Small-Angle Ultra-Narrowband Tunable Mid-Infrared Absorber Composing from Graphene and Dielectric Metamaterials

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Article Small-Angle Ultra-Narrowband Tunable Mid-Infrared Absorber Composing from Graphene and Dielectric Metamaterials

Yan-Lin Liao 1,2,*, Huilin Wang 1, Yan Zhao 3,*, Xiang Chen 1, Jin Wu 1 and Zhenggen Chen 1

1 School of Physics and Materials Science, Anhui University, Hefei 230039, China; [email protected] (H.W.); [email protected] (X.C.); [email protected] (J.W.); [email protected] (Z.C.) 2 Key Laboratory of Functional Materials and Devices for Informatics of Anhui Higher Education Institutes, Fuyang Normal University, Fuyang 236041, China 3 School of Biomedical Engineering, Anhui Medical University, Hefei 230032, China * Correspondence: [email protected] (Y.-L.L.); [email protected] (Y.Z.)

Abstract: We report a small-angle ultra-narrowband mid-infrared tunable absorber that uses graphene and dielectric metamaterials. The absorption bandwidth of the absorber at the graphene Fermi level of 0.2 eV is 0.055 nm, and the absorption peaks can be tuned from 5.14803 to 5.1411 µm by changing the graphene Fermi level. Furthermore, the resonance absorption only occurs in the angle range of several degrees. The simulation ﬁeld distributions show the magnetic resonance and Fabry–Pérot resonance at the resonance absorption peak. The one-dimensional photonic crystals (1DPCs) in this

absorber act as a Bragg mirror to efﬁciently reﬂect the incidence light. The simulation results also show that the bandwidth can be further narrowed by increasing the resonance cavity length. As a

Citation: Liao, Y.-L.; Wang, H.; Zhao, tunable mid-infrared thermal source, this absorber can possess both high temporal coherence and Y.; Chen, X.; Wu, J.; Chen, Z. near-collimated angle characteristics, thus providing it with potential applications. Small-Angle Ultra-Narrowband Tunable Mid-Infrared Absorber Keywords: absorption; graphene; near-collimation; mid-infrared absorber Composing from Graphene and Dielectric Metamaterials. Coatings 2021, 11, 825. https://doi.org/ 10.3390/coatings11070825 1. Introduction Metamaterial, which is an artiﬁcial electromagnetic material, has extraordinary physi- Academic Editor: Anna Palau cal properties that natural materials do not have. Metamaterial absorbers have been widely studied in recent years because they have such potential applications as photo-detection [1], Received: 2 June 2021 sensing [2], solar cell [3], and thermal emission source [4]. For photo-detection and solar cell Accepted: 7 July 2021 Published: 9 July 2021 applications, broadband or multiband absorbers are needed [5–17]. However, for sensing and coherent thermal emission source applications, the narrower the absorption bandwidth

Publisher’s Note: MDPI stays neutral is, the better performance it will have [18,19]. Thus, to achieve better performance, many with regard to jurisdictional claims in schemes have been proposed to narrow the absorption bandwidths for ultra-narrowband published maps and institutional affil- absorbers [20–25]. Unlike the conventional metal metamaterials, dielectric metamaterials iations. have almost no absorption loss; therefore, their use provides an extremely efficient way to produce ultra-narrowband absorbers [26–29]. On the other hand, tunable absorbers are generally desirable because they can work at different resonance wavelengths to meet various requirements. By combining active medium and resonant microstructures, several tunable absorbers have been proposed based on vanadium dioxide, Ge Sb Te , etc. [30–33]. Copyright: © 2021 by the authors. 2 2 5 Licensee MDPI, Basel, Switzerland. Recently, great attention has been paid to graphene because it possesses many unprece- This article is an open access article dented properties such as high optical transparency, high electron mobility, flexibility, and distributed under the terms and tunable conductivity [34–40]. In addition, due to the advantage of rapid-response conduc- conditions of the Creative Commons tivity by applying the bias voltage upon graphene, tunable ultra-narrowband mid-infrared Attribution (CC BY) license (https:// absorbers with graphene are very desirable. creativecommons.org/licenses/by/ Particularly, manipulation of the incidence angles with perfect absorption is another 4.0/). important topic in the research of metamaterial absorbers. For example, for solar cell and

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Particularly, manipulation of the incidence angles with perfect absorption is another important topic in the research of metamaterial absorbers. For example, for solar cell and photo-detection applications, absorbers are expected to operate within a wide-angle range to collect more incident electromagnetic energy [6–8]. On the other hand, similarly to lasers, mid-infrared thermal emission sources based on the metamaterial absorbers are expected to emit near-collimated light, which means that the emissions occur within a small angle range to focus the radiation energy in space [41]. However, to date, no small-angle Coatings 2021, 11, 825 2 of 9 ultra-narrowband tunable mid-infrared absorber has been reported. In this paper, a small-angle ultra-narrowband tunable mid-infrared absorber is pro- photo-detectionposed based on applications, graphene absorbers and dielectric are expected metamaterials. to operate within The a wide-angle ultra-narrowband range resonance toabsorption collect more in incident the mid-infrared electromagnetic regime energy can [6– be8]. tuned On the by other changing hand, similarly the Fermi to level of gra- lasers,phene. mid-infrared In this proposed thermal emissionstructure, sources a Bragg based mirror on the metamaterialconsisting of absorbers the 1DPCs are efficiently re- expectedflects the to incident emit near-collimated light. Furthermore, light, which means the re thatsonance the emissions absorption occur withinonly occurs a small within several angle range to focus the radiation energy in space [41]. However, to date, no small-angle degrees. Such an absorber can be used as a tunable near-collimated coherence thermal ultra-narrowband tunable mid-infrared absorber has been reported. emissionIn this source. paper, a small-angle ultra-narrowband tunable mid-infrared absorber is proposed based on graphene and dielectric metamaterials. The ultra-narrowband resonance absorption2. Structure in the of mid-infrared the Proposed regime Absorber can be tuned by changing the Fermi level of graphene. In this proposed structure, a Bragg mirror consisting of the 1DPCs efficiently reflects the incident light.Figure Furthermore, 1 shows the the resonance schematic absorption diagram only of occurs the withinproposed several absorber. degrees. Such The top-layer ma- anterial absorber is graphene, can be used which as a tunable is placed near-collimated on the periodic coherence micro-structured thermal emission source. Ge material determined by period p, height h, and width w. A ZnS film layer is inserted between the peri- 2. Structure of the Proposed Absorber odic micro-structured Ge material and 1DPCs, which consist of N = 10 pairs of CaF2 and Figure1 shows the schematic diagram of the proposed absorber. The top-layer material Ge film layers. The thickness of ZnS is t. The substrate material is calcium fluoride. Com- is graphene, which is placed on the periodic micro-structured Ge material determined bypared period withp, height graphene,h, and reduced width w. Agraphene ZnS film layeroxide is (RGO) inserted has between a larger the periodic imaginary part of re- micro-structuredfractive index due Ge material to G–O and bonding 1DPCs, whichof RGO; consist therefore of N = 10 RGO pairs is of difficult CaF2 and Geto use in narrow- filmband layers. absorption The thickness [42,43]. of ZnS Although is t. The substrate RGO is material a material is calcium that fluoride. is commonly Compared available at scale withfor practical graphene, applications, reduced graphene we oxidechoose (RGO) graphene has a larger in Figure imaginary 1 instead part of refractiveof RGO to obtain ultra- index due to G–O bonding of RGO; therefore RGO is difficult to use in narrowband absorptionnarrowband [42,43 absorption]. Although in RGO our is design. a material We that use is commonly Ge microstructures available at scale because for Ge has high practicalrefractive applications, indices, which we choose are grapheneoften used in Figure to localize1 instead the of RGOelectromagnetic to obtain ultra- field in the mid- narrowbandinfrared regime absorption [44]. in ZnS our design.is an optical We use thin Ge microstructures film material because with middle Ge has high refractive indices, refractiveand it is indices,placed whichunder are the often Ge usedmicrostructures to localize the electromagneticin order to decrease field in the mid-transmission from infrared regime [44]. ZnS is an optical thin film material with middle refractive indices, and itthe is placedupper under layer. the A Ge plane microstructures electromagnetic in order wave to decrease with the the transmission transverse-magnetic from the (TM) polar- upperization layer. is incident A plane electromagnetic on the proposed wave structure with the transverse-magnetic with angle θ. Rigorous (TM) polarization coupled-wave analy- issis incident (RCWA), on thewhich proposed is a semi-analytical structure with angle method,θ. Rigorous is utilized coupled-wave to study analysis the light absorption (RCWA),characteristics which is[45]. a semi-analytical In the simulation method, process, is utilized the to reflection study the lightR and absorption the transmission T are characteristicsthe sum of reflected [45]. In theFourier simulation components process, theand reflection the transmittedR and the Fourier transmission components,T respec- are the sum of reflected Fourier components and the transmitted Fourier components, respectively.tively. The Theabsorption absorption AA cancan be evaluatedevaluated with withA = A 1 −= 1R − RT .− The T. refractiveThe refractive index index of air is ofset air as is 1. set The as 1. refractive The refractive indices indices of of calcium fluoride, fluoride, zinc zinc sulfide sulfide and Ge and are obtained Ge are obtained from frompreviously previously publishe publishedd studies studies [ 46[46,47].,47].

FigureFigure 1. 1.Schematic Schematic diagram diagram of the of proposed the proposed absorber. absorber.

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The surface conductivity σs of graphene can be expressed by using the Kubo formula with The surface conductivity σs of graphene can be expressed by using the Kubo formula − with 22+−ωτ1 2eik Τ E ie2Eif () σ = B f +  s 21− ln2 cosh ln − πτ−ω k Τ 4π  1 (1)  i 2 B 2Ei"−−()ωτ − # 2e2k T i  E ie2f 2E + h ω − iτ 1 = B f + f σs 2 −1 ln 2cosh ln −1 (1) πh iτ − ω 2kBT 4πh 2Ef − h(ω − iτ ) where kB is Boltzmann’s constant, τ is the relaxation time, T is the temperature, e is the electron charge,  = h 2π is the reduced Planck’s constant and Ef is the Fermi energy [48]. where kB is Boltzmann’s constant, τ is the relaxation time, T is the temperature, e is the h = h π =−E σωε Thus,electron the charge,refractive index/2 of isgraphene the reduced can be Planck’s expressed constant as ni andg 1f is thesg() Fermi0 t energy with the [48 ]. q approximateThus, the refractive graphene index thickness of graphene tg = 0.34 can nm be and expressed vacuum as permittivityng = 1 − εi0σ. sIn/ addition,ωε0tg with T the approximate graphene thickness tg = 0.34 nm and vacuum permittivity ε . In addition, and τ are 300 K and 1 ps, respectively. 0 T and τ are 300 K and 1 ps, respectively. 3. Results and Discussion 3. Results and Discussion To provide efficient reflection with 1DPCs, the optical thickness of each film layer in To provide efficient reflection with 1DPCs, the optical thickness of each film layer 1DPCs should be equal to one quarter of the interested wavelength [49]. In addition, to in 1DPCs should be equal to one quarter of the interested wavelength [49]. In addition, obtain higher reflection with less film layer pairs, the refractive index ratio of two dielec- to obtain higher reflection with less film layer pairs, the refractive index ratio of two trics in 1DPCs should be large. CaF2 and Ge have little absorption loss in the mid-infrared dielectrics in 1DPCs should be large. CaF2 and Ge have little absorption loss in the mid- regime. Furthermore, CaF2 has low refractive indices. Therefore, to achieve high reflection infrared regime. Furthermore, CaF2 has low refractive indices. Therefore, to achieve in the mid-infrared regime, we choose CaF2 and Ge as the two primitive dielectrics of high reflection in the mid-infrared regime, we choose CaF2 and Ge as the two primitive 1DPCs, and the thicknesses of the CaF2 and Ge layers are set as tC = 0.55 μm and, tG = 0.31 μm dielectrics of 1DPCs, and the thicknesses of the CaF and Ge layers are set as t = 0.55 µm respectively. Other parameters are optimized with p = 2.02 μm, N = 10, w = 1.0 μm, Ch = 1.0 μm, and, tG = 0.31 µm respectively. Other parameters are optimized with p = 2.0 µm, N = 10, θ = 0° and t = 1.027 μm. Figure 2a shows that, at Ef = 0.2 eV, there is an absorption peak at w = 1.0 µm, h = 1.0 µm, θ = 0◦ and t = 1.027 µm. Figure2a shows that, at E = 0.2 eV, there the wavelength of 5.14803 μm with a full width half maximum (FWHM)f of 0.055 nm, is an absorption peak at the wavelength of 5.14803 µm with a full width half maximum which is much less than those with metallic metamaterials [21–25]. The parameters used (FWHM) of 0.055 nm, which is much less than those with metallic metamaterials [21–25]. inThe the parameters next parts are used the in same the next as those parts in are Fi thegure same 2a if as they those are in not Figure specified.2a if they Figure are not2b showsspecified. that Figurethe absorption2b shows peak that thecan absorption shift from peak5.14803 can to shift 5.1411 from μm 5.14803 by changing to 5.1411 Ef µfromm by 0.2 to 0.6 eV. changing Ef from 0.2 to 0.6 eV.

FigureFigure 2. 2.(a) (Absorptiona) Absorption spectrum spectrum with withEf = 0.2E feV;= 0.2(b) eV;absorption (b) absorption spectra with spectra Ef = 0.2 with eVE andf = E 0.2f = 0.6 eV eV. and Ef = 0.6 eV. To investigate the influence of the incidence angle on absorption, we plot the absorp- To investigate the inﬂuence of the incidence angle on absorption, we plot the absorption spectra with different incidence angles in Figure 3a. As seen in Figure 3a, we can find tion spectra with different incidence angles in Figure3a. As seen in Figure3a, we can ﬁnd that the ultra-narrowband resonance absorption exists in two angle regions. One is from that the ultra-narrowband resonance absorption exists in two angle regions. One is from 0° to 4°, and the other is from 5° to 8°. To further show the angle-dependent absorption 0◦ to 4◦, and the other is from 5◦ to 8◦. To further show the angle-dependent absorption characteristics, we plot the absorption spectra with small angle ranges in Figure 3b,c. From characteristics, we plot the absorption spectra with small angle ranges in Figure3b,c. From Figure 3b, we can see that the absorption peak shift in the angle range from 0° to 2° is Figure3b, we can see that the absorption peak shift in the angle range from 0 ◦ to 2◦ is smaller than 0.2 nm, and the absorption rate is still larger than 0.95 for angles up to 2°. smaller than 0.2 nm, and the absorption rate is still larger than 0.95 for angles up to 2◦. Furthermore, the absorption rate decreases drastically in the angle range from 2° to 4°. Furthermore, the absorption rate decreases drastically in the angle range from 2◦ to 4◦. Figure3c shows that the absorption peaks will shift to the shorter wavelengths as the

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Figure 3c shows that the absorption peaks will shift to the shorter wavelengths as the in- cidenceincidence angles angles increase increase in in the the angle angle range range from from 5° 5◦ toto 8°. 8◦ .In In addition, addition, we we can can see see that, inin the angle range from 55°◦ to 8°, 8◦, the the resonance resonance absorption absorption rate decreases when the incidence angle deviates from 66°.◦. From the above discussion, we can conclude that the resonanceresonance absorption only occurs in a small angle range, which means that our absorber can be used as a mid-infrared thermal source with a near-collimated lightlight beam.beam.

Figure 3. ((aa)) AbsorptionAbsorption spectra spectra with with different different incidence incidence angles; angles; (b) absorption(b) absorption spectra spectra with with incidence inci- denceangles angles from 0 from◦ to 4 ◦0°;( toc) 4°; absorption (c) absorption spectra spectra with incidence with incidence angles angles from 5 from◦ to 8 5°◦. to 8°.

To reveal the physical mechanism of the pe perfectrfect absorption, we calculate the electro- electro-

magnetic field distributions of Hy and |Ez| within one-unit cell at the resonance absorption magnetic field distributions of H and E within one-unit cell at the resonance ab- peak of 5.14803 µm in Figure4. Fromy Figurez4a, we can find that the magnetic field is sorptionmainly localized peak of in5.14803 the Ge μ microstructurem in Figure 4. layer,From which Figure causes 4a, we strong can find magnetic that the resonance magnetic to fieldoccur. is Inmainly addition, localized the magnetic in the Ge field microstructure distribution inlayer, the ZnSwhich film causes layer strong exhibits magnetic Fabry–P éres-rot onanceresonance to occur. [50] at In the addition, absorption the peak. magnetic Furthermore, field distribution the intensity in the in ZnS the 1DPCsfilm layer from exhibits top to Fabry–Pérotbottom decrease resonance to zero; [50] thus, at the the 1DPCs absorption with 10peak. pairs Furthermore, of CaF2 and Gethe film intensity layer actin asthe a perfect1DPCs from Bragg top mirror to bottom to totally decrease reflect to the zero; incidence thus, the light. 1DPCs Figure with4b 10 shows pairs that of CaF the2 electricand Ge filmfield layer is mainly act localizedas a perfect at the Bragg top-surface mirror ofto thetotally microstructures reflect the incidence where graphene light. Figure is located. 4b Therefore,shows that due the toelectric the electromagnetic field is mainly resonance localized in at the the Ge top-surface microstructures of the andmicrostructures Fabry–Pérot whereresonance graphene inside is the located. ZnS film Therefore, layer, near-perfect due to the absorptionelectromagnetic can be resonance realized. in the Ge mi- crostructuresWe notice and that Fabry–Pérot the optical resonance path in the inside ZnS layerthe ZnS is approximately film layer, near-perfect equal to theabsorp- half- tionresonance can be wavelength.realized. To further demonstrate the Fabry–Pérot resonance effect, we optimize the ZnS film thicknesses of t = 2.15 µm and t = 3.286 µm with different high- order resonance modes. Figure5a,b show the absorption spectra with t = 2.15 µm and t = 3.286 µm, respectively. As seen in Figure5a,b, the absorption bandwidths are narrower than that in Figure2a. In addition, the bandwidth in Figure5b is narrower than that in Figure5a. The magnetic field distributions with t = 2.15 µm and t = 3.286 µm are presented in Figure5c,d, respectively. The magnetic field distributions in the ZnS film layer indicate the first-order mode and second-order mode in Figure5c,d, respectively. The results in Figure5 indicate that the bandwidths can be further narrowed by increasing the thickness of the ZnS film layer, and the related mechanism can be interpreted based on the Fabry–

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Pérot resonance effect [20]. Based on the Fabry–Pérot resonance theory, the FWHM at the resonance absorption wavelength can be expressed as [50]

λ 2 1 − R ∆λ = 0 √ , (2) 2πnZnSt 2 R √ where λ0 is the resonance wavelength, R = R1R2, and R1 and R2 are the reflections of Coatings 2021, 11, x FOR PEER REVIEWthe top layer of the ZnS film layer and the 1DPCs, respectively. Equation (2) shows5 of that 9 the FWHM is inversely proportional to the ZnS layer thickness. Thus, an absorber with narrower bandwidth can be realized by adding the thickness of the ZnS film layer.

Coatings 2021, 11, x FOR PEER REVIEW 6 of 9 FigureFigure 4. 4.FieldField distributions distributions at atthe the resonanc resonancee absorption absorption wavelength wavelength of of5.14803 5.14803 μm:µm: (a) ( amagnetic) magnetic field;ﬁeld; (b) ( belectric) electric field. ﬁeld.

We notice that the optical path in the ZnS layer is approximately equal to the half- resonance wavelength. To further demonstrate the Fabry–Pérot resonance effect, we optimize the ZnS film thicknesses of t = 2.15 μm and t = 3.286 μm with different high-order resonance modes. Figure 5a,b show the absorption spectra with t = 2.15 μm and t = 3.286 μm, respectively. As seen in Figure 5a,b, the absorption bandwidths are narrower than that in Figure 2a. In addition, the bandwidth in Figure 5b is narrower than that in Figure 5a. The magnetic field distributions with t = 2.15 μm and t = 3.286 μm are presented in Figure 5c,d, respectively. The magnetic field distributions in the ZnS film layer indicate the first-order mode and second-order mode in Figure 5c,d, respectively. The results in Figure 5 indicate that the bandwidths can be further narrowed by increasing the thickness of the ZnS film layer, and the related mechanism can be interpreted based on the Fabry–Pérot resonance effect [20]. Based on the Fabry–Pérot resonance theory, the FWHM at the resonance absorption wavelength can be expressed as [50]

λ 2 1− R Δλ= 0 π , (2) 2 ntZnS 2 R

where λ0 is the resonance wavelength, R= R12 R , and R1 and R2 are the reflections of the top layer of the ZnS film layer and the 1DPCs, respectively. Equation (2) shows that the FWHM is inversely proportional to the ZnS layer thickness. Thus, an absorber with narrower bandwidth can be realized by adding the thickness of the ZnS film layer. Figure 5. 5. AbsorptionAbsorption spectra spectra with with different different silica silica layer layer thickness: thickness: (a (a) )t t== 2.15 2.15 μµmm and and ( (bb)) tt == 3.286 3.286 μµm.m. Magnetic field ﬁeld distributions: ( c)) t = 2.15 2.15 μµmm and and ( (dd)) tt = 3.286 3.286 μµm.m.

To investigate the influence inﬂuence of the pair layers ( N)) on on the the transmission transmission and and absorption, absorption, we have calculatedcalculated thethe spectraspectra of of transmission transmission and and absorption absorption with with different different values values of ofN inN inFigure Figure6. As6. As seen seen in Figurein Figure6a, the6a, the transmission transmission decreases decreases to zero to zero as asN increasesN increases from from 6 to 6 to 10. In addition, the absorption rate increases to 100% as N increases to 10 in Figure 6b, and it maintains a constant value of 100% when N is larger than 10. To reduce computation costs, we set N as 10, which indicates that the 1DPCs can act as a perfect Bragg mirror to provide efficient reflection.

Figure 6. (a) Transmission spectra with different N; (b) absorption spectra with different N.

Next, we calculate the absorption spectra with the different geometric parameters of w, h and t in Figure 7. As seen in Figure 7a, the absorption rate of the absorber will decrease as w deviates from 1 μm, and it remains above 0.85 as w ranges from 0.994 to 1.006 μm. The absorption spectra with different values of h are shown in Figure 7b. From Figure 7b, we can see that the absorption peaks shift to longer wavelengths as the grating heights increase, and the absorption rate is still larger than 0.8 in the grating height range from 0.98 and 1.02 μm. Figure 7c gives the absorption spectra with different t. As seen in Figure

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Figure 5. Absorption spectra with different silica layer thickness: (a) t = 2.15 μm and (b) t = 3.286 μm. Magnetic field distributions: (c) t = 2.15 μm and (d) t = 3.286 μm. Coatings 2021, 11, 825 6 of 9 To investigate the influence of the pair layers (N) on the transmission and absorption, we have calculated the spectra of transmission and absorption with different values of N in Figure 6. As seen in Figure 6a, the transmission decreases to zero as N increases from 6 10.to 10. In In addition, addition, the the absorption absorption rate rate increases increases to to 100% 100% as asN Nincreases increases toto 1010 inin FigureFigure6 6b,b,and itand maintains it maintains a constant a constant value value of of 100% 100% whenwhen N isis larger larger than than 10. 10. To Toreduce reduce computation computation costs, we set set NN asas 10, 10, which which indicates indicates that that the the 1DPCs 1DPCs can can act actas a as perfect a perfect Bragg Bragg mirror mirror to to provide efficient efﬁcient reflection. reﬂection.

Figure 6. ((aa)) Transmission Transmission spectra spectra with with different different N;N (b;() babsorption) absorption spectra spectra with with different different N. N.

Next, we we calculate calculate the the absorp absorptiontion spectra spectra with with the the different different geometric geometric parameters parameters of of w, h and tt inin Figure Figure 7.7. As As seen seen in in Figure Figure 7a,7a, the the absorption absorption rate rate of ofthe the absorber absorber will will decrease decrease as w deviates from from 11 μµm,m, and and it itremains remains above above 0.85 0.85 as w as rangesw ranges from from 0.994 0.994 to 1.006 to 1.006 μm. µm. The absorption spectra spectra with with different different values values of ofh areh are shown shown in Figure in Figure 7b. 7Fromb. From Figure Figure 7b, 7b, we can see that that the the absorption absorption peaks peaks shift shift to tolonger longer wavelengths wavelengths as the as thegrating grating heights heights Coatings 2021, 11, x FOR PEER REVIEW 7 of 9 increase, and the absorptionabsorption rate is stillstill largerlarger thanthan 0.80.8 inin thethe gratinggrating heightheight rangerange fromfrom 0.98 and0.98 and 1.02 1.02µm. μ Figurem. Figure7c gives 7c gives the the absorption absorption spectra spectra with with different different tt.. As As seen seen in in FigureFigure 7c , the resonance absorption peaks shift to the longer wavelengths as the t increases. This 7c, the resonance absorption peaks shift to the longer wavelengths as the t increases. This phenomenon can be explained by increasing of the optical path g. The above discussion phenomenon can be explained by increasing of the optical path g. The above discussion indicates that that our our proposed proposed structure structure still stillhas good has goodabsorption absorption characteristics characteristics if the related if the related parameters only only slightly slightly deviate deviate from from the optimized the optimized values. values.

Figure 7. 7. (a()a Absorption) Absorption spectra spectra with with different different w; (b)w absorption;(b) absorption spectra spectra with different with different h; (c) ab- h;(c) absorp- sorptiontion spectra spectra with with different differentt. t.

4. Conclusions A small-angle ultra-narrowband mid-infrared tunable absorber that uses graphene and dielectric metamaterials has been reported. The absorption bandwidth of the absorber at the graphene Fermi level of 0.2 eV is 0.055 nm, and the absorption peaks can be tuned by changing the graphene Fermi level. Furthermore, the resonance absorption only occurs in the angle range of several degrees. The simulation results also show that the bandwidth can be further narrowed by increasing the resonance cavity length. This absorber has potential applications as a tunable near-collimated coherent thermal source.

Author Contributions: Conceptualization, Y.-L.L.; methodology, H.W.; validation, Y.Z.; formal analysis, X.C. and J.W.; investigation, Z.C. All authors have read and agreed to the published version of the manuscript. Funding: This work is supported by the National Natural Science Foundation of China (No. 51901001), the Anhui Provincial Natural Science Foundation (No. 2008085MF221 and 1908085MF198) and the Provincial Natural Science Foundation of Anhui Higher Education Institution of China (No. KJ2019A0016 and KJ2018A0175). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data is contained within the article. Conflicts of Interest: The authors declare no conflict of interest.

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4. Conclusions A small-angle ultra-narrowband mid-infrared tunable absorber that uses graphene and dielectric metamaterials has been reported. The absorption bandwidth of the absorber at the graphene Fermi level of 0.2 eV is 0.055 nm, and the absorption peaks can be tuned by changing the graphene Fermi level. Furthermore, the resonance absorption only occurs in the angle range of several degrees. The simulation results also show that the bandwidth can be further narrowed by increasing the resonance cavity length. This absorber has potential applications as a tunable near-collimated coherent thermal source.

Author Contributions: Conceptualization, Y.-L.L.; methodology, H.W.; validation, Y.Z.; formal analysis, X.C. and J.W.; investigation, Z.C. All authors have read and agreed to the published version of the manuscript. Funding: This work is supported by the National Natural Science Foundation of China (No. 51901001), the Anhui Provincial Natural Science Foundation (No. 2008085MF221 and 1908085MF198) and the Provincial Natural Science Foundation of Anhui Higher Education Institution of China (No. KJ2019A0016 and KJ2018A0175). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data is contained within the article. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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