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Numerical and Analytical Modeling of Guided Modes of a Planar Gradient Waveguide

  • Edik Ayrjan
  • Migran Gevorkyan
  • Dmitry Kulyabov
  • Konstantin Lovetskiy
  • Nikolai Nikolaev
  • Anton Sevastianov
  • Leonid Sevastianov
  • Eugeny Laneev
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 678)

Abstract

The mathematical model of light propagation in a planar gradient optical waveguide consists of the Maxwell’s equations supplemented by the matter equations and boundary conditions. In the coordinates adapted to the waveguide geometry, the Maxwell’s equations are separated into two independent sets for the TE and TM polarizations. For each there are three types of waveguide modes in a regular planar optical waveguide: guided modes, substrate radiation modes, and cover radiation modes. We implemented in our work the numerical-analytical calculation of typical representatives of all the classes of waveguide modes.

In this paper we consider the case of a linear profile of planar gradient waveguide, which allows for the most complete analytical description of the solution for the electromagnetic field of the waveguide modes. Namely, in each layer we are looking for a solution by expansion in the fundamental system of solutions of the reduced equations for the particular polarizations and subsequent matching them at the boundaries of the waveguide layer.

The problem on eigenvalues (discrete spectrum) and eigenvectors is solved in the way that first we numerically calculate (approximately, with double precision) eigenvalues, then numerically and analytically—eigenvectors. Our modelling method for the radiation modes consists in reducing the initial potential scattering problem (in the case of the continuous spectrum) to the equivalent ones for the Jost functions: the Jost solution from the left for the substrate radiation modes and the Jost solution from the right for the cover radiation modes.

Keywords

Waveguide propagation of electromagnetic radiation Equations of waveguide modes of regular waveguide Numerical-analytical modelling 

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Edik Ayrjan
    • 1
    • 4
  • Migran Gevorkyan
    • 2
  • Dmitry Kulyabov
    • 1
    • 2
  • Konstantin Lovetskiy
    • 2
  • Nikolai Nikolaev
    • 2
  • Anton Sevastianov
    • 2
  • Leonid Sevastianov
    • 2
    • 3
  • Eugeny Laneev
    • 2
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubna, Moscow RegionRussia
  2. 2.RUDN University (Peoples’ Friendship University of Russia)MoscowRussia
  3. 3.Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear ResearchDubna, Moscow RegionRussia
  4. 4.Yerevan Physics InstituteYerevanArmenia

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