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Abstract
In this study, we simulate how much solar energy a proposed planar dielectric-metal (SiO2-Ti-SiO2-Ti-SiO2-Ti-SiO2-W) structure can absorb by employing FDTD solutions. The proposed structure is ultrathin (510.1 nm). It can absorb incident light within a wavelength range of 345 to at least 2500 nm with an average absorption of 97.8% for the incident light in the 345–2500 nm band while maintaining efficient absorption for a wide range of incident light when its angle changes and being insensitive to the polarization angle of the incident light. In addition, the Particle Swarm Optimization algorithm was used to optimize the proposed planar structure, and the optimality of the 8-layer structure was investigated. In addition, we compare the proposed structure to those of others, analyze the reasons for the structure's perfect absorption, and discuss the resonance mode that occurs during the absorption process, which demonstrates the rationale behind its perfect absorption. As a result, the proposed device can efficiently and sustainably collect solar energy.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fossil fuels are the main source of energy used in the world. However, the combustion of fossil fuels releases greenhouse emissions, which will impact many aspects of human lives, including food and energy supply [1], and their mental health, creating many serious problems [2]. Moreover, greenhouse emissions have a detrimental impact on the environment. Owing to the limitations of fossil energy, renewable energy transitions are of great necessity for mitigating global climate change [3]. As a clean and renewable form of energy, solar energy has attracted widespread attention. There is an abundance of studies confirming the potential of solar energy, particularly on how to obtain and store solar energy [4].
In this study, Finite Difference Time Domain (FDTD) solutions downloaded from Lumerical website was used to design a solar absorber numerically. FDTD solutions is a professional nano photonics simulation and analysis software based on the finite time difference method. It can simulate the interaction between electromagnetic waves in the ultraviolet, visible, infrared, and even terahertz bands and complex structures with typical subwavelength dimensions. Therefore, the simulator can be used in the design, analysis, and optimization of nano optical materials and photonic devices. Since the 1980s, the FDTD method has been employed as a fundamental method for electromagnetic field numerical calculations. Many researches have designed absorbers for the solar band based on FDTD solutions. However, previous studies have several shortcomings; for example, the design process of previous absorbers is complex, and there is still room for the improvement of their absorption performance.
Ran wang et al. proposed a three-layer absorber consisting of a disk, an antireflection layer SiO2, and a thick gold substrate. It can achieve an average absorption of 95.7% in the wavelength range of 400–700 nm. However, the structure does not effectively absorb solar energy in the near infrared band [5]. In Li’s study, a tunable, polarization independent and incident insensitive broadband solar absorber was proposed that could achieve high absorption in the visible region. However, it contains noble metal Au and has a complex structure [6]. Samira Mehrabi presented a combination of two TiN metasurface resonators with a high average absorption of 94% in the 250–3000 nm wavelength range [7]. Haitham Alsaif et al. proposed an absorber consisting of a plus-shaped multilayer resonator and a SiO2 substrate with a graphene spacer. The absorber exhibits the highest absorption of 93.8% in the visible spectrum and 90% in the infrared spectrum from 700 to 2000nm [8]. Didi Song et al. designed a periodically aligned titanium (Ti) nanoarraycan absorber that reaches up to 99.84% in the broad spectrum between 200 nm and 3000 nm [9]. Mojtaba Ehsanikachosang used PSO to design a structure composed of three-layer Ti/TiO2/Ti square disks surrounded by a Ti square ring, with an average absorption of 95.5% within the wavelength range of 280–3200 nm [10]. Finally, Shobhit K. Patel et al. proposed a Te plus-shaped slotted absorber capable of 91%, 97%, and 86% average absorption in the UV, visible, and NIR regions, respectively [11]. Table 1 compares the characteristics and performance of all absorbers mentioned above.
Table 1. Comparison of related absorbers with the structure proposed in this work
Prior research has made significant contributions; for instance, we now know how to achieve perfect absorption with a wider bandwidth; previously, researchers primarily employed scanning and other methods for parameter optimization. However, the performance of absorbers that rely on scanning to adjust parameters is typically inferior to that of absorbers that employ algorithm optimization. Therefore, we can conclude that employing an optimization technique during the design process is preferable.
In this study, we used FDTD solutions and the Particle Swarm Optimization (PSO) algorithm to optimize an eight-layer solar energy absorbing structure. In doing so, an eight-layer absorber with the structure of SiO2-Ti-SiO2-Ti-SiO2-Ti-SiO2-W was obtained, which can absorb incident light within the wavelength range from 300–2500 nm. The average absorption of the structure for incident light in the wavelength range 345–2500 nm is 97.9%. The proposed structure exhibits significant potential for use in solar cells [12,13] and solar evaporation [14–16].
2. Design of the proposed absorber
The designed structure is continuous and remains the same in both X and Y dimensions. Its absorption characteristic can be conveniently adjusted by only changing its parameters in the Z direction. The structure is called a planar structure, and its main advantage is that it can be developed via electron beam evaporation without using a complex lithography or an etching process [17].
To obtain the best absorption, we have optimized the combination of several metals through a comparison of absorption. It was found that SiO2-Ti-SiO2-Ti-SiO2-Ti-SiO2-W is the best combination as it can not only achieve the most efficient absorption of the incident wave in the range of 300–2500 nm, but also achieve broadband absorption, that is, absorb the largest wavelength range of incident light.
The proposed structure contains eight layers from top to bottom. As shown in Fig. 1, the thickness of each layer is n1 = 91.9 nm, n2 = 4.9 nm, n3 = 98.3 nm, n4 = 8.5 nm, n5 = 83.5 nm, n6 = 14.5 nm, n7 = 78.5 nm, and n8 = 130 nm (tolerance for the thickness of each layer is 10%), while the 1st, 3rd, 5th, and 7th layers are SiO2, the 2nd, 4th, and 6th layers are Ti, and the 8th layer is W. No expensive metal was used in the proposed structure, and the selected materials are commonly used materials, which enables large-scale manufacturing and application. In addition, W, Ti, and SiO2 have high melting points, so the proposed structure has good thermal stability.
The simulation of the solar energy absorption effect of the proposed structure was completed using FDTD solutions. The accuracy of FDTD solutions has been proved in many studies, that is, the numerical simulation results of FDTD solutions are highly similar to the experimental results [18,19].
Generally, the formula $A(\lambda ) = 1 - R(\lambda ) - T(\lambda )$ can be used to calculate the absorption of the proposed structure, where: $A(\lambda )$ represents the absorption, $R(\lambda )$ represents the reflection of the structure, and $T(\lambda )$ indicates the transmission. Owing to the sufficient thickness of the substrate Ti, almost no incident light could pass through the absorber, and the perfect absorption condition was set in the Z direction. In addition, periodic conditions were applied to both the X and Y dimensions, thereby enabling us to simulate the infinite extension in the X and Y directions under real conditions.
In this study, the refractive indexes of W and Ti were obtained from the CRC Handbook, and the refractive index of SiO2 was set to 1.45 [20]. On setting the simulation environment and the refractive index of the material, reasonable range for each parameter were set. Overall, to obtain a better optimization, we used the PSO algorithm to optimize the parameters. According to the simulation results, as shown in Fig. 2, the absorption of the proposed structure is almost always above 95% for sunlight, which confirms its superior characteristics.
James Kennedy and Russell Eberhart developed PSO in 1995 [20] after being inspired by the law of bird predation. In PSO, the solution of each optimization problem is represented by a “particle” in the search space, referred to as the “search space”. All particles possess a quality factor determined by the optimized function (figure of merit) and indicates whether the particle parameters are optimal. Subsequently, the particles search the solution space by following the optimal particle. In most cases, PSO is initialized with a collection of random particles, and the optimal solution is found via iteration. When the maximum number of iterations is reached, the particle parameters with the highest quality factor will be output. Ref.10 provides complete explanations of the PSO algorithm [10].
In this study, 20 particles were set to iterate. Each particle contains eight parameters, that is, n1–n8, and we set an appropriate iteration range for each parameter. At the beginning of PSO, the algorithm automatically assigns random parameter values to particles before applying the parameters of this generation of particles to the absorption structure. Second, figure of merit is calculated. It can be obtained by the following formula:
In Eq. (1), M represents figure of merit, and $A(\lambda )$ and $R(\lambda )$ represent the absorption and solar radiation intensity at different incident light wavelength, respectively.
Before the end of each iteration, PSO records the parameter and figure of merit of each particle, and then adjusts the speed and direction of particle parameter change according to pbest and gbest.
From Fig. 3(b), it can be observed that when the number of iterations is small, the best figure of merit in one generation is always in a low but fast growth state. Following an iteration, the figure of merit suddenly achieved great progress because PSO found a set of suitable parameters. When the number of iterations is large, figure of merit gradually reaches its peak, which means that the number of particles and iterations were set appropriately, enabling us to successfully search for a group of excellent parameters globally. This optimization method is extremely useful and convenient to obtain the size of an absorber.
Fig. 3. (a) Flow chart of the PSO algorithm. (a) Process of the change of figure of merit with the increase of generation.
Simultaneously, Fig. 4(a) shows that as the number of iterations increases, the color of the picture gradually darkens, which means that the quality of the particles is improving with the addition of iterations. The main reason underlying the quality improvement is because the particles have been changing with their own pBest and gBest, which gradually optimizes the particle, thus realizing the optimization function. The change trend of the maximum figure of merit of particles with the number of iterations in the proposed structure optimization process is illustrated in Fig. 4(b). Evidently, the figure of merit of particles increases with the number of iterations; meanwhile, when the number of iterations is large, the rising speed of particle quality gradually slows down. Figure 4 depicts the final figure of merit and the absorption following the combination of different metals using PSO. It is clear that the combination Ti-W(SiO2-Ti-SiO2-Ti-SiO2-Ti-SiO2-W) yields the best outcome.
Fig. 4. (a) Figure of merit during the optimization process. (b) Absorption performance of different material combinations.
3. Analysis of the perfect-absorption
According to previous studies [21,22], under the condition of subwavelength, that is when the size of the absorber is smaller than the wavelength of the incident light, the free electrons in the metal will strongly interact with the incident light, which creates a good coupling between photons and the absorber, and a strong electromagnetic field will be excited around the absorber. Therefore, the cause of high absorption could be analyzed as long as we observe the electromagnetic field around the absorber.
For this absorber, there are two primary reasons for the strong coupling between the incident light, namely propagating surface plasmon resonance (PSPR) and Fano resonance [23,24]. PSPR occurs between an adjacent metal and dielectric layers. When electromagnetic waves incident on metals, the electrons in the metals will respond to the electric and magnetic field of light in the surrounding dielectric [25]. Fano resonance is produced by the combination of metal, dielectric, and metal. When the incident light is reflected by the lower metal, it will be offset by the incident light to enhance the absorption [26]. Therefore, Fano resonance provides the entire structure with a better absorption effect.
A monitor on the XOZ plane of the proposed structure was set so as to scan its electric field. Figure 5 shows that the electric field intensity above the absorber is higher, and the electric field intensity around the absorber decreases as the distance of the incident light entering the absorber increases, which is due to the effective absorption of the incident light by the absorber.
Furthermore, it can be seen that the electric field intensity around SiO2 is higher than that around Ti, while there is almost no electric field around W. This indicates that the multilayer Ti absorbs almost all the incident light. As the Z distance decreases, the electric field of the absorber decreases gradually, and the top layer of Ti contributes more to the absorption.
According to the definition of PSPR and Fano resonance, the top layer of Ti and the SiO2 above it jointly results in the generation of PSPR. In addition, a strong electric field is generated in the SiO2 with metal at the top and bottom, which is the result of Fano resonance.
When the top layer of the absorption structure is a non-metallic medium, the medium can help the metal material to couple with the incident light due to the existence of PSPR, enabling the overall structure to achieve a better absorption effect. When there is no anti reflective medium on the top, the absorption effect is often inadequate. In fact, previous studies have also proved this.
A recent case reported by Cheng et al shows us an absorber based on a four-corner star that has a layer of SiO2 on top of it. In their study, they placed the four-corner star array in different positions, such as above SiO2 and inside SiO2 to examine the absorption capability. Finally, they concluded that SiO2 can provide the best absorption when it is located above the four-corner star array [27].
Chen et al. illustrated that when there is an anti-reflection layer on top of an absorber, its absorption will be enhanced. The absorber has high absorption because the anti-reflection layer makes the incident light with shorter wavelength value better coupled with the entire structure, thereby enhancing the absorption effect [28].
According to these cases, to explore whether similar plane structures can achieve the best absorption effect, we set the number of layers of the plane structure and explored the absorption effect of the structure with PSO when the layers are 4, 6, 8, and 10.
One reason why the absorption curves change at different speeds and trends is because perfect absorption usually only occurs when the size of the absorber is subwavelength, that is, when the wavelength value of the incident light is several times that of the absorber. When the absorber size is too small, the absorber better absorbs the incident light with a smaller wavelength.
From Fig. 6, cases 1,2,3, and 4 represent the structure with 4,6,8, and 10 layers. Additionally, each case has more than one absorption peak. When the absorber has 4 and 6 layers, the absorption starts decaying rapidly when the incident light wavelength is greater than 1500 nm and 2000nm, respectively, and the absorption of these two structures attenuates at a similar rate. When the absorber has eight layers, the perfect absorption bandwidth covers the entire solar radiation band. However, when the number of layers reaches ten, the entire structure tends to absorb the incident light with larger wavelength, and when the wavelength is 1500–2000nm, the absorption curve has a significant downward trend. When the wavelength of incident light increases, the absorption increases again. However, the solar energy is primarily concentrated in the incident light with the wavelength of 400–1500 nm. When the incident light wavelength is large, the high absorption of the ten-layer absorber cannot bring better overall absorption. In addition, the average absorptivity of the ten-layer absorber is lower than that of the eight-layer absorber. Therefore, the eight-layer structure is more suitable for absorbing sunlight. Table 2 shows the thickness of each layer of four absorption structures.
Table 2. Thickness of each layer of four absorption structures with different layers(n1-top layer, n10-bottom layer). (Unit: nm)
Fig. 6. (a-d) Side view of four absorption structures. (e) Absorption curve of structure with different layers.
Knowing that the proposed structure can achieve a good absorption effect at a particular incident light wavelength range, the impedance matching principle could be used to verify it by calculating the impedance of the proposed structure using the following formula [29,30]:
Knowing the impedance of the structure, it is easy to find out whether it could have good absorption performance by using the following formula:
where Z0 is the impedance of the free space, and Zin is the impedance of the whole structure. The real portion of free space's impedance is 1, while the imaginary portion is 0. When the wavelength of the incident light is 500 nm, Fig. 7 demonstrates that the real part of the impedance is close to 1 and the imaginary part is close to 0, proving that R is close to 0. Due to the fact that the less the R, the more incident light the structure can absorb, so the impedance matching principle demonstrates that our proposed structure achieves premium absorption performance.In the FDTD solutions, infinite extensions were set in the X and Y directions to study the absorption effect of this absorption structure under actual conditions, and set full absorption in the Z direction. However, it is impossible for sunlight to be unpolarized and vertically incident on the absorber, therefore, it is essential to scan the absorption of the structure when the absorber is polarized in TM and TE mode (the polarization angle of the incident light is between 0 and 90°) respectively, and when the incident light is incident at 0–80°.
From Fig. 8. (a), it can be observed that the absorption structure can provide consistent absorption regardless of the polarization mode of the incident light entering the absorption structure. Since the structure is symmetrical, the polarization mode has minimal effect on the absorption efficiency. Therefore, it is reasonable to discover whether the proposed structure is insensitive to the change of the incident light’s angle when it is polarized at TM mode (polarization angle is 0°). From Fig. 8. (b) it is evident that the structure has a good absorption effect for incident light at various angles: when the incident angle is close to 70°, the perfect absorption band includes the band with high incident light intensity: 300–1500 nm. The solar spectrum (Fig. 2) demonstrates that the majority of solar energy is concentrated in this band so that the structure can absorb the majority of solar scattering energy despite the large incident angle. Thus, the proposed structure has a practical absorption effect.
Fig. 8. (a) Absorption at different polarization angles. (b) Absorption at different incident angles.
4. Conclusion
To summarize, FDTD solutions and PSO were used to optimize the proposed planar structure and obtained a perfect absorber that can absorb 97.8% of the incident light (wavelength range: 300–2500 nm). This study explores the feasibility of PSO design, and performs a comprehensive analysis on how to achieve perfect absorption. Accordingly, the most suitable planar structure absorber for solar energy absorption was found by changing the composition materials of the absorption structure and the number of layers of the structure. Moreover, the electric field scanning diagram of the structure is analyzed, and the reason for the perfect absorption of the structure is studied. In conclusion, compared with other absorbers, the proposed absorber has the following advantages: perfect absorption, simple structure, easy preparation, polarization and incidence angle insensitivity, not requiring precious metals, and potential for large-scale manufacturing.
Funding
Natural Science Foundation of Fujian Province (2020J01712); National Natural Science Foundation of China (62275102); Science Fund for Distinguished Young Scholars of Fujian Province (2020J06025); Science and Technology Major Project of of Fujian Province (2022HZ01130025); Innovation Fund for Young Scientists of Xiamen (2020FCX012501010105); Xiamen Marine and Fishery Development Special Fund (20CZB014HJ03); Youth Talent Support Program of Jimei University (ZR2019002).
Acknowledgements
The authors would like to thank Shiyanjia Lab (www.shiyanjia.com) for the language editing service.
Disclosures
The authors declare that there are no conflicts of interest related to this article
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. S. Skendzic, M. Zovko, I.P. Zivkovic, V. Lesic, and D. Lemic, “The impact of climate change on agricultural insect pests,” Insects 12(5), 2 (2021). [CrossRef]
2. K.L. Ebi, J. Vanos, J.W. Baldwin, J.E. Bell, D.M. Hondula, N.A. Errett, K. Hayes, C.E. Reid, S. Saha, J. Spector, and P. Berry, “Extreme weather and climate change: population health and health system implications,” in Annual Review of Public Health, Vol 42, 2021, J.E. Fielding, ed. (Annual Review, 2021), p. 293–315.
3. A.M. Levenda, I. Behrsin, and F. Disano, “Renewable energy for whom? A global systematic review of the environmental justice implications of renewable energy technologies,” Energy Research & Social Science 71, 101837 (2021. [CrossRef]
4. C. B. Tabelin, J. Dallas, S. Casanova, T. Pelech, G. Bournival, S. Saydam, and I. Canbulat, “Towards a low-carbon society: A review of lithium resource availability, challenges and innovations in mining, extraction and recycling, and future perspectives,” Miner. Eng. 163, 106743 (2021). [CrossRef]
5. R. Wang, S. Yue, Z. Zhang, Y. Hou, H. D. Zhao, S. T. Qu, M. Li, and Z. C. Zhang, “Broadband perfect absorber in the visible range based on metasurface composite structures,” Materials 15(7), 2612 (2022). [CrossRef]
6. J. Li, Z. Chen, H. Yang, Z. Yi, X. Chen, W. Yao, T. Duan, P. Wu, G. Li, and Y. Yi, “Tunable broadband solar energy absorber based on monolayer transition metal dichalcogenides materials using Au nanocubes,” Nanomaterials 10(2), 257 (2020). [CrossRef]
7. S. Mehrabi, M. H. Rezaei, and M. R. Rastegari, “High-efficient plasmonic solar absorber and thermal emitter from ultraviolet to near-infrared region,” Opt. Laser Technol. 143, 107323 (2021). [CrossRef]
8. H. Alsaif, S. K. Patel, N. B. Ali, A. Armghan, and K. Aliqab, “Numerical simulation and structure optimization of multilayer metamaterial plus-shaped solar absorber design based on graphene and SiO2 substrate for renewable energy generation,” Mathematics 11(2), 282 (2023). [CrossRef]
9. D. Song, K. Zhang, M. Qian, Y. Liu, X. Wu, and K. Yu, “Ultra-broadband perfect absorber based on titanium nanoarrays for harvesting solar energy,” Nanomaterials 13(1), 91 (2022). [CrossRef]
10. M. Ehsanikachosang, K. Karimi, M. H. Rezaei, and H. Pourmajd, “Metamaterial solar absorber based on titanium resonators for operation in the ultraviolet to near-infrared region,” J. Opt. Soc. Am. B 39(12), 3178–3186 (2022). [CrossRef]
11. S. K. Patel, J. Parmar, and V. Katkar, “Ultra-broadband, wide-angle plus-shape slotted metamaterial solar absorber design with absorption forecasting using machine learning,” Sci. Rep. 12(1), 10166 (2022). [CrossRef]
12. V. V. Akshay, S. Benny, and S. V. Bhat, “Solution-processed antimony chalcogenides based thin film solar cells: A brief overview of recent developments,” Sol. Energy 241, 728–737 (2022). [CrossRef]
13. B. Ankaiah and S. Hampannavar, “perovskite solar cells with electron and hole transport absorber layers of high-power conversion efficiency by numerical simulations design using SCAPS,” International Conference on Mobile Networks and Wireless Communications (ICMNWC) (IEEE, 2021).
14. Y. Liu, J. Zhao, S. Y. Zhang, D. Y. Li, X. J. Zhang, Q. Zhao, and B. S. Xing, “Advances and challenges of broadband solar absorbers for efficient solar steam generation,” Environ. Sci.: Nano 9(7), 2264–2296 (2022). [CrossRef]
15. P. F. Wang, X. Y. Wang, S. Y. Chen, J. H. Zhang, X. J. Mu, Y. L. Chen, Z. Q. Sun, A. Y. Wei, Y. Z. Tian, J. H. Zhou, X. X. Liang, L. Miao, and N. Saito, “Reduced Red Mud as the Solar Absorber for Solar-Driven Water Evaporation and Vapor-Electricity Generation,” ACS Appl. Mater. Interfaces 13(26), 30556–30564 (2021). [CrossRef]
16. Y. Yang, G. Y. Xu, S. F. Huang, and Y. G. Yin, “Experimental study of the solar-driven interfacial evaporation based on a novel magnetic nano solar absorber,” Appl. Therm. Eng. 217, 119170 (2022). [CrossRef]
17. A. K. Azad, W. J. M. Kort-Kamp, M. Sykora, N. R. Weisse-Bernstein, T. S. Luk, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Metasurface broadband solar absorber,” Sci. Rep. 6, 20347 (2016). [CrossRef]
18. W. J. Hou, F. Yang, Z. M. Chen, J. W. Dong, and S. J. Jiang, “Wide-angle and broadband solar absorber made using highly efficient large-area fabrication strategy,” Opt. Express 30(3), 4424–4433 (2022). [CrossRef]
19. N. Roostaei, H. Mbarak, S. A. Monfared, and S. M. Hamidi, “Plasmonic wideband and tunable absorber based on semi etalon nano structure in the visible region,” Phys. Scr. 96(3), 035805 (2021). [CrossRef]
20. J.A.D. Matthew, “CRC Handbook Of Chemistry and Physics: book review,” Nature 331(6152), 127 (1988).
21. H. Ammari, B. Fitzpatrick, E. O. Hiltunen, and S. Yu, “Subwavelength localized modes for acoustic waves in bubbly crystals with a defect,” SIAM J. Appl. Math. 78(6), 3316–3335 (2018). [CrossRef]
22. A. Sanchez-Postigo, P. Ginel-Moreno, D. Pereira-Martin, A. Hadij-ElHouati, J.M. Luque-Gonzalez, C. Perez-Armenta, J.G. Wanguemert-Perez, A. Ortega-Monux, R. Halir, J.H. Schmid, J.S. Penades, M. Nedeljkovic, W.N. Ye, G.Z. Mashanovich, P. Cheben, and I. Molina-Fernandez, “Subwavelength-engineered metamaterial devices for integrated photonics.,” in Conference on Smart Photonic and Optoelectronic Integrated Circuits at SPIE OPTO Conference (2022.)
23. Y. Liang, K. Koshelev, F. C. Zhang, H. Lin, S. R. Lin, J. Y. Wu, B. H. Jia, and Y. Kivshar, “Bound states in the continuum in anisotropic plasmonic metasurfaces,” Nano Lett. 20(9), 6351–6356 (2020). [CrossRef]
24. B. Wang, P. Yu, W. Wang, X. Zhang, H.-C. Kuo, H. Xu, and Z. M. Wang, “High-Q plasmonic resonances: fundamentals and applications,” Adv. Opt. Mater. 9(7), 2001520 (2021). [CrossRef]
25. R. J. Bell, “Boundary effects,” Nature 306(5938), 95 (1983). [CrossRef]
26. V. J. Sorger, R. F. Oulton, J. Yao, G. Bartal, and X. Zhang, “Plasmonic Fabry-Pérot nanocavity,” Nano Lett. 9(10), 3489–3493 (2009). [CrossRef]
27. Y. Cheng, M. Xiong, M. Chen, S. Deng, H. Liu, C. Teng, H. Yang, H. Deng, and L. Yuan, “Numerical study of ultra-broadband metamaterial perfect absorber based on four-corner star array,” Nanomaterials 11(9), 2172 (2021). [CrossRef]
28. Y. S. Chen, K. W. You, J. Z. Lin, J. W. Zhao, W. Z. Ma, D. Meng, Y. Y. Cheng, and J. Liu, “Design of a broadband perfect solar absorber based on a four-layer structure with a cross-shaped resonator and triangular array,” Photonics 9(8), 565 (2022). [CrossRef]
29. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005). [CrossRef]
30. Z. Szabo, G.-H. Park, R. Hedge, and E.-P. Li, “A unique extraction of metamaterial parameters based on Kramers-Kronig relationship,” IEEE Trans. Microwave Theory Tech. 58(10), 2646–2653 (2010). [CrossRef]
