- PII
- 10.31857/S0374064123090054-1
- DOI
- 10.31857/S0374064123090054
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 59 / Issue number 9
- Pages
- 1199-1204
- Abstract
- We consider the problem of leaky waves in an inhomogeneous waveguide structure covered with a layer of graphene, which is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. A variational statement of the problem is used to determine the solution. The variational problem is reduced to the study of an operator function. The properties of the operator function necessary for the analysis of its spectral properties are investigated. Theorems on the discreteness of the spectrum and on the distribution of the characteristic numbers of the operator function on the complex plane are proved.
- Keywords
- Date of publication
- 19.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 8
References
- 1. Geim A.K., Novoselov K.S. The rise of graphene // Nature Materials. 2007. V. 6. P. 183-191.
- 2. Hanson G.W. Dyadic Green's functions and guided surface waves for a surface conductivity model of graphene // J. of Appl. Phys. 2008. V. 103. Art. 064302.
- 3. Falkovsky L.A. Optical properties of graphene // J. of Phys.: Conf. Ser. 2008. V. 129. Art. 012004.
- 4. Mikhailov S.A. Quantum theory of the third-order nonlinear electrodynamic effects of graphene // Phys. Rev. B. 2016. V. 93. Art. 085403.
- 5. Смирнов Ю.Г. Математические методы исследования задач электродинамики. Пенза, 2009.
- 6. Shestopalov Y., Smirnov Y., Smolkin E. Optical Waveguide Theory. Mathematical Models, Spectral Theory and Numerical Analysis. Springer Ser. in Optical Sciences. V. 237. Singapore, 2022.
- 7. Hajian H., Rukhlenko I.D., Leung P.T., Caglayan H., Ozbay E. Guided plasmon modes of a graphene-coated Kerr slab // Plasmonics. 2016. V. 11. P. 735-741.
- 8. Smirnov Y., Tikhov S. The nonlinear eigenvalue problem of electromagnetic wave propagation in a dielectric layer covered with graphene // Photonics. 2023. V. 10. P. 523.
- 9. Смирнов Ю.Г., Тихов С.В., Гусарова Е.В. О распространении электромагнитных волн в диэлектрическом слое, покрытом графеном // Изв. вузов. Поволжский регион. Физ.-мат. науки. 2022. № 3. С. 11-18.
- 10. Никифоров А.Ф., Уваров В.Б. Специальные функции математической физики. М., 1978.
- 11. Adams R. Sobolev Spaces. New York, 1975.
- 12. Като Т. Теория возмущений линейных операторов. М., 1972.
- 13. Смирнов Ю.Г., Смолькин Е.Ю. О дискретности спектра в задаче о нормальных волнах открытого неоднородного волновода // Дифференц. уравнения. 2017. Т. 53. № 10. С. 1298-1309.
- 14. Абрамовиц М., Стиган И. Справочник по специальным функциям. М., 1979.
- 15. Гохберг И.Ц., Сигал Е.И. Операторное обобщение теоремы о логарифмическом вычете и теоремы Руше // Мат. сб. 1971. Т. 84 (126). № 4. С. 607-629.
