Abstract

We report an ultrabroadband perfect metamaterial absorber, comprising a two-dimensional array of a hemi-ellipsoid shaped metallo-dielectric multilayered structure. What we believe, to the best of our knowledge, is an unprecedented average absorbance of ${\sim}99\%$ is theoretically demonstrated in the 300 to 4500 nm spectral range at normal incidence. We use 20 pairs of molybdenum–germanium metallo-dielectric layers with tungsten as the ground metal placed on a silicon substrate. Our design is polarization-independent as well as angle-insensitive (up to 60°), making it a perfect “superabsorber.” Theoretical modeling based on effective medium theory validates our full-wave simulation results. The figure-of-merit calculations suggest that our superabsorber can outperform recently reported broadband absorbers. The proposed design has potential application in thermophotovoltaics for solar energy harvesting.

© 2021 Optical Society of America

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2020 (12)

A. Rastgordani and Z. G. Kashani, “Robust design method for metasurface high-sensitivity sensors and absorbers,” J. Opt. Soc. Am. B 37, 2006–2011 (2020).
[Crossref]

Y. Cheng, H. Zhao, and C. Li, “Broadband tunable terahertz metasurface absorber based on complementary-wheel-shaped graphene,” Opt. Mater. 109, 110369 (2020).
[Crossref]

R.-H. Fan, B. Xiong, R.-W. Peng, and M. Wang, “Constructing metastructures with broadband electromagnetic functionality,” Adv. Mater. 32, 1904646 (2020).
[Crossref]

S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” Nanophotonics 9, 1189–1241 (2020).
[Crossref]

Y. Cheng, F. Chen, and H. Luo, “Multi-band giant circular dichroism based on conjugated bilayer twisted-semicircle nanostructure at optical frequency,” Phys. Lett. A 384, 126398 (2020).
[Crossref]

Y. Cheng, F. Chen, and H. Luo, “Triple-band perfect light absorber based on hybrid metasurface for sensing application,” Nanoscale Res. Lett. 15, 103 (2020).
[Crossref]

W. Li and Y. Cheng, “Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure,” Opt. Commun. 462, 125265 (2020).
[Crossref]

C. Liang, Z. Yi, X. Chen, Y. Tang, Y. Yi, Z. Zhou, X. Wu, Z. Huang, Y. Yi, and G. Zhang, “Dual-band infrared perfect absorber based on a Ag-dielectric-Ag multilayer films with nanoring grooves arrays,” Plasmonics 15, 93–100 (2020).
[Crossref]

B. Wu, Z. Liu, G. Du, Q. Chen, X. Liu, G. Fu, and G. Liu, “Polarization and angle insensitive ultra-broadband mid-infrared perfect absorber,” Phys. Lett. A 384, 126288 (2020).
[Crossref]

J. Liu, W. Chen, W. Z. Ma, G. X. Yu, J. C. Zheng, Y. S. Chen, and C. F. Yang, “Ultra-broadband infrared absorbers using iron thin layers,” IEEE Access 8, 43407–43412 (2020).
[Crossref]

S. K. Patel, J. Parmar, D. Katrodiya, T. K. Nguyen, E. Holdengreber, and V. Dhasarathan, “Broadband metamaterial-based near-infrared absorber using an array of uniformly placed gold resonators,” J. Opt. Soc. Am. B 37, 2163–2170 (2020).
[Crossref]

T. Amotchkina, M. Trubetskov, D. Hahner, and V. Pervak, “Characterization of e-beam evaporated Ge, YbF3, ZnS, and LaF3 thin films for laser-oriented coatings,” Appl. Opt. 59, A40–A47 (2020).
[Crossref]

2019 (16)

G. Liu, X. Liu, J. Chen, Y. Li, L. Shi, G. Fu, and Z. Liu, “Near-unity, full-spectrum, nanoscale solar absorbers and near-perfect blackbody emitters,” Sol. Energy Mater. Sol. Cells 190, 20–29 (2019).
[Crossref]

N. T. Q. Hoa, P. H. Lam, P. D. Tung, T. S. Tuan, and H. Nguyen, “Numerical study of a wide-angle and polarization-insensitive ultrabroadband metamaterial absorber in visible and near-infrared region,” IEEE Photon. J. 11, 4600208 (2019).
[Crossref]

M. C. Soydan, A. Ghobadi, D. U. Yildirim, V. B. Erturk, and E. Ozbay, “All ceramic-based metal-free ultra-broadband perfect absorber,” Plasmonics 14, 1801–1815 (2019).
[Crossref]

M. Aalizadeh, A. Khavasi, A. E. Serebryannikov, G. A. E. Vandenbosch, and E. Ozbay, “A route to unusually broadband plasmonic absorption spanning from visible to mid-infrared,” Plasmonics 14, 1269–1281 (2019).
[Crossref]

H. Lin, B. C. P. 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, 270–276 (2019).
[Crossref]

H. Gao, W. Peng, W. Cui, S. Chu, L. Yu, and X. Yang, “Ultraviolet to near infrared titanium nitride broadband plasmonic absorber,” Opt. Mater. 97, 109377 (2019).
[Crossref]

H. Gao, D. Zhou, W. Cui, Z. Liu, Y. Liu, Z. Jing, and W. Peng, “Ultraviolet broadband plasmonic absorber with dual visible and near-infrared narrow bands,” J. Opt. Soc. Am. A 36, 264–269 (2019).
[Crossref]

H. Zhang, C. Guan, J. Luo, Y. Yuan, N. Song, Y. Zhang, J. Fang, and H. Liu, “Facile film-nanoctahedron assembly route to plasmonic metamaterial absorbers at visible frequencies,” ACS Appl. Mater. Interfaces 11, 20241–20248 (2019).
[Crossref]

Y. Huang, J. Luo, M. Pu, Y. Guo, Z. Zhao, X. Ma, X. Li, and X. Luo, “Catenary electromagnetics for ultra-broadband lightweight absorbers and large-scale flat antennas,” Adv. Sci. 6, 1801691 (2019).
[Crossref]

H. Zou and Y. Cheng, “Design of a six-band terahertz metamaterial absorber for temperature sensing application,” Opt. Mater. 88, 674–679 (2019).
[Crossref]

Y. Cheng, H. Luo, F. Chen, and R. Gong, “Triple narrow-band plasmonic perfect absorber for refractive index sensing applications of optical frequency,” OSA Contin. 2, 2113–2122 (2019).
[Crossref]

Y. Wang, H. Liu, and J. Zhu, “Solar thermophotovoltaics: progress, challenges, and opportunities,” APL Mater. 7, 080906 (2019).
[Crossref]

P. Yu, L. V. Besteiro, Y. Huang, J. Wu, L. Fu, H. H. Tan, C. Jagadish, G. P. Wiederrecht, A. O. Govorov, and Z. Wang, “Broadband metamaterial absorbers,” Adv. Opt. Mater. 7, 1800995 (2019).
[Crossref]

L. Escoubas, M. Carlberg, J. L. Rouzo, F. Pourcin, J. Ackermann, O. Margeat, C. Reynaud, D. Duche, J. J. Simon, R. M. Sauvage, and G. Berginc, “Design and realization of light absorbers using plasmonic nanoparticles,” Prog. Quantum Electron. 63, 1–22 (2019).
[Crossref]

H. Hajian, A. Ghobadi, B. Butun, and E. Ozbay, “Active metamaterial nearly perfect light absorbers: a review,” J. Opt. Soc. Am. B 36, F131–F143 (2019).
[Crossref]

J. Xie, S. Quader, F. Xiao, C. He, X. Liang, J. Geng, R. Jin, W. Zhu, and I. D. Rukhlenko, “Truly all-dielectric ultra-broadband metamaterial absorber: water-based and ground-free,” IEEE Antennas Wireless Propag. Lett. 18, 536–540 (2019).
[Crossref]

2018 (4)

S. Ogawa and M. Kimata, “Metal-insulator-metal-based plasmonic metamaterial absorbers at visible and infrared wavelengths: a review,” Materials 11, 458 (2018).
[Crossref]

W. Li and S. Fan, “Nanophotonic control of thermal radiation for energy applications,” Opt. Express 26, 15995–16021 (2018).
[Crossref]

Y. Guo, X. Ma, M. Pu, X. Li, Z. Zhao, and X. Luo, “High-efficiency and wide-angle beam steering based on catenary optical fields in ultrathin metalens,” Adv. Opt. Mater. 6, 1800592 (2018).
[Crossref]

Y. Cheng, H. Zhang, X. S. Mao, and R. Gong, “Dual-band plasmonic perfect absorber based on all-metal nanostructure for refractive index sensing application,” Mater. Lett. 219, 123–126 (2018).
[Crossref]

2017 (4)

W. Zhu, I. D. Rukhlenko, F. Xiao, C. He, J. Geng, X. Liang, M. Premaratne, and R. Jin, “Multiband coherent perfect absorption in a water-based metasurface,” Opt. Express 25, 15737–15745 (2017).
[Crossref]

B. Tang, Y. Zhu, X. Zhou, L. Huang, and X. Lang, “Wide-angle polarization independent broadband absorbers based on concentric multisplit ring arrays,” IEEE Photon. J. 9, 4502707 (2017).
[Crossref]

W. Wang, Y. Qu, K. Du, S. Bai, J. Tian, M. Pan, H. Ye, M. Qiu, and Q. Li, “Broadband optical absorption based on single-sized metal-dielectric metal plasmonic nanostructures with high-ε metals,” Appl. Phys. Lett. 110, 101101 (2017).
[Crossref]

Y. Lin, Y. Cui, F. Ding, K. H. Fung, T. Ji, D. Li, and Y. Hao, “Tungsten based anisotropic metamaterial as an ultra-broadband absorber,” Opt. Mater. Express 7, 606–617 (2017).
[Crossref]

2015 (1)

W. Li, Z. J. Coppens, L. V. Besteiro, W. Wang, A. O. Govorov, and J. Valentine, “Circularly polarized light detection with hot electrons in chiral plasmonic metamaterials,” Nat. Commun. 6, 8379 (2015).
[Crossref]

2014 (6)

S. He, F. Ding, L. Mo, and F. Bao, “Light absorber with an ultra-broad flat band based on multi-sized slow-wave hyperbolic metamaterial thin-films,” Prog. Electromagn. Res. 147, 69–79 (2014).
[Crossref]

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 Photon. 1, 618–624 (2014).
[Crossref]

W. Li and J. Valentine, “Metamaterial perfect absorber based hot electron photodetection,” Nano Lett. 14, 3510–3514 (2014).
[Crossref]

K.-T. Lin, H.-L. Chen, Y.-S. Lai, and C.-C. Yu, “Silicon-based broadband antenna for high responsivity and polarization-insensitive photodetection at telecommunication wavelengths,” Nat. Commun. 5, 3288 (2014).
[Crossref]

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[Crossref]

J. Zhu, Z. Ma, W. Sun, F. Ding, Q. He, L. Zhou, and Y. Ma, “Ultra-broadband terahertz metamaterial absorber,” Appl. Phys. Lett. 105, 021102 (2014).
[Crossref]

2013 (1)

H. Hu, D. Ji, X. Zeng, K. Liu, and Q. Gan, “Rainbow trapping in hyperbolic metamaterial waveguide,” Sci. Rep. 3, 1249 (2013).
[Crossref]

2012 (3)

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, 1443–1447 (2012).
[Crossref]

H. Noh, Y. Chong, A. D. Stone, and H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref]

W. Zhu, Y. Huang, I. D. Rukhlenko, G. Wen, and M. Premaratne, “Configurable metamaterial absorber with pseudo wideband spectrum,” Opt. Express 20, 6616–6621 (2012).
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2011 (1)

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
[Crossref]

2010 (1)

2009 (1)

W. S. M. Werner, K. Glantschnig, and C. A. Draxl, “Optical constants and inelastic electron-scattering data for 17 elemental metals,” J. Phys. Chem. Ref. Data 38, 1013–1092 (2009).
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2008 (3)

T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
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N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
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E. Rephaeli and S. Fan, “Tungsten black absorber for solar light with wide angular operation range,” Appl. Phys. Lett. 92, 211107 (2008).
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2007 (3)

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, “Total light absorption in plasmonic nanostructures,” J. Opt. A 9, S458–S462 (2007).
[Crossref]

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
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K. Tsakmakidis, A. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450, 397–401 (2007).
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1988 (1)

1983 (1)

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T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
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S. Abdollahramezani, O. Hemmatyar, M. Taghinejad, H. Taghinejad, Y. Kiarashinejad, M. Zandehshahvar, T. Fan, S. Deshmukh, A. A. Eftekhar, W. Cai, E. Pop, M. El-Sayed, and A. Adibi, “Dynamic hybrid metasurfaces,” arXiv:2008.03905 [physics.optics] (2020).

Ackermann, J.

L. Escoubas, M. Carlberg, J. L. Rouzo, F. Pourcin, J. Ackermann, O. Margeat, C. Reynaud, D. Duche, J. J. Simon, R. M. Sauvage, and G. Berginc, “Design and realization of light absorbers using plasmonic nanoparticles,” Prog. Quantum Electron. 63, 1–22 (2019).
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S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” Nanophotonics 9, 1189–1241 (2020).
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S. Abdollahramezani, O. Hemmatyar, H. Taghinejad, A. Krasnok, Y. Kiarashinejad, M. Zandehshahvar, A. Alu, and A. Adibi, “Tunable nanophotonics enabled by chalcogenide phase-change materials,” Nanophotonics 9, 1189–1241 (2020).
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K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
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Y. Cheng, F. Chen, and H. Luo, “Multi-band giant circular dichroism based on conjugated bilayer twisted-semicircle nanostructure at optical frequency,” Phys. Lett. A 384, 126398 (2020).
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Y. Cheng, F. Chen, and H. Luo, “Triple-band perfect light absorber based on hybrid metasurface for sensing application,” Nanoscale Res. Lett. 15, 103 (2020).
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Y. Cheng, H. Luo, F. Chen, and R. Gong, “Triple narrow-band plasmonic perfect absorber for refractive index sensing applications of optical frequency,” OSA Contin. 2, 2113–2122 (2019).
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Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2, 770–774 (2007).
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B. Wu, Z. Liu, G. Du, Q. Chen, X. Liu, G. Fu, and G. Liu, “Polarization and angle insensitive ultra-broadband mid-infrared perfect absorber,” Phys. Lett. A 384, 126288 (2020).
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C. Liang, Z. Yi, X. Chen, Y. Tang, Y. Yi, Z. Zhou, X. Wu, Z. Huang, Y. Yi, and G. Zhang, “Dual-band infrared perfect absorber based on a Ag-dielectric-Ag multilayer films with nanoring grooves arrays,” Plasmonics 15, 93–100 (2020).
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J. Liu, W. Chen, W. Z. Ma, G. X. Yu, J. C. Zheng, Y. S. Chen, and C. F. Yang, “Ultra-broadband infrared absorbers using iron thin layers,” IEEE Access 8, 43407–43412 (2020).
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W. Li and Y. Cheng, “Dual-band tunable terahertz perfect metamaterial absorber based on strontium titanate (STO) resonator structure,” Opt. Commun. 462, 125265 (2020).
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Y. Cheng, F. Chen, and H. Luo, “Triple-band perfect light absorber based on hybrid metasurface for sensing application,” Nanoscale Res. Lett. 15, 103 (2020).
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Y. Cheng, F. Chen, and H. Luo, “Multi-band giant circular dichroism based on conjugated bilayer twisted-semicircle nanostructure at optical frequency,” Phys. Lett. A 384, 126398 (2020).
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Y. Cheng, H. Zhao, and C. Li, “Broadband tunable terahertz metasurface absorber based on complementary-wheel-shaped graphene,” Opt. Mater. 109, 110369 (2020).
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H. Zou and Y. Cheng, “Design of a six-band terahertz metamaterial absorber for temperature sensing application,” Opt. Mater. 88, 674–679 (2019).
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Y. Cheng, H. Luo, F. Chen, and R. Gong, “Triple narrow-band plasmonic perfect absorber for refractive index sensing applications of optical frequency,” OSA Contin. 2, 2113–2122 (2019).
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K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
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B. Wu, Z. Liu, G. Du, Q. Chen, X. Liu, G. Fu, and G. Liu, “Polarization and angle insensitive ultra-broadband mid-infrared perfect absorber,” Phys. Lett. A 384, 126288 (2020).
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Figures (7)

Fig. 1.
Fig. 1. Design of an infinite 2D array of hemi-ellipsoid shaped metallo-dielectric (MD) multilayered structure showing (a) 3D schematic representation along with (b) side and (c) top views of its unit cell considered for 3D numerical simulation. We consider TM polarization, where the $\textbf{H}$ field is aligned along ${y}$ axis. Plane wave propagates along the ${z}$ axis from port 1 and the optical response is measured using ${S}$ parameters. This design consists of 20 pairs ( $L$ ) of MD layers [made of molybdenum (Mo)–germanium (Ge)], with tungsten (W) as the ground metal, standing over a silicon substrate. A perfectly matched layer (PML) is applied at the top and the bottom of the unit cell. In (a) and (c): $d$ (400 nm), length of each minor axis of a prolate hemi-ellipsoid; $g$ (20 nm), the gap between the base of two adjacent hemi-ellipsoids; and $p$ (420 nm), the period of the unit cell. In (b), the thickness of each layer of the simulation model is presented within the parentheses.
Fig. 2.
Fig. 2. Numerically calculated spectral response for our design showing (a) absorbance ( $A$ ), reflectance ( $R$ ), and transmittance ( $T$ ) for design with 20 pairs ( $L$ ) of metallo-dielectric (MD) layer between the 300 and 5000 nm spectral window at normal incidence, and (b) a trend for gradually increasing average absorbance with an increasing number of MD pairs ( $L$ ) at five discrete values between 2 and 40. Note that the average absorbance is calculated between the 300 and 4500 nm spectral range at normal incidence.
Fig. 3.
Fig. 3. Normalized (a) magnetic and (b) electric field distribution (color plots) with corresponding energy flow (arrow plot) at arbitrarily chosen incident frequencies, $f$ (wavelengths, $\lambda$ ) between 67 and 750 THz (between 400 and 4500 nm), simulated for 20 pairs ( $L$ ) of metallo-dielectric layers. In (a), for the incident wavelengths between 2000 and 4500 nm, the presence of fundamental order magnetic resonance modes is clearly shown at different locations of the structure using horizontal white arrows (pointing toward the right). At $\lambda = 1600\;{\rm nm}$ , higher-order resonance modes can be seen in the magnetic field plot. In (b), dotted white circles highlight the electric modes, corresponding to the magnetic resonance modes in (a), which depict the pattern of near-field interaction between adjacent hemi-ellipsoids with incident wavelength.
Fig. 4.
Fig. 4. (a) Comparison of numerically calculated absorbance spectra between 20 pairs ( $L$ ) of metallo-dielectric (MD) layers (solid line) and the effective medium theory (EMT) approximation (dashed line) over the 300–5000 nm spectral range at normal incidence, and (b) normalized magnetic field ( $\textbf{H}$ ) distribution (color plot) and energy flow (arrow plot) using the EMT approximation at arbitrarily chosen incident frequencies, $f$ (wavelengths, $\lambda$ ) between 150 and 750 THz (between 400 and 2000 nm). Note that in (a), the EMT approximation is valid between the 400 and 1900 nm spectral range, shown by the shaded region.
Fig. 5.
Fig. 5. Simulation-based parametric analysis of our design showing color contour plot for varying (a) metal thickness, ${t_{{\rm M1}}}$ , (b) dielectric thickness, ${t_{\rm D}}$ , and (c) length of each minor axis, $d$ , while keeping all other parameters constant for each case. The white dashed lines show the optimized parameter value between the 300 and 4500 nm spectral range in each case.
Fig. 6.
Fig. 6. Numerically calculated optical fabrication tolerance of our design showing an average absorbance between the 300 and 4500 nm spectral range at normal incidence for varying (a) metal thickness, ${t_{{\rm M1}}}$ , (b) dielectric thickness, ${t_{\rm D}}$ , and (c) length of each minor axis, $d$ , while keeping other parameters constant in each case. The shadowed regions show the tolerance limit for our design with $\pm {0.5}\%$ maximum allowable variance on average absorbance.
Fig. 7.
Fig. 7. Simulation results for our design showing (a) the absorbance spectra (between 300 and 4500 nm) for both the TM and TE polarizations at normal incidence; the contour plot of absorbance spectrum for (b) the TM and (c) TE polarization as a function of incident angle, ranging from 0° to 60°, and (d) the average absorbance (between 300 and 4500 nm) for TM, TE, and unpolarized waves incident at different angles, showing over 90% average absorbance efficiency ( $\eta$ ) for the oblique angle of incidence up to 50° and a nearly 80% absorption efficiency for the oblique angle of incidence up to 60°.

Tables (2)

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Table 1. Optical Fabrication Tolerance Limit for Our Design Shown in Fig. 1 with ± 0.5 % Maximum Allowable Variance on Average Absorbance (All Dimensions Are in nm)

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Table 2. Comparative Overview of a Few Recently Reported Broadband Absorbers for Solar Energy Harvesting a

Equations (2)

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1 / ϵ = f / ϵ m ( ω ) + ( 1 f ) / ϵ d ,
ϵ = f ϵ m ( ω ) + ( 1 f ) ϵ d ,

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