[1-4]。但是由自然界存在的材料構(gòu)成的吸收器因缺乏磁響應(yīng)導(dǎo)致阻抗失配，因此它們不能完全抑制光反射，從而降低了吸收器光吸收能力[5]。因此，人們提出了基于超材料的吸收器，由于超材料吸收器（Metamaterial Absorber，MA）對電磁波具有高吸收效率，且具有體積小、可設(shè)定工作波長等優(yōu)點，逐漸被人們所關(guān)注并成為研究熱點之一[6]。

經(jīng)深入研究，人們設(shè)計并制備出了不同類型的MA，如寬帶寬MA、窄帶寬MA、太赫茲MA、可調(diào)諧MA等[7-9]。窄帶寬MA被人們所關(guān)注是因為窄帶寬MA用在探測和熱發(fā)射器上時相比于寬帶寬MA效率更高[10-11]，而且在光調(diào)制、光探測和熱輻射剪裁中只有窄帶寬MA才能滿足要求[12-13]。目前已經(jīng)有不同結(jié)構(gòu)的窄帶寬MA被提出，如基于裂環(huán)諧振器陣列（Split Ring Resonator，SRR）、金屬/介質(zhì)周期光柵、金屬/介質(zhì)狹縫（narrow slits）等。2014年瑞典皇家理工學(xué)院的Min-Qiu等人提出在銀（Ag）金屬襯底上刻蝕金屬光柵，基于Ag光柵與空氣介質(zhì)形成的表面等離子激元共振成功使MA在波長1400 nm處實現(xiàn)了窄帶寬吸收，其線寬（Full Width Half Maximum，F(xiàn)WHM）可以達(dá)到0.4 nm[14]；2018年香港中文大學(xué)的FENG A等人提出一種由非對稱金屬光柵和金屬襯底構(gòu)成的窄帶寬MA，而且在光柵和襯底之間添加了一層二氧化硅過渡層，經(jīng)模擬計算發(fā)現(xiàn)該窄帶寬MA在光通信波段實現(xiàn)了超窄吸收，F(xiàn)WHM僅 有0.28 nm[15]；2019年，東 南 大學(xué)KANG S等人提出在二氧化硅襯底上刻蝕出由金（Au）材料構(gòu)成的十字型納米陣列，與此同時在二氧化硅另一面生長一層Au薄層抑制透射，經(jīng)測試發(fā)現(xiàn)該MA可在太赫茲波段實現(xiàn)窄帶寬吸收[16]。

從以上研究可以發(fā)現(xiàn)，這些窄帶寬MA中的微納結(jié)構(gòu)所使用的材料都是金屬材料，但是金屬材料存在歐姆損耗，而且在高頻處精細(xì)金屬材料存在加工問題，這會在一定程度上影響MA在將來的應(yīng)用推廣。因此，一些課題組提出利用介質(zhì)材料設(shè)計、制造窄帶寬MA。2019年哈爾濱工業(yè)大學(xué)的Zhibin Ren等人利用氮化硅、氧化銦錫材料設(shè)計并制備出在紅外波段具有窄帶寬吸收的MA，經(jīng)測試可得該窄帶寬MA的FWHM可達(dá)2.6 nm[17]；2020年，安徽大學(xué)的Yan Zhao等人提出在金屬襯底上直接刻蝕出由硅材料構(gòu)成的介質(zhì)光柵，經(jīng)模擬計算可知該窄帶寬MA的FWHM可達(dá)0.38 nm[18]。

雖然利用介質(zhì)材料設(shè)計制備窄帶寬MA可以降低制造成本，提高吸收效率，而且吸收帶寬可保持在亞納米級別，但目前鮮有實現(xiàn)多波長窄帶寬亞納米級別吸收的MA，這會限制窄帶寬MA在一些場合的應(yīng)用，如在光譜探測、氣體探測中，多波長窄帶寬MA更能提高它們的工作效率[19-20]。針對上述需求，本文提出由非對稱介質(zhì)光柵、介質(zhì)過渡層、金屬襯底構(gòu)成的雙波長窄帶寬介質(zhì)MA，并利用時域有限差分法(Finite Difference Time Domain, FDTD)對該MA進行設(shè)計和分析。FDTD在時域中對麥克斯韋方程組的微分形式進行數(shù)值求解，以差商代替方程中的微分。在求解時電場與磁場交替分布，隨著時間的推移求解出仿真區(qū)域的電場和磁場。經(jīng)模擬計算發(fā)現(xiàn)雙波長窄帶寬MA的FWHM最低可達(dá)0.077 nm，品質(zhì)因素（Figure Of Merit，F(xiàn)OM）可達(dá)1524/RIU，而且經(jīng)對比可以發(fā)現(xiàn)本文設(shè)計的窄帶寬MA最窄的吸收帶寬相比文獻[14-18]都下降了一個數(shù)量級。本文研究可為生物傳感器、熱發(fā)射器、光調(diào)制器等提供高質(zhì)量的雙波長窄帶寬介質(zhì)MA。

2 器件結(jié)構(gòu)

圖1是雙波長窄帶寬介質(zhì)MA結(jié)構(gòu)圖，它自下而上由Au襯底、二氧化硅（SiO2）介質(zhì)層、硅（Si）材料形成的非對稱光柵組成。Au襯底的主要作用是抑制光的透射，因此它的厚度必須大于入射電磁波的趨膚深度，本實驗中Au的厚度設(shè)為0.2 μm。從圖1中可以看到，一個周期內(nèi)具有兩個同高度（h）、不同寬度的光柵，它們的寬度分別是W1和W2，同周期內(nèi)光柵之間的間距為g，另外SiO2的厚度為t。在將來實際器件制備中，本文的雙波長窄帶寬介質(zhì)MA的制備工藝與現(xiàn)今的微納加工工藝兼容，通過磁控濺射在Au襯底上先后生長SiO2和Si薄層，緊接著在Si薄層上旋涂電子束抗蝕膠，經(jīng)電子束曝光和顯影后在抗蝕膠上形成非對稱光柵圖形，去膠并利用感應(yīng)耦合等離子體刻蝕技術(shù)，將圖形轉(zhuǎn)移到Si薄層上，最終制備出雙波長窄帶寬介質(zhì)MA[21]。

Au的介質(zhì)常數(shù)由Drude模型表示，即

式中ωp、γ和ω分別是等離子體頻率、阻尼系數(shù)和入射光角頻率。為了保證模擬計算結(jié)果正確，ωp和γ均是從實驗數(shù)據(jù)中獲得，根據(jù)文獻[22]可知，ωp=1.32×1016rad/s，γ=1.2×1014rad/s。SiO2和Si的折射率分別為nSiO2=1.45和nSi=3.45。

3 結(jié)果與討論

3.1 雙波長窄帶寬高吸收的實現(xiàn)

首先利用FDTD軟件建立雙波長窄帶寬介質(zhì)MA單個周期的二維物理模型，然后在x方向添加周期性邊界條件，在z方向添加完美匹配層邊界條件，y方向默認(rèn)為光柵無限長。最后在雙波長窄帶寬介質(zhì)MA正上方添加光源，光源偏振設(shè)為TE偏振，入射角設(shè)為0°，并且MA周圍為空氣，折射率n=1。

圖2所示的是雙波長窄帶寬介質(zhì)MA的吸收光譜，此時P=1.05 μm、t=1.2 μm、h=0.78 μm、W1=0.2 μm、W2=0.3 μm、g=0.2 μm，上述光柵參數(shù)是基于FDTD優(yōu)化后獲得的。從圖2中可以看到MA分別在波長λ1=1.2085 μm和λ2=1.2382 μm處具有超高吸收效率，吸收線寬FWHM分別為0.735 nm和0.077 nm。相比于文獻[14-15, 17]結(jié)果，雙波長窄帶寬介質(zhì)MA在波長λ2處的線寬明顯下降，實現(xiàn)了窄帶寬吸收。若無特殊說明，上述所有參數(shù)保持不變。

MA能在波長λ1=1.2085 μm和λ2=1.2382 μm實現(xiàn)超窄帶寬高吸收，是因為MA在這兩個波長處的有效阻抗剛好與自由空間阻抗相匹配，這可有效地抑制MA對波長λ1和λ2的反射[23]。因為MA的吸收效率A可表示為A=1-T-R，由于Au襯底的厚度大于光的趨膚深度，所以T=0，而當(dāng)MA在波長λ1和λ2的反射得到抑制后，MA對這兩個波長的吸收效率就接近1。MA的有效阻抗Z可由式（2）表示：

式中S11和S21分別是TE偏振光垂直照射下反射和透射的散射矩陣系數(shù)，其中R=(S11)2,T=(S21)2，由于T=0，所以S21=0。圖3是由式（2）計算得到的MA的有效阻抗，從圖3（a）中可知阻抗的實部Zreal在波長λ1和λ2處接近為1，而從圖3（b）中可以發(fā)現(xiàn)阻抗的虛部Zimag在波長λ1和λ2接近為0。

為了探索MA實現(xiàn)雙波長窄帶寬吸收的內(nèi)在物理機制，本文計算了MA分別在波長λ1和λ2處的電場分布，具體如圖4（彩圖見期刊電子版）所示。從圖4（a）中可知，窄帶寬介質(zhì)MA之所以在波長λ1出現(xiàn)窄帶寬高吸收是因為大部分光被限制在SiO2介質(zhì)層當(dāng)中，少部分光限制在非對稱光柵當(dāng)中。由此可知，入射光在SiO2介質(zhì)層當(dāng)中形成了法布里-珀羅(Fabry-Pérot, FP)腔共振。圖4（b）所示的是窄帶寬介質(zhì)MA在波長λ2的電場分布，與在波長λ1的電場分布不同，此時光不再被限制在SiO2介質(zhì)層當(dāng)中，反而是被限制在光柵當(dāng)中，依據(jù)電場分布可以判斷這是由于入射光在光柵中形成了導(dǎo)模共振[24]，也因為導(dǎo)模共振導(dǎo)致MA在波長λ2處的帶寬更窄。

3.2 結(jié)構(gòu)參數(shù)對MA吸收特性的影響

為了探究雙波長窄帶寬介質(zhì)MA結(jié)構(gòu)參數(shù)對其吸收特性的影響規(guī)律，本文模擬計算了MA結(jié)構(gòu)參數(shù)對其吸收特性的影響。圖5（彩圖見期刊電子版）是不同SiO2介質(zhì)層厚度t對MA吸收特性的影響。從圖5（a）中可知，隨著t的增加，MA的吸收波長λ1會出現(xiàn)紅移現(xiàn)象，但是t的變化對吸收波長λ2的影響非常微弱。由圖5（b）可得，當(dāng)t從1.2 μm增加到1.215 μm，吸收波長λ1從1.2085 μm紅移到1.2115 μm，增加了3 nm。t的變化能夠?qū)A吸收波長λ1有顯著影響，是因為由圖4（a）可知光在SiO2介質(zhì)層中形成了FP腔共振。FP腔共振波長與SiO2層厚度t的關(guān)系為[25]：

式中，neq是FP腔的等效折射率，Φ是FP腔上下界面相位之和，N是整數(shù)，λFP是FP腔共振波長。根據(jù)式（3）可知t增大會導(dǎo)致FP腔共振波長λFP增大，從而導(dǎo)致MA的吸收波長λ1出現(xiàn)紅移現(xiàn)象。

由圖4（b）可知，MA在波長λ2處實現(xiàn)窄帶寬高吸收是因為導(dǎo)模共振效應(yīng)，而根據(jù)文獻[26]可知，導(dǎo)模共振波長主要與光柵參數(shù)、入射角等有關(guān)。但是可以發(fā)現(xiàn)隨著t的增大，MA在吸收波長λ2的吸收效率會逐漸下降，這可由圖6（彩圖見期刊電子版）解釋。圖6是t=1.205 μm時MA在波長λ2處電場分布，將圖6與圖4（b）相比，可以發(fā)現(xiàn)在圖6中聚集在光柵中的電場明顯低于圖4（b），故此導(dǎo)致MA在t變大后的吸收率會下降。

圖7（彩圖見期刊電子版）所示的是光柵寬度W1對雙波長窄帶寬介質(zhì)MA吸收特性的影響。由圖7（a）可知，隨著W1的變寬，MA的吸收波長λ1和λ2都分別出現(xiàn)了紅移現(xiàn)象。從圖7（b）可知，當(dāng)W1從0.2 μm增加到0.202 μm，MA的吸收波長λ2紅移了將近7 nm，而MA的吸收波長λ1紅移了1.46 nm。

W1的變化能夠?qū)ξ詹ㄩLλ1產(chǎn)生影響是因為根據(jù)等效介質(zhì)原理可知光柵寬度的變化會導(dǎo)致非對稱光柵的等效折射率發(fā)生變化，而FP腔的等效折射率neq又受非對稱光柵等效折射率nw的影響。而且文獻[27]也已經(jīng)證明，光柵寬度增加會導(dǎo)致FP腔等效折射率neq增大，由式（3）可知，neq增大，F(xiàn)P腔共振波長λFP也將會增大。λFP增大就會導(dǎo)致MA的吸收波長λ1紅移。圖8是當(dāng)W1取不同值時neq的變化情況，它是由FDTD計算獲得。從圖8中可以發(fā)現(xiàn)，當(dāng)W1從0.2 μm增加到0.202 μm，neq則從1.510增加到1.512.

光柵、SiO2層、空氣形成了光波導(dǎo)，根據(jù)光柵導(dǎo)模共振理論可知，光柵等效折射率的改變將會影響導(dǎo)模共振波長[26]，即

式中λg是導(dǎo)模共振波長，m為光柵的衍射階數(shù)。由等效介質(zhì)理論可知，W1增大將會使光柵等效折射率nw增大，而根據(jù)式（4）可知，nw增大則使導(dǎo)模共振波長λg紅移，從而使MA吸收波長λ2紅移。在本文中之所以沒有展示W(wǎng)2對MA吸收特性的影響，是因為W2的變化對MA吸收特性的影響與W1對MA的影響相似，而且內(nèi)在物理機理也基本相同。

通過圖4（b）的電場分布可知，有一部分電場分布在介質(zhì)光柵縫隙中，由此可知，周圍氣體的變化將會對MA的吸收波長λ2產(chǎn)生影響，因此本文提出的窄帶寬介質(zhì)MA可應(yīng)用在氣體或生物探測等領(lǐng)域當(dāng)中。為了評估窄帶寬介質(zhì)MA在氣體探測中的工作性能，定義了靈敏度和品質(zhì)因素兩個參數(shù)，即

式中S是窄帶寬MA的靈敏度，△n和△λ分別是周圍氣體折射率的變化量和吸收波長的變化量[18]。

從圖9（a）（彩圖見期刊電子版）可知，隨著n的增加，MA的吸收波長λ1和λ2都出現(xiàn)了紅移的現(xiàn)象。因為n變大會導(dǎo)致光柵低折射率材料折射率nl變大，而nl變大又會導(dǎo)致光柵對不同波長的等效折射率變大。而由前面所述可知，光柵折射率變大會導(dǎo)致FP腔等效折射率neq變大，所以根據(jù)式（3）可知，n的增加會導(dǎo)致MA吸收波長λ1紅移。與導(dǎo)致MA吸收波長λ1紅移的機理不同，MA吸收波長λ2之所以會隨著n變大而紅移，是因為其增大了光柵等效折射率nw，這意味著增大了光波導(dǎo)中心層的折射率，而根據(jù)導(dǎo)模共振理論和式（4）可知[27]，這必定會導(dǎo)致光柵導(dǎo)模共振波長的紅移。

從圖9（b）可知，當(dāng)n從1增加到1.03，吸收波長λ2會從1.2382 μm增加到1.2417 μm，紅移了3.5 nm，根據(jù)式（5）和式（6）可得，S=117.3 nm/RIU，F(xiàn)OM=1524/RIU。本文的FOM相比文獻[14-15, 18]有了明顯提高。

最后分析了非對稱光柵周期P對介質(zhì)MA吸收特性的影響，具體結(jié)果如圖10（彩圖見期刊電子版）所示。從圖10中可以發(fā)現(xiàn)，隨著P的增加，MA的吸收波長λ1和λ2都產(chǎn)生了紅移現(xiàn)象。當(dāng)P從1.05 μm增加到1.1 μm后，波長λ1則從1.2085 μm增加到了1.2249 μm，而波長λ2則從1.2382 μm增加到了1.2525 μm。由式（4）可知，波長λ2之所以會隨著P的增大而增大[24]，是因為周期增大時若要維持導(dǎo)模共振，則必須使得共振波長向長波長方向移動。

隨著P的增加FP腔的相位Φ會顯著下降，因為P的變化對neq的影響并無相位Φ的顯著，所以根據(jù)式（3）可知，隨著P的增加FP腔共振波長λFP會增大，從而導(dǎo)致MA的吸收波長λ1出現(xiàn)紅移現(xiàn)象。P對相位Φ的影響趨勢如圖11所示，該結(jié)果由FDTD計算得到，從圖11中可知當(dāng)P從1.05 μm增大到1.1 μm，Φ會從4.64 rad下降到0.22 rad。

4 結(jié)論

為了拓寬窄帶寬MA的應(yīng)用領(lǐng)域，本文基于時域有限差分法設(shè)計了在紅外波段上可實現(xiàn)雙波長窄帶寬吸收的介質(zhì)MA，經(jīng)模擬分析發(fā)現(xiàn)，本文的窄帶寬介質(zhì)MA在波長λ1=1.2085 μm和λ2=1.2382 μm具有超高吸收效率，而且FWHM也分別只有0.735 nm和0.077 nm。由于MA在λ1和λ2上形成窄帶寬高吸收的機理不同，所以經(jīng)本文研究發(fā)現(xiàn)，λ1對SiO2過渡層的厚度t變化非常敏感，但是λ2卻對介質(zhì)光柵寬度W1的變化非常敏感，隨著t和W1的增加，MA的吸收波長λ1和λ2都會分別出現(xiàn)紅移現(xiàn)象。而當(dāng)光柵周期P增加時，MA的吸收波長λ1和λ2會同時向長波長方向偏移。從MA在λ2處的電場分布可知，其電場有一大部分是分布在光柵之間的空隙當(dāng)中，因此空氣折射率的變化對λ2有顯著影響，這可使其應(yīng)用在探測領(lǐng)域當(dāng)中，經(jīng)計算可得本文的窄帶寬介質(zhì)MA的FOM可達(dá)1524/RIU。