Dual-wavelength narrow-bandwidth dielectric metamaterial absorber

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图1 双波长窄带宽介质MA结构图

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图2 双波长窄带宽介质MA吸收光谱

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图3 介质MA的有效阻抗。（a）阻抗实部；（b）阻抗虚部

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图4 双波长窄带宽介质MA在不同波长处的电场分布。（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图5 t对双波长窄带宽介质MA吸收特性的影响。（a）吸收光谱；（b）吸收波长

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图6 t=1.205 μm时MA在波长λ2处的电场分布

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图7 W1对双波长窄带宽介质MA吸收特性的影响。（a）吸收光谱；（b）吸收波长

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图8 W1对neq的影响

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图9 n对双波长窄带宽介质MA吸收特性的影响。（a）吸收光谱；（b）吸收波长

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图10 P对双波长窄带宽介质MA吸收特性的影响

Fig.11 Effect of P on Φ图11 P对Φ的影响

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.

——中文对照版——

1 引言

在许多应用中都有需要对电磁波实现完美吸收，如太阳能电池、热发射器、辐射冷却、通信等[1-4]。但是由自然界存在的材料构成的吸收器因缺乏磁响应导致阻抗失配，因此它们不能完全抑制光反射，从而降低了吸收器光吸收能力[5]。因此，人们提出了基于超材料的吸收器，由于超材料吸收器（Metamaterial Absorber，MA）对电磁波具有高吸收效率，且具有体积小、可设定工作波长等优点，逐渐被人们所关注并成为研究热点之一[6]。

经深入研究，人们设计并制备出了不同类型的MA，如宽带宽MA、窄带宽MA、太赫兹MA、可调谐MA等[7-9]。窄带宽MA被人们所关注是因为窄带宽MA用在探测和热发射器上时相比于宽带宽MA效率更高[10-11]，而且在光调制、光探测和热辐射剪裁中只有窄带宽MA才能满足要求[12-13]。目前已经有不同结构的窄带宽MA被提出，如基于裂环谐振器阵列（Split Ring Resonator，SRR）、金属/介质周期光栅、金属/介质狭缝（narrow slits）等。2014年瑞典皇家理工学院的Min-Qiu等人提出在银（Ag）金属衬底上刻……