## Abstract

Photonic topological transitions (PTTs) in metamaterials open up a novel approach to design a variety of high-performance optical devices and provide a flexible platform for manipulating light-matter interactions at nanoscale. Here, we present a wideband spectral-selective solar absorber based on multilayered hyperbolic metamaterial (HMM). Absorptivity of higher than 90% at normal incidence is supported over a wide wavelength range from 300 to 2215 nm, due to the topological change in the isofrequency surface (IFS). The operating bandwidth can be flexibly tailored by adjusting the thicknesses of the metal and dielectric layers. Moreover, the near-ideal absorption performance can be retained well at a wide angular range regardless of the incident light polarization. These features make the proposed design hold great promise for practical applications in energy harvesting.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

In light of the global energy crisis and the rapid deterioration of ecological environment, the utilization and development of renewable energy is urgently needed. The importance of solar energy as a clean, safe and abundant source of sustainable energy has been recognized. As one of the most commonly used methods of harvesting solar energy, solar thermal systems can directly convert solar radiation into heat energy, which can be widely applied in many industrial processes, such as steam generation, desalination and wastewater treatment [1–3]. Specifically, in such applications, the solar absorbers, as an indispensable component, have a great impact on the performance of the entire systems. In order to maximize the utilization of solar energy, a solar absorber with spectral selective absorption is essential, which means it can absorb all the solar energy efficiently while suppressing mid-infrared emission [4–6]. Since solar radiation varies with time and place, polarization- and angle-independence are also crucial for assessing the overall performance of solar absorbers. Therefore, the design of near-ideal solar selective absorbers is of fundamental significance for many practical applications, and the improvement of absorption efficiency of solar absorber will greatly promote the development of solar-thermal industry.

In 2008, Landy et al. presented a single-wavelength metamaterial perfect absorber made of two metallic split-ring resonators and a metallic cutting wire [7]. Later on, various types of ingenious designs have been proposed to tailor the optical properties of the metamaterial absorbers [8–10]. Unfortunately, these schemes suffer common disadvantage of limited bandwidth, which will reflect a great amount of incident energy. To achieve perfect absorption over a broadband, the most common strategy is to combine several different strong resonators together [11–13], but the absorption bandwidth of metamaterial absorbers cannot be broadened significantly, and these multi-sized resonators will add complexity to the nanofabrication. Besides, the slow-light waveguide constructed from a periodic array of sawtoothed anisotropic metamaterial provides another effective approaches for absorbing the electromagnetic radiation over an ultrawide band [14–16]. However, the poor selectivity of absorption spectrum and low melting point metals in HMM nanostructures impede its application potential in solar-thermal energy harvesting. Therefore, it still remains challenging to achieve a wideband spectral-selective solar absorber with simultaneous low cost, high efficiency, and fabrication simplicity.

In this paper, we propose a near-ideal solar selective absorber which exhibits near-perfect absorption covering almost the whole solar spectrum. It is realized based on photonic topological transition (PTT) in HMM nanostructure consisting of a periodic SiO$_{2}$/TiO$_{2}$/W multilayer on tungsten substrate. Both simulations and theoretical calculations show that the absorption performance is superior with absorptivity higher than 90% covering the range from 300 to 2215 nm and a near-ideal total photothermal conversion efficiency up to 91.8% at 1000 K, which indicates that most of the incident energy can be absorbed and utilized efficiently. In addition, we give a detailed theoretical description of the underlying physics and prove that the transition point of PTT can be employed to manipulate the multilayer’s absorbing characteristics by changing structural parameters of the metamaterial. Moreover, the proposed nanostructure can maintain the performance of very high and broadband absorption even when the incident angle reaches up to $70^\circ$ for TM polarization, while for TE polarization the absorption efficiency is still satisfactory when the incident angle approaches $60^\circ$. Compared with previous works, our proposed metamaterial absorber is cost-effective and spectral-selective, showing broad prospects for large-scale applications that require omnidirectional, and ultra-broadband perfect absorption, such as energy harvesting, optical modulators and thermal emitters.

## 2. Structure and model

As shown in Fig. 1(a), the proposed solar absorber is formed by periodically deposited unit cells consisting of a metal layer and two dielectric layers. The metal layer is selected as W, and the dielectric layers are made of SiO$_{2}$ and TiO$_{2}$, respectively. The total number of SiO$_{2}$/TiO$_{2}$/W pairs ($N$) is 18. For W with good thermal stability, its optical properties is taken from the experimental data [17]. The refractive indices of SiO$_{2}$ and TiO$_{2}$ are 1.46 and 2.56, respectively [18]. The geometrical parameters are initially assumed as $d_1=70$ nm, $d_2=15$ nm, $d_3=3$ nm, $P=50$ nm, and $d=200$ nm. To ensure the reliability and precision of the numerical results, the optical characteristics can be numerically investigated using the transfer matrix method (TMM) and finite-difference time-domain (FDTD) method, respectively [19]. The FDTD calculation is performed by a commercial software package (Lumerical FDTD solutions). In the simulation, periodic boundary conditions are employed in the **x** and **y** directions, and perfectly matched layers are utilized in the **z** direction. In order to balance the simulation time and accuracy, the mesh cell size along the **x**-, **y**-, and **z**-direction is set to 2.5 nm $\times$ 2.5 nm $\times$ 0.5 nm, respectively. A plane wave with a wavelength ($\lambda$) is launched onto the proposed multilayer configuration with an angle ($\theta$), the absorptivity based on the Poynting theorem can be calculated by $A(\lambda ) = 1- R(\lambda ) - T(\lambda )$, where $R(\lambda )$ and $T(\lambda )$ represent the reflectivity and transmissivity, respectively. Here, considering that an opaque W film is used as substrate, the transmissivity of the nanostructure can be ignored.

## 3. Results and analysis

Since the period of multilayer ($D$) is much smaller than the wavelength of light, such metamaterial behaves as a uniform uniaxial media with effective parameters [20]. According to the effective medium theory (EMT) [21], the effective permittivity tensor of the stacked multilayer can be described by the mixing formulae [18]

To understand the physical mechanism of absorption in our structure, we start by studying the isofrequency surface of extraordinary electromagnetic waves, which is given by [23]

**x**-,

**y**-, and

**z**-directions. In the bidimensional $\boldsymbol {k}$-space, the tangential component of wavevector ($k_x$) is conserved at the interface between air and the multilayer [24]. As shown in Fig. 3(a), the IFS at the wavelength of 1949 nm is ellipsoidal. The wavevectors of excited modes depend on the surface of the ellipsoid and its tangential components ($k_x$) can match to that of vacuum modes. Thus the modes from free space (black curve) can be efficiently coupled to the modes from metamaterial (blue curve) maximizing the incident energy absorption. In other words, since the multilayer supports radiative modes, light from free space can penetrate into the nanostructure and get absorbed, leading to high absorptivity. With the increasing wavelength, $Re(\varepsilon _{\rVert })$ turns into negative around the ENZ regime and the proposed metamaterial undergoes a PTT from an effective dielectric to an HMM. Correspondingly, the IFS turns from an ellipsoid into a hyperboloid as shown in Fig. 3(b). In this case, such as $\lambda =3075$ nm, the HMM only supports high-$\boldsymbol {k}$ modes with large tangential components of the wavevectors ($k_{rx}$), which cannot match to the low-$\boldsymbol {k}$ modes propagating in vacuum. Thus there is no coupling between the vacuum modes and the hyperbolic modes leading to a strong suppression of light absorption in the hyperbolic regime. As a result, only above the critical angle ($\theta _c$), the total internal reflection (TIR) occurs at the first TiO$_{2}$/W interface, producing an evanescent wave with little energy that can be coupled to the multilayered structure to achieve high reflection and low absorption in this regime [25]. To further verify the absorption characteristics, we study the normalized distributions of the electric field |$E$| at the above two wavelengths in Fig. 4(a). It is found that the electric field intensity at $\lambda =1949$ nm is attenuated with propagating in the SiO$_{2}$/TiO$_{2}$/W multilayered structure, which indicates that most of the incident power within the studied wavelength range can be absorbed. However, for a longer wavelength of $\lambda =3075$ nm, the multilayered system works as an HMM so that most of the incident power propagates downwards along the

**z**-direction in the air layer without penetrating into the nanostructure, leading to a strong suppression of absorption in this wavelength range. Here, it should be noted that, our approach is based on intrinsic material properties, which is fundamentally different from structural resonances or interference effects, thus the unique electromagnetic responses in the nanostructure are also slightly different from before.

According to the aforementioned analyses, the PTT occurs around the ENZ regime, where $Re(\varepsilon _{\rVert }) \simeq 0$ and $Re(\varepsilon _{\bot }) > 0$. Correspondingly, the topology of IFS undergoes the transition from the closed (ellipsoid $\varepsilon _{\rVert }\varepsilon _{\bot }>0$) to the open (hyperboloid $\varepsilon _{\rVert }\varepsilon _{\bot }<\,0$) one through the transform point. In this case, the incident light is strongly absorbed in the ellipsoidal regime and remarkably suppressed in the hyperbolic regime, which contributes to the excellent spectral selectivity of absorption in our nanostructure. Therefore, we can utilize the PTT to tailor the bandwidth of the near-perfect absorption by adjusting the structural thickness in the multilayered system. Figure 4(b) is the calculated absorption efficiency as a function of metal (W) layer thickness $d_3$, when $d_1=70$ nm, $d_2=15$ nm, and $N=18$. It is found that the bandwidth of the absorption spectrum decreases gradually with an increasing of $d_3$. And meanwhile the PTT points are calculated by Eq. (2) with different $d_3$, which matches nicely with the end of the near-unity absorption broadband. Furthermore, to determine the tunability of the proposed solar absorber, we further investigate the influence of dielectric layers thicknesses on the absorption performance. As shown on Figs. 5(a)–5(b), the end wavelength of the broadband absorption possesses a linear redshift with the increase of the SiO$_{2}$ thickness ($d_1$) and TiO$_{2}$ thickness ($d_2$). It is well explained from the effective permittivity of the HMM based on the effective medium theory. In other words, with the increment of dielectric layer thickness, the ENZ regime shifts toward the long wavelength due to the increase of $f_1$ (or $f_2$), which also leads to an ultra-broad absorbing band. Meanwhile, topological transition points of the IFS correspond well to the end of broadband, and these results provide more freedom to control the operating bandwidth of the absorption spectrum.

Furthermore, as depicted in Fig. 5(a), it is found that, the Bloch mode can be generated at the shorter wavelengths, which leads to a dip in absorption spectrum [26]. To further verify this phenomena, the absorption spectra of the multilayer with $d_1=105$ nm, $d_2=15$ nm, $d_3=3$ nm, and $N=18$ under normal incidence at the shorter wavelengths is calculated by the FDTD method, as shown in Fig. 6(a). The obvious dip around 360 nm is observed in the absorption spectrum due to the generation of Bloch mode, which can be proved by the distribution of the electric field in the metamaterial structure. Judging from the electric field distribution, smaller optical power is trapped within nanostructure due to Bloch effect, indicating the weak interaction between light and matter, and resulting in a low light absorption as illustrated in Fig. 4(a). According to the photonic crystal bandgap critical condition [27], one can move the location of Bloch mode toward the shorter wavelength by reducing the thickness of the dielectric layer, but with decreasing of the absorption band within the studied wavelength range, which degrades the absorption performance of solar absorber for energy harvesting. Therefore, in this work, we propose a novel way to replace the conventional two-layer (dielectric/ metal) structure unit with a three-layer one, which not only avoids the effect of Bloch mode at the shorter wavelengths by changing the critical condition of the photonic bandgap, but also can achieve a superior absorption performance based on PTT in HMM. In addition, increasing the period number $N$ of the multilayered metamaterial can effectively improve the accuracy of PTT point as predicted by the EMT method and further enhance the stability of the high-efficiency light absorption in the nanostructure. As shown in Fig. 6(b), we numerically simulate the absorption of light in the multilayered structure with different $N$. It is found that the period number hardly affects the absorption performance and the location of PTT point when $N \ge 18$. With the decrement of $N$, the absorption performance of the nanostructure also degrades gradually due to the large nonlocal dispersion effect [24], especially the hyperbolic character alters when $N<10$, and in this case, other more complex shaped isofrequency contours are generated, leading to the inability of PTT based on the EMT to accurately predict the absorption bandwidth.

Due to the central symmetry of the nanostructure, the proposed spectral-selective absorber is polarization-insensitive under normal incidence. Moreover, the angular tolerance of a solar absorber is also crucial to maximize the solar energy absorption owing to the sunlight coming from random directions. Figure 7 shows the calculated absorption spectrum at the incident angles ($\theta$) from $0^\circ$ to $70^\circ$ for both TM and TE polarizations. As shown in Fig. 7(a), for the TM case, the proposed absorber can still maintain an excellent absorption performance even when $\theta$ increases to $70^\circ$, resembling that at normal incidence. While for the case of TE polarization, the broadband absorption keeps close to unity up to $60^\circ$ incidence angle $\theta$ over wavelengths ranging from 300 to 2161 nm, and for larger angles, the absorptivities drop down to zero due to the increase of Fresnel reflectivity. Although there is a slight divergence at relatively large angles (see Fig. 7(b)), the averaged absorptivity and spectral selectivity are still satisfactory. Therefore, all these results clearly reveal that the designed solar absorber has a robust absorption performance, which is omni-directional at the entire solar spectrum.

For solar thermal systems, the total photothermal conversion efficiency ($\eta$) is an important parameter to quantitatively evaluate the performance of solar absorber, which can be calculated by [28]

## 4. Conclusions

In summary, a planar multi-layer metamaterial is proposed to work as a wideband spectral-selective solar absorber for efficient light harvesting. Our numerical simulations demonstrate that the light absorption can significantly exceed 90% over the wavelengths from 300 nm to 2215 nm, due to the topological change in IFS. It is also found that the bandwidth and efficiency of absorption spectrum can be flexibly tailored by adjusting the thicknesses of the metal (W) and dielectric (SiO$_{2}$ or TiO$_{2}$) layers, which agree well with theoretical calculations based on PTT in HMM. Moreover, the designed solar absorber is polarization-insensitive and its absorbing characteristics can be maintained very well over a wide incident angle of $60^\circ$ for both TM and TE polarizations. It is worth noting that, owing to the selective spectral response of the absorber, the total solar-thermal conversion efficiency can reach as high as 91.8% at operating temperature of 1000 K. And with varying the operating temperature, the solar absorber exhibit a high practicability, which shows a remarkable photothermal performance. The attractive properties, together with the designed method, indicate that such a solar absorber can readily serve as a potential candidate for many high-performance solar thermal applications, such as thermal emitters, photodetectors and energy harvesting.

## Funding

National Natural Science Foundation of China (61775064); Fundamental Research Funds for the Central Universities (HUST: 2016YXMS024).

## Acknowledgments

The author Xiaoyun Jiang (XYJIANG) expresses her deepest gratitude to her PhD advisor Tao Wang for providing guidance during this project.

## Disclosures

The authors declare no conflicts of interest.

## References

**1. **G. Ni, G. Li, S. V. Boriskina, H. Li, W. Yang, T. Zhang, and G. Chen, “Steam generation under one sun enabled by a floating structure with thermal concentration,” Nat. Energy **1**(9), 16126 (2016). [CrossRef]

**2. **X. Hu, W. Xu, L. Zhou, Y. Tan, Y. Wang, S. Zhu, and J. Zhu, “Tailoring graphene oxide-based aerogels for efficient solar steam generation under one sun,” Adv. Mater. **29**(5), 1604031 (2017). [CrossRef]

**3. **H. Lin, B. C. Sturmberg, K.-T. Lin, Y. Yang, X. Zheng, T. K. Chong, C. M. de Sterke, and B. Jia, “A 90-nm-thick graphene metamaterial for strong and extremely broadband absorption of unpolarized light,” Nat. Photonics **13**(4), 270–276 (2019). [CrossRef]

**4. **I. E. Khodasevych, L. Wang, A. Mitchell, and G. Rosengarten, “Micro-and nanostructured surfaces for selective solar absorption,” Adv. Opt. Mater. **3**(7), 852–881 (2015). [CrossRef]

**5. **P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. **7**(1), 11809 (2016). [CrossRef]

**6. **M. Chirumamilla, A. Chirumamilla, Y. Yang, A. S. Roberts, P. K. Kristensen, K. Chaudhuri, A. Boltasseva, D. S. Sutherland, S. I. Bozhevolnyi, and K. Pedersen, “Large-area ultrabroadband absorber for solar thermophotovoltaics based on 3d titanium nitride nanopillars,” Adv. Opt. Mater. **5**(22), 1700552 (2017). [CrossRef]

**7. **N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. **100**(20), 207402 (2008). [CrossRef]

**8. **X. Jiang, T. Wang, S. Xiao, X. Yan, and L. Cheng, “Tunable ultra-high-efficiency light absorption of monolayer graphene using critical coupling with guided resonance,” Opt. Express **25**(22), 27028–27036 (2017). [CrossRef]

**9. **S. Xiao, T. Liu, L. Cheng, C. Zhou, X. Jiang, Z. Li, and C. Xu, “Tunable anisotropic absorption in hyperbolic metamaterials based on black phosphorous/dielectric multilayer structures,” J. Lightwave Technol. **37**(13), 3290–3297 (2019). [CrossRef]

**10. **T. Liu, X. Jiang, C. Zhou, and S. Xiao, “Black phosphorus-based anisotropic absorption structure in the mid-infrared,” Opt. Express **27**(20), 27618–27627 (2019). [CrossRef]

**11. **S. Liu, H. Chen, and T. J. Cui, “A broadband terahertz absorber using multi-layer stacked bars,” Appl. Phys. Lett. **106**(15), 151601 (2015). [CrossRef]

**12. **A. K. Azad, W. J. Kort-Kamp, M. Sykora, N. R. Weisse-Bernstein, T. S. Luk, A. J. Taylor, D. A. Dalvit, and H.-T. Chen, “Metasurface broadband solar absorber,” Sci. Rep. **6**(1), 20347 (2016). [CrossRef]

**13. **J. Cong, Z. Zhou, B. Yun, L. Lv, H. Yao, Y. Fu, and N. Ren, “Broadband visible-light absorber via hybridization of propagating surface plasmon,” Opt. Lett. **41**(9), 1965–1968 (2016). [CrossRef]

**14. **Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. **12**(3), 1443–1447 (2012). [CrossRef]

**15. **Q. Liang, T. Wang, Z. Lu, Q. Sun, Y. Fu, and W. Yu, “Metamaterial-based two dimensional plasmonic subwavelength structures offer the broadest waveband light harvesting,” Adv. Opt. Mater. **1**(1), 43–49 (2013). [CrossRef]

**16. **J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and theory of the broadband absorption by a tapered hyperbolic metamaterial array,” ACS Photonics **1**(7), 618–624 (2014). [CrossRef]

**17. **E. D. Palik, * Handbook of optical constants of solids*, vol. 3 (Academic University, 1998).

**18. **A. Leviyev, B. Stein, A. Christofi, T. Galfsky, H. Krishnamoorthy, I. Kuskovsky, V. Menon, and A. Khanikaev, “Nonreciprocity and one-way topological transitions in hyperbolic metamaterials,” APL Photonics **2**(7), 076103 (2017). [CrossRef]

**19. **N.-h. Liu, S.-Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E **65**(4), 046607 (2002). [CrossRef]

**20. **C. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. **14**(6), 063001 (2012). [CrossRef]

**21. **V. Agranovich and V. Kravtsov, “Notes on crystal optics of superlattices,” Solid State Commun. **55**(1), 85–90 (1985). [CrossRef]

**22. **X. Jiang, T. Wang, S. Xiao, X. Yan, L. Cheng, and Q. Zhong, “Approaching perfect absorption of monolayer molybdenum disulfide at visible wavelengths using critical coupling,” Nanotechnology **29**(33), 335205 (2018). [CrossRef]

**23. **X. Jiang, T. Wang, L. Cheng, Q. Zhong, R. Yan, and X. Huang, “Tunable optical angular selectivity in hyperbolic metamaterial via photonic topological transitions,” Opt. Express **27**(13), 18970–18979 (2019). [CrossRef]

**24. **L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. **40**, 1–40 (2015). [CrossRef]

**25. **J. Zhou, X. Chen, and L. J. Guo, “Efficient thermal–light interconversions based on optical topological transition in the metal-dielectric multilayered metamaterials,” Adv. Mater. **28**(15), 3017–3023 (2016). [CrossRef]

**26. **Y. Kan, C. Zhao, X. Fang, and B. Wang, “Designing ultrabroadband absorbers based on bloch theorem and optical topological transition,” Opt. Lett. **42**(10), 1879–1882 (2017). [CrossRef]

**27. **J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, * Photonic Crystals: Molding the Flow of Light*, vol. 2 (Princeton University, 2008).

**28. **A. Sakurai and T. Kawamata, “Electromagnetic resonances of solar-selective absorbers with nanoparticle arrays embedded in a dielectric layer,” J. Quant. Spectrosc. Radiat. Transfer **184**, 353–359 (2016). [CrossRef]

**29. **Air Mass 1.5 Spectra, “American Society for Testing and Materials(ASTM),” http://rredc.nrel.gov/solar/spectra/am1.5/.

**30. **S. Han, J.-H. Shin, P.-H. Jung, H. Lee, and B. J. Lee, “Broadband solar thermal absorber based on optical metamaterials for high-temperature applications,” Adv. Opt. Mater. **4**(8), 1265–1273 (2016). [CrossRef]

**31. **Y. Li, D. Li, D. Zhou, C. Chi, S. Yang, and B. Huang, “Efficient, scalable, and high-temperature selective solar absorbers based on hybrid-strategy plasmonic metamaterials,” Sol. RRL **2**(8), 1800057 (2018). [CrossRef]

**32. **M. Chen and Y. He, “Plasmonic nanostructures for broadband solar absorption based on the intrinsic absorption of metals,” Sol. Energy Mater. Sol. Cells **188**, 156–163 (2018). [CrossRef]

**33. **Y. Li, C. Lin, D. Zhou, Y. An, D. Li, C. Chi, H. Huang, S. Yang, C. Y. Tso, C. Y. Chao, and B. Huang, “Scalable all-ceramic nanofilms as highly efficient and thermally stable selective solar absorbers,” Nano Energy **64**, 103947 (2019). [CrossRef]