Numerical modeling of leaky electromagnetic waves in planar dielectric waveguides

D. Divakov; A. Drevitskiy; A. Egorov; L. Sevastianov

doi:10.1117/12.2530175

3 June 2019 Numerical modeling of leaky electromagnetic waves in planar dielectric waveguides

D. Divakov, A. Drevitskiy, A. Egorov, L. Sevastianov

Proceedings Volume 11066, Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling; 110660R (2019) https://doi.org/10.1117/12.2530175
Event: International Symposium on Optics and Biophotonics VI: Saratov Fall Meeting 2018, 2018, Saratov, Russian Federation

Abstract

In the case of guided and radiation modes of open waveguides, the Sturm-Liouville problem is formulated for self-adjoint second-order operators on the axis and the corresponding eigenvalues are real quantities for dielectric media. The search for eigenvalues and eigenfunctions corresponding to the leaky modes involves a number of difficulties: the boundary conditions for the leaky modes are not self-adjoint, so that the eigenvalues can turn out to be complex quantities. The problem of finding eigenvalues and eigenfunctions is associated with finding the complex roots of the nonlinear dispersion equation. Leaky modes, by analogy with radiation and guided modes, are considered as solutions of the Helmholtz equation. The presence of complex eigenvalues corresponding to the leaky modes leads to an infinite increase of eigen- functions corresponding to the leaky modes. In the present work, the leaky modes are considered as solutions of the problem for the wave equation and are analyzed as a wave process. Complex eigenvalues define the leaky modes as inhomogeneous waves. The proposed approach allows to obtain a mathematically sound representation of the leaky modes, within which one can see the region of existence of each particular leaky mode. The calculations of model structure, demonstrating the application of the described approach, are presented in the paper.

Citation Download Citation

D. Divakov, A. Drevitskiy, A. Egorov, and L. Sevastianov "Numerical modeling of leaky electromagnetic waves in planar dielectric waveguides", Proc. SPIE 11066, Saratov Fall Meeting 2018: Laser Physics, Photonic Technologies, and Molecular Modeling, 110660R (3 June 2019); https://doi.org/10.1117/12.2530175

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available