Modelling Leaky Waves in Planar Dielectric Waveguides
Joint Institute for Nuclear Research,
Dubna, Moscow Region,
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
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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