Wideband Near-Infrared Absorber with high manufacturing tolerance utilizing MXene Metasurface for industrial thermal applications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Wideband Near-Infrared Absorber with high manufacturing tolerance utilizing MXene Metasurface for industrial thermal applications Ammar Armghan, Meshari Alsharari, Muhammad Abuzar Baqir, Xiaohu Wu, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4991208/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents a polarization-insensitive, wideband solar absorber and thermal emitter made of plus-shaped fractal MXene metasurface. The proposed structure shows a high average absorption rate and photon-to-thermal energy conversion efficiency of above 90% from 750 to 3300 nm. The result findings reveal that wideband high absorption and excellent photothermal conversion efficiency is a result of localized surface plasmon resonance (LSPR) exists within the design structure. Besides that, the proposed structure also shows incident wave angular stability over the wide angular range up to 60 0 . Moreover, the proposed structure shows high manufacturing tolerance when different parameters of unit cell design varies up to ± 10–15%. The understanding of high absorption characteristics is explored by surface electric field at various operating wavelengths. The proposed wideband absorption would be useful for energy harvesting applications, thermophotovoltaic, high power electronics devices, and infrared imaging. Absorber Fractal geometry MXene Thermal emitter Wideband Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Over the years, metamaterials (MMs) have gained the attention of researchers due to their excellent features that make them useful for several modern applications such as filtering, imaging, absorber, imaging, and sensing, etc. that operate in different frequency regions starting from the microwave to optical and beyond [ 1 – 3 ]. Absorption is one of the properties of MM-based devices called absorbers. So far, several research studies present MM-based absorbers with distinctive features such as high absorption, small size, filtering capabilities, etc., and operate in different frequency bands [ 4 – 7 ]. In this regard, researchers in this area have been working to improve the following characteristics: absorption, tuneability, and small size of metasurface unit cell, etc [ 8 – 12 ]. A simple structure of the MM-absorber comprises a stack of multilayers made of the combination of metal-dielectric-metal and a periodic pattern to achieve high absorption under the plasmonic resonance condition when light falls upon the metasurface. Typically, most MM-based absorbers designs operate for a single band [ 13 – 16 ]. The number of published works also shows the operation of MM-based absorbers in more than one operating band [ 17 – 24 ]. From a future perspective, dual-band absorbers would be in high demand for different potential applications based on the sensing operation in the chemical and biological fields. Recently, several state-of-the-art works about multi-band absorbers based on the plasmonic MMs that operate in visible, infrared, and even in the THz regions have been presented [ 25 – 31 ]. For example, the ref. [ 27 ] shows a nanostructure (Au-disks/SiO 2 /Au-film) design of the absorber and its absorption bands works by exciting the localized and surface plasmonic resonances in their desired operating bands. Similarly, another work [ 28 ] shows the MM-absorber that consists of metal-insulator-metal coupling capability to support the plasmon resonances and can be used for color printing. Authors in ref. [ 29 ] present the dual-band MM-absorber that works in the THz band. The resonance phenomena in the THz band are due to the existence of an electric and a magnetic dipole. The manufacturing perspective always demands low-cost materials when considering the design process. Within this context, some MM-based absorber designs contain noble metals such as nickel, gold, and tungsten [ 32 – 35 ]. These materials have the feature to operate in a very high-temperature environment and have a melting point of 1000°C and even more; that would show their potential for solar energy system-based applications. Recent research has shown that 2D transition metal MXene (Ti 3 C 2 T x ) consists of a combination of carbides and nitrides and has gained the great interest of the research community due to its silent features that include high tuneability and better efficiency in converting heat into light. Therefore, this material shows suitability for several modern applications [ 36 – 39 ]. Hence, MM-absorber made of MXene material can be useful in developing solar energy systems. The present research literature reveals that the study on MXene-based MM absorbers concerning plasmonics [ 40 , 41 ] is limited in both theoretical [ 42 , 43 ] and experiments [ 44 , 45 ]. Besides that, the shape of the MM-based absorbers has significance in the design process. Among numerous reported designs [ 46 – 50 ], fractal geometry structure for MM-based absorbers is considered a promising platform for attaining wideband and multiband absorption. Most recent published works have been focused on achieving high absorption characteristics in a single operating band. Therefore, it is desirable to present the study of the optical absorber with dual-band operation that can be useful for modern applications. In addition, MXene is a newly explored material for use in the manufacturing of optical devices due to its several prominent features such as high tunability, large surface area, high absorption efficiency, availability in the powdered form, etc. This study investigates the wideband MXene-based metasurface absorber and thermal emitter using etched fractal geometry resonators that operate in visible and infrared regimes of electromagnetic spectra. The unit cell design of the proposed device comprises MXene at top followed by a Ni metallic layer on a glass substrate of silicon dioxide (SiO 2 ) and nickel nanolayer of 100 nm thickness acts as a reflector to the striking light waves. The localized surface plasmon resonance (LSPR) effect and fractal structure of MXene produce absorption and, therefore, permit the light energy to keep inside the substrate, SiO 2 . Furthermore, the proposed absorber features high absorption characteristics over the wideband (750 to 3300 nm) and high photothermal conversion efficiency within the near-infrared spectra and shows high manufacturing tolerance while evaluating the parametric analysis. Besides that, the proposed absorber shows angular stability, polarization-independent nature. Therefore, this device shows potential for several practical applications such as solar cells, photovoltaic systems, thermal imaging, and energy harvesting, etc. 2. Design and Simulation Figure. 1 shows the geometry details of the proposed fractal-shaped wideband metasurface absorber (FSWMA). The top metasurface layer is etched plus shaped fractal resonators made of MXene, and has a thickness t 1 . The middle layer contains nickel ( Ni ) with thickness t N = 150 nm mounted on a silicon dioxide (SiO 2 ) substrate and has a thickness of t , and the reflected surface is made of nickel with a thickness of 100 nm. The formation of the proposed absorber unit cell comprises materials with high melting points; Ni and SiO 2 are 1453 0 C [ 51 ], 1414 0 C [ 52 ], respectively and MXene has thermal stability up to 600 0 C [ 53 ]. Moreover, Fig. 1 (a) provides the detail of different dimensions of the unit cell and their values are given: P = 300 nm, C = 160 nm, l = 250 nm b = 50 nm, x = 60 nm, d = 45 nm, and e = 25 nm. The substrate thickness is represented by t = 320 nm , and t 2 = 100 nm represents the ground layer thickness. The dimension of the proposed unit cell is p×p = 300 × 300 nm 2 . Figure. 1(b) shows the 3D view of the proposed unit cell and similarly, 3D view of the proposed structure panel is provided in Fig. 1 (c), respectively. Please note that we have used the dielectric constant value of the MXene that is reported in the reference [ 51 ]. The absorptivity of a metamaterial can be calculated from the given equation [ 48 ]. $$\:A=1-\left|{\Gamma\:}\right|-\left|T\right|$$ 1 . Where A, Γ and Τ represents the absorption, reflection, and transmission, respectively. Eq. ( 1 ) can also be defined in terms of S-parameters: $$\:A=1-{\left|{S}_{11}\right|}^{2}-{\left|{S}_{21}\right|}^{2}.$$ 2 The absorber is backed with perfect reflector; therefore, transmission is almost zero, \(\:\left|{S}_{11}\right|\) ≈ 0. Hence, Eq. ( 2 ) can be further simplified as $$\:A=1-{\left|{S}_{11}\right|}^{2}$$ 3 . Heat radiation efficiency \(\:{\eta\:}_{E}\) is defined as \(\:{\eta\:}_{E}\) = \(\:{\text{A}}_{avg}\) – [5.67 × 10 −8 × \(\:\frac{{{\epsilon\:}}_{th}({T}^{4}-\:{T}_{ambient}^{4})}{C\times\:{I}_{s}}\) ] (4) here \(\:{\text{A}}_{avg}\) , C , T, T ambient , and I s are representing aggregative absorption within the operating range, solar concentration factor, operating temperature in Kelvin, ambient temperature (273 K), and solar flux intensity, respectively. 3. Results and Discussion In this section, we discuss the relationship of wavelength-dependent absorption of the proposed absorber. Using (3), Figure 2 (a) shows the absorption results of the proposed MXene fractal-shaped absorber when considering TE/TM mode of excitation. Whereas, using (4), temperature dependent photothermal efficiency is calculated and presented in the part (b) of Figure. 2. Here, we are representing MXene, having a thickness of 40 nm described in ref. [ 54 ]. For the absorption and photothermal conversion analysis, the operating wavelength is considered from 750 to 3300 nm. It is clearly observed that the aggregative absorption rate remains above 90% in the wide spectrum of the infrared regime of the operating wavelength. The given spectra cover the near-infrared, short-infrared and some portion of the far-infrared regime of the electromagnetic spectra. Therefore, the proposed absorber is used for several applications – such as, NIR absorbers are useful for photovoltaic solar cell, photothermal therapy to kill cancer cells, infrared imaging and infrared sensors for night vision. Whereas, short-infrared absorber is useful in semiconductor industry for inspection and detection of defects, medical imaging, and security and surveillance. Moreover, photothermal conversion efficiency is calculated for different operating temperature ranging from 500 K to 1300 K within the 750-3300 nm operating window. For \(\:{\eta\:}_{avg}\) calculation, we have set the parameters as; C = 1000, T = 300 K to 700 K, T ambient = 273 K, I s = 1000 W. m -2 , and A avg is the aggregative absorption exists in the operating window. From the bar plot, it can be seen that photothermal efficiency value remain above 90% for the operating temperature of 500 K and 700 K and remains 85% at 1100 K due to high absorption characteristics of the proposed device. Hence the proposed device shows its potential for the photothermal-based applications under the high temperature environment. To better understand the absorption mechanism of the proposed FSWMA, the effective permittivity, permeability, impedance and refractive index of the absorber were analyzed using the amplitudes and phases of the S-parameters for the normal incidence of the light [ 46 ]. The impedance of the absorber is an important parameter to evaluate the absorption feature of the proposed WMA absorber and can be defined as \(\:Z=\sqrt{{\mu\:}/\epsilon\:}\) . Notably, at resonance, the impedance of the absorber matches with the free-space impedance and unity absorption is attained for the perfect matching condition. The impedance, refractive index, effective permittivity, and permeability values of the material used in the designed absorber are extracted by using [ 46 ]. $$\:Z=\:\sqrt{\frac{{\left(1+{S}_{11}\right)}^{2}-{S}_{21}^{2}}{{\left(1-{S}_{11}\right)}^{2}-{S}_{21}^{2}}}$$ 4 $$\:n=\frac{-i{ln}\left({e}^{i{k}_{0}d}\right)}{{k}_{0}d}$$ 5 where k 0 and d represent the wavenumber and thickness of the absorber, respectively. In Eq. ( 5 ), \(\:{\varvec{e}}^{\varvec{i}{\varvec{k}}_{0}\varvec{d}}=\varvec{X}\pm\:\varvec{i}\sqrt{1-{\varvec{X}}^{2}}\) where \(\:\varvec{X}=1/2{\varvec{S}}_{21}\left(1-{{\varvec{S}}_{11}}^{2}+{{\varvec{S}}_{21}}^{2}\right)\) . The remaining parameters, effective permittivity and effective permeability are calculated as $$\:{\varvec{\epsilon\:}}_{\varvec{r}}=\frac{\varvec{n}}{\varvec{Z}}$$ 6 $$\:{\varvec{\mu\:}}_{\varvec{r}}=\varvec{n}\varvec{Z}$$ 7 Figure 3 shows the extracted parameters of the proposed FSWMA. To understand the absorption mechanism, we present the analysis related to the impedance of the proposed absorber for the normal incidence of light. Figure 3 (a) show the normalized impedance of the absorber. It is noticed at 1500 nm that both the real part of the normalized impedance is unity and imaginary part of the normalized impedance is zero which corresponds to the perfect. However, the impedance fluctuates above and below the unity for the remaining operating regime, as well as the imaginary part of impendence swings above and below the unity. The unity real impedance and zero imaginary impedance allows the incoming electromagnetic waves to completely penetrate inside the substrate of the proposed FSWMA. Figure 3 (b) shows the effective refractive index of the proposed metamaterial absorber. It is observed that the real part of the refractive index remains negative from 1782 to 3300 nm. The negative index medium is used negative reflection/refraction and backward wave propagation. However, the imaginary refractive index remains positive for the entire operating wavelength, as shown by solid red line. Part c and d of Fig. 3 show real and imaginary parts of the permittivity and permeability, respectively. It is noticed that the real part of permittivity and permeability is negative from 1782 to 3330 nm which lead to the negative refraction. Here, we further discuss the angle-dependent absorption when light falls on the metasurface. Figure 5 shows the absorptivity of the proposed absorber for different polarization of the excited light. It observed that the change in polarization does not affect the absorptivity. Therefore, the proposed absorber shows polarization-independent characteristics due to the symmetric nature of the unit cell structure. As a result, the LSPR remains unaltered due to the change in the polarization of the incidence light. Therefore, the absorptivity remains the same. Figure 6 shows the absorption results for the obliquity of incidence of light. Here, we take the angle of incidence from 0 \(\:^\circ\:\) to 60 \(\:^\circ\:\) and a step size of 15 \(\:^\circ\:\) . Figure 6 (a) for the TE mode of excitation, reveals that the angle of excitation has profound effects on the absorption due to the anisotropic nature of the proposed absorber. The corresponding plot shows a blueshift in the absorption bands that exist in the visible and near-infrared regimes of the spectra with the increase in the obliquity of the incidence. Furthermore, considering the absorption band in the near-infrared regime, the increase in the absorptivity value is noticed as the obliquity of incidence increases. However, the absorption band is reduced with the increase of obliquity of incidence. The blue shift in the absorption spectra is observed. On the contrary, for TM mode, the absorptivity reduces with the increase of the incidence angle. However, the blue shift in the absorption spectra is noticed unchanged. Nanostructure fabrication and design process may reduce performance of the device. Therefore, the devices with high manufacturing tolerance are more desirable. In this section, we present the parametric analysis of the proposed device and vary the different parameters of the unit cell and reveal the performance of the device for ± 10–15% tolerance rate. Figure 7 shows the absorption by varying the parametric values of the absorber under investigation. Figure 7 (a) shows the absorptivity for the different thicknesses of the substrate of the absorber while keeping the unit cell period P = 320 nm. The absorptivity is analyzed by varying the thickness of the SiO 2 substrate from 272 to 368 nm. Please note that the absorptivity almost remains same by altering the substrate thickness as obvious in Fig. 7 (b) shows the absorption by varying the unit cell period from P = 255 to 345 nm. It is noticed that wideband high absorption of above 80% is observed for P = 180 nm from 1050 to 1800 nm. It is noticed that absorptivity is increased with the increase of the period of the unit cell, however, the absorption band is reduced. For P = 220 nm, the high absorption value such as above 80% is attained from 1000 to 1550 nm and is shown by the solid blue line. Figure 7 (c) shows the absorption for different thickness of the Ni layer in the absorbing device. It is can be observed from the figure that impact of the thickness of the Ni remains less ineffectual on the absorption. Henceforth, the device has high manufacturing tolerance. Table 1 presents the comparison summary of the proposed absorber with several state-of-the-art works while considering some performance metrics. The proposed absorber features a simple design and is low-cost compared to reported studies where gold or other expensive metals have been used. The proposed absorber performs wideband operation with significant absorption in the visible and near-infrared regions. The narrowband operation of the proposed absorber may support sensing and wideband absorption characteristics would be beneficial in solar applications. Table 1 Performance comparison of proposed absorber with reported works Geometry Material Bandwidth Absorption > 90% Angular Stability Absorption > 50% Photothermal efficiency \(\:\varvec{\eta\:}\) / T(K) Nano disks [21] W and SiO 2 295– 2500nm (2205 nm) TE (θ = 60°) TM (θ = 60°) Not discussed 1D multilayered [26] W and SiO 2 400–1750nm (1350 nm) TE (θ = 60°) TM (θ = 50°) 91.2% (T abs = 1273 K) Nano-disk [37] TiO 2 , SiO 2 and TiN 288.5 -2157.5 nm (1869 nm) TE (θ = 60°) TM (θ = 60°) 92.83% (T abs = 1273 K) 1D multilayered [55] W and SiO 2 300–2000 nm (1700 nm) --- 90.02% (T abs = 373 K) Octagonal prism array [56] W and SiO 2 373–1656 nm (1283 nm) TE (θ = 50°) TM (θ = 50°) 94.72% (T abs = 1073 K) Present Work Fractal shaped MXene, SiO 2 , Ag 436–528 nm (92 nm) 1090–1750 nm (660 nm) TE (θ = 60°) TM (θ = 50°) 92.2% at 500 K 4. Conclusion In the aforesaid discussion, we investigated a fractal absorber and thermal emitter made of MXene operating in the near-infrared, short and far-infrared regimes. The analysis results indicate a high average absorption rate of above 90% and high photothermal efficiency of 92.2% at 500 K within the operating window ranging from 750 to 3300 nm in the near-infrared region. Moreover, the device retains high manufacturing tolerance rate of ± 10–15% for the change in the different parameters of the unit cell and maintain the aggregative absorption rate above 80%. Whereas, for a better understanding of the absorption mechanism, the parametric extraction and surface electric field over the different operating wavelengths is analyzed. The analysis results show that the proposed absorber has attained polarization-independent absorption in its operating bands when the phase of incident light has been varied over the wide angular range. Besides that, the proposed absorber features excellent obliquity to incidence light for TM and TE modes. This device can be useful for the practical use in energy harvesting applications, thermal emitter-based applications, and infrared imaging, etc. Declarations Acknowledgment Not applicable. Funding Not applicable. Contributions AA, MA, and MAB conceived idea and design of the presented work. MS and KA put forward theory and worked out results. MAB and XW verified the analytical methods employed. AA and MA concluded the results with support of MAB and MS. AA, MAB, and MS wrote the manuscript with support of XW and KA. All authors deliberated the results and contributed to the final manuscript. Supplementary information There is no supplementary information related to this article. Ethical Statement Ethical approval is not applicable for this article. Conflict of Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled. References Ziolkowski RW, Engheta N (2020) Metamaterials: Two decades past and into their electromagnetics future and beyond, IEEE Trans. Antennas Propag ., vol. 68, no. 3, pp. 1232–1237, Mar Rhee JY, Kim YJ, Yi C, Hwang JS, Lee YP (2020) Recent progress in perfect absorbers by utilizing metamaterials, J. Electromagn. Waves Appl ., vol. 34, no. 10, pp. 1338–1371, Jul Patel SK, Parmar J, Katrodiya D, Nguyen TK, Holdengreber E, Dhasarathan V (2020) Broadband metamaterial-based near-infrared absorber using an array of uniformly placed gold resonators, J. Opt. Soc. Amer. B, Opt. 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Plasmonics 18(5):1865–1871 Xu M, Guo L, Zhang P, Qiu Y, Li Q, Wang J (2022) Near-perfect spectrally-selective metasurface solar absorber based on tungsten octagonal prism array. RSC Adv 12(26):16823–16834 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4991208","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":354934177,"identity":"b2137293-b62d-4f24-900f-86fca2344e4f","order_by":0,"name":"Ammar Armghan","email":"","orcid":"","institution":"Jouf University","correspondingAuthor":false,"prefix":"","firstName":"Ammar","middleName":"","lastName":"Armghan","suffix":""},{"id":354934178,"identity":"5c5583e3-b0cd-472a-9fef-e7f2cc1d3a9b","order_by":1,"name":"Meshari Alsharari","email":"","orcid":"","institution":"Jouf University","correspondingAuthor":false,"prefix":"","firstName":"Meshari","middleName":"","lastName":"Alsharari","suffix":""},{"id":354934179,"identity":"a8a363ef-0167-4e2b-9501-17590aafb0fd","order_by":2,"name":"Muhammad Abuzar Baqir","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVRIiWNgGAWjYDACCTBpw8DADEIGDAx8UEEDAlrSEFrYiNRyGEwygwiCWvhn9xh/+LnnvLzBcfaHnwsKDsuzMTAfvM3DcMcYpyV3zhgY9jy7bbjhMI+x9AyDw4ZtDGzJ1jwMz8xwOuxGjkECz4HbCQaHeRikeQxuM7Yx8JhJ8zActsGlQx6o5eCfA+eAWtgf/wZqsW9j4P+GV4vBjRzDZp4DB4BaGMxAtiQCbWEDacHpMMM7x4qZZQ4kG848zGNmzWPwP7mNmc3Yco7BM5zel7vdvPnjmwN28nznjz++zfMnzbafvfnhjTcVdwwbcPofA4Bjx+AA8RpggAwto2AUjIJRMFwBAKAvUjUxnAojAAAAAElFTkSuQmCC","orcid":"","institution":"COMSATS University Islamabad","correspondingAuthor":true,"prefix":"","firstName":"Muhammad","middleName":"Abuzar","lastName":"Baqir","suffix":""},{"id":354934180,"identity":"e63346b5-1e8f-4b1b-858f-a8eb06913707","order_by":3,"name":"Xiaohu Wu","email":"","orcid":"","institution":"Shandong Institute of Advanced Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiaohu","middleName":"","lastName":"Wu","suffix":""},{"id":354934181,"identity":"18bf0d86-7eef-407e-b4ad-1f68639ef0fe","order_by":4,"name":"Muhammad saqlain","email":"","orcid":"","institution":"COMSATS University Islamabad","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"saqlain","suffix":""},{"id":354934182,"identity":"51f27418-3d7a-4d25-bbd5-566b468b4e53","order_by":5,"name":"Khaled Aliqab","email":"","orcid":"","institution":"Jouf University","correspondingAuthor":false,"prefix":"","firstName":"Khaled","middleName":"","lastName":"Aliqab","suffix":""}],"badges":[],"createdAt":"2024-08-28 12:53:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4991208/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4991208/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":66867555,"identity":"aeb1d9f2-9f75-4c76-b3c9-6fd310731e2e","added_by":"auto","created_at":"2024-10-17 09:21:09","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":147245,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the proposed absorber (a) 2D view of the unit cell (b) 3D view of the unit cell (c) 3D panel of the absorber.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/462fa7e494432be5779e7aff.png"},{"id":66867559,"identity":"72f0f030-7fcc-4f1a-90e9-c09018c05aa7","added_by":"auto","created_at":"2024-10-17 09:21:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":32403,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra and photothermal efficiency plots of the proposed device made of MXene metasurface.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/bd7ef7674de4f2375646e354.png"},{"id":66867563,"identity":"e7c6c8de-9dbb-48a3-b7f4-eb34470987f5","added_by":"auto","created_at":"2024-10-17 09:21:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":49939,"visible":true,"origin":"","legend":"\u003cp\u003eParametric extraction of FSWMA (a) Real and imaginary part of the impedance (b) Real and imaginary part of refractive index (c) Real and imaginary part of permittivity (d) Real and Imaginary part of permeability.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/daa35075dfa24c7b026a8b46.png"},{"id":66867557,"identity":"713559d1-c696-4427-961b-6a2c15f8dcaa","added_by":"auto","created_at":"2024-10-17 09:21:10","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":275670,"visible":true,"origin":"","legend":"\u003cp\u003eSurface electric field of the proposed absorber for different operating wavelengths (a) λ= 1000 nm (b) λ= 1500 nm (c) λ= 2000 nm (d) λ= 2500 nm.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/8d519c185b27c112aca816c1.png"},{"id":66867565,"identity":"24bc19ec-d43d-4016-a1c0-c463e1d61e34","added_by":"auto","created_at":"2024-10-17 09:21:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":21458,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption of the proposed by varying the phase of the excited light.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/f5908bbf918a900df5a84fa1.png"},{"id":66867560,"identity":"7e603910-2713-4756-b699-315a4002dc4a","added_by":"auto","created_at":"2024-10-17 09:21:10","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":35950,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption of the absorber for the obliquity of incidence (a) for TE mode (b) for TM mode.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/3c0befa4558b19f5952e43e0.png"},{"id":66867569,"identity":"1e61e54a-a939-42bd-8040-f5a200d987ee","added_by":"auto","created_at":"2024-10-17 09:21:12","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":39992,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption of the proposed absorber when varying different parameters (a) substrate thickness (b) period of the unit cell and (c) thickness of Ni layer.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/5271f3d394a9ddc114d839b6.png"},{"id":66869200,"identity":"642b130e-28f8-46a4-b06b-e4f13cc2af40","added_by":"auto","created_at":"2024-10-17 09:29:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":955155,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4991208/v1/f2b2b7b8-5a82-447d-be4b-7794b9ae7268.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Wideband Near-Infrared Absorber with high manufacturing tolerance utilizing MXene Metasurface for industrial thermal applications","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOver the years, metamaterials (MMs) have gained the attention of researchers due to their excellent features that make them useful for several modern applications such as filtering, imaging, absorber, imaging, and sensing, etc. that operate in different frequency regions starting from the microwave to optical and beyond [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Absorption is one of the properties of MM-based devices called absorbers. So far, several research studies present MM-based absorbers with distinctive features such as high absorption, small size, filtering capabilities, etc., and operate in different frequency bands [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. In this regard, researchers in this area have been working to improve the following characteristics: absorption, tuneability, and small size of metasurface unit cell, etc [\u003cspan additionalcitationids=\"CR9 CR10 CR11\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. A simple structure of the MM-absorber comprises a stack of multilayers made of the combination of metal-dielectric-metal and a periodic pattern to achieve high absorption under the plasmonic resonance condition when light falls upon the metasurface. Typically, most MM-based absorbers designs operate for a single band [\u003cspan additionalcitationids=\"CR14 CR15\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The number of published works also shows the operation of MM-based absorbers in more than one operating band [\u003cspan additionalcitationids=\"CR18 CR19 CR20 CR21 CR22 CR23\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. From a future perspective, dual-band absorbers would be in high demand for different potential applications based on the sensing operation in the chemical and biological fields.\u003c/p\u003e \u003cp\u003eRecently, several state-of-the-art works about multi-band absorbers based on the plasmonic MMs that operate in visible, infrared, and even in the THz regions have been presented [\u003cspan additionalcitationids=\"CR26 CR27 CR28 CR29 CR30\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. For example, the ref. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] shows a nanostructure (Au-disks/SiO\u003csub\u003e2\u003c/sub\u003e/Au-film) design of the absorber and its absorption bands works by exciting the localized and surface plasmonic resonances in their desired operating bands. Similarly, another work [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] shows the MM-absorber that consists of metal-insulator-metal coupling capability to support the plasmon resonances and can be used for color printing. Authors in ref. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] present the dual-band MM-absorber that works in the THz band. The resonance phenomena in the THz band are due to the existence of an electric and a magnetic dipole.\u003c/p\u003e \u003cp\u003eThe manufacturing perspective always demands low-cost materials when considering the design process. Within this context, some MM-based absorber designs contain noble metals such as nickel, gold, and tungsten [\u003cspan additionalcitationids=\"CR33 CR34\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. These materials have the feature to operate in a very high-temperature environment and have a melting point of 1000\u0026deg;C and even more; that would show their potential for solar energy system-based applications. Recent research has shown that 2D transition metal MXene (Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e) consists of a combination of carbides and nitrides and has gained the great interest of the research community due to its silent features that include high tuneability and better efficiency in converting heat into light. Therefore, this material shows suitability for several modern applications [\u003cspan additionalcitationids=\"CR37 CR38\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Hence, MM-absorber made of MXene material can be useful in developing solar energy systems. The present research literature reveals that the study on MXene-based MM absorbers concerning plasmonics [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e] is limited in both theoretical [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e] and experiments [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Besides that, the shape of the MM-based absorbers has significance in the design process. Among numerous reported designs [\u003cspan additionalcitationids=\"CR47 CR48 CR49\" citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e], fractal geometry structure for MM-based absorbers is considered a promising platform for attaining wideband and multiband absorption. Most recent published works have been focused on achieving high absorption characteristics in a single operating band. Therefore, it is desirable to present the study of the optical absorber with dual-band operation that can be useful for modern applications. In addition, MXene is a newly explored material for use in the manufacturing of optical devices due to its several prominent features such as high tunability, large surface area, high absorption efficiency, availability in the powdered form, etc.\u003c/p\u003e \u003cp\u003eThis study investigates the wideband MXene-based metasurface absorber and thermal emitter using etched fractal geometry resonators that operate in visible and infrared regimes of electromagnetic spectra. The unit cell design of the proposed device comprises MXene at top followed by a Ni metallic layer on a glass substrate of silicon dioxide (SiO\u003csub\u003e2\u003c/sub\u003e) and nickel nanolayer of 100 nm thickness acts as a reflector to the striking light waves. The localized surface plasmon resonance (LSPR) effect and fractal structure of MXene produce absorption and, therefore, permit the light energy to keep inside the substrate, SiO\u003csub\u003e2\u003c/sub\u003e. Furthermore, the proposed absorber features high absorption characteristics over the wideband (750 to 3300 nm) and high photothermal conversion efficiency within the near-infrared spectra and shows high manufacturing tolerance while evaluating the parametric analysis. Besides that, the proposed absorber shows angular stability, polarization-independent nature. Therefore, this device shows potential for several practical applications such as solar cells, photovoltaic systems, thermal imaging, and energy harvesting, etc.\u003c/p\u003e"},{"header":"2. Design and Simulation","content":"\u003cp\u003eFigure. 1 shows the geometry details of the proposed fractal-shaped wideband metasurface absorber (FSWMA). The top metasurface layer is etched plus shaped fractal resonators made of MXene, and has a thickness \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e. The middle layer contains nickel (\u003cem\u003eNi\u003c/em\u003e) with thickness \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003eN\u003c/em\u003e\u003c/sub\u003e = 150 nm mounted on a silicon dioxide (SiO\u003csub\u003e2\u003c/sub\u003e) substrate and has a thickness of \u003cem\u003et\u003c/em\u003e, and the reflected surface is made of nickel with a thickness of 100 nm. The formation of the proposed absorber unit cell comprises materials with high melting points; Ni and SiO\u003csub\u003e2\u003c/sub\u003e are 1453 \u003csup\u003e0\u003c/sup\u003eC [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e], 1414 \u003csup\u003e0\u003c/sup\u003eC [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e], respectively and MXene has thermal stability up to 600 \u003csup\u003e0\u003c/sup\u003eC [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. Moreover, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) provides the detail of different dimensions of the unit cell and their values are given: \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;300 nm, \u003cem\u003eC\u003c/em\u003e\u0026thinsp;=\u0026thinsp;160 nm, \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;250 nm \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;50 nm, \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;60 nm, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;45 nm, and \u003cem\u003ee\u003c/em\u003e\u0026thinsp;=\u0026thinsp;25 nm. The substrate thickness is represented by \u003cem\u003et\u0026thinsp;=\u0026thinsp;320 nm\u003c/em\u003e, and \u003cem\u003et\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;100 nm represents the ground layer thickness. The dimension of the proposed unit cell is \u003cem\u003ep\u0026times;p\u003c/em\u003e\u0026thinsp;=\u0026thinsp;300 \u0026times; 300 nm\u003csup\u003e2\u003c/sup\u003e. Figure. 1(b) shows the 3D view of the proposed unit cell and similarly, 3D view of the proposed structure panel is provided in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (c), respectively. Please note that we have used the dielectric constant value of the MXene that is reported in the reference [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe absorptivity of a metamaterial can be calculated from the given equation [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:A=1-\\left|{\\Gamma\\:}\\right|-\\left|T\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eWhere A, Γ and Τ represents the absorption, reflection, and transmission, respectively. Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) can also be defined in terms of S-parameters:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:A=1-{\\left|{S}_{11}\\right|}^{2}-{\\left|{S}_{21}\\right|}^{2}.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe absorber is backed with perfect reflector; therefore, transmission is almost zero, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left|{S}_{11}\\right|\\)\u003c/span\u003e\u003c/span\u003e\u0026asymp; 0. Hence, Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) can be further simplified as\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:A=1-{\\left|{S}_{11}\\right|}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e.\u003c/p\u003e \u003cp\u003eHeat radiation efficiency \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\eta\\:}_{E}\\)\u003c/span\u003e\u003c/span\u003e is defined as\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\eta\\:}_{E}\\)\u003c/span\u003e \u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{A}}_{avg}\\)\u003c/span\u003e\u003c/span\u003e \u003csub\u003e\u0026ndash;\u003c/sub\u003e [5.67 \u0026times; 10\u003csup\u003e\u0026minus;8\u003c/sup\u003e \u0026times; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{{\\epsilon\\:}}_{th}({T}^{4}-\\:{T}_{ambient}^{4})}{C\\times\\:{I}_{s}}\\)\u003c/span\u003e\u003c/span\u003e] (4)\u003c/p\u003e \u003cp\u003ehere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{A}}_{avg}\\)\u003c/span\u003e\u003c/span\u003e, \u003cem\u003eC\u003c/em\u003e, \u003cem\u003eT, T\u003c/em\u003e\u003csub\u003e\u003cem\u003eambient\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e are representing aggregative absorption within the operating range, solar concentration factor, operating temperature in Kelvin, ambient temperature (273 K), and solar flux intensity, respectively.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eIn this section, we discuss the relationship of wavelength-dependent absorption of the proposed absorber. Using (3), Figure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (a) shows the absorption results of the proposed MXene fractal-shaped absorber when considering TE/TM mode of excitation. Whereas, using (4), temperature dependent photothermal efficiency is calculated and presented in the part (b) of Figure. 2. Here, we are representing MXene, having a thickness of 40 nm described in ref. [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. For the absorption and photothermal conversion analysis, the operating wavelength is considered from 750 to 3300 nm. It is clearly observed that the aggregative absorption rate remains above 90% in the wide spectrum of the infrared regime of the operating wavelength. The given spectra cover the near-infrared, short-infrared and some portion of the far-infrared regime of the electromagnetic spectra. Therefore, the proposed absorber is used for several applications \u0026ndash; such as, NIR absorbers are useful for photovoltaic solar cell, photothermal therapy to kill cancer cells, infrared imaging and infrared sensors for night vision. Whereas, short-infrared absorber is useful in semiconductor industry for inspection and detection of defects, medical imaging, and security and surveillance. Moreover, photothermal conversion efficiency is calculated for different operating temperature ranging from 500 K to 1300 K within the 750-3300 nm operating window. For \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\eta\\:}_{avg}\\)\u003c/span\u003e\u003c/span\u003e calculation, we have set the parameters as; C = 1000, T = 300 K to 700 K, T\u003csub\u003eambient\u003c/sub\u003e = 273 K, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e = 1000 \u003cem\u003eW. m\u003c/em\u003e\u003csup\u003e\u003cem\u003e-2\u003c/em\u003e\u003c/sup\u003e, and A\u003csub\u003eavg\u003c/sub\u003e is the aggregative absorption exists in the operating window. From the bar plot, it can be seen that photothermal efficiency value remain above 90% for the operating temperature of 500 K and 700 K and remains 85% at 1100 K due to high absorption characteristics of the proposed device. Hence the proposed device shows its potential for the photothermal-based applications under the high temperature environment.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo better understand the absorption mechanism of the proposed FSWMA, the effective permittivity, permeability, impedance and refractive index of the absorber were analyzed using the amplitudes and phases of the S-parameters for the normal incidence of the light [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The impedance of the absorber is an important parameter to evaluate the absorption feature of the proposed WMA absorber and can be defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Z=\\sqrt{{\\mu\\:}/\\epsilon\\:}\\)\u003c/span\u003e\u003c/span\u003e. Notably, at resonance, the impedance of the absorber matches with the free-space impedance and unity absorption is attained for the perfect matching condition. The impedance, refractive index, effective permittivity, and permeability values of the material used in the designed absorber are extracted by using [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:Z=\\:\\sqrt{\\frac{{\\left(1+{S}_{11}\\right)}^{2}-{S}_{21}^{2}}{{\\left(1-{S}_{11}\\right)}^{2}-{S}_{21}^{2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:n=\\frac{-i{ln}\\left({e}^{i{k}_{0}d}\\right)}{{k}_{0}d}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere k\u003csub\u003e0\u003c/sub\u003e and d represent the wavenumber and thickness of the absorber, respectively. In Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{e}}^{\\varvec{i}{\\varvec{k}}_{0}\\varvec{d}}=\\varvec{X}\\pm\\:\\varvec{i}\\sqrt{1-{\\varvec{X}}^{2}}\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{X}=1/2{\\varvec{S}}_{21}\\left(1-{{\\varvec{S}}_{11}}^{2}+{{\\varvec{S}}_{21}}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e. The remaining parameters, effective permittivity and effective permeability are calculated as\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{\\epsilon\\:}}_{\\varvec{r}}=\\frac{\\varvec{n}}{\\varvec{Z}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{\\mu\\:}}_{\\varvec{r}}=\\varvec{n}\\varvec{Z}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the extracted parameters of the proposed FSWMA. To understand the absorption mechanism, we present the analysis related to the impedance of the proposed absorber for the normal incidence of light. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) show the normalized impedance of the absorber. It is noticed at 1500 nm that both the real part of the normalized impedance is unity and imaginary part of the normalized impedance is zero which corresponds to the perfect. However, the impedance fluctuates above and below the unity for the remaining operating regime, as well as the imaginary part of impendence swings above and below the unity. The unity real impedance and zero imaginary impedance allows the incoming electromagnetic waves to completely penetrate inside the substrate of the proposed FSWMA. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b) shows the effective refractive index of the proposed metamaterial absorber. It is observed that the real part of the refractive index remains negative from 1782 to 3300 nm. The negative index medium is used negative reflection/refraction and backward wave propagation. However, the imaginary refractive index remains positive for the entire operating wavelength, as shown by solid red line. Part c and d of Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e show real and imaginary parts of the permittivity and permeability, respectively. It is noticed that the real part of permittivity and permeability is negative from 1782 to 3330 nm which lead to the negative refraction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eHere, we further discuss the angle-dependent absorption when light falls on the metasurface. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the absorptivity of the proposed absorber for different polarization of the excited light. It observed that the change in polarization does not affect the absorptivity. Therefore, the proposed absorber shows polarization-independent characteristics due to the symmetric nature of the unit cell structure. As a result, the LSPR remains unaltered due to the change in the polarization of the incidence light. Therefore, the absorptivity remains the same.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the absorption results for the obliquity of incidence of light. Here, we take the angle of incidence from 0\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e to 60\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e and a step size of 15\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a) for the TE mode of excitation, reveals that the angle of excitation has profound effects on the absorption due to the anisotropic nature of the proposed absorber. The corresponding plot shows a blueshift in the absorption bands that exist in the visible and near-infrared regimes of the spectra with the increase in the obliquity of the incidence. Furthermore, considering the absorption band in the near-infrared regime, the increase in the absorptivity value is noticed as the obliquity of incidence increases. However, the absorption band is reduced with the increase of obliquity of incidence. The blue shift in the absorption spectra is observed. On the contrary, for TM mode, the absorptivity reduces with the increase of the incidence angle. However, the blue shift in the absorption spectra is noticed unchanged.\u003c/p\u003e \u003cp\u003eNanostructure fabrication and design process may reduce performance of the device. Therefore, the devices with high manufacturing tolerance are more desirable. In this section, we present the parametric analysis of the proposed device and vary the different parameters of the unit cell and reveal the performance of the device for \u0026plusmn;\u0026thinsp;10\u0026ndash;15% tolerance rate. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the absorption by varying the parametric values of the absorber under investigation. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a) shows the absorptivity for the different thicknesses of the substrate of the absorber while keeping the unit cell period \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;320 nm. The absorptivity is analyzed by varying the thickness of the SiO\u003csub\u003e2\u003c/sub\u003e substrate from 272 to 368 nm. Please note that the absorptivity almost remains same by altering the substrate thickness as obvious in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(b) shows the absorption by varying the unit cell period from \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;255 to 345 nm. It is noticed that wideband high absorption of above 80% is observed for \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;180 nm from 1050 to 1800 nm. It is noticed that absorptivity is increased with the increase of the period of the unit cell, however, the absorption band is reduced. For \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;220 nm, the high absorption value such as above 80% is attained from 1000 to 1550 nm and is shown by the solid blue line. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(c) shows the absorption for different thickness of the Ni layer in the absorbing device. It is can be observed from the figure that impact of the thickness of the Ni remains less ineffectual on the absorption. Henceforth, the device has high manufacturing tolerance.\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the comparison summary of the proposed absorber with several state-of-the-art works while considering some performance metrics. The proposed absorber features a simple design and is low-cost compared to reported studies where gold or other expensive metals have been used. The proposed absorber performs wideband operation with significant absorption in the visible and near-infrared regions. The narrowband operation of the proposed absorber may support sensing and wideband absorption characteristics would be beneficial in solar applications.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePerformance comparison of proposed absorber with reported works\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeometry\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMaterial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBandwidth\u003c/p\u003e \u003cp\u003eAbsorption\u0026thinsp;\u0026gt;\u0026thinsp;90%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAngular Stability\u003c/p\u003e \u003cp\u003eAbsorption\u0026thinsp;\u0026gt;\u0026thinsp;50%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePhotothermal efficiency\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{\\eta\\:}\\)\u003c/span\u003e\u003c/span\u003e/ T(K)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNano disks [21]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eW and SiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e295\u0026ndash; 2500nm (2205 nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTE (θ\u0026thinsp;=\u0026thinsp;60\u0026deg;)\u003c/p\u003e \u003cp\u003eTM (θ\u0026thinsp;=\u0026thinsp;60\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNot discussed\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1D multilayered [26]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eW and SiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e400\u0026ndash;1750nm (1350 nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTE (θ\u0026thinsp;=\u0026thinsp;60\u0026deg;)\u003c/p\u003e \u003cp\u003eTM (θ\u0026thinsp;=\u0026thinsp;50\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e91.2% (T\u003csub\u003eabs\u003c/sub\u003e = 1273 K)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNano-disk [37]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTiO\u003csub\u003e2\u003c/sub\u003e, SiO\u003csub\u003e2\u003c/sub\u003e and TiN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e288.5 -2157.5 nm (1869 nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTE (θ\u0026thinsp;=\u0026thinsp;60\u0026deg;)\u003c/p\u003e \u003cp\u003eTM (θ\u0026thinsp;=\u0026thinsp;60\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e92.83% (T\u003csub\u003eabs\u003c/sub\u003e = 1273 K)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1D multilayered [55]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eW and SiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300\u0026ndash;2000 nm (1700 nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e90.02% (T\u003csub\u003eabs\u003c/sub\u003e = 373 K)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOctagonal prism array [56]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eW and SiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e373\u0026ndash;1656 nm (1283 nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTE (θ\u0026thinsp;=\u0026thinsp;50\u0026deg;)\u003c/p\u003e \u003cp\u003eTM (θ\u0026thinsp;=\u0026thinsp;50\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e94.72% (T\u003csub\u003eabs\u003c/sub\u003e = 1073 K)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePresent Work\u003c/p\u003e \u003cp\u003eFractal shaped\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMXene, SiO\u003csub\u003e2\u003c/sub\u003e, Ag\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e436\u0026ndash;528 nm (92 nm)\u003c/p\u003e \u003cp\u003e1090\u0026ndash;1750 nm (660 nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTE (θ\u0026thinsp;=\u0026thinsp;60\u0026deg;)\u003c/p\u003e \u003cp\u003eTM (θ\u0026thinsp;=\u0026thinsp;50\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e92.2% at 500 K\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn the aforesaid discussion, we investigated a fractal absorber and thermal emitter made of MXene operating in the near-infrared, short and far-infrared regimes. The analysis results indicate a high average absorption rate of above 90% and high photothermal efficiency of 92.2% at 500 K within the operating window ranging from 750 to 3300 nm in the near-infrared region. Moreover, the device retains high manufacturing tolerance rate of \u0026plusmn;\u0026thinsp;10\u0026ndash;15% for the change in the different parameters of the unit cell and maintain the aggregative absorption rate above 80%. Whereas, for a better understanding of the absorption mechanism, the parametric extraction and surface electric field over the different operating wavelengths is analyzed. The analysis results show that the proposed absorber has attained polarization-independent absorption in its operating bands when the phase of incident light has been varied over the wide angular range. Besides that, the proposed absorber features excellent obliquity to incidence light for TM and TE modes. This device can be useful for the practical use in energy harvesting applications, thermal emitter-based applications, and infrared imaging, etc.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAA, MA, and MAB conceived idea and design of the presented work. MS and KA put forward theory and worked out results. MAB and XW verified the analytical methods employed. AA and MA concluded the results with support of MAB and MS. AA, MAB, and MS wrote the manuscript with support of XW and KA. All authors deliberated the results and contributed to the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere is no supplementary information related to this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEthical approval is not applicable for this article.\u003c/p\u003e\n\u003cp\u003eConflict of Interest\u003c/p\u003e\n\u003cp\u003eWe declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eZiolkowski RW, Engheta N (2020) Metamaterials: Two decades past and into their electromagnetics future and beyond, \u003cem\u003eIEEE Trans. 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RSC Adv 12(26):16823\u0026ndash;16834\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"
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