DOI: https://doi.org/10.26089/NumMet.v17r325

Hybrid methods for modeling waveguides containing local inhomogeneous insets of multilayer structure

Authors

  • A.A. Petukhov
  • A.N. Bogolyubov
  • M.K. Trubetskov

Keywords:

nonregular waveguide
multilayer inset
hybrid numerical methods
incomplete Galerkin’s method
finite difference method
transfer matrix method

Abstract

A mathematical model of wave diffraction on a local inhomogeneous multilayer inset placed inside a rectangular waveguide is considered. An algorithm for the numerical solution of the corresponding diffraction problem based on the application of hybrid numerical and numerical-analytical methods is described. In particular, the hybrid methods based on the joint application of the incomplete Galerkin’s method together with the finite difference method and the transfer matrix method are discussed. A comparative analysis of the described methods is given, including an efficiency analysis of these methods in application to modeling the wave diffraction on a multilayer inhomogeneous inset in a waveguide.

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Published

2016-07-04

Issue

Vol. 17 (2016): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

A.A. Petukhov

Lomonosov Moscow State University
• Leading Programmer

A.N. Bogolyubov

Lomonosov Moscow State University
• Professor

M.K. Trubetskov

Lomonosov Moscow State University
• Leading Researcher

References

  1. A. N. Bogolyubov, A. L. Delitsyn, A. V. Krasil’nikova, et al., “Mathematical Modeling of Waveguides Using the Finite-Difference Method,” Usp. Sovremen. Radioelektron., № 5, 39-54 (1998).
  2. M. Wik, D. Dumas, and D. Yevick, “Comparison of Vector Finite-Difference Techniques for Modal Analysis,” J. Opt. Soc. Am. A 22 (7), 1341-1347 (2005).
  3. A. G. Sveshnikov, “The Principle of Radiation,” Dokl. Akad. Nauk SSSR 3 (5), 511-520 (1950).
  4. A. N. Bogolyubov and A. V. Lavrenova, “Mathematical Modeling of the Diffraction on the Heterogeneity in the Waveguide with the Application of the Hybrid Finite Elements,” Mat. Model. 20 (2), 122-128 (2008) [Math. Models Comput. Simul. 1 (1), 131-137 (2009)].
  5. A.G. Sveshnikov, “Incomplete Galerkin Method,” Dokl. Akad. Nauk SSSR 236 (5), 1076-1079 (1977).
  6. A. A. Bykov, A. G. Sveshnikov, and M. K. Trubetskov, “Reduced Galerkin’s Method Application to Calculations of Eigenwaves in Open Waveguides,” Mat. Model. 3 (7), 111-123 (1991).
  7. D. Marcuse, “Solution of the Vector Wave Equation for General Dielectric Waveguides by the Galerkin Method,” IEEE J. Quantum Electron. 28 (2), 459-465 (1992).
  8. A. A. Bykov and A. S. Il’inskii, “Solution of Boundary Value Problems for Linear Systems of Ordinary Differential Equations by the Method of Directed Orthogonalization,” Zh. Vychisl. Mat. Mat. Fiz. 19 (3), 631-639 (1979) [USSR Comput. Math. Math. Phys. 19 (3), 74-82 (1979)].
  9. A. A. Bykov, “Stability to Rounding Errors of Directed Orthogonalization,” Zh. Vychisl. Mat. Mat. Fiz. 21 (5), 1154-1167 (1981) [USSR Comput. Math. Math. Phys. 21 (5), 80-94 (1981)].
  10. M. Born and E. Wolf, Principles of Optics (Pergamon, London, 1970; Nauka, Moscow, 1973).
  11. A. S. Il’inskii, V. V. Kravtsov, and A. G. Sveshnikov, Mathematical Models of Electrodynamics (Vysshaya Shkola, Moscow, 1991) [in Russian].
  12. N. N. Kalitkin, Numerical Methods (Nauka, Moscow, 1978) [in Russian].
  13. D. W. Berreman, “Optics in Stratified and Anisotropic media: 4×4-Matrix Formulation,” J. Opt. Soc. Am. 62 (4), 502-510 (1972).
  14. M. R. Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Freeman, New York, 1991; Inst. Komp’yut. Issled., Izhevsk, 2005).
  15. A. N. Bogolyubov, A. A. Petukhov, and N. E. Shapkina, “Mathematical Modeling of Waveguides with Fractal Insets,” Vestn. Mosk. Univ., Ser. 3: Fiz., No. 2, 20-23 (2011) [Moscow Univ. Phys. Bull. 66 (2), 122-125 (2011)].
  16. A. A. Petukhov, “Joint Application of the Incomplete Galerkin Method and Scattering Matrix Method for Modeling Multilayer Diffraction Gratings,” Mat. Model. 25 (6), 41-53 (2013) [Math. Models Comput. Simul. 6 (1), 92-100 (2014)].