Abstract
The purpose of this study is develop a method for mathematical simulation of nonlinear effects (parametric generation and parametric excitation of waves and instabilities) caused by the interaction between electromagnetic waves and highly nonlinear multilayer graphene nanostructures based on the solution of a nonlinear diffraction problem for Maxwell’s equations with allowance for confining geometries. A numerical method has been developed for bifurcation analysis of nonlinear effects (parametric generation and parametric excitation of waves) arising in graphene nanostructures in the terahertz range. It consists of finding the bifurcation points of the nonlinear Maxwell operator using the developed computational algorithm, which was improved by a qualitative analysis method based on the Lyapunov stability theory. The developed computational algorithm has been applied to obtain results of the electrodynamic calculation of the terahertz wave generation thresholds and instability regions in a multilayer graphene nanostructure depending on the bifurcation parameters: pump wave amplitude and normalized frequency. It follows from the results of rigorous mathematical simulation that the terahertz wave generation thresholds depend on the chemical potential; therefore, characteristics of parametric terahertz generators based on multilayer graphene nanostructures can be tuned by an external bias electric field and controlled by the configuration and sizes of the nanostructures.
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REFERENCES
T. Jiang, V. Kravtsov, M. Tokman, A. Belyanin, et al., Nat. Nanotechnol. 14, 838 (2019).
J. C. Deinert, D. Alcaraz Iranzo, R. Pérez, X. Jia, et al., ACS Nano 15, 1145 (2021).
J. D. Cox, A. Marini, and F. J. García de Abajo, Opt. Commun. 406, 183 (2018).
P. M. Romanenko and S. A. Mikaeva, in Informatics and Technology. Innovative Technologies in Industry and Informatics (MIREA, Moscow, 2019), Vol. 2, p. 268 [in Russian].
D. Rodrigo, A. Tittl, O. Limaj, F. J. García de Abajo, et al., Light: Sci. Appl., 16277 (2017).
G. A. Menendez and B. Maes, Phys. Rev. B 95, 144307 (2017).
J. D. Cox and F. J. García de Abajo, Acc. Chem. Res. 52, 2536 (2019).
G. S. Makeeva and O. A. Golovanov, J. Commun. Technol. Electron. 52, 96 (2007).
O. A. Golovanov, J. Commun. Technol. Electron. 51, 1338 (2006).
G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
O. A. Golovanov and G. S. Makeeva, J. Commun. Technol. Electron. 54, 1345 (2009).
O. A. Golovanov, Radiotekh. Elektron. 35, 1853 (1990).
O. A. Golovanov, G. S. Makeeva, and A. B. Rinkevich, Tech. Phys. 86, 274 (2016).
V. V. Nikol’skii, Projection Methods in Electrodynamics: Collection of Scientific and Methodological Articles on Applied Electrodynamics (Vysshaya Shkola, Moscow, 1977) [in Russian].
A. M. Lyapunov, General Problem of the Stability of Motion (Gostekhizdat, Moscow, 1950; CRC, Boca Raton, FL, 1992).
M. A. Krasnosel’skii, Functional Analysis (Nauka, Moscow, 1964) [in Russian].
ACKNOWLEDGMENTS
Development of the computational method and the related algorithm was performed by O.A. Golovanov.
Funding
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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Translated by A. Sin’kov
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Makeeva, G.S. Bifurcation Analysis of the Thresholds of Parametric Generation of Terahertz Waves in Nonlinear Multilayer Graphene Nanostructures. Tech. Phys. Lett. 49, 55–63 (2023). https://doi.org/10.1134/S1063785023050012
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DOI: https://doi.org/10.1134/S1063785023050012