An iterative method for solving the problem of diffraction on a nonlinear dielectric lattice in strong electromagnetic fields
A.M. Lerer1, I.N. Ivanova1, V.I. Kravchenko 1
1Southern Federal University, Rostov-on-Don, Russia
Email: erer@sfedu.ru
Three problems of nonlinear electrodynamics have been solved. An analytical solution of boundary value problems on the reflection of an electromagnetic wave from a dielectric layer coated with nonlinear graphene and from a nonlinear dielectric layer is presented. A method for solving a nonlinear integro-differential equation (IDE) of the second kind for diffraction problems on a nonlinear dielectric body is proposed. It is shown that an IDE can be transformed to an IDE with a linear integral term and a nonlinear free term. This significantly increases the speed of calculations. An iterative method has been implemented to solve the transformed IDE. Keywords: nonlinear dielectric, graphene, reflection, diffraction, integro-differential equation, Galerkin method, perturbation method.
- J. Wang, S.A. Maier, A. Tittl. Adv. Opt. Mater., 10 (7), 2102366 (2022)
- A.S. Solntsev, G.S. Agarwal, Y.S. Kivshar. Nat. Photonics, 15, 327 (2021)
- M.J. Huttunen, S. Bin-Alam, O. Reshef, Y. Mamchur, T. Stolt, J.-M. Menard, K. Dolgaleva, R.W. Boyd, M. Kauranen. 2020 22nd Int. Conf. on Transparent Optical Networks (ICTON). DOI: 10.1109/ICTON51198.2020.9203026
- T. Santiago-Cruz, S.D. Gennaro, O. Mitrofanov, S. Addamane, J. Reno, I. Brener, M.V. Chekhova. Science, 377, 991(2022)
- M.J. Huttunen, R. Czaplicki, M. Kauranen. J. Nonlinear Opt. Phys. Mater., 28, 1950001 (2019)
- D. Hahnel, C. Golla, M. Albert, T. Zentgraf, V. Myroshnychenko, J. Forstner, C. Meier. Light Sci. Appl., 12, 97 (2023). https://doi.org/10.1038/s41377-023-01134-1
- Hui-Hsin Hsiao, Jou-Chun Hsieh, Ai-Yin Liu, Kuang-I Lin, Yi-Chien Hsu. Nanophotonics, 13 (17), (2024). DOI: org/10.1515/nanoph-2024-0194
- Y. Ra'di, N. Nefedkin, P. Popovski, A. Al\`u. IEEE Antennas and Propagation Magazine, 66 (5), 52 (2024)
- J. Noh, T. Santiago-Cruz, S.D. Gennaro. V. Sultanov, I. Brener, M.V. Chekhova. CLEO Optica Publishing Group, FM3O.1 (2024)
- J.H. Krakofsky, S. Stich, G. Boohm, M.A. Belkin. CLEO Optica Publishing Group, SM4P.3. (2024)
- M.D. Feinstein1, A. Adronikides, E. Almeida. CLEO Optica Publishing Group, FTh1P.6. (2024)
- I. Brener. 2024 Intern. Conf. on Optical MEMS and Nanophotonics (OMN). DOI: 10.1109/OMN61224.2024.10685263
- S.A. Mikhailov. Europhys. Lett., 79, 27002 (2007)
- E. Hendry, P.J. Hale, J. Moger, A.K. Savchenko, S.A. Mikhailov. Phys. Rev. Lett., 105, 097401 (2010)
- V.V. Cherepanov. Electrodinamicheskiy analis plasmonnykh ustroistv na osnove grafena v TGz i IK diapazone (Avtoref. kand. diss. YuF, Rostov-on-Don, 2023) (in Russian)
- A.M. Lerer. J. Commun. Technol. Electron., 57 (11), 1151 (2012). DOI: 10.1134/S106422691210004X
- G.W. Hanson. J. Appl. Phys., 103 (6), 064302 (2008)
- J.L. Cheng, N. Vermeulen, J. Sipe. Phys. Rev. B, 91, 235320 (2015)
- S.A. Mikhailov. Phys. Rev. B, 93 (8), 085403 (2016)
- V.V. Cherepanov. Physicheskie osnovy pryborostroeniya 9 (4), 2 (2020) (in Russian)
- G.A. Kalinchenko, A. Lerer. J. Electromagnetic Waves and Application, 13 (11), 1539 (1999)
- A.M. Lerer, I.N. Ivanova. Tr. conf. Analyticheskiye i chislenniye metody modelyrovania estestvenno-nauchnykh i sotsialnykh problem AChM-2023. Set of articles on materials of the XVIII all-Russian conference ANM-2023 with the participation of foreign organizations. (Pensa, Russia, 2023), v. 1. v. 44
- A.M. Lerer. J. Commun. Technol. Electron., 57 (11), 1151 (2012). DOI: 10.1134/S106422691210004X
- A.M. Lerer, G.S. Makeeva, V.V. Cherepanov. J. Commun. Technol. Electron., 66 (6), 656 (2021). DOI: 10.1134/S1064226921060188
- M.E. Abbassi, L. Posa, P. Makk, C. Nef, K. Thodkar, A. Halbritter., M. Calame. Nanoscale, 9, 17312 (2017). DOI: 10.1039/C7NR05348G