Abstract

The guided and leaky modes of the optical waveguides (fibers) are analyzed by the finite-element method (FEM) with the integral boundary conditions. The initial equations are reduced to the algebraic general eigenvalue problem, which is solved by the Arnoldi algorithm. The mode dispersion characteristics, fields, and cutoff frequencies are calculated for several waveguide structures, including flat and multilayer fibers with different shapes of cross sections.

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  1. M. J. Steel and R. M. J. Osgood, "Polarization and dispersive properties of elliptical-hole photonic crystal fibers", J. Lightw. Technol., vol. 19, no. 4, pp. 495-503, Apr. 2001.
  2. Y. Xu, G. Ouyang, R. Lee and A. Yariv, "Asymptotic matrix theory of Bragg fibers", J. Lightw. Technol., vol. 20, no. 3, pp. 428-440, Mar. 2002.
  3. N. A. Issa and L. Poladian, "Vector wave expansion method for leaky modes of microstructured optical fibers", J. Lightw. Technol., vol. 21, no. 4, pp. 1005-1012, Apr. 2003.
  4. T. H. Wang, "Calculation of cutoff frequency of arbitrary weak guidance optical waveguides by extended boundary condition method", Opt. Quantum Electron., vol. 32, no. 1, pp. 31-42, 2000.
  5. Y. Liu and B. Rachman, "Analysis of the birefringence properties of optical fibers mode by a preform deformation technique", J. Lightw. Technol., vol. 13, no. 2, pp. 142-147, Feb. 1995.
  6. P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 2nd ed. Cambridge: U.K.: Cambridge Univ. Press, 1990.
  7. A. I. Kleev, A. B. Manenkov and A. G. Rozhnev, "Numerical methods of calculating dielectric waveguides (optical fibers). Universal methods", J. Commun. Technol. Electron., vol. 39, no. 2, pp. 90-115, 1994.
  8. A. B. Manenkov and A. G. Rozhnev, "Optical dielectric waveguide analysis, based on the modified finite element and integral equation methods", Opt. Quantum Electron., vol. 30, no. 1, pp. 61-70, 1998.
  9. C.-C. Su, "A combined method for dielectric waveguides using the finite-element technique and surface integral equations method", IEEE Trans. Microw. Theory Tech., vol. 34, no. 11, pp. 1140-1145, Nov. 1986.
  10. J. W. Demmel, Applied Numerical Linear Algebra, Philadelphia, PA: SIAM, 1997.
  11. D. Sorensen, "Implicit application of polynomial filters in k -step Arnoldi method", SIAM J. Matrix Anal. Appl., vol. 13, no. 2, pp. 357-385, 1992.
  12. R. B. Lehoucq, D. C. Sorensen and C. Yang, "ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods", Rice Univ., Houston, TX, 1997.
  13. A. W. Snyder and J. D. Love, Optical Waveguide Theory, London: U.K.: Chapman & Hall, 1983.
  14. C. A. J. Fletcher, Computational Galerkin Method, New York: Springer-Verlag, 1984.
  15. A. B. Manenkov, T. M. Benson, P. D. Sewell and P. Kendall, "Fast and accurate reflectivity calculations for shaped core optical fibres", Opt. Quantum Electron., vol. 32, no. 11, pp. 1245-1255, 2000.
  16. R. A. Sammut, "Mode cutoff frequencies in elliptical and large numerical aperture optical fibres", Opt. Quantum Electron., vol. 14, no. 5, pp. 419-424, 1982.
  17. A. B. Manenkov, "Quasioptics of waveguide with selective reflecting walls", in Proc. 5th Colloq. Microwave Communications, vol. 3, Budapest, Hungary, 1974, pp. 219-226.
  18. A. B. Manenkov and V. N. Melekhin, "Calculation of the quasi-single-mode optical fibers with selective reflecting multilayer covers", Radiotekhnika i elektronika, vol. 24, no. 7, pp. 1282-1289, 1979.
  19. Y. Xu, R. Lee and A. Yariv, "Asymptotic analysis theory of Bragg fibers", Opt. Lett., vol. 25, no. 24, pp. 1756-1758, 2000.
  20. A. B. Manenkov, "Excitation of open homogeneous waveguides", Radiophys. Quantum Electron., vol. 13, no. 5, pp. 578-586, 1970.
  21. A. B. Manenkov, "Orthogonality relations for the eigenmodes of lossy anisotropic waveguides (fibres)", Proc. Inst. Elect. Eng., J Optoelectron., vol. 140, no. 3, pp. 206-212, 1993.
  22. A. V. Brovko, A. G. Rozhnev and A. B. Manenkov, "Finite-element model of a fiber-optic polarizer", Radiophys. Quantum Electron., vol. 44, no. 7, pp. 567-574, 2001.

Other (22)

M. J. Steel and R. M. J. Osgood, "Polarization and dispersive properties of elliptical-hole photonic crystal fibers", J. Lightw. Technol., vol. 19, no. 4, pp. 495-503, Apr. 2001.

Y. Xu, G. Ouyang, R. Lee and A. Yariv, "Asymptotic matrix theory of Bragg fibers", J. Lightw. Technol., vol. 20, no. 3, pp. 428-440, Mar. 2002.

N. A. Issa and L. Poladian, "Vector wave expansion method for leaky modes of microstructured optical fibers", J. Lightw. Technol., vol. 21, no. 4, pp. 1005-1012, Apr. 2003.

T. H. Wang, "Calculation of cutoff frequency of arbitrary weak guidance optical waveguides by extended boundary condition method", Opt. Quantum Electron., vol. 32, no. 1, pp. 31-42, 2000.

Y. Liu and B. Rachman, "Analysis of the birefringence properties of optical fibers mode by a preform deformation technique", J. Lightw. Technol., vol. 13, no. 2, pp. 142-147, Feb. 1995.

P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers, 2nd ed. Cambridge: U.K.: Cambridge Univ. Press, 1990.

A. I. Kleev, A. B. Manenkov and A. G. Rozhnev, "Numerical methods of calculating dielectric waveguides (optical fibers). Universal methods", J. Commun. Technol. Electron., vol. 39, no. 2, pp. 90-115, 1994.

A. B. Manenkov and A. G. Rozhnev, "Optical dielectric waveguide analysis, based on the modified finite element and integral equation methods", Opt. Quantum Electron., vol. 30, no. 1, pp. 61-70, 1998.

C.-C. Su, "A combined method for dielectric waveguides using the finite-element technique and surface integral equations method", IEEE Trans. Microw. Theory Tech., vol. 34, no. 11, pp. 1140-1145, Nov. 1986.

J. W. Demmel, Applied Numerical Linear Algebra, Philadelphia, PA: SIAM, 1997.

D. Sorensen, "Implicit application of polynomial filters in k -step Arnoldi method", SIAM J. Matrix Anal. Appl., vol. 13, no. 2, pp. 357-385, 1992.

R. B. Lehoucq, D. C. Sorensen and C. Yang, "ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods", Rice Univ., Houston, TX, 1997.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, London: U.K.: Chapman & Hall, 1983.

C. A. J. Fletcher, Computational Galerkin Method, New York: Springer-Verlag, 1984.

A. B. Manenkov, T. M. Benson, P. D. Sewell and P. Kendall, "Fast and accurate reflectivity calculations for shaped core optical fibres", Opt. Quantum Electron., vol. 32, no. 11, pp. 1245-1255, 2000.

R. A. Sammut, "Mode cutoff frequencies in elliptical and large numerical aperture optical fibres", Opt. Quantum Electron., vol. 14, no. 5, pp. 419-424, 1982.

A. B. Manenkov, "Quasioptics of waveguide with selective reflecting walls", in Proc. 5th Colloq. Microwave Communications, vol. 3, Budapest, Hungary, 1974, pp. 219-226.

A. B. Manenkov and V. N. Melekhin, "Calculation of the quasi-single-mode optical fibers with selective reflecting multilayer covers", Radiotekhnika i elektronika, vol. 24, no. 7, pp. 1282-1289, 1979.

Y. Xu, R. Lee and A. Yariv, "Asymptotic analysis theory of Bragg fibers", Opt. Lett., vol. 25, no. 24, pp. 1756-1758, 2000.

A. B. Manenkov, "Excitation of open homogeneous waveguides", Radiophys. Quantum Electron., vol. 13, no. 5, pp. 578-586, 1970.

A. B. Manenkov, "Orthogonality relations for the eigenmodes of lossy anisotropic waveguides (fibres)", Proc. Inst. Elect. Eng., J Optoelectron., vol. 140, no. 3, pp. 206-212, 1993.

A. V. Brovko, A. G. Rozhnev and A. B. Manenkov, "Finite-element model of a fiber-optic polarizer", Radiophys. Quantum Electron., vol. 44, no. 7, pp. 567-574, 2001.

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