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Simulation of the evolution of laser beams in impurity carbon nanotubes using the Madelung approach
E.A. Kuvshinov 1, R.R. Trofimov 1, N.N. Konobeeva 1

1 Volgograd State University, 400062, Volgograd, University avenue 100

 PDF, 704 kB

DOI: 10.18287/2412-6179-CO-1545

Pages: 200-204.

Full text of article: English language.

Abstract:
The relevance of modeling the interaction of electromagnetic waves with various materials exhibiting nonlinear properties is increasing every year. In this work, we studied the dynamics of laser beams propagating in a medium of single-walled carbon nanotubes with impurities, placed in a dielectric. By multilevel impurity, we mean an impurity whose energy levels are separated from the conduction band and valence band in carbon nanotubes and lie inside the band gap of the dielectric medium. The novelty of this work lies in the development of a model for the evolution of electromagnetic radiation in the infrared range is constructed using the Madelung transform for the nonlinear Schrödinger equation, the numerical implementation of which is carried out using the smoothed-particle hydrodynamics. The influence of impurity parameters on the laser beam propagation in a given medium, namely, the energy of electron transitions from impurity levels to the first and second sublattices of nanotubes, is analyzed.

Keywords:
laser beam, carbon nanotubes, impurities, hydrodynamic approach.

Citation:
Kuvshinov EA, Trofimov RR, Konobeeva NN. Simulation of the evolution of laser beams in impurity carbon nanotubes using the Madelung approach. Computer Optics 2025; 49(2): 200-204. DOI: 10.18287/2412-6179-CO-1545.

Acknowledgements:
The study was supported by the Russian Science Foundation (RSF) (grant no. 23-71-00016, https://rscf.ru/project/23-71-00016/). The work was carried out using the equipment of the Center for Collective Use of Ultra-High-Performance Computing Resources of Moscow State University named after M.V. Lomonosov.

References:
  1. Bulat PV, Volkov KN, Ilyina EYe. Model of interaction of laser radiation with a drop of liquid. Int Elect J Math Ed 2016; 11(8): 3009-3020.
  2. Miloshevsky G. Ultrafast laser matter interactions: modeling approaches, challenges, and prospects. Model Simul Mater Sci Eng 2022: 30(8); 083001. DOI: 10.1088/1361-651X/ac8abc.
  3. Khalyapin VA, Bugay AN. Analytical study of light bullets stabilization in the ionized medium. Chaos, Solitons & Fractals 2022; 156: 111799. DOI: 10.1016/j.chaos.2022.111799.
  4. Iijima S. Synthesis of carbon nanotubes. Nature 1991; 354: 56-58. DOI: 10.1038/354056a0.
  5. Yamashita S. Nonlinear optics in carbon nanotube, graphene, and related 2D materials. APL Photonics 2019; 4(3): 034301. DOI: 10.1063/1.5051796.
  6. Zhan J, Qin J, Tan S, Liu S, Zhou R, Chen Y. A novel nanotube-based fiber laser for ultrashort pulse generation and fast measurements. Modern Instrumentation 2018; 7(2); 24-34. DOI: 10.4236/mi.2018.72003.
  7. Liu X, Popa D, Akhmediev N. Revealing the transition dynamics from Q switching to mode locking in a soliton laser. Phys Rev Lett 2019; 123(3): 093901. DOI: 10.1103/PhysRevLett.123.093901.
  8. Pyatkov F, Khasminskaya S, Kovalyuk V, Frank Hennrich F, Kappes MM, Goltsman GN, Pernice WHP, Krupke R. Sub-nanosecond light-pulse generation with waveguide-coupled carbon nanotube transducers. Beilstein J Nanotechnol 2017; 8: 38-44. DOI: 10.3762/bjnano.8.5.
  9. Uda T, Ishii A, Kato YK. Single carbon nanotubes as ultrasmall all-optical memories. ACS Photonics 2018; 5(2): 559-565. DOI: 10.1021/acsphotonics.7b01104.
  10. Belonenko MB, Lebedev NG, Popov AS. Two-dimensional light bullets in an array of carbon nanotubes. JETP Lett 2010; 91(9): 461-465. DOI: 10.1134/S0021364010090067.
  11. Konobeeva NN, Fedorov EG, Rosanov NN, Zhukov AV, Bouffanais R, Belonenko MB. Stabilization of ultrashort pulses by external pumping in an array of carbon nanotubes subject to piezoelectric effects. J Appl Phys 2019; 126(20): 203103. DOI: 10.1063/1.5128365.
  12. Fedorov EG, Zhukov AV, Bouffanais R, Konobeeva NN, Boroznina EV, Malomed BA, Leblond H, Mihalache D, Belonenko MB, Rosanov NN, George TF. External light control of three-dimensional ultrashort far-infrared pulses in an inhomogeneous array of carbon nanotubes. Phys Rev B 2021; 103(8): 085111. DOI: 10.1103/PhysRevB.103.085111.
  13. Konobeeva NN, Belonenko MB. Influence of a magnetic field on the propagation of ultrashort optical pulses in anisotropic optical media with carbon nanotubes. Nanosystems: Physics, Chemistry, Mathematics. 2021; 12(4): 430-435. DOI: 10.17586/2220-8054-2021-12-4-430-435.
  14. Madelung E. Quantentheorie in hydrodynamischer Form. Zeitschrift für Physik 1927; 40(3-4): 322-326. DOI: 10.1007/BF01400372.
  15. Auletta G. Foundation and interpretation of quantum mechanics. Singapore: World Scientific; 2000. ISBN: 981-02-4614-5.
  16. Lee J-H, Lin C-K. The behavior of solutions of NLS equation of derivative type in the semiclassical limit. Chaos, Solitons & Fractals 2002; 13(7); 1475-1492. DOI: 10.1016/S0960-0779(01)00157-6.
  17. Khesin B, Misiolek G, Modin K. Geometry of the Madelung transform. Arch Ration Mech Anal 2019; 234(2): 549-573. DOI: 10.1007/s00205-019-01397-2.
  18. Zylberman J, Di Molfetta G, Brachet M, Loureiro NF, Debbasch F. Quantum simulations of hydrodynamics via the Madelung transformation. Phys Rev A 2022; 106(3): 032408. DOI: 10.1103/PhysRevA.106.032408.
  19. Fedorov EG, Konobeeva NN, Belonenko MB. Two-dimensional electromagnetic breathers in an array of nanotubes with multilevel impurities. Russ J Phys Chem B 2014: 8: 409-415. DOI: 10.1134/S1990793114030051.
  20. Epshtein EM. Solitons in a superlattice [In Russian]. Fizika Tverdogo Tela 1976; 19: 3456-3458.
  21. Eletskii AV. Carbon nanotubes. Phys Usp 1977; 40(9): 899-924. DOI: 10.1070/PU1997v040n09ABEH000282.
  22. Akhmediev N, Ankiewicz A. Solitons. Non-linear pulses and beams [In Russian]. Moscow: "Fizmatlit" Publisher; 2003.
  23. Mocz P, Succi S. Numerical solution of the nonlinear Schrödinger equation using smoothed-particle hydrodynamics. Phys Rev E 2015; 91(5): 053304. DOI: 10.1103/PhysRevE.91.053304.
  24. Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 1977; 181(3): 375-389. DOI: 10.1093/mnras/181.3.375.
  25. Monaghan JJ, Lattanzio JC. A refined particle method for astrophysical problems. Astron Astrophys 1985; 149(1): 135-143.
  26. Balac S, Mahé F. An Embedded Split-Step method for solving the nonlinear Schrödinger equation in optics. J Comput Phys 2015; 280: 295-305. DOI: 10.1016/j.jcp.2014.09.018.
  27. Monin EO, Khonina SN. Modeling the propagation of autofocusing beams in a linear and nonlinear optical medium. 2021 Int Conf on Information Technology and Nanotechnology (ITNT) 2021: 1-4. DOI: 10.1109/ITNT52450.2021.9649114.
  28. Jiang T, Chen Z-C, Lu W-G, Yuan J-Y, Wang D-S. An efficient split-step and implicit pure mesh-free method for the 2D/3D nonlinear Gross–Pitaevskii equations. Comput Phys Commun 2018; 231: 19-30. DOI: 10.1016/j.cpc.2018.05.007.

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