Complex band structure of two-dimensional thermal wave crystals
DOI:
https://doi.org/10.31349/RevMexFis.70.061603Keywords:
Complex band; Cattaneo-VernotteAbstract
We investigate the complex band structure of temperature oscillations in a two-dimensional thermal wave crystal. We use the Cattaneo-Vernotte heat model to describe the thermal properties. We apply the plane wave method to calculate the complex band structure of a square lattice composed of an infinite array of square bars. We find that a complete band gap exists across the whole Brillouin zone, where temperature oscillations are forbidden. This has potential applications in thermal management, thermal cloaking, and other areas.
References
H. D.Weymann, Finite speed of propagation in heat conduction, diffusion, and viscous shear motion, American Journal of Physics 35 (1967) 488. https://doi.org/10.1119/1.1974155
M. Chester, Second sound in solids, Physical Review 131 (1963) 2013. https://doi.org/10.1103/physrev.131.2013
D. D. Joseph and L. Preziosi, Heat waves, Reviews of Modern Physics 61 (1989) 41. https://doi.org/10.1103/revmodphys.61.41
M. Wang, N. Yang, and Z.-Y. Guo, Non-fourier heat conductions in nanomaterials, Journal of Applied Physics 110 (2011) 064310. https://doi.org/10.1063/1.3634078
A. I. Zhmakin, Non-Fourier Heat Conduction (Springer International Publishing, 2023). https://doi.org/10.1007/978-3-031-25973-9
C. Cattaneo, A form of heat-conduction equations which eliminates the paradox of instantaneous propagation, Comptes Rendus 247 (1958) 431
P. Vernotte, Les paradoxes de la theorie continue de l’equation de la chaleur, Comptes rendus 246 (1958) 3154
D. S. Chandrasekharaiah, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Reviews 51 (1998) 705. https://doi.org/10.1115/1.3098984
D. Y. Tzou, The generalized lagging response in smallscale and high-rate heating, International Journal of Heat and Mass Transfer 38 (1995) 3231. https://doi.org/10.1016/0017-9310(95)00052-b
S. K. R. Choudhuri, On a thermoelastic three-phase-lag model, Journal of Thermal Stresses 30 (2007) 231. https://doi.org/10.1080/01495730601130919
A.-L. Chen, Z.-Y. Li, T.-X. Ma, X.-S. Li, and Y.- S.Wang, Heat reduction by thermal wave crystals, International Journal of Heat and Mass Transfer 121 (2018) 215. https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.136
R. D. V. Meade, S. G. Johnson, and J. N. Winn, Photonic crystals: Molding the flow of light (2008)
E. Guevara-Cabrera, M. Palomino-Ovando, B. Flores- Desirena, and J. Gaspar-Armenta, Dispersive photonic crystals from the plane wave method, Physica B: Condensed Matter 484 (2016) 53. https://doi.org/10.1016/j.physb.2015.12.030
S. Brand, R. Abram, and M. Kaliteevski, Complex photonic band structure and effective plasma frequency of a twodimensional array of metal rods, Physical Review B 75 (2007) 035102. https://doi.org/10.1103/PhysRevB.75.035102
M. Maldovan, Narrow low-frequency spectrum and heat management by thermocrystals, Physical Review Letters 110 (2013) 025902. https://doi.org/10.1103/physrevlett.110.025902
L. Xu, J. Huang, and X. Ouyang, Tunable thermal wave nonreciprocity by spatiotemporal modulation, Phys. Rev. E 103 (2021) 032128. https://doi.org/10.1103/PhysRevE.103.032128
Z. Zhang, L. Xu, X. Ouyang, and J. Huang, Guiding temperature waves with graded metamaterials, Thermal Science and Engineering Progress 23 (2021) 100926. https://doi.org/10.1016/j.tsep.2021.100926
A. Camacho de la Rosa, D. Becerril, M. G. Gómez- Farfán, and R. Esquivel-Sirvent, Bragg mirrors for thermal waves, Energies 14 (2021). https://doi.org/10.3390/en14227452
G. Morales-Morales and J. Manzanares-Martinez, Enlargement of band gaps on thermal wave crystals by using heterostructures, Results in Physics 42 (2022) 106019. https://doi.org/10.1016/j.rinp.2022.106019
K. Xu and C. Jiang, Expanding the bandgap of thermal phonons by using supercrystals, Results in Physics 17 (2020) 103015. https://doi.org/10.1016/j.rinp.2020.103015
J. Ordonez-Miranda, Y. Guo, J. J. Alvarado-Gil, S. Volz, and M. Nomura, Thermal-wave diode, Phys. Rev. Appl. 16 (2021) L041002. https://doi.org/10.1103/PhysRevApplied.16.L041002
J. Wang, G. Dai, and J. Huang, Thermal metamaterial: Fundamental, application, and outlook, iScience 23 (2020) 101637. https://doi.org/10.1016/j.isci.2020.101637
T.-Z. Yang, Y. Su, W. Xu, and X.-D. Yang, Transient thermal camouflage and heat signature control, Applied Physics Letters 109 (2016). https://doi.org/10.1063/1.4963095
A. A. Zul Karnain, S. A. R. Kuchibhatla, T. Thomas, and P. Rajagopal, Semiconductor-based thermal wave crystals, ISSS Journal of Micro and Smart Systems 9 (2020) 181. https://doi.org/10.1007/s41683-020-00061-2
A. Camacho de la Rosa, D. Becerril, M. G. Gómez- Farfán, and R. Esquivel-Sirvent, Bragg mirrors for thermal waves, Energies 14 (2021) 7452. https://doi.org/10.3390/en14227452
G. Morales-Morales and J. Manzanares-Martinez, Enlargement of band gaps on thermal wave crystals by using heterostructures, Results in Physics 42 (2022) 106019. https://doi.org/10.1016/j.rinp.2022.106019
Z.-Y. Li, T.-X. Ma, A.-L. Chen, Y.-S. Wang, and C. Zhang, Thermal wave crystals based on the dualphase- lag model, Results in Physics 19 (2020) 103371. https://doi.org/10.1016/j.rinp.2020.103371
C. A. Romero-Ramos, B. Manzanares-Martinez, D. SotoPuebla, and J. Manzanares-Martinez, Complex band structure of thermal wave crystals: The plane-wave method, Rev. Mex. Fis. 70 (2024) 031601. https://doi.org/10.31349/RevMexFis.70.031601
R. Shirzadkhani, S. Eskandari, and A. Akbarzadeh, Nonfourier thermal wave in 2d cellular metamaterials: From transient heat propagation to harmonic band gaps, International Journal of Heat and Mass Transfer 205 (2023) 123917. https://doi.org/10.1016/j.ijheatmasstransfer.2023.123917
Z.-Y. Li et al. Non-fourier heat conduction in 2d thermal metamaterials, Materials Today Communications 38 (2024) 107828. https://doi.org/10.1016/j.mtcomm.2023.107828
J. D. Jackson, Classical electrodynamics (1999)
M. Botey et al., Unlocked evanescent waves in periodic structures, Optics Letters 38 (2013) 1890. https://doi.org/10.1364/OL.38.001890
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 C. A. Romero-Ramos, J. Manzanares-Martinez, D. Soto-Puebla, B. Manzanares Martínez
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.