Complex band structure of thermal wave crystals: The plane-wave method
DOI:
https://doi.org/10.31349/RevMexFis.70.031601Keywords:
Heat; non-Fourier; crystalAbstract
In this paper, we present an extension of the plane-wave method (PWM) to compute the complex band structure of thermal wave crystals (TWCs). The structural periodicity of TWC allows the possibility to manipulate non-Fourier heat via wave interference. While the Cattaneo-Vernotte (CV) heat conduction theory accurately models oscillatory wave-like propagation of heat in TWCs, obtaining an eigenvalue equation for frequency using the CV wave equation is not possible. To overcome this limitation, we propose a novel approach that solves a complex eigenvalue equation for the Bloch wave vectors
References
A.-L. Chen, et al., Heat reduction by thermal wave crystals, International Journal of Heat and Mass Transfer 121 (2018) 215
G.-L. Dai, Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics, Frontiers of Physics 16 (2021) 1
A. Camacho de la Rosa, et al., Bragg Mirrors for Thermal Waves, Energies 14 (2021) 7452
G. Morales-Morales and J. Manzanares-Martinez, Enlargement of band gaps on thermal wave crystals by using heterostructures, Results in Physics 42 (2022) 106019
A. C. de la Rosa and R. Esquivel-Sirvent, Causality in nonfourier heat conduction, Journal of Physics Communications 6 (2022) 105003, https://doi.org/10.1088/2399-6528/ac9774
Z.-Y. Li, et al., Thermal wave crystals based on the dualphaselag model, Results in Physics 19 (2020) 103371
A. A. Z. Karnain, et al., Semiconductor-based thermal wave crystals, ISSS Journal of Micro and Smart Systems 9 (2020) 181
D. Chandrasekharaiah, Hyperbolic Thermoelasticity: A Review of Recent Literature, Applied Mechanics Reviews 51 (1998) 705
E. Yablonovitch, Inhibited Spontaneous Emission in Solid State Physics and Electronics, Phys. Rev. Lett. 58 (1987) 2059
M. S. Kushwaha, et al., Acoustic band structure of periodic elastic composites, Phys. Rev. Lett. 71 (1993) 2022
S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58 (1987) 2486
E. Yablonovitch and T. J. Gmitter, Photonic band structure: The face-centered-cubic case, Phys. Rev. Lett. 63 (1989) 1950
K. M. Ho, C. T. Chan, and C. M. Soukoulis, Existence of a photonic gap in periodic dielectric structures, Phys. Rev. Lett. 65 (1990) 3152
S. Brand, R. A. Abram, and M. A. Kaliteevski, Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods, Phys. Rev. B 75 (2007) 035102
V. Kuzmiak, A. A. Maradudin, and F. Pincemin, Photonic band structures of two-dimensional systems containing metallic components, Phys. Rev. B 50 (1994) 16835
V. Kuzmiak and A. A. Maradudin, Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation, Phys. Rev. B 55 (1997) 7427
V. Kuzmiak, A. Maradudin, and A. McGurn, Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal, Physical Review B 55 (1997) 4298
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
E. Guevara-Cabrera, et al., Dispersive photonic crystals from the plane wave method, Physica B: Condensed Matter 484 (2016) 53
L. Schalcher, J. Dos Santos, and E. Miranda Jr, Extended plane wave expansion formulation for 1-D viscoelastic phononic crystals, Partial Differential Equations in Applied Mathematics (2023) 100489
M. Plihal, et al., Two-dimensional photonic band structures, Optics Communications 80 (1991) 199
S. G. Romanov, et al., Diffraction of light from thin-film polymethylmethacrylate opaline photonic crystals, Phys. Rev. E 63 (2001) 056603
J. Flores Méndez, et al., Phononic Band Structure by Calculating Effective Parameters of One-Dimensional Metamaterials, Crystals 13 (2023)
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
T. Suzuki and K. Paul, Complex photonic band structures of a conductive metal lattice by a quadratic eigensystem, Optics letters 20 (1995) 2520
A. Beardo, et al., Observation of second sound in a rapidly varying temperature field in Ge, Science advances 7 (2021) eabg4677
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Cesar Augusto Romero-Ramos, Betsabe Manzanares-Martinez, Diego Soto-Puebla, Jesus Manzanares-Martinez
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.
