| Issue |
EPJ Web Conf.
Volume 226, 2020
Mathematical Modeling and Computational Physics 2019 (MMCP 2019)
|
|
|---|---|---|
| Article Number | 02003 | |
| Number of page(s) | 4 | |
| Section | Mathematical Modeling, Numerical Methods, and Simulation | |
| DOI | https://doi.org/10.1051/epjconf/202022602003 | |
| Published online | 20 January 2020 | |
https://doi.org/10.1051/epjconf/202022602003
Modelling Leaky Waves in Planar Dielectric Waveguides
1
Joint Institute for Nuclear Research,
Joliot-Curie 6,
141980
Dubna, Moscow Region,
Russia
2
Peoples’ Friendship University of Russia (RUDN University),
Miklukho-Maklaya 6,
117198
Moscow,
Russia
3
Prokhorov General Physics Institute, Russian Academy of Sciences,
Vavilova 38,
119991
Moscow,
Russia
★ e-mail: ayrjan@jinr.ru
★★ e-mail: divakov_dv@rudn.ru
★★★ e-mail: yegorov@kapella.gpi.ru
★★★★ e-mail: lovetskiy_kp@rudn.ru
† e-mail: sevastianov_la@rudn.ru
Published online: 20 January 2020
Experimentally observed leaky modes of a dielectric waveguide are characterised by a weak tunnelling of the light through the waveguide and its long-time propagation along the waveguide. Traditional mathematical models of leaky waveguide modes meet some contradictions resolved using additional considerations. We propose a model of leaky modes in a waveguide free from the above contradictions, akin to the quantum mechanical model of the “pseudo-stable” Gamow-Siegert states.
By separating variables, from the complete problem for plane inhomogeneous waves we obtain a non-self-adjoint Sturm-Liouville problem to determine the complex coefficient of the phase delay of the studied mode. The solution of the complete wave problem determines the propagation cone for the leaky mode of the waveguide, inside which there are no contradictions. Thus, solution is in qualitative agreement with experimental data.
© The Authors, published by EDP Sciences, 2020
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