Abstract
In this study, we have theoretically introduced the reflectance spectrum of the one-dimensional metamaterial photonic crystals (PCs) based on the effective medium theory (EMT) and the well-defined transfer matrix formulism. The candidate structure is composed of two metamaterials, including hyperbolic (CD) and gyroidal (G) metamaterials, such as [G (CD)m]s. In this regard, the gyroidal metamaterial is designed from Silver (Ag) of a gyroidal configuration in a dielectric host material (TiO2). Then, the hyperbolic metamaterial appears as a composite design of Indium Arsenide (InAs) and Ag for m periods. The numerical findings showed the emergence of an angle-insensitive photonic bandgap, extending from 2.5 μm to 4 μm. Meanwhile, we have considered the impact of the filling fraction, periodicity number (m and S), and thicknesses on the reflectivity of the proposed reflector. We believe that this structure could be promising as an angle-insensitive reflector for various solar energy applications, such as reflectors, wavelength-selective absorbers, smart widows, and an intermediate layer for solar cells.
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This manuscript has associated data in a data repository. [Authors’ comment: Requests should be addressed to the corresponding author.]
References
T.A. Taha, H. Sayed, A.H. Aly, H.A. Elsayed, Textured concave anti-reflecting coating and convex back reflector to enhance the absorbance of amorphous Si solar cells. Phys. Scr. 97(5), 055503 (2022)
A.G. Mohamed, W. Sabra, A. Mehaney, A.H. Aly, H.A. Elsayed, Multiplication of photonic band gaps in one-dimensional photonic crystals by using hyperbolic metamaterial in IR range. Sci. Rep. 13(1), 324 (2023)
F.A. Sayed, H.A. Elsayed, A. Mehaney, M.F. Eissa, A.H. Aly, A doped-polymer based porous silicon photonic crystal sensor for the detection of gamma-ray radiation. RSC Adv. 13(5), 3123–3138 (2023)
N. Kumar, B. Suthar, Advances in Photonic Crystals and Devices (CRC Press, Boca Raton, 2019)
M. Castillo, D. Cunha, C. Estévez-Varela, D. Miranda, I. Pastoriza-Santos, S. Núñez-Sánchez, M. Vasilevskiy, M. Lopez-Garcia, Tunable narrowband excitonic optical Tamm states enabled by a metal free all organic structure. Nanophotonics 11(21), 4879–4888 (2022)
A.H.M. Almawgani, H.A. Elsayed, A. Mehaney, T.A. Taha, Z.A. Alrowaili, G.A. Ali, W. Sabra, S. Asaduzzaman, A.M. Ahmed, Photonic crystal nanostructure as a photodetector for NaCl solution monitoring: theoretical approach. RSC Adv. 13(10), 6737–6746 (2023)
N. Kumar, B. Suthar, A. Rostami, Novel optical behaviors of metamaterial and polymer-based ternary photonic crystal with lossless and lossy features. Opt Commun 529, 129073 (2023)
T.A. Taha, A. Mehaney, H.A. Elsayed, Detection of heavy metals using one-dimensional gyroidal photonic crystals for effective water treatment. Mater. Chem. Phys. 285, 126125 (2022)
S. Stutzer, Y. Plotnik, Y. Lumer Y, et al., Photonic topological Anderson insulators. Nature 560, 461–465 (2018)
L. Lu, Z. Wang, D. Ye et al., Experimental observation of Weyl points. Science 349, 622–624 (2015)
A.H. Aly, S.A. El-Naggar, H.A. Elsayed, Tunability of two dimensional n-doped semiconductor photonic crystals based on the Faraday effect. Opt. Express 23(11), 15038–15046 (2015)
A.G. Mohamed, H.A. Elsayed, A. Mehaney, A.H. Aly, W. Sabra, Transmittance properties of one-dimensional metamaterial nanocomposite photonic crystal in GHz range. Sci. Rep. 12(1), 18331 (2022)
M. Xiao, Q. Lin, S. Fan, Hyperbolic weyl point in reciprocal chiral metamaterials. Phys. Rev. Lett. 117, 057401 (2016)
C. Lv, W. Li, X. Jiang, J. Cao, Far field super resolution imaging with a planar hyperbolic metamaterial lens. Europhys. Lett. 105, 28003 (2014)
F. Wu, D. Liu, H.-J. Li, M. Feng, A redshifted photonic bandgap and wide-angle polarization selection in an all-hyperbolic-metamaterial one-dimensional photonic crystal. Phys. Chem. Chem. Phys. 25(15), 10785–10794 (2023)
L.Q. Cong, S.K. Valiyaveedu, J.H. Shi, X.Q. Zhang, Terahertz radiation: materials and applications. Front. Phys. 9, 671647 (2021)
R. Zhang, Q. Chen, K. Liu, Z. Chen, K. Li, X. Zhang, J. Xu, E.P. MacPherson, Terahertz microfluidic metamaterial biosensor for sensitive detection of small-volume liquid samples. IEEE Trans. Terahertz Sci. Technol. 9(2), 209–214 (2019)
M.-R. Nickpay, M. Danaie, A. Shahzadi, Highly sensitive THz refractive index sensor based on folded split ring metamaterial graphene resonators. Plasmonics 17(1), 237–248 (2022)
H. Ou, F. Lu, Z. Xu, Y.S. Lin, Terahertz metamaterial with multiple resonances for biosensing application. Nanomaterials 10(6), 1038 (2020)
K. Yao, Y. Liu, “Plasmonic metamaterials. Nanotechnol. Rev. 3, 177–210 (2014)
M. Seo, H.R. Park, Terahertz biochemical molecule-specific sensors. Adv. Opt. Mater. 8(3), 1900662 (2020)
S. Niknam, M. Yazdi, S. Behboudi Amlashi, Enhanced ultra-sensitive metamaterial resonance sensor based on double corrugated metal stripe for terahertz sensing. Sci. Rep. 9(1), 7516 (2019)
F. Meng, M.D. Thomson, B. Klug, H.G. Roskos, Strong interaction between two photons and a plasmon of a complementary metamaterial in a terahertz dual cavity. Opt. Express 29(26), 42420–42434 (2021)
F. Meng, M.D. Thomson, B. Klug, D. Cibiraite, Q. Ul-Islam, H.G. Roskos, “Nonlocal collective ultrastrong interaction of plasmonic metamaterials and photons in a terahertz photonic crystal cavity. Opt. Express 27(17), 24455–24468 (2019)
S. Vignolini, N.A. Yufa, P.S. Cunha, S. Guldin, I. Rushkin, M. Stefik, K. Hur, U. Wiesner, J.J. Baumberg, U. Steiner, A 3D optical metamaterial made by self-assembly. Adv. Mater. 24, OP23–OP27 (2012)
S.K. Srviastava, A. Aghajamali, Analysis of reflectance properties in 1D photonic crystal containing metamaterial and high-temperature superconductor. J. Supercond. Novel Magn. 30(2), 343–351 (2017)
B.D.F. Casse, W.T. Lu, Y.J. Huang, E. Gultepe, L. Menon, S. Sridhar, Super resolution imaging using a three-dimensional metamaterial nanolens. Appl. Phys. Lett. 96, 023114 (2010)
L. Ferrari, C. Wu, D. Lepage, X. Zhang, Z. Liu, Hyperbolic metamaterials and their applications. Prog. Quantum Electron. 40, 1–40 (2015)
B. Janaszek, P. Szczepański, Distributed feedback laser based on tunable photonic hypercrystals. Materials 14, 4065 (2021)
O.N. Kozina, L.A. Melnikov, I.S. Nefedov, A theory for terahertz lasers based on a graphene hyperbolic metamaterial. J. Opt. 22, 095003 (2020)
M.A. Baqir, P.K. Choudhury, Design of hyperbolic metamaterial-based absorber comprised of Ti nanospheres. IEEE Photon. Technol. Lett. 31, 735 (2019)
E.E. Narimanov, Photonic hypercrystals. Phys. Rev. X 4, 041014 (2014)
S.V. Zhukovsky, A.A. Orlov, V.E. Babicheva, A.V. Lavrinenko, J.E. Sipe, Photonic bandgap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials. Phys. Rev. A 90, 013801 (2014)
F. Wu, X. Wu, S. Xiao, G. Liu, H. Li, Broadband wide-angle multilayer absorber based on a broadband omnidirectional optical Tamm state. Opt. Express 29, 23976 (2021)
A. Poddubny, I. Iorsh, P. Belov, Y. Kivshar, Hyperbolic metamaterials. Nat. Photonics 7, 948 (2013)
O. Takayama, A.V. Lavrinenko, Optics with hyperbolic materials. J. Opt. Soc. Am. B 36, F38 (2019)
R.G. Bikbaev, S.Y. Vetrov, I.V. Timofeev, Hyperbolic metamaterial for the Tamm plasmon polariton application. J. Opt. Soc. Am. B 37, 2215 (2020)
S. Hu, S. Du, J. Li, C. Gu, Multidimensional image and beam splitter based on hyperbolic. Nano Lett. 21(4), 1792–1799 (2021)
C. Xue, Y. Ding, H. Jiang, Y. Li, Z. Wang, Y. Zhang, H. Chen, Dispersionless gaps and cavity modes in photonic crystals containing hyperbolic metamaterials. Phys. Rev. B 93(12), 125310 (2016)
Y. Li, B.P. Bastakoti, Y. Yamauchi, Research update: triblock copolymers as templates to synthesize inorganic nanoporous materials. APL Mater. 4, 040703 (2016)
I. Vukovic, G.T. Brinke, K. Loos, Block copolymer template-directed synthesis of well-ordered metallic nanostructures. Polymer 54, 2591–2605 (2013)
H.-Y. Hsueh, H.-Y. Chen, Y.-C. Ling, W.-S. Huang, Y.-C. Hung, S. Gwo, R.-M. Ho, A polymer-based SERS-active substrate with gyroid-structured gold multibranches. J. Mater. Chem. C 2, 4667–4675 (2014)
B.D. Wilts, K. Michielsen, H. De Raedt, D.G. Stavenga, Iridescence and spectral filtering of the gyroid-type photonic crystals in parides sesostris wing scales. Interface Focus 2, 681–687 (2012)
S. Prayakarao, S. Robbins, N. Kinsey, A. Boltasseva, V.M. Shalaev, U.B. Wiesner, C.E. Bonner, R. Hussain, N. Noginova, M.A. Noginov, Gyroidal titanium nitride as nonmetallic metamaterial. Opt. Mater. Express 5, 1316–1322 (2015)
K. Hur, Y. Francescato, V. Giannini, S.A. Maier, R.G. Hennig, U. Wiesner, Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks. Angew. Chem. 123, 12191–12195 (2011)
O. Buchnev, N. Podoliak, K. Kaltenecker, M. Walther, V.A. Fedotov, Metasurface-based optical liquid crystal cell as an ultrathin spatial phase modulator for THz applications. ACS Photonics 7(11), 3199–3206 (2020)
W. Zhang, S. Yu, Bistable switching using an optical Tamm cavity with a Kerr medium. Opt. Commun. 283, 2622–2626 (2010)
J. Wu, Z. Shen, S. Ge et al., Liquid crystal programmable metasurface for terahertz beam steering. Appl. Phys. Lett. 116(13), 131104 (2020)
M.M. Born, E. Wolf, Principles of Optics (Cambridge University Press, London, 1999)
S.J. Orfanidis, Electromagnetic Waves and Antennas (Rutger University, 2008)
S. Sharma, R. Kumar, K.S. Singh, A. Kumar, V. Kumar, Omnidirectional reflector using linearly graded refractive index profile of 1D binary and ternary photonic crystal. Optik 126, 1146–1149 (2015)
S.A. El-Naggar, Tunable terahertz omnidirectional photonic gap in one dimensional graphene-based photonic crystals. Opt. Quant. Electron. 47(7), 1627–1636 (2015)
W. Sabra, H.A. Elsayed, A. Mehaney, A.H. Aly, Numerical optimization of 1D superconductor photonic crystals pressure sensor for low temperatures applications. Solid State Commun. 343, 114671 (2022)
V.E. Babicheva, M.Y. Shalaginov, S. Ishii, A. Boltasseva, A.V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding. Opt. Express 23(8), 9681–9689 (2015)
B. Janaszek, M. Kieliszczyk, A. Tyszka-Zawadzka, P. Szczepanski, Multi resonance response in hyperbolic metamaterials. Appl. Opt. 57, 2135 (2018)
A.H.M. Almawgani, M.G. Daher, S.A. Taya, M. Mashagbeh, I. Colak, Optical detection of fat concentration in milk using MXene based surface plasmon resonance structure. Biosensors 12, 535 (2022)
B. Han, Y. Zhang, S.E.X. Wang, D. Yang, T. Wang, K. Lu, F. Wang, Simultaneous measurement of temperature and strain based on dual SPR effect in PCF. Opt. Laser Technol. 113, 46–51 (2019)
D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, M. Qiu, Ultra-narrowband light dissipation by a stack of lamellar silver and alumina. Appl. Phys. Lett. 104, 221107 (2014)
J. Kim, V.P. Drachev, Z. Jacob, G.V. Naik, A. Boltasseva, E.E. Narimanov, V.M. Shalaev, Improving the radiative decay rate for dye molecules with hyperbolic metamaterials. Opt. Express 20, 8100–8116 (2012)
M.Y. Shalaginov, S. Ishii, J. Liu, J. Liu, J. Irudayaraj, A. Lagutchev, A.V. Kildishev, V.M. Shalaev, Broadband enhancement of spontaneous emission from nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials. Appl. Phys. Lett. 102, 173114 (2013)
B.W. Stuart, X. Tao, D. Gregory, H.E. Assender, Roll-to-roll patterning of Al/Cu/Ag electrodes on flexible poly(ethylene terephthalate) by oil masking: a comparison of thermal evaporation and magnetron sputtering. Appl. Surf. Sci. 505, 144294 (2020)
M. Shaban, A.M. Ahmed, E. Abdel-Rahman, H. Hamdy, Tunability and sensing properties of plasmonic/1D photonic crystal. Sci. Rep. 7, 41983 (2017)
J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, X. Zhang, Spherical hyperlens for two-dimensional sub-diffractional imaging at visible frequencies. Nat. Commun. 1, 143 (2010)
A.J. Hoffman, L. Alekseyev, S.S. Howard, K.J. Franz, D. Wasserman, V.A. Podolskiy, E.E. Narimanov, D.L. Sivco, C. Gmachl, Negative refraction in semiconductor metamaterials. Nat. Mater. 6, 946–950 (2007)
H. Shen, Z. Wang, Y. Wu, B. Yang, One-dimensional photonic crystals: fabrication, responsiveness and emerging applications in 3D construction. RSC Adv. 6, 4505–4520 (2016)
L. González-García, S. Colodrero, H. Míguez, A.R. González-Elipe, Single-step fabrication process of 1-D photonic crystals coupled to nanocolumnar TiO2 layers to improve DSC efficiency. Opt. Express 23(24), A1642–A1650 (2015)
K. Fukukawa, M. Ueda, recent progress of photosensitive polyimides. Polym. J. 40, 281–296 (2008)
J.P.-P. González, A. Lamure, F. Senocq, Surf. Coat. Technol. 201, 9437–9944 (2007)
S.-M. Lian, K.-M. Chen, R.-J. Lee, J.-P. Pan, A. Hung, Chemical etching of polyimide film. J. Appl. Polym. Sci. 58(9), 1577–1584 (1995)
A.M. Ahmed, A. Mehaney, Ultra-high sensitive 1D porous silicon photonic crystal sensor based on the coupling of Tamm/Fano resonances in the mid-infrared region. Sci. Rep. 9, 6973 (2019)
R. Xiong, J. Luan, S. Kang, C. Ye, S. Singamaneni, V. V. Tsukruk, Biopolymeric photonic structures: design, fabrication, and emerging applications. Chem. Soc. Rev. 49, 983–1031 (2020)
J. Hoffmann, T. Lehnert, D. Hoffmann, H. Fouckhardt, Advantages and disadvantages of sulfur passivation of InAs/GaSb superlattice waveguide photodiodes. Semicond. Sci. Technol. 24(6), 65008 (2009)
D.A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, I. Vendik, How far are we from making metamaterials by self-organization? The microstructure of highly anisotropic particles with an srr-like geometry. Adv. Funct. Mater. 20, 1116 (2010)
A.C. Edrington, A.M. Urbas, P. DeRege, C.X. Chen, T.M. Swager, N. Hadjichristidis, M. Xenidou, L.J. Fetters, J.D. Joannopoulos, Y. Fink, Polymer-based photonic crystals. Adv. Mater. 13, 421 (2001)
I. Vukovic, S. Punzhin, Z. Vukovic, P. Onck, J.T.M. De Hosson, G. ten Brinke, K. Loos, Supramolecular route to well-ordered metal nanofoams. ACS Nano 5, 6339 (2011)
S.S. Oh, A. Demetriadou, S. Wuestner, O. Hess, On the origin of chirality in nanoplasmonic gyroid metamaterials. Adv. Mater. 25, 612 (2013)
P. Farah, A. Demetriadou, S. Salvatore, S. Vignolini, M. Stefik, U. Wiesner, O. Hess, U. Steiner, V.K. Valev, J.J. Baumberg, Ultrafast nonlinear response of gold gyroid three-dimensional meta-materials. Phys. Rev. Appl. 2, 044002 (2014)
F. Wu, G. Lu, C. Xue, H. Jiang, Z. Guo, M. Zheng, C. Chen, G. Du, H. Chen, Experimental demonstration of angle-independent gaps in one-dimensionalphotonic crystals containing layered hyperbolic metamaterials and dielectrics atvisible wavelengths. Appl. Phys. Lett. 112, 041902 (2018)
A. Demetriadou, O. Hess, Analytic theory of optical nanoplasmonic metamaterias. Phys. Rev. B 87, 161101 (2013)
A. Demetriadou, S.S. Oh, S. Wuestner, O. Hess, A trihelical model for nanoplasmonic gyroid metamaterials. New J. Phys. 14, 083032 (2012)
F. Wu, G. Lu, Z. Guo, H. Jiang, C. Xue, M. Zheng, C. Chen, G. Du, H. Chen, Redshift gaps in one-dimensional photonic crystals containing hyperbolic metamaterials. Phys. Rev. Appl. 10(6), 064022 (2018)
F. Wang, Y.Z. Cheng, X. Wang, D. Qi, H. Luo, R.Z. Gong, Effective modulation of the photonic band gap based on Ge/ZnS one-dimensional photonic crystal at the infrared band. Opt. Mater. 75, 373–378 (2018)
D.M. Calvo-Velasco, R. Sanchez-Cano, Omnidirectional photonic band gaps in one-dimensional gradient refractive index photonic crystals considering linear and quadratic profiles. Curr. Appl. Phys. 35, 72–77 (2022)
G. Lu, X. Zhou, Y. Zhao, K. Zhang, H. Zhou, J. Li, C. Diao, F. Liu, A. Wu, G. Du, Omnidirectional photonic bandgap in one-dimensional photonic crystals containing hyperbolic metamaterials. Opt. Express 29(20), 31915–31923 (2021)
B.K. Singh, M.K. Chaudhari, P.C. Pandey, Photonic and omnidirectional band gap engineering in one-dimensional photonic crystals consisting of linearly graded index material. J. Lightwave Technol. 34(10), 2431–2438 (2016)
Y. Kang, H. Liu, Wideband absorption in one dimensional photonic crystal with graphene-based hyperbolic metamaterials. Superlattices Microstruct. 114, 355–360 (2018)
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The authors are thankful to the Deanship of Scientific Research at Najran University for funding this work under the Research Priorities and Najran Research funding program grant code (NU/NRP/SERC/12/5).
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Project administration, AHMA, GAA, MI, MM, HAE, and AM; Supervision, AHMA, GAA, MI, MM, HAE, and AM; Software, AHMA, and GAA; Visualization, AM, and MM; Writing—review & editing, AHMA, MM, HAE, and AM; Writing—original draft, MM; Methodology, MM, and HAE; Data curation, HAE, and MM; All authors have read and agreed to the published version of the manuscript.
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Almawgani, A.H.M., Medhat, M., Mehaney, A. et al. One-dimensional metamaterial photonic crystals comprising gyroidal and hyperbolic layers as an angle-insensitive reflector for energy applications in IR regions. Eur. Phys. J. Plus 138, 483 (2023). https://doi.org/10.1140/epjp/s13360-023-04080-4
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DOI: https://doi.org/10.1140/epjp/s13360-023-04080-4