Broadband perfect absorption achieved by double-square-slotted Ti3 C2 Tx layer

Broadband perfect absorption achieved by double-square-slotted Ti3 C2 Tx layer | 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 Broadband perfect absorption achieved by double-square-slotted Ti3 C2 Tx layer Dong Mei Liu, Sheng Wei Ji, Jiu Fu Ruan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4690367/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Jun, 2025 Read the published version in Optical and Quantum Electronics → Version 1 posted 9 You are reading this latest preprint version Abstract There are a few reports on broadband optical MAs using a whole unpatterned Ti 3 C 2 T x layer or patch-type Ti 3 C 2 T x resonators, and this paper presents a broadband optical MA using the slotted 30-nm-thick Ti 3 C 2 T x layer. The proposed MA can achieve the absorptivity over 90% in the wavelength range of 674–1021 nm. More significantly, the absorptivity beyond 98% is achieved in the wavelength range of 763–965 nm. The function of the slotted 30-nm-thick Ti 3 C 2 T x layer is demonstrated by the comparison between the proposed MA and a similarly constructed structure with the top material replaced by gold. The absorption mechanism is investigated by the distribution of electric field, in which the local surface plasmon resonance (SPR) is quantitatively identified to contribute to the enhancement of absorption. Moreover, the proposed MA is insensitive to incident angles within 60°. Furthermore, the simulated results as well as the design robustness is demonstrated by the calculated ones using the multi-reflection interference theory. metamaterial absorber broadband Ti3C2Tx slotted optical Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Metamaterial absorbers (MAs) have garnered intensive and extensive attention for more than a decade due to the outstanding and angularly stable absorption performance as well as compact structure and high design flexibility [1]. The first experimentally demonstrated MA [2] can only achieve perfect (near-unity) absorption at one frequency point and its absorption bandwidth is narrow even according to the absorption rate of 90%, which is generally used as a standard to determine whether a frequency is located in the absorption band. To achieve broadband absorption in MAs, researchers have come up with a method naturally to overcome the limitation of narrow bandwidth caused by the inherent mechanism of electromagnetic (EM) resonance. In this method, multiple resonators with adjacent resonant frequencies are used in the same layer [3–5] or different layers [6–9] to realize the overlap of two or more adjacent narrow absorption bands so that an extended absorption band is achieved. Although the above-mentioned method is effective for implementing broadband MAs, the MAs designed by this method generally suffer from complex pattern resulting from multiple resonators in the same layer or thick structure stemming from multiple resonator in different layers. To address this issue, the functional materials such as graphene [10], semiconductor materials [11], vanadium dioxide [12], water [13–17] and MoS 2 [18], have been used to develop broadband MAs. Here, it must be pointed out that the broad absorption bands of these MAs above refer to the frequency bands in which the absorption rate reaches 90%, rather than perfect absorption. Ti 3 C 2 T x [19], the first prepared member of 2D MXene family [20], has the metal-like properties due to high electronic mobility and thus is considered to support surface plasmon resonance (SPR) [21–23], which is excited at the interface between thin metal films and dielectric materials and can enhance optical absorption greatly [24–26]. For this reason, Ti 3 C 2 T x has been applied into the design of broadband optical MAs in the last two years. A four-layer-structured MA composed of PMMA layer embedded with tungsten nanosphere, Ti 3 C 2 T x layer, tungsten film and silicon dioxide substrate was reported [27] in 2022, and the MA has an average absorption of 95% in the wavelength range of 400–2500 nm. A three-layer-structured MA consisting of the top aluminum resonators, an intermediate Ti 3 C 2 T x layer and a ground aluminum layer was reported [28] in 2023, this MA can achieve the absorption rate exceeding 90% in the wavelength range of 497–833 nm. A six-layer-structured MA composed of a top gold resonator with hollow cylinder form and five layers of silicon dioxide, MXene, tungsten and MgF 2 was reported [29] in 2024 and the MA exhibits superior absorption performance that the absorptivity exceeds 99.99% over a broad wavelength range of 187–3000 nm. It is noted that Ti 3 C 2 T x in the three MAs reviewed above takes the form of a whole unpatterned layer. In addition, two three-layer-structured MAs composed of the top Ti 3 C 2 T x resonators, the intermediate silicon dioxide layer and the ground gold layer have been reported [30, 31], and they achieve perfect absorption across the wavelength range of 728–890 nm and 693–897 nm, respectively. It is worth mentioning that they both use the patch-type Ti 3 C 2 T x resonators. To the best of our knowledge, there have been no reports on MAs using slotted Ti 3 C 2 T x resonators. In this paper, a broadband MA using slotted Ti 3 C 2 T x resonators is presented, which can achieve the absorptivity beyond 90% in the wavelength range of 674–1021 nm with a simple three-layer structure. It is remarkable that the absorption rate of the presented MA exceeds 98% (very close to perfect absorption) over the wavelength range of 763–965 nm. 2. Design and structure The topology of the unit cell that constitutes the proposed MA is depicted in Fig. 1 . As can be observed, the unit cell with a simple three-layer structure is composed of a top layer of slotted Ti 3 C 2 T x , an intermediate layer of SiO 2 and a ground layer of gold. The slotted Ti 3 C 2 T x at the top layer is in the shape of double square ring. The width and the length of the outer square ring are w 1 and P , respectively, while the width and the length of the inner square ring are w 2 and l , respectively. It is noted that the period of the unit cell is also P . The middle and bottom layers are the whole unpatterned layer of SiO 2 and gold. As Fig. 1 c shows, the thicknesses of the three layers from top to bottom are t 1 , t 2 , and t 3 , respectively. In this study, SiO 2 is regarded as losses and its permittivity is 2.126. Since the role of the ground gold layer is to block the penetration of EM waves, it is enough that the thickness t 3 is greater than the skin depth of EM waves so that the EM waves cannot pass through. The thickness of the Ti 3 C 2 T x layer t 1 is determined to be 30 nm as only the EM properties of 30-nm-thick Ti 3 C 2 T x layer is available by public reports and the Ti 3 C 2 T x layer with other thickness cannot be found in terms of EM properties at present. According to Drude-Lorentz model, the permittivity of 30-nm-thick Ti 3 C 2 Tx layer is expressed as [32] $$\:\begin{array}{c}{\epsilon\:}_{Drude}={\epsilon\:}_{1}-{\left(\frac{{\omega\:}_{p}}{\omega\:}\right)}^{2}+i\left({\epsilon\:}_{2}-\frac{{\omega\:}_{p}^{2}\gamma\:}{{\omega\:}^{3}+\omega\:{\gamma\:}^{2}}\right)\#\left(1\right)\end{array}$$ $$\:\begin{array}{c}{\epsilon\:}_{Lorentz}={\epsilon\:}_{3}\left[1+\frac{{\omega\:}_{p}^{2}\left({\omega\:}_{0}^{2}-{\omega\:}^{2}\right)+i\omega\:{\omega\:}_{0}\gamma\:}{{\left({\omega\:}_{0}^{2}-{\omega\:}^{2}\right)}^{2}+{\omega\:}^{2}{\gamma\:}^{2}}\right]\#\left(2\right)\end{array}$$ where the plasma frequency ω p = 4.21×10 14 rad/s, scattering losses γ = 8.65×10 14 rad/s, Lorentz pole frequency ω 0 = 2.30×10 15 rad/s, ε 1 = 6.0, ε 2 = 3.0, ε 3 = 0.2. The relative permittivity of gold can be expressed with Drude model [14], where the plasmon frequency and scattering losses are 1.37×10 16 rad/s and 8.04×10 13 rad/s. To determine the optimized values of the structure parameters, parameter sweeping is conducted by full-wave simulation using the commercial software CST Microwave Studio. The optimal values of these parameters in Fig. 1 other than t 1 and t 3 are as follows: P = 400 nm, l = 200 nm, w 1 = 100 nm, w 2 = 100 nm, and t 2 = 100 nm. 3. Results and discussion The absorption performance of the proposed MA is obtained as follows. When EM waves hit the MA, part is reflected, a portion of them is absorbed by the MA, and part may pass through the MA. The proportion that is reflected, absorbed and transmitted are denoted as R(ω) , T(ω) and A(ω) , respectively, which are called the reflection coefficient, the transmission coefficient and the absorptivity, respectively. And the absorptivity A(ω) can be calculated as A(ω) = 1- R(ω)-T ( ω ). The reflection coefficient R(ω) and the transmission coefficient T(ω) is expressed by R(ω) =| S 11 (ω) | 2 and T(ω) =| S 21 (ω) | 2 , in which S 11 (ω) and S 21 (ω) are the scattering parameters of the MA. As noted above, the ground gold layer that is thicker than the skin depth of the incident EM waves can prevent the incident EM waves from passing through, thereby leading to a zero transmission coefficient. Therefore, the equation A(ω) = 1- R(ω)-T ( ω ) can be written as A(ω) = 1- R(ω) = 1-| S 11 (ω) | 2 . In this way, the absorptivity can be obtained only by obtaining the scattering parameter S 11 (ω) in the full-wave simulation according to the above optimized parameters. Figure 2 plots the absorption performance of the proposed MA. It can be observed that the proposed MA exhibits excellent absorption ability to the normal incident EM waves. Specifically, the absorptivity over 90% is achieved across the wide wavelength range of 674–1021 nm and the maximum absorptivity is 99.2% at the wavelength of 900 nm. More critically, the absorptivity is beyond 98% in the wavelength range of 763–965 nm. To clarify the function or the advantage of using Ti 3 C 2 T x , a structure similar to the proposed MA is constructed, except that the top layer is made of gold. And the constructed structure is illustrated in Fig. 3 . Then the absorption performance of the constructed structure is examined and compared with that of the proposed MA. As shown in Fig. 4 , in the wavelength range examined, the absorptivity of the constructed structure is much less than 20% and it is obvious that the absorption performance of the proposed MA is much better than the constructed structure shown in Fig. 3 . As described above, the only difference between the two is that the proposed MA uses Ti 3 C 2 T x at the top layer, while the material at the top layer of the constructed structure is gold. Consequently, the conclusion can be drawn that the 30-nm-thick Ti 3 C 2 T x layer contributes to the excellent absorption significantly and can effectively improve the absorption performance. In order to obtain a deep insight into the operating principle of the proposed MA, the electric field at 900 nm where the maximum absorptivity is achieved is investigated. Figure 5 plots the top view and side view of the electric field distribution. As seen in Fig. 5 a, the electric field is concentrated at the inner edge of the outer square ring and the outer edge of the inner square ring as well as the interface between Ti 3 C 2 T x layer and SiO 2 layer. The electric field at the inner edge of the outer square ring and the outer edge of the inner square ring on the top Ti 3 C 2 T x layer is easily interpreted to be caused by the resonance of Ti 3 C 2 T x , which possesses the metal-like properties. The electric filed at the interface between Ti 3 C 2 T x layer and SiO 2 layer in the top view Fig. 5 a can be understood in conjunction with that in the side view Fig. 5 b. Due to the metal-like properties of Ti 3 C 2 T x , local SPR occurs when EM waves reach the interface of Ti 3 C 2 T x layer and SiO 2 layer and thus the electric field in this region is enhanced, thereby resulting in high energy loss and high absorption to EM waves. To quantitatively determine the resonance attribute at the interface between Ti 3 C 2 T x layer and SiO 2 layer, the normalized electric field along the direction normal to the interface is examined as shown in Fig. 6 . It can be observed that as the distance from the interface increases, the electric field changes in a manner very close to exponential decay, which is consistent with the attenuation law of SPR. It can be easily asserted that the proposed MA is insensitive to polarization and polarization angles due to the rotational symmetry of 90°. Next, it is necessary to investigate the absorption performance of the proposed MA at different incident angles. After all, its desired application scenario is not only the case of normal incidence considered above. The absorption spectra of the proposed MA at different incident angles are shown in Fig. 7 . For TE mode, the absorption bandwidth decreases gradually with the increase of incident angle as depicted in Fig. 7 a. When the incident angle is less than 45°, the absorptivity remains above 98% in the wavelength range of 763–965 nm. As the incident angle continues to increase and passes 60°, the absorptivity decreases, but the overall absorptivity is still beyond 90% over the wide wavelength range of 674–1021 nm. For TM mode, the absorptivity changes little within 45° as shown in Fig. 7 b, and the stability of the absorption performance is better than that in TE mode. It can be claimed that the proposed MA has good stability of the absorption performance within 60°, which basically meets the practical application in the scenario of large-angle oblique incidence. 4. Calculation for demonstration To date, simulation results have been presented in most of the published articles on optical MAs and there are few experimental results reported limited by the lack of experiment setup. In this study, the absorption performance is calculated using the theory of multi-reflection interference to compensate the lack of the experimental results. The multi-reflection interference model of the proposed MA is plotted in Fig. 8 . In this model, the absorption of the incident EM waves in the proposed MA is interpreted or described as follows. It is noted that the proposed MA is viewed as consisting of a uniform medium and a ground gold layer in this model. When the EM waves come from the air to the surface of the proposed MA at an angle of θ 1 , part of incident waves is reflected back to the air, while the rest is refracted between the air and the upper surface of the MA and enters the MA. The reflection coefficient and the transmission coefficient are \(\:{r}_{11}exp\left(j{\theta\:}_{11}\right)\) and \(\:{t}_{12}exp\left(j{\theta\:}_{12}\right)\) , respectively. The refracted part moves on in the uniform medium until it reaches the ground gold layer, which blocks the EM waves passing through. Hence, at the interface between the ground layer and the uniform medium, only reflection occurs and the reflected waves propagate to the interface between the medium and the air, in which the reflection and refraction occurs and the reflected waves continues to the next cycle. Based on the multi-reflection interference theory, the overall reflection coefficient of the absorber is [33] $$\:r={r}_{11}{e}^{{j\theta\:}_{11}}-\frac{{t}_{21}{t}_{12}{e}^{j({\theta\:}_{21}+{\theta\:}_{12}-2\beta\:)}}{1-{r}_{21}{e}^{j({\theta\:}_{21}-2\beta\:)}}$$ 3 where \(\:\beta\:=\sqrt{\epsilon\:}kd/cos\left({\alpha\:}_{s}\right)\) , k is the free space wave number, \(\:d=t/\text{c}\text{o}\text{s}\left({\alpha\:}_{s}\right)\) is the propagation distance from top to bottom layer and \(\:{\alpha\:}_{s}=arcsin(sin\alpha\:/\sqrt{\epsilon\:})\) propagation phase. As a result, the absorptivity can be calculated as A(ω) =1-| r(ω) | 2 , which is depicted in Fig. 9 . The simulated absorptivity above is also plotted as a comparison. It can be seen that there is a good agreement between the simulated and calculated results, which demonstrates the design robustness. 5. Conclusion The previously reported broadband Ti 3 C 2 T x -based MAs generally use a whole unpatterned Ti 3 C 2 T x layer or patch-type Ti 3 C 2 T x resonators. In this paper, a broadband optical MA using the slotted 30-nm-thick Ti 3 C 2 T x layer is presented. The absorptivity beyond 90% in the wavelength range of 674–1021 nm is realized by the proposed MA. It is worth mentioning that the absorptivity exceeding 98% is achieved in the wavelength range of 763–965 nm. The function of the slotted 30-nm-thick Ti 3 C 2 T x layer is clarified by the fact that the absorption performance of a similar structure with the top material replaced by gold is far inferior to that of the proposed MA. The distribution of electric field is investigated in detail to provide a deep insight into the absorption mechanism and it is found that the broadband and effective absorption is attributed to local SPR, which occurs and is identified at the interface between Ti 3 C 2 T x layer and SiO 2 layer. Additionally, the absorption performance of the proposed MA is stable within incident angles of 60°. Finally, the multi-reflection interference theory is used to calculate the absorptivity and a good agreement between the simulated results and the calculated one demonstrates the design robustness. Declarations Funding: No funding was obtained for executing this research. Author Contribution: Dong Mei Liu: Investigation, Visualization, Resources, and Writing. Sheng Wei Ji: Data curation, Investigation, Methodology, Software, Visualization, and Validation. Jiu Fu Ruan: Software, Conceptualization, Project administration, Supervision. Conflicts of interest/Competing interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Costa, F., Monorchio, A., Manara, G.: Theory, design and perspectives of electromagnetic wave absorbers. IEEE Electromagn. Compat. Mag. 5 (2), 66-74 (2016). Landy, N.L., Sajuyigbe, S., Mock, J.J., Smith, D.R., Padilla, W.J.: Perfect metamaterial absorber. Phys. Rev. Lett. 100 (20), 207402 (2008). Bilal, R.M.H., Baqir, M.A., Choudhury, P.K., Karaaslan, M., Ali, M.M., Altintas, Q., Rahim, A.A., Unal, E., Sabah, C.: Wideband microwave absorber comprising metallic split-ring resonators surrounded with E-shaped fractal metamaterial. IEEE Access. 9 , 5670-5677 (2021). Saadeldin, A.S., Sayed, A.M., Amr, A.M., Sayed, M.O., Hameed, M.F., Obayya, S.S.A.: Broadband polarization insensitive metamaterial absorber. Opt. Quantum Electron. 55 (7), 652 (2023). Bilal, R.M.H., Baqir, M.A., Choudury, P.K., Naveed, M.A., Ali, M.M., Rahim, A.A.: Ultrathin broadband metasurface-based absorber comprised of tungsten nanowires. Results Phys. 19 , 103471 (2020). Liu, S., Chen, H., Cui, T.J.: A broadband terahertz absorber using multi-layer stacked bars. Appl. Phys. Lett. 106 (15), 151601 (2015). Wang, T., Ding, M.-D., He, H.-H., Mao, J.-B., Ruan, J.-F.: Ultra-wideband polarization- and angle-insensitive metamaterial absorber based on multilayer resistive ink. J. Electromagn. Waves Appl. 36 (2), 272-284 (2022). Ruan, J.F., Meng, Z.F., Zou, R.Z., Pan, S.M., Ji, S.W.: Ultra-wideband metamaterial absorber based on frequency selective resistive film for 5G spectrum. Microw. Opt. Technol. Lett. 65 (1), 20-27 (2023). Rezaei, M.H., Vatandoust, Y., Afshari-Bavil, M., Liu, D.: Ultra-broadband, polarization-independent and wide-angle metamaterial absorber based on fabrication-friendly Ti and TiO 2 resonators. Opt. Quantum Electron. 56 (3), 400 (2024). Patel, S.K., Charola, S., Jani, C., Ladumor M., Parmar, J., Guo, T.: Graphene-based highly efficient and broadband solar absorber. Opt. Mater. 96 , 109330 (2019). Meng, Q., Zhang, Y., Zhong, Z., Zhang, B.: Optically tuneable broadband terahertz metamaterials using photosensitive semiconductor material. J. Modern Opt. 65 (18), 2086-2092 (2018). Zhang, H., Ling, F., Zhang, B.: Broadband tunable terahertz metamaterial absorber based on vanadium dioxide and Fabry-Perot cavity. Opt. Mater. 112 , 110803 (2021). Yoo, Y.J., Ju, S., Park, S.Y., Kim, Y.J., Bong, J., Lim, T., Kim, K.W., Rhee, J.Y., Lee, Y.: Metamaterial absorber for electromagnetic waves in periodic water droplets. Sci. Rep. 5 , 14018 (2015). Xie, J., Quader, S., Xiao, F., He, C., Liang, X., Geng, J., Jin, R., Zhu, W., Rukhlenko, I.D.: Truly all-dielectric ultrabroadband metamaterial absorber: water-based and ground-free. IEEE Antenn. Wireless Propag. Lett. 18 (3), 536-540 (2019). Lan, F., Meng, Z.-F., Ruan, J.-F., Zou, R.-Z., Ji, S.-W.: All-dielectric water-based metamaterial absorber in terahertz domain. Opt. Mater. 121 , 111572 (2021). Gao, Z., Fan, Q., Tian, X., Xu, C., Meng, Z., Huang, S., Xiao, T., Tian, C.: An optically transparent broadband metamaterial absorber for radar-infrared bi-stealth. Opt. Mater. 112 , 110793 (2021). Bahloli, M.D., Bordbar, A., Basiri, R., Jam, S.: A tunable multi-band absorber based on graphene metasurface in terahertz band. Opt. Quantum Electron. 54 (11), 708 (2022). Wu, J.: Polarization-insensitive broadband absorption enhancement with few-layer MoS 2 film. Phys. Lett. A. 408 , 127511 (2021). Naguib, M., Kurtoglu, M., Presser, V., Lu, J., Niu, J., Heon, M., Hultman, L., Gogotsi, Y., Barsoum, M.W.: Two-dimensional nanocrystals produced by exfoliation of Ti 3 AlC 2 . Adv. Mater. 23 (37), 4248-4253 (2011). Hantanasirisakul, K., Gogotsi, Y.: Electronic and optical properites of 2D transition metal carbides and nitrides (MXenes). Adv. Mater. 30 (52), 1804779 (2018). Wood, R.W.: On a remarkable case of uneven distribution of light in a diffraction grating spectrum. London Edinburgh Dublin Philos. Mag. J. Sci. 4, 396-402 (1902). Otto, A.: Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection. Zeitschrift Phys. 216, 398-410 (1968). Kretschmann, E., Raether, H.: Radiative decay of nonradiative surface plasmons excited by light. Z. Naturforsch. 23 , 2135-2136 (1968). Anderson, M.S.: Surface enhanced infrared absorption by coupling phonon and plasma resonance. Appl. Phys. Lett. 87 (14), 144102 (2005). Hasegawa, K., Rohde, C., Deutsch, M.: Enhanced surface-plasmon resonance absorption in metal-dielectric-metal layered microspheres. Opt. Lett. 31 (8), 1136-1138 (2006). Zhong, M., Liu, S.J., Xu, B.L., Wang, J., Huang, H.Q.: Single-band high absorption and coupling between localized surface plasmons modes in a metamaterials absorber. Opt. Mater. 72 , 283-288 (2017). Jia, Y., Wu, T., Wang, G., Jiang, J., Miao, F., Gao, Y.: Visible and near-infrared broadband absorber based on Ti 3 C 2 T x MXene-Wu. Nanomaterials. 12 (16), 2753 (2022). Korkmaz, H., Hasar, U.C., Ramahi, O.M.: Thin-film MXene-based metamaterial absorber design for solar cell applications. Opt. Quantum Electron. 55 (6), 530 (2023). Ngobeh, J.M., Sorathiya, V., Alwabli, A., Malky, S.F.: Broad-spectrum infrared metamaterial absorber based on MXenes for solar cell applications. Opt. Quantum Electron. 56 (6), 530 (2024). Ruan, J.F., Tao, Z., Zhu, D.W., Meng, Z.F., Pan, S.M.: Surface plasmon resonance-enhanced broadband perfect absorption in a Ti 3 C 2 T x -based metamaterial absorber. J. Phys. D-Appl. Phys. 55 (48), 485102 (2022). Ruan, J.F., Tu, J.Y., Wang, D.L., Tao, Z., Yuan, Y., Ji, S.W.: Perfect absorption based on Ti 3 C 2 T x surface plasmon resonance. Opt. Mater. 137 , 113604 (2023). Cui, W., Li, L., Xue, W., Xu, H., He, Z., Liu, Z.: Enhanced absorption for MXene/Au-based metamaterials. Results Phys. 23 , 104072 (2021). Chen, H.T.: Interference theory of metamaterial perfect absorbers. Opt. Express. 20 (7), 7165-7172 (2012). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 21 Jun, 2025 Read the published version in Optical and Quantum Electronics → Version 1 posted Editorial decision: Revision requested 08 Apr, 2025 Reviews received at journal 08 Apr, 2025 Reviews received at journal 22 Mar, 2025 Reviewers agreed at journal 22 Mar, 2025 Reviewers agreed at journal 18 Mar, 2025 Reviewers invited by journal 07 Mar, 2025 Editor assigned by journal 05 Jul, 2024 Submission checks completed at journal 05 Jul, 2024 First submitted to journal 05 Jul, 2024 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-4690367","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":326429718,"identity":"fd7f3830-7d26-4e3f-8e36-4edca4519b7b","order_by":0,"name":"Dong Mei Liu","email":"","orcid":"","institution":"Hefei University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Dong","middleName":"Mei","lastName":"Liu","suffix":""},{"id":326429719,"identity":"2bc54021-2ed5-4353-bffe-85984a974cd3","order_by":1,"name":"Sheng Wei Ji","email":"","orcid":"","institution":"Shandong University","correspondingAuthor":false,"prefix":"","firstName":"Sheng","middleName":"Wei","lastName":"Ji","suffix":""},{"id":326429720,"identity":"1467426a-412c-4a0d-865a-e5c8721b0128","order_by":2,"name":"Jiu Fu Ruan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYBACxuYDIMomgb0BRLMRo6UtAUSlJfAcYCZSCwMbWMthErQwt/E+k/i543wej0T+AYYPZYcZ+Gc3EHIYu5lk75nbxTwSyQyMM84dZpC4c4CAlvltbBK8bbcT9wO1MPO2HWYwkEggZAsbm+TftnOJPSAtf4nVIs3bdgCihZFILczWsm3JiT08jw0O9pxL55G4QUCLYRsb4823bXaJPeyJDx/8KLOW459BSEsDEucAEPPgVw8E8gRVjIJRMApGwSgAAK0QPeRQ35tQAAAAAElFTkSuQmCC","orcid":"","institution":"Hefei University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Jiu","middleName":"Fu","lastName":"Ruan","suffix":""}],"badges":[],"createdAt":"2024-07-05 07:23:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4690367/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4690367/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11082-025-08313-x","type":"published","date":"2025-06-21T15:57:47+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":61305480,"identity":"23d8af7f-75b2-4026-aed7-e38556c55b28","added_by":"auto","created_at":"2024-07-29 09:57:02","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":234839,"visible":true,"origin":"","legend":"\u003cp\u003eUnit cell of the proposed MA. \u003cstrong\u003ea\u003c/strong\u003e 3D view. \u003cstrong\u003eb\u003c/strong\u003e Top view. \u003cstrong\u003ec\u003c/strong\u003e Side view.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/2d3aa8f9e1dda3a202573469.png"},{"id":61304896,"identity":"904f280f-7f5d-48e2-83b5-2cf4429cf882","added_by":"auto","created_at":"2024-07-29 09:49:02","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":33586,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra of the proposed MA.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/ef569366ef0db5b02cbc6b69.png"},{"id":61305482,"identity":"947904b7-a793-453a-85fa-eb0cbdc87dca","added_by":"auto","created_at":"2024-07-29 09:57:02","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":264428,"visible":true,"origin":"","legend":"\u003cp\u003eConstructed structure that is compared with the proposed MA in terms of the absorption performance.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/1f6c5ed7a537313efb7fe3df.png"},{"id":61304894,"identity":"b3e4d836-315b-4407-bad0-b7f517edc47b","added_by":"auto","created_at":"2024-07-29 09:49:02","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":47581,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the absorption performance between the proposed MA and the constructed structure.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/ca12cd756a2695c051a15466.png"},{"id":61304900,"identity":"9dcef48f-93e8-4947-a142-86b7a318cfa7","added_by":"auto","created_at":"2024-07-29 09:49:02","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":101016,"visible":true,"origin":"","legend":"\u003cp\u003eElectric field distribution at the wavelength of 900 nm. \u003cstrong\u003ea\u003c/strong\u003e Top veiw. \u003cstrong\u003eb\u003c/strong\u003e Side view.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/72e81d9e855d01193c7d5ebf.png"},{"id":61304899,"identity":"2738987b-5b28-4fb9-8a57-8ed1a723b3c1","added_by":"auto","created_at":"2024-07-29 09:49:02","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":43624,"visible":true,"origin":"","legend":"\u003cp\u003eNormalized electric field along the direction normal to the interface between Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer and SiO\u003csub\u003e2\u003c/sub\u003e layer.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/3236f7f74a0643da03cb44d2.png"},{"id":61304892,"identity":"e7469fca-5050-421a-b96c-80eb1900db0f","added_by":"auto","created_at":"2024-07-29 09:49:02","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":44664,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra of the proposed MA under different incident angles in (\u003cstrong\u003ea\u003c/strong\u003e) TE and (\u003cstrong\u003eb\u003c/strong\u003e) TM modes.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/caaf083a802b25cfc53e9203.png"},{"id":61305481,"identity":"d1dd4c15-912c-4461-b594-8d6535fb56eb","added_by":"auto","created_at":"2024-07-29 09:57:02","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":28434,"visible":true,"origin":"","legend":"\u003cp\u003eMulti-reflection interference model of the proposed MA.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/438937a41501508800109152.png"},{"id":61305483,"identity":"a23b6f90-86ca-4193-b0c6-3037d4b9954b","added_by":"auto","created_at":"2024-07-29 09:57:02","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":72357,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the calculated and the simulated absorptivity\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/89a9230d5082ed25f21dac33.png"},{"id":85231417,"identity":"740dc51a-7eda-48d3-bf03-a1b16fe80f36","added_by":"auto","created_at":"2025-06-23 16:07:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1475303,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4690367/v1/e8f64738-7963-4f5f-a4a9-ba883e4aab12.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Broadband perfect absorption achieved by double-square-slotted Ti3 C2 Tx layer","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eMetamaterial absorbers (MAs) have garnered intensive and extensive attention for more than a decade due to the outstanding and angularly stable absorption performance as well as compact structure and high design flexibility [1]. The first experimentally demonstrated MA [2] can only achieve perfect (near-unity) absorption at one frequency point and its absorption bandwidth is narrow even according to the absorption rate of 90%, which is generally used as a standard to determine whether a frequency is located in the absorption band. To achieve broadband absorption in MAs, researchers have come up with a method naturally to overcome the limitation of narrow bandwidth caused by the inherent mechanism of electromagnetic (EM) resonance. In this method, multiple resonators with adjacent resonant frequencies are used in the same layer [3\u0026ndash;5] or different layers [6\u0026ndash;9] to realize the overlap of two or more adjacent narrow absorption bands so that an extended absorption band is achieved.\u003c/p\u003e \u003cp\u003eAlthough the above-mentioned method is effective for implementing broadband MAs, the MAs designed by this method generally suffer from complex pattern resulting from multiple resonators in the same layer or thick structure stemming from multiple resonator in different layers. To address this issue, the functional materials such as graphene [10], semiconductor materials [11], vanadium dioxide [12], water [13\u0026ndash;17] and MoS\u003csub\u003e2\u003c/sub\u003e [18], have been used to develop broadband MAs. Here, it must be pointed out that the broad absorption bands of these MAs above refer to the frequency bands in which the absorption rate reaches 90%, rather than perfect absorption.\u003c/p\u003e \u003cp\u003eTi\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e [19], the first prepared member of 2D MXene family [20], has the metal-like properties due to high electronic mobility and thus is considered to support surface plasmon resonance (SPR) [21\u0026ndash;23], which is excited at the interface between thin metal films and dielectric materials and can enhance optical absorption greatly [24\u0026ndash;26]. For this reason, Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e has been applied into the design of broadband optical MAs in the last two years. A four-layer-structured MA composed of PMMA layer embedded with tungsten nanosphere, Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer, tungsten film and silicon dioxide substrate was reported [27] in 2022, and the MA has an average absorption of 95% in the wavelength range of 400\u0026ndash;2500 nm. A three-layer-structured MA consisting of the top aluminum resonators, an intermediate Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer and a ground aluminum layer was reported [28] in 2023, this MA can achieve the absorption rate exceeding 90% in the wavelength range of 497\u0026ndash;833 nm. A six-layer-structured MA composed of a top gold resonator with hollow cylinder form and five layers of silicon dioxide, MXene, tungsten and MgF\u003csub\u003e2\u003c/sub\u003e was reported [29] in 2024 and the MA exhibits superior absorption performance that the absorptivity exceeds 99.99% over a broad wavelength range of 187\u0026ndash;3000 nm. It is noted that Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e in the three MAs reviewed above takes the form of a whole unpatterned layer. In addition, two three-layer-structured MAs composed of the top Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e resonators, the intermediate silicon dioxide layer and the ground gold layer have been reported [30, 31], and they achieve perfect absorption across the wavelength range of 728\u0026ndash;890 nm and 693\u0026ndash;897 nm, respectively. It is worth mentioning that they both use the patch-type Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e resonators. To the best of our knowledge, there have been no reports on MAs using slotted Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e resonators.\u003c/p\u003e \u003cp\u003eIn this paper, a broadband MA using slotted Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e resonators is presented, which can achieve the absorptivity beyond 90% in the wavelength range of 674\u0026ndash;1021 nm with a simple three-layer structure. It is remarkable that the absorption rate of the presented MA exceeds 98% (very close to perfect absorption) over the wavelength range of 763\u0026ndash;965 nm.\u003c/p\u003e"},{"header":"2. Design and structure","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003eThe topology of the unit cell that constitutes the proposed MA is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. As can be observed, the unit cell with a simple three-layer structure is composed of a top layer of slotted Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e, an intermediate layer of SiO\u003csub\u003e2\u003c/sub\u003e and a ground layer of gold. The slotted Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e at the top layer is in the shape of double square ring. The width and the length of the outer square ring are \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e, respectively, while the width and the length of the inner square ring are \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003el\u003c/em\u003e, respectively. It is noted that the period of the unit cell is also \u003cem\u003eP\u003c/em\u003e. The middle and bottom layers are the whole unpatterned layer of SiO\u003csub\u003e2\u003c/sub\u003e and gold. As Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec shows, the thicknesses of the three layers from top to bottom are \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, respectively. In this study, SiO\u003csub\u003e2\u003c/sub\u003e is regarded as losses and its permittivity is 2.126. Since the role of the ground gold layer is to block the penetration of EM waves, it is enough that the thickness \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e is greater than the skin depth of EM waves so that the EM waves cannot pass through. The thickness of the Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e is determined to be 30 nm as only the EM properties of 30-nm-thick Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer is available by public reports and the Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer with other thickness cannot be found in terms of EM properties at present.\u003c/p\u003e \u003cp\u003eAccording to Drude-Lorentz model, the permittivity of 30-nm-thick Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eTx layer is expressed as [32]\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{\\epsilon\\:}_{Drude}={\\epsilon\\:}_{1}-{\\left(\\frac{{\\omega\\:}_{p}}{\\omega\\:}\\right)}^{2}+i\\left({\\epsilon\\:}_{2}-\\frac{{\\omega\\:}_{p}^{2}\\gamma\\:}{{\\omega\\:}^{3}+\\omega\\:{\\gamma\\:}^{2}}\\right)\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{\\epsilon\\:}_{Lorentz}={\\epsilon\\:}_{3}\\left[1+\\frac{{\\omega\\:}_{p}^{2}\\left({\\omega\\:}_{0}^{2}-{\\omega\\:}^{2}\\right)+i\\omega\\:{\\omega\\:}_{0}\\gamma\\:}{{\\left({\\omega\\:}_{0}^{2}-{\\omega\\:}^{2}\\right)}^{2}+{\\omega\\:}^{2}{\\gamma\\:}^{2}}\\right]\\#\\left(2\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere the plasma frequency \u003cem\u003eω\u003c/em\u003e\u003csub\u003ep\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;4.21\u0026times;10\u003csup\u003e14\u003c/sup\u003e rad/s, scattering losses \u003cem\u003eγ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;8.65\u0026times;10\u003csup\u003e14\u003c/sup\u003e rad/s, Lorentz pole frequency \u003cem\u003eω\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.30\u0026times;10\u003csup\u003e15\u003c/sup\u003e rad/s, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;6.0, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.0, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.2. The relative permittivity of gold can be expressed with Drude model [14], where the plasmon frequency and scattering losses are 1.37\u0026times;10\u003csup\u003e16\u003c/sup\u003e rad/s and 8.04\u0026times;10\u003csup\u003e13\u003c/sup\u003e rad/s.\u003c/p\u003e \u003cp\u003eTo determine the optimized values of the structure parameters, parameter sweeping is conducted by full-wave simulation using the commercial software CST Microwave Studio. The optimal values of these parameters in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e other than \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e are as follows: \u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;400 nm, \u003cem\u003el\u003c/em\u003e\u0026thinsp;=\u0026thinsp;200 nm, \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;100 nm, \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;100 nm, and \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;100 nm.\u003c/p\u003e"},{"header":"3. Results and discussion","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003eThe absorption performance of the proposed MA is obtained as follows. When EM waves hit the MA, part is reflected, a portion of them is absorbed by the MA, and part may pass through the MA. The proportion that is reflected, absorbed and transmitted are denoted as \u003cem\u003eR(ω)\u003c/em\u003e, \u003cem\u003eT(ω)\u003c/em\u003e and \u003cem\u003eA(ω)\u003c/em\u003e, respectively, which are called the reflection coefficient, the transmission coefficient and the absorptivity, respectively. And the absorptivity \u003cem\u003eA(ω)\u003c/em\u003e can be calculated as \u003cem\u003eA(ω)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1-\u003cem\u003eR(ω)-T\u003c/em\u003e(\u003cem\u003eω\u003c/em\u003e). The reflection coefficient \u003cem\u003eR(ω)\u003c/em\u003e and the transmission coefficient \u003cem\u003eT(ω)\u003c/em\u003e is expressed by \u003cem\u003eR(ω)\u003c/em\u003e=|\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(ω)\u003c/em\u003e|\u003csup\u003e2\u003c/sup\u003e and \u003cem\u003eT(ω)\u003c/em\u003e=|\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e21\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(ω)\u003c/em\u003e|\u003csup\u003e2\u003c/sup\u003e, in which \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(ω)\u003c/em\u003e and \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e21\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(ω)\u003c/em\u003e are the scattering parameters of the MA. As noted above, the ground gold layer that is thicker than the skin depth of the incident EM waves can prevent the incident EM waves from passing through, thereby leading to a zero transmission coefficient. Therefore, the equation \u003cem\u003eA(ω)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1-\u003cem\u003eR(ω)-T\u003c/em\u003e(\u003cem\u003eω\u003c/em\u003e) can be written as \u003cem\u003eA(ω)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1-\u003cem\u003eR(ω)\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1-|\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(ω)\u003c/em\u003e|\u003csup\u003e2\u003c/sup\u003e. In this way, the absorptivity can be obtained only by obtaining the scattering parameter \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(ω)\u003c/em\u003e in the full-wave simulation according to the above optimized parameters. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e plots the absorption performance of the proposed MA. It can be observed that the proposed MA exhibits excellent absorption ability to the normal incident EM waves. Specifically, the absorptivity over 90% is achieved across the wide wavelength range of 674\u0026ndash;1021 nm and the maximum absorptivity is 99.2% at the wavelength of 900 nm. More critically, the absorptivity is beyond 98% in the wavelength range of 763\u0026ndash;965 nm.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo clarify the function or the advantage of using Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e, a structure similar to the proposed MA is constructed, except that the top layer is made of gold. And the constructed structure is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Then the absorption performance of the constructed structure is examined and compared with that of the proposed MA. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, in the wavelength range examined, the absorptivity of the constructed structure is much less than 20% and it is obvious that the absorption performance of the proposed MA is much better than the constructed structure shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. As described above, the only difference between the two is that the proposed MA uses Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e at the top layer, while the material at the top layer of the constructed structure is gold. Consequently, the conclusion can be drawn that the 30-nm-thick Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer contributes to the excellent absorption significantly and can effectively improve the absorption performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to obtain a deep insight into the operating principle of the proposed MA, the electric field at 900 nm where the maximum absorptivity is achieved is investigated. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e plots the top view and side view of the electric field distribution. As seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea, the electric field is concentrated at the inner edge of the outer square ring and the outer edge of the inner square ring as well as the interface between Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer and SiO\u003csub\u003e2\u003c/sub\u003e layer. The electric field at the inner edge of the outer square ring and the outer edge of the inner square ring on the top Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer is easily interpreted to be caused by the resonance of Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e, which possesses the metal-like properties. The electric filed at the interface between Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer and SiO\u003csub\u003e2\u003c/sub\u003e layer in the top view Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea can be understood in conjunction with that in the side view Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb. Due to the metal-like properties of Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e, local SPR occurs when EM waves reach the interface of Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer and SiO\u003csub\u003e2\u003c/sub\u003e layer and thus the electric field in this region is enhanced, thereby resulting in high energy loss and high absorption to EM waves. To quantitatively determine the resonance attribute at the interface between Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer and SiO\u003csub\u003e2\u003c/sub\u003e layer, the normalized electric field along the direction normal to the interface is examined as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. It can be observed that as the distance from the interface increases, the electric field changes in a manner very close to exponential decay, which is consistent with the attenuation law of SPR.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt can be easily asserted that the proposed MA is insensitive to polarization and polarization angles due to the rotational symmetry of 90\u0026deg;. Next, it is necessary to investigate the absorption performance of the proposed MA at different incident angles. After all, its desired application scenario is not only the case of normal incidence considered above. The absorption spectra of the proposed MA at different incident angles are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. For TE mode, the absorption bandwidth decreases gradually with the increase of incident angle as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea. When the incident angle is less than 45\u0026deg;, the absorptivity remains above 98% in the wavelength range of 763\u0026ndash;965 nm. As the incident angle continues to increase and passes 60\u0026deg;, the absorptivity decreases, but the overall absorptivity is still beyond 90% over the wide wavelength range of 674\u0026ndash;1021 nm. For TM mode, the absorptivity changes little within 45\u0026deg; as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb, and the stability of the absorption performance is better than that in TE mode. It can be claimed that the proposed MA has good stability of the absorption performance within 60\u0026deg;, which basically meets the practical application in the scenario of large-angle oblique incidence.\u003c/p\u003e"},{"header":"4. Calculation for demonstration","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003eTo date, simulation results have been presented in most of the published articles on optical MAs and there are few experimental results reported limited by the lack of experiment setup. In this study, the absorption performance is calculated using the theory of multi-reflection interference to compensate the lack of the experimental results. The multi-reflection interference model of the proposed MA is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. In this model, the absorption of the incident EM waves in the proposed MA is interpreted or described as follows. It is noted that the proposed MA is viewed as consisting of a uniform medium and a ground gold layer in this model. When the EM waves come from the air to the surface of the proposed MA at an angle of \u003cem\u003eθ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e, part of incident waves is reflected back to the air, while the rest is refracted between the air and the upper surface of the MA and enters the MA. The reflection coefficient and the transmission coefficient are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{r}_{11}exp\\left(j{\\theta\\:}_{11}\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{t}_{12}exp\\left(j{\\theta\\:}_{12}\\right)\\)\u003c/span\u003e\u003c/span\u003e, respectively. The refracted part moves on in the uniform medium until it reaches the ground gold layer, which blocks the EM waves passing through. Hence, at the interface between the ground layer and the uniform medium, only reflection occurs and the reflected waves propagate to the interface between the medium and the air, in which the reflection and refraction occurs and the reflected waves continues to the next cycle. Based on the multi-reflection interference theory, the overall reflection coefficient of the absorber is [33]\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:r={r}_{11}{e}^{{j\\theta\\:}_{11}}-\\frac{{t}_{21}{t}_{12}{e}^{j({\\theta\\:}_{21}+{\\theta\\:}_{12}-2\\beta\\:)}}{1-{r}_{21}{e}^{j({\\theta\\:}_{21}-2\\beta\\:)}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:=\\sqrt{\\epsilon\\:}kd/cos\\left({\\alpha\\:}_{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cem\u003ek\u003c/em\u003e is the free space wave number, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d=t/\\text{c}\\text{o}\\text{s}\\left({\\alpha\\:}_{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the propagation distance from top to bottom layer and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\alpha\\:}_{s}=arcsin(sin\\alpha\\:/\\sqrt{\\epsilon\\:})\\)\u003c/span\u003e\u003c/span\u003e propagation phase. As a result, the absorptivity can be calculated as \u003cem\u003eA(ω)\u003c/em\u003e =1-|\u003cem\u003er(ω)\u003c/em\u003e|\u003csup\u003e2\u003c/sup\u003e, which is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. The simulated absorptivity above is also plotted as a comparison. It can be seen that there is a good agreement between the simulated and calculated results, which demonstrates the design robustness.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThe previously reported broadband Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e-based MAs generally use a whole unpatterned Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer or patch-type Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e resonators. In this paper, a broadband optical MA using the slotted 30-nm-thick Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer is presented. The absorptivity beyond 90% in the wavelength range of 674\u0026ndash;1021 nm is realized by the proposed MA. It is worth mentioning that the absorptivity exceeding 98% is achieved in the wavelength range of 763\u0026ndash;965 nm. The function of the slotted 30-nm-thick Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer is clarified by the fact that the absorption performance of a similar structure with the top material replaced by gold is far inferior to that of the proposed MA. The distribution of electric field is investigated in detail to provide a deep insight into the absorption mechanism and it is found that the broadband and effective absorption is attributed to local SPR, which occurs and is identified at the interface between Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer and SiO\u003csub\u003e2\u003c/sub\u003e layer. Additionally, the absorption performance of the proposed MA is stable within incident angles of 60\u0026deg;. Finally, the multi-reflection interference theory is used to calculate the absorptivity and a good agreement between the simulated results and the calculated one demonstrates the design robustness.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e No funding was obtained for executing this research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution:\u003c/strong\u003e Dong Mei Liu: Investigation, Visualization, Resources, and Writing. Sheng Wei Ji: Data curation, Investigation, Methodology, Software, Visualization, and Validation. Jiu Fu Ruan: Software, Conceptualization, Project administration, Supervision.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests:\u0026nbsp;\u003c/strong\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCosta, F., Monorchio, A., Manara, G.: Theory, design and perspectives of electromagnetic wave absorbers. IEEE Electromagn. Compat. Mag. \u003cstrong\u003e5\u003c/strong\u003e(2), 66-74 (2016).\u003c/li\u003e\n\u003cli\u003eLandy, N.L., Sajuyigbe, S., Mock, J.J., Smith, D.R., Padilla, W.J.: Perfect metamaterial absorber. Phys. Rev. Lett. \u003cstrong\u003e100\u003c/strong\u003e(20), 207402 (2008).\u003c/li\u003e\n\u003cli\u003eBilal, R.M.H., Baqir, M.A., Choudhury, P.K., Karaaslan, M., Ali, M.M., Altintas, Q., Rahim, A.A., Unal, E., Sabah, C.: Wideband microwave absorber comprising metallic split-ring resonators surrounded with E-shaped fractal metamaterial. IEEE Access. \u003cstrong\u003e9\u003c/strong\u003e, 5670-5677 (2021).\u003c/li\u003e\n\u003cli\u003eSaadeldin, A.S., Sayed, A.M., Amr, A.M., Sayed, M.O., Hameed, M.F., Obayya, S.S.A.: Broadband polarization insensitive metamaterial absorber. Opt. Quantum Electron. \u003cstrong\u003e55\u003c/strong\u003e(7), 652 (2023).\u003c/li\u003e\n\u003cli\u003eBilal, R.M.H., Baqir, M.A., Choudury, P.K., Naveed, M.A., Ali, M.M., Rahim, A.A.: Ultrathin broadband metasurface-based absorber comprised of tungsten nanowires. Results Phys. \u003cstrong\u003e19\u003c/strong\u003e, 103471 (2020).\u003c/li\u003e\n\u003cli\u003eLiu, S., Chen, H., Cui, T.J.: A broadband terahertz absorber using multi-layer stacked bars. Appl. Phys. Lett. \u003cstrong\u003e106\u003c/strong\u003e(15), 151601 (2015).\u003c/li\u003e\n\u003cli\u003eWang, T., Ding, M.-D., He, H.-H., Mao, J.-B., Ruan, J.-F.: Ultra-wideband polarization- and angle-insensitive metamaterial absorber based on multilayer resistive ink. J. Electromagn. Waves Appl. \u003cstrong\u003e36\u003c/strong\u003e(2), 272-284 (2022).\u003c/li\u003e\n\u003cli\u003eRuan, J.F., Meng, Z.F., Zou, R.Z., Pan, S.M., Ji, S.W.: Ultra-wideband metamaterial absorber based on frequency selective resistive film for 5G spectrum. Microw. Opt. Technol. Lett. \u003cstrong\u003e65\u003c/strong\u003e(1), 20-27 (2023).\u003c/li\u003e\n\u003cli\u003eRezaei, M.H., Vatandoust, Y., Afshari-Bavil, M., Liu, D.: Ultra-broadband, polarization-independent and wide-angle metamaterial absorber based on fabrication-friendly Ti and TiO\u003csub\u003e2\u003c/sub\u003e resonators. Opt. Quantum Electron. \u003cstrong\u003e56\u003c/strong\u003e(3), 400 (2024).\u003c/li\u003e\n\u003cli\u003ePatel, S.K., Charola, S., Jani, C., Ladumor M., Parmar, J., Guo, T.: Graphene-based highly efficient and broadband solar absorber. Opt. Mater. \u003cstrong\u003e96\u003c/strong\u003e, 109330 (2019). \u003c/li\u003e\n\u003cli\u003eMeng, Q., Zhang, Y., Zhong, Z., Zhang, B.: Optically tuneable broadband terahertz metamaterials using photosensitive semiconductor material. J. Modern Opt. \u003cstrong\u003e65\u003c/strong\u003e(18), 2086-2092 (2018).\u003c/li\u003e\n\u003cli\u003eZhang, H., Ling, F., Zhang, B.: Broadband tunable terahertz metamaterial absorber based on vanadium dioxide and Fabry-Perot cavity. Opt. Mater. \u003cstrong\u003e112\u003c/strong\u003e, 110803 (2021). \u003c/li\u003e\n\u003cli\u003eYoo, Y.J., Ju, S., Park, S.Y., Kim, Y.J., Bong, J., Lim, T., Kim, K.W., Rhee, J.Y., Lee, Y.: Metamaterial absorber for electromagnetic waves in periodic water droplets. Sci. Rep. \u003cstrong\u003e5\u003c/strong\u003e, 14018 (2015).\u003c/li\u003e\n\u003cli\u003eXie, J., Quader, S., Xiao, F., He, C., Liang, X., Geng, J., Jin, R., Zhu, W., Rukhlenko, I.D.: Truly all-dielectric ultrabroadband metamaterial absorber: water-based and ground-free. IEEE Antenn. Wireless Propag. Lett. \u003cstrong\u003e18\u003c/strong\u003e(3), 536-540 (2019).\u003c/li\u003e\n\u003cli\u003eLan, F., Meng, Z.-F., Ruan, J.-F., Zou, R.-Z., Ji, S.-W.: All-dielectric water-based metamaterial absorber in terahertz domain. Opt. Mater. \u003cstrong\u003e121\u003c/strong\u003e, 111572 (2021).\u003c/li\u003e\n\u003cli\u003eGao, Z., Fan, Q., Tian, X., Xu, C., Meng, Z., Huang, S., Xiao, T., Tian, C.: An optically transparent broadband metamaterial absorber for radar-infrared bi-stealth. Opt. Mater. \u003cstrong\u003e112\u003c/strong\u003e, 110793 (2021).\u003c/li\u003e\n\u003cli\u003eBahloli, M.D., Bordbar, A., Basiri, R., Jam, S.: A tunable multi-band absorber based on graphene metasurface in terahertz band. Opt. Quantum Electron. \u003cstrong\u003e54\u003c/strong\u003e(11), 708 (2022).\u003c/li\u003e\n\u003cli\u003eWu, J.: Polarization-insensitive broadband absorption enhancement with few-layer MoS\u003csub\u003e2\u003c/sub\u003e film. Phys. Lett. A. \u003cstrong\u003e408\u003c/strong\u003e, 127511 (2021).\u003c/li\u003e\n\u003cli\u003eNaguib, M., Kurtoglu, M., Presser, V., Lu, J., Niu, J., Heon, M., Hultman, L., Gogotsi, Y., Barsoum, M.W.: Two-dimensional nanocrystals produced by exfoliation of Ti\u003csub\u003e3\u003c/sub\u003eAlC\u003csub\u003e2\u003c/sub\u003e. Adv. Mater. \u003cstrong\u003e23\u003c/strong\u003e(37), 4248-4253 (2011).\u003c/li\u003e\n\u003cli\u003eHantanasirisakul, K., Gogotsi, Y.: Electronic and optical properites of 2D transition metal carbides and nitrides (MXenes). Adv. Mater. \u003cstrong\u003e30\u003c/strong\u003e(52), 1804779 (2018).\u003c/li\u003e\n\u003cli\u003eWood, R.W.: On a remarkable case of uneven distribution of light in a diffraction grating spectrum. London Edinburgh Dublin Philos. Mag. J. Sci. \u003cstrong\u003e4,\u003c/strong\u003e 396-402 (1902).\u003c/li\u003e\n\u003cli\u003eOtto, A.: Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection. Zeitschrift Phys. \u003cstrong\u003e216,\u003c/strong\u003e 398-410 (1968).\u003c/li\u003e\n\u003cli\u003eKretschmann, E., Raether, H.: Radiative decay of nonradiative surface plasmons excited by light. Z. Naturforsch. \u003cstrong\u003e23\u003c/strong\u003e, 2135-2136 (1968).\u003c/li\u003e\n\u003cli\u003eAnderson, M.S.: Surface enhanced infrared absorption by coupling phonon and plasma resonance. Appl. Phys. Lett. \u003cstrong\u003e87\u003c/strong\u003e(14), 144102 (2005).\u003c/li\u003e\n\u003cli\u003eHasegawa, K., Rohde, C., Deutsch, M.: Enhanced surface-plasmon resonance absorption in metal-dielectric-metal layered microspheres. Opt. Lett. \u003cstrong\u003e31\u003c/strong\u003e(8), 1136-1138 (2006).\u003c/li\u003e\n\u003cli\u003eZhong, M., Liu, S.J., Xu, B.L., Wang, J., Huang, H.Q.: Single-band high absorption and coupling between localized surface plasmons modes in a metamaterials absorber. Opt. Mater. \u003cstrong\u003e72\u003c/strong\u003e, 283-288 (2017).\u003c/li\u003e\n\u003cli\u003eJia, Y., Wu, T., Wang, G., Jiang, J., Miao, F., Gao, Y.: Visible and near-infrared broadband absorber based on Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e MXene-Wu. Nanomaterials. \u003cstrong\u003e12\u003c/strong\u003e(16), 2753 (2022).\u003c/li\u003e\n\u003cli\u003eKorkmaz, H., Hasar, U.C., Ramahi, O.M.: Thin-film MXene-based metamaterial absorber design for solar cell applications. Opt. Quantum Electron. \u003cstrong\u003e55\u003c/strong\u003e(6), 530 (2023).\u003c/li\u003e\n\u003cli\u003eNgobeh, J.M., Sorathiya, V., Alwabli, A., Malky, S.F.: Broad-spectrum infrared metamaterial absorber based on MXenes for solar cell applications. Opt. Quantum Electron. \u003cstrong\u003e56\u003c/strong\u003e(6), 530 (2024).\u003c/li\u003e\n\u003cli\u003eRuan, J.F., Tao, Z., Zhu, D.W., Meng, Z.F., Pan, S.M.: Surface plasmon resonance-enhanced broadband perfect absorption in a Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e-based metamaterial absorber. J. Phys. D-Appl. Phys. \u003cstrong\u003e55\u003c/strong\u003e(48), 485102 (2022).\u003c/li\u003e\n\u003cli\u003eRuan, J.F., Tu, J.Y., Wang, D.L., Tao, Z., Yuan, Y., Ji, S.W.: Perfect absorption based on Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e surface plasmon resonance. Opt. Mater. \u003cstrong\u003e137\u003c/strong\u003e, 113604 (2023).\u003c/li\u003e\n\u003cli\u003eCui, W., Li, L., Xue, W., Xu, H., He, Z., Liu, Z.: Enhanced absorption for MXene/Au-based metamaterials. Results Phys. \u003cstrong\u003e23\u003c/strong\u003e, 104072 (2021).\u003c/li\u003e\n\u003cli\u003eChen, H.T.: Interference theory of metamaterial perfect absorbers. Opt. Express. \u003cstrong\u003e20\u003c/strong\u003e(7), 7165-7172 (2012).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"metamaterial absorber, broadband, Ti3C2Tx, slotted, optical","lastPublishedDoi":"10.21203/rs.3.rs-4690367/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4690367/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThere are a few reports on broadband optical MAs using a whole unpatterned Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer or patch-type Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e resonators, and this paper presents a broadband optical MA using the slotted 30-nm-thick Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer. The proposed MA can achieve the absorptivity over 90% in the wavelength range of 674\u0026ndash;1021 nm. More significantly, the absorptivity beyond 98% is achieved in the wavelength range of 763\u0026ndash;965 nm. The function of the slotted 30-nm-thick Ti\u003csub\u003e3\u003c/sub\u003eC\u003csub\u003e2\u003c/sub\u003eT\u003csub\u003ex\u003c/sub\u003e layer is demonstrated by the comparison between the proposed MA and a similarly constructed structure with the top material replaced by gold. The absorption mechanism is investigated by the distribution of electric field, in which the local surface plasmon resonance (SPR) is quantitatively identified to contribute to the enhancement of absorption. Moreover, the proposed MA is insensitive to incident angles within 60\u0026deg;. Furthermore, the simulated results as well as the design robustness is demonstrated by the calculated ones using the multi-reflection interference theory.\u003c/p\u003e","manuscriptTitle":"Broadband perfect absorption achieved by double-square-slotted Ti3 C2 Tx layer","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-29 09:48:57","doi":"10.21203/rs.3.rs-4690367/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-08T14:24:26+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-08T09:55:51+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-03-22T19:21:12+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"243704989048870099080333501778582896703","date":"2025-03-22T13:54:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"132464203512485577220160844022580013919","date":"2025-03-18T12:26:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-07T05:19:02+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-05T07:49:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-05T07:27:14+00:00","index":"","fulltext":""},{"type":"submitted","content":"Optical and Quantum Electronics","date":"2024-07-05T07:19:09+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"optical-and-quantum-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"oqel","sideBox":"Learn more about [Optical and Quantum Electronics](https://www.springer.com/journal/11082)","snPcode":"11082","submissionUrl":"https://submission.nature.com/new-submission/11082/3","title":"Optical and Quantum Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f5c2be9a-e044-499b-8a37-be3a63c6c213","owner":[],"postedDate":"July 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-06-23T16:02:32+00:00","versionOfRecord":{"articleIdentity":"rs-4690367","link":"https://doi.org/10.1007/s11082-025-08313-x","journal":{"identity":"optical-and-quantum-electronics","isVorOnly":false,"title":"Optical and Quantum Electronics"},"publishedOn":"2025-06-21 15:57:47","publishedOnDateReadable":"June 21st, 2025"},"versionCreatedAt":"2024-07-29 09:48:57","video":"","vorDoi":"10.1007/s11082-025-08313-x","vorDoiUrl":"https://doi.org/10.1007/s11082-025-08313-x","workflowStages":[]},"version":"v1","identity":"rs-4690367","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4690367","identity":"rs-4690367","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}