Effective medium theory of a concentric metamaterial bifunctional cloak
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Oleg Rybin
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Sergey Shulga
Abstract
This study investigates a bifunctional cloak composed of concentric metamaterials arranged in 4N thin layers, where N denotes the number of periodic layer pairs within the structure. The structure includes an inner circular domain, an outer domain, and alternating sequences of 2N layers between them. We explore two models: one using isotropic materials and another one using anisotropic materials. The anisotropic model demonstrates superior cloaking performance for both electrical and thermal fields. Analytical solutions based on the Effective Medium Theory and boundary-value problems reveal the structure’s response under quasi-static conditions. Numerical simulations using COMSOL validate these findings, highlighting the cloak’s and concentration’s ability to manipulate external thermal and electric fields efficiently.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The authors state no conflict of interest.
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Research funding: None declared.
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Data availability: Not applicable.
References
[1] U. Leonhardt, “Optical conformal mapping,” Science, vol. 312, no. 5781, pp. 1777–1780, 2006. https://doi.org/10.1126/science.1126493.Search in Google Scholar PubMed
[2] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science, vol. 312, no. 5781, pp. 1780–1782, 2006. https://doi.org/10.1126/science.1125907.Search in Google Scholar PubMed
[3] U. Brosa, “Electromagnetic waves in variable media,” Z. Naturforsch. A, vol. 67, nos. 3–4, pp. 111–131, 2012. https://doi.org/10.5560/zna.2011-0069.Search in Google Scholar
[4] L. Xu and H. Chen, “Transformation metamaterials,” Adv. Mater., vol. 33, no. 52, p. 2005489, 2021. https://doi.org/10.1002/adma.202005489.Search in Google Scholar PubMed
[5] M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt., vol. 18, no. 4, p. 044002, 2016. https://doi.org/10.1088/2040-8978/18/4/044002.Search in Google Scholar
[6] F. J. F. Gonçalves, R. C. Mesquita, and E. J. Silva, “Hybrid nonsingular mappings in the multi-objective design of a transverse-magnetic reduced cloak,” J. Electromagn. Waves Appl., vol. 35, no. 2, pp. 220–232, 2021. https://doi.org/10.1080/09205071.2020.1829092.Search in Google Scholar
[7] A. Golgoon and A. Yavari, “Transformation cloaking in elastic plates,” J. Nonlinear Sci., vol. 31, no. 1, pp. 1–76, 2021. https://doi.org/10.1007/s00332-020-09660-7.Search in Google Scholar
[8] P. Ang and G. V. Eleftheriades, “Incident-field estimation for active cloaking,” Phys. Rev. Appl., vol. 16, no. 6, p. 064005, 2021. https://doi.org/10.1103/PhysRevApplied.16.064005.Search in Google Scholar
[9] A. Steckiewicz and A. Choroszucho, “Numerical investigation of quasi-static magnetic cloak performance in time-varying magnetic field,” Rom. J. Phys., vol. 64, no. 606, pp. 1–11, 2019.Search in Google Scholar
[10] W. Ahmad, B. B. Amin, U. Wahid, A. Ullah, and M. Haneef, “Distortion-free conductivity-dependent temporal cloak based on tunnelling chiral medium,” Eur. Phys. J. Plus, vol. 136, no. 3, p. 275, 2021. https://doi.org/10.1140/epjp/s13360-021-01268-4.Search in Google Scholar
[11] S. Eslamzadeh, M. Ghaffari-Miab, and B. Abbasi-Arand, “Design of a broadband metamaterial-based acoustic lens using elaborated carpet cloak strategy,” Appl. Phys. A, vol. 127, no. 12, p. 897, 2021. https://doi.org/10.1007/s00339-021-05043-1.Search in Google Scholar
[12] M. Raza, M. Ahsan, M. F. M. R. Wee, and M. A. Baqir, “Investigation of open cloaking of acoustic fields via transformation optics,” Acoust. Phys., vol. 70, no. 1, pp. 76–81, 2024. https://doi.org/10.1134/S1063771023600444.Search in Google Scholar
[13] H. Wang, N.-Z. Yao, and X. Wang, “A transient transformation theory for the design of convective thermal metamaterials: cloaks, concentrators, and rotators,” Int. J. Heat Mass Transport, vol. 221, 2024. https://doi.org/10.1016/j.ijheatmasstransfer.2023.125088.Search in Google Scholar
[14] H. M. Nguyen, “Cloaking an arbitrary object via anomalous localized resonance: the cloak is independent of the object,” SIAM J. Math. Anal., vol. 49, no. 4, pp. 3208–3232, 2017. https://doi.org/10.1137/16M1086017.Search in Google Scholar
[15] T. Chen, et al.., “Direct current remote cloak for arbitrary objects,” Light: Sci. Appl., vol. 8, no. 1, pp. 1–6, 2019. https://doi.org/10.1038/s41377-019-0141-2.Search in Google Scholar PubMed PubMed Central
[16] G. Fujii and Y. Akimoto, “Dc electric cloak concentrator via topology optimization,” Phys. Rev. E, vol. 102, no. 3, p. 033308, 2020. https://doi.org/10.1103/PhysRevE.102.033308.Search in Google Scholar PubMed
[17] L. Zhang and Y. Shi, “Bifunctional arbitrarily-shaped cloak for thermal and electric manipulations,” Opt. Mater. Express, vol. 8, no. 9, pp. 2600–2613, 2018. https://doi.org/10.1364/OME.8.002600.Search in Google Scholar
[18] M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys., vol. 117, no. 2, p. 024502, 2015. https://doi.org/10.1063/1.4905618.Search in Google Scholar
[19] G. Fujii and Y. Akimoto, “Electromagnetic-acoustic biphysical cloak designed through topology optimization,” Opt. Express, vol. 30, no. 4, pp. 6090–6106, 2022. https://doi.org/10.1364/OE.450787.Search in Google Scholar PubMed
[20] N. Xiang, et al.. “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express, vol. 8, no. 9, p. 092601, 2015. https://doi.org/10.7567/APEX.8.092601.Search in Google Scholar
[21] Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously.” Phys. Rev. Lett., vol. 113, no. 20, p. 205501, 2014. https://doi.org/10.1103/PhysRevLett.113.205501.Search in Google Scholar PubMed
[22] X. Zhang, X. He, and L. Wu, “Ellipsoidal bifunctional thermal-electric transparent device,” Compos. Struct., vol. 234, 2020. https://doi.org/10.1016/j.compstruct.2019.111717.Search in Google Scholar
[23] M. Raza, “An electric concentrator and thermal cloaking device,” Mater. Res. Express, vol. 7, no. 5, p. 055802, 2020. https://doi.org/10.1088/2053-1591/ab8fba.Search in Google Scholar
[24] C. Jiang, C. Fang, and X. Shen, “Multi-physics bi-Functional intelligent meta-device based on the shape memory alloys,” Crystals, vol. 9, no. 9, p. 438, 2019. https://doi.org/10.3390/cryst9090438.Search in Google Scholar
[25] M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electric current via bifunctional metamaterials,” Phys. Rev. X, vol. 4, no. 2, p. 021025, 2014. https://doi.org/10.1103/PhysRevX.4.021025.Search in Google Scholar
[26] I. Peralta, V. D. Fachinotti, and J. C. Alvarez Hostos. “A brief review on thermal metamaterials for cloaking and heat flux manipulation,” Adv. Eng. Mater., vol. 22, no 2, p. 1901034, 2020. https://doi.org/10.1002/adem.201901034.Search in Google Scholar
[27] M. Raza, M. Ahsan, W. B. Alonazi, S. A. Naqvi, and B. Braaten, “Design and analysis of arbitrary shaped bifunctional cloaks for multifunctional material composites,” Phys. Scr., vol. 98, no. 11, p. 115020, 2023. https://doi.org/10.1088/1402-4896/acfc6e.Search in Google Scholar
[28] M. Raza, O. Rybin, M. Ahsan, W. B. Alonazi, and K. Rameen, “Controlling the thermal and electric fields in isotropic and anisotropic media,” Phys. Scr., vol. 98, no. 10, p. 105913, 2023. https://doi.org/10.1088/1402-4896/acf3ae.Search in Google Scholar
[29] R. Wang, L. Xu, Q. Ji, and J. Huang, “A thermal theory for unifying and designing transparency, concentrating and cloaking,” J. Appl. Phys., vol. 123, no. 11, p. 115117, 2018. https://doi.org/10.1063/1.5019306.Search in Google Scholar
[30] F. Yang, L. Xu, and J. Huang, “Thermal illusion of porous media with convection-diffusion process: transparency, concentrating, and cloaking,” ES Energy Environ., vol. 6, no. 8, pp. 45–50, 2019. https://doi.org/10.30919/esee8c329.Search in Google Scholar
[31] C. W. Qiu, L. Hu, X. Xu, and Y. Feng, “Spherical cloaking with homogeneous isotropic multilayered structures,” Phys. Rev. E, vol. 79, no. 4, p. 047602, 2009. https://doi.org/10.1103/PhysRevE.79.047602.Search in Google Scholar PubMed
[32] D. S. Filonov, A. P. Slobozhanyuk, P. A. Belov, and Y. S. Kivshar, “Double-shell metamaterial coatings for plasmonic cloaking,” Phys. Status Solidi RRL, vol. 6, no. 1, pp. 46–48, 2012. https://doi.org/10.1002/pssr.201105475.Search in Google Scholar
[33] S. Batool, M. Nissar, F. Frezza, and F. Mangini, “Cloaking using the anisotropic multilayer sphere,” Photonics, vol. 7, no. 3, p. 52, 2020. https://doi.org/10.3390/photonics7030052.Search in Google Scholar
[34] K. Schulgasser, “Sphere assemblage model for polycrystals and symmetric materials,” J. Appl. Phys., vol. 54, no. 3, pp. 1380–1382, 1983. https://doi.org/10.1063/1.332161.Search in Google Scholar
[35] N. L. Tsitsas, H. M. Alkhoori, and A. Lakhtakia, “Theory of perturbation of electrostatic field by A coated anisotropic dielectric sphere,” Q. J. Mech. Appl. Math., vol. 76, no. 3, pp. 297–314, 2023. https://doi.org/10.1093/qjmam/hbad005.Search in Google Scholar
[36] A. Lakhtakia, N. L. Tsitsas, and H. M. Alkhoori, “Theory of perturbation of electrostatic field by an anisotropic dielectric sphere,” Q. J. Mech. Appl. Math., vol. 74, no. 4, pp. 467–490, 2021. https://doi.org/10.1093/qjmam/hbab013.Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Atomic, Molecular & Optical Physics
- Quantum chemical concept of oxidation states
- Dynamical Systems & Nonlinear Phenomena
- Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system
- Fundamental Concepts of Physical Science
- Fermi motion in nucleons and the generalized Heisenberg uncertainty relation
- Hydrodynamics & Plasma Physics
- Stability and convection in compressible partially ionized plasma layers: nonlinear and linear analysis
- Solid State Physics & Materials Science
- Effective medium theory of a concentric metamaterial bifunctional cloak
- Morphological impact on energy storage properties of 2D-MoS2 and its nanocomposites: a comprehensive review
- Exploring the implications of CoCrFeNiCu high entropy alloy coatings on tribomechanical, wetting behavior, and interfacial microstructural characterizations in microwave-clad AISI 304 stainless steels
Articles in the same Issue
- Frontmatter
- Atomic, Molecular & Optical Physics
- Quantum chemical concept of oxidation states
- Dynamical Systems & Nonlinear Phenomena
- Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system
- Fundamental Concepts of Physical Science
- Fermi motion in nucleons and the generalized Heisenberg uncertainty relation
- Hydrodynamics & Plasma Physics
- Stability and convection in compressible partially ionized plasma layers: nonlinear and linear analysis
- Solid State Physics & Materials Science
- Effective medium theory of a concentric metamaterial bifunctional cloak
- Morphological impact on energy storage properties of 2D-MoS2 and its nanocomposites: a comprehensive review
- Exploring the implications of CoCrFeNiCu high entropy alloy coatings on tribomechanical, wetting behavior, and interfacial microstructural characterizations in microwave-clad AISI 304 stainless steels
