Abstract

The purpose of this paper is to develop high-order vectorial finite-element methods to characterize the bending loss in optical waveguides. In order to avoid the use of approximate models based on equivalent refraction index or conformal mapping, the fully vectorial Maxwell system is expressed in a general orthogonal coordinate system. Boundary reflections are circumvented by a proper adaptation of the perfectly matched layer technique. Application to bent rib optical waveguides in cylindrical coordinates and bent circular fiber in toroidal coordinates is presented. In the latter case, a suitable family of quadrangular finite elements has been developed and was shown to give interesting results, both in that situation and in the Cartesian coordinate situation.

© 2007 IEEE

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  1. Y. Tsuji, M. Koshiba, "Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions," Electromagn. 24, 39-48 (2004).
  2. D. Dai, S. He, "Analysis of characteristics of bent rib waveguides," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 113-121 (2004).
  3. D. M. Shyroki, "Exact equivalent-profile formulation for bent optical waveguides," ArXiv: Phys. 1, (2006).
  4. R. Jedidi, R. Pierre, "Efficient analytical and numerical methods for the computation of bent loss in planar waveguides ," J. Lightw. Technol. 23, 2278-2284 (2005).
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  9. P. Petropoulos, "Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of maxwell equations in rectangular, cylindrical, and spherical coordinates," SIAM J. Appl. Math. 60, 1037-1058 (2000).
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  17. L. Faustini, G. Martini, "Bend loss in single-mode fibers," J. Lightw. Technol. 15, 671-679 (1997).
  18. Q. Wang, G. Farrell, T. Freir, "Theoretical and experimental investigations of macro-bend losses for standard single mode fibers ," Opt. Express 13, 4476-4484 (2005).
  19. A. Harris, P. Castle, "Bend loss measurement on high numerical aperture single-mode fibers as function of wavelength and bend radius," J. Lightw. Technol. LT-4, 34-40 (1986).

2006

2005

K. Dossou, M. Fontaine, "A high order isoparametric finite element method for the computation of waveguides modes ," Comput. Methods Appl. Mech. Eng. 194, 837-858 (2005).

R. Jedidi, R. Pierre, "Efficient analytical and numerical methods for the computation of bent loss in planar waveguides ," J. Lightw. Technol. 23, 2278-2284 (2005).

Q. Wang, G. Farrell, T. Freir, "Theoretical and experimental investigations of macro-bend losses for standard single mode fibers ," Opt. Express 13, 4476-4484 (2005).

2004

Y. Tsuji, M. Koshiba, "Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions," Electromagn. 24, 39-48 (2004).

D. Dai, S. He, "Analysis of characteristics of bent rib waveguides," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 113-121 (2004).

2002

L. Vardapetyan, L. Demkowicz, "Full-wave analysis of dielectric waveguides at a given frequency," Math. Comput. 72, 105-129 (2002).

2000

P. Petropoulos, "Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of maxwell equations in rectangular, cylindrical, and spherical coordinates," SIAM J. Appl. Math. 60, 1037-1058 (2000).

1997

L. Faustini, G. Martini, "Bend loss in single-mode fibers," J. Lightw. Technol. 15, 671-679 (1997).

1994

K. Yamamoto, M. Koshiba, "Analysis of curvature losses of whispering gallery modes in an optical dielectric disk by the finite-element method," J. Lightw. Technol. 12, 59-63 (1994).

1993

K. Yamamoto, M. Koshiba, "Numerical analysis of curvature loss in optical waveguides by the finite-element method ," J. Lightw. Technol. 11, 1579-1583 (1993).

1989

F. Kikuchi, "On a discrete compactness property for the Nedelec element," J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math. 36, 479-490 (1989).

1988

1987

A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, "Numerical analysis of planar optical waveguides using the matrix approach," J. Lightw. Technol. LT-5, 660-667 (1987).

1986

A. Harris, P. Castle, "Bend loss measurement on high numerical aperture single-mode fibers as function of wavelength and bend radius," J. Lightw. Technol. LT-4, 34-40 (1986).

1985

F. Brezzi, J. Douglas, L. Marini, "Two families of mixed finite elements for second order elliptic problems," Numer. Math. 47, 217-235 (1985).

1980

J. Nedelec, "Mixed finite elements in IR3," Numer. Math. 35, 315-341 (1980).

ArXiv: Phys.

D. M. Shyroki, "Exact equivalent-profile formulation for bent optical waveguides," ArXiv: Phys. 1, (2006).

Comput. Methods Appl. Mech. Eng.

K. Dossou, M. Fontaine, "A high order isoparametric finite element method for the computation of waveguides modes ," Comput. Methods Appl. Mech. Eng. 194, 837-858 (2005).

Electromagn.

Y. Tsuji, M. Koshiba, "Complex modal analysis of curved optical waveguides using a full-vectorial finite element method with perfectly matched layer boundary conditions," Electromagn. 24, 39-48 (2004).

J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math.

F. Kikuchi, "On a discrete compactness property for the Nedelec element," J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math. 36, 479-490 (1989).

J. Lightw. Technol.

A. K. Ghatak, K. Thyagarajan, M. R. Shenoy, "Numerical analysis of planar optical waveguides using the matrix approach," J. Lightw. Technol. LT-5, 660-667 (1987).

L. Faustini, G. Martini, "Bend loss in single-mode fibers," J. Lightw. Technol. 15, 671-679 (1997).

R. Jedidi, R. Pierre, "Efficient analytical and numerical methods for the computation of bent loss in planar waveguides ," J. Lightw. Technol. 23, 2278-2284 (2005).

K. Yamamoto, M. Koshiba, "Numerical analysis of curvature loss in optical waveguides by the finite-element method ," J. Lightw. Technol. 11, 1579-1583 (1993).

K. Yamamoto, M. Koshiba, "Analysis of curvature losses of whispering gallery modes in an optical dielectric disk by the finite-element method," J. Lightw. Technol. 12, 59-63 (1994).

A. Harris, P. Castle, "Bend loss measurement on high numerical aperture single-mode fibers as function of wavelength and bend radius," J. Lightw. Technol. LT-4, 34-40 (1986).

J. Opt. Soc. Amer. A, Opt. Image Sci.

D. Dai, S. He, "Analysis of characteristics of bent rib waveguides," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 113-121 (2004).

Math. Comput.

L. Vardapetyan, L. Demkowicz, "Full-wave analysis of dielectric waveguides at a given frequency," Math. Comput. 72, 105-129 (2002).

Numer. Math.

F. Brezzi, J. Douglas, L. Marini, "Two families of mixed finite elements for second order elliptic problems," Numer. Math. 47, 217-235 (1985).

J. Nedelec, "Mixed finite elements in IR3," Numer. Math. 35, 315-341 (1980).

Opt. Express

Opt. Lett.

SIAM J. Appl. Math.

P. Petropoulos, "Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of maxwell equations in rectangular, cylindrical, and spherical coordinates," SIAM J. Appl. Math. 60, 1037-1058 (2000).

Other

R. Jedidi, Modélisation des guides d'ondes optiques courbés et caractérisation des pertes par des méthodes d’éléments finis hiérarchiques thèse de doctorat Bib. Univ. LavalQuebec CityQCCanada (2007).

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