Abstract

In this paper, a new vectorial boundary element method is introduced and applied to the modal analysis of dielectric waveguides with piecewise homogeneous refractive indexes. The procedure, which is free of spurious modes,determines the full field distribution from the longitudinal fields at the refractive index boundaries. Singular kernels are evaluated through series solutions while the electric field discontinuity at corners is accommodated through either a grid refinement technique or a semianalytic approach. Our formalism generates propagation constants and modal field distributions for several representative refractive index profiles with far higher accuracy than standard finite-difference or finite-element procedures.

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J. Lightwave Technol. (7)

Opt. Lett. (1)

Other (24)

W. Bardyszewski, D. Yevick, J. Yu and M. Glasner, "Stability issues in vector electric field propagation", IEEE Photon. Technol. Lett., vol. 7, pp. 656-658, June 1995.

D. Yevick, "The application of complex Padé approximants to vector field propagation", IEEE Photon. Technol. Lett., vol. 108, pp. 1636-1638, Feb. 2000.

M. S. Stern, C. L. Xu, W. P. Huang and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method", Inst. Elec. Eng. Proc: Optoelectron., vol. 141, pp. 281-286, Oct. 1994.

D.-U. Li and H. C. Chang, "An efficient full-vectorial finite-element modal analysis of dielectric waveguides incorporating inhomogeneous elements across dielectric discontinuities", IEEE J. Quantum Electron., vol. 36, pp. 1251-1261, Nov. 2000.

T. Lu and D. Yevick, "Boundary element analysis of dielectric waveguides", J. Opt. Soc. Amer. A, vol. 19, no. 6, pp. 1197-1206, 2002 .

W. Yang and A. Gopinath, "A boundary integral method for propagation problems in integrated optical structures", IEEE Photon. Technol. Lett., vol. 7, pp. 777-779, July 1995.

G. E. Stewart, K. E. Golden and D. C. Pridmore-Brown, "Approximation techniques for the mutual admittance of slot antennas on metallic cones", IEEE Trans. Antennas Propagat., vol. AP-22, pp. 43-48, 1974.

L. B. Felsen, Z. W. Chang and A. Hessel, "Surface Ray Methods for Mutual Coupling in Conformal Arrays on Cylinder and Conical Surface", Polytechnic Institute of New York,Final Report, 1976.

Numerical Recipes in C, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1992.

W. Van Etten and J. Van der Plaats, Fundamentals of Optical Fiber Communications, Englewood Cliffs, NJ: Prentice-Hall, 1990.

A. Yariv, Optical Electronics, 4th ed. : Saunders College, California Institute of Technology, 1991.

Y. Sun, Y. Kagawa and Z. Mahmood, "Regular boundary integral formulation for the analysis of open dielectric/optical waveguides", IEEE Trans. Microwave Theory Tech., vol. 44, no. 8, pp. 1441-1450, Aug. 1996.

S. Walker, "Approximate fundamental solutions and alternative formulations," in Boundary Element Methods Proceedings of the Third International Seminar, C. A. Brebbia, Ed. Irvine, CA: CML Publications, July 1981, pp. 472-484.

T. Lu, "Boundary Element Analysis of Dielectric Waveguides", M.S. thesis, Queen's University at Kingston, Sept. 1998.

J. Meixner, "The behavior of electromagnetic fields at edges", IEEE Trans. Antennas Propagat., vol. AP-20, pp. 442-446, July 1972.

J. B. Andersen and V. V. Solodukhov, "Field behavior near a dielectric wedge", IEEE Trans. Antennas Propag., vol. AP-26, pp. 598 -602, July 1978.

G. I. Makarov and A. V. Osipov, "Structure of Meixner's series", UDC,, 1986.

Y. Tsuji and M. Koshiba, "Adaptive mesh generation for full-vectorial guided-mode and beam-propagation solutions", IEEE J. Select. Topics Quantum Electron. , vol. 6, pp. 163-169, Jan. 2000.

H. Noro and T. Nakayama, "Mode analysis of optical waveguides: a new approach", Opt. Lett., vol. 20, no. 11, pp. 1227-1229, June 1995.

K. L. Johnson, Z.-E. Abid and A. Gopinath, "Analysis of dielectric guides by vector transverse magnetic field finite elements", J. Lightwave Technol. , vol. 11, pp. 1545-1549, Oct. 1993.

B. M. A. Rahman and J. B. Davies, "Vector-finite-element solution of GaAs/GaALAs rib waveguides", Proc. Inst. Elec. Eng., vol. 132, pp. 349-353, 1985.

M. Eguchi, M. Koshiba, H. Saitoh and K. Hirayama, "Simple scalar finite element approach to optical rib waveguides", Proc. Inst. Elec. Eng. Pt. J, vol. 139, pp. 166-171, Apr. 1992.

M. S. Stern, "Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles", Proc. Inst. Elec. Eng. Pt. J, vol. 135, pp. 56-63, Feb.

C. Vassallo, "Mode solvers, 1993-1995 optical mode solvers", Optic. Quantum Electron., vol. 29, pp. 95-114, 1997.

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