Abstract

An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orthogonal basis functions and patched at these interfaces by matching the physical boundary conditions. In addition, a new technique incorporating the effective index method and the Wentzel-Kramers-Brillouin method for the a-priori determination of the scaling factor in Hermite-Gauss or Laguerre-Gauss basis functions is introduced to considerably save computational time without experimenting with it. This method shares the same desirable property of the spectral collocation method of providing a fast and accurate solution but avoids the oscillatory solutions and improves the poor convergence problem of the simple spectral collocation method with single domain where regions of discontinuous refractive index profiles exist. Applications to several two-and three-dimensional waveguide structures having exact or accurate approximate solutions are given to test the accuracy and efficiency; all the results are found to be in excellent agreement.

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Appl. Opt.

J. Lightwave Technol.

W. Y. Lee and S. Y. Wang, "Guided-wave characteristics of optical graded-index planar waveguides with metal-cladding: A simple analysis method", J. Lightwave Technol., vol. 13, pp. 416-421, Mar. 1995.

T. Wongcharoen, B. M. A. Rahman and K. T. V. Grattan, "Electro-optic directional coupler switch characterization", J. Lightwave Technol., vol. 15, pp. 377-382, Feb. 1997.

H. Noro and T. Nakayama, "A new approach to scalar and semivector mode analysis of optical waveguides", J. Lightwave Technol., vol. 14, pp. 1546-1556, June 1996.

N. Ramanujam, L. Li, J. J. Burke and M. A. Gribbons, "Determination of the truncation order and numerical window for modeling general dielectric waveguides by the Fourier method", J. Lightwave Technol., vol. 14, pp. 500-508, Mar. 1996 .

W. P. Huang, C. L. Xu, S. T. Chu and S. K. Chaudhuri, "The finite difference vector beam propagation method-Analysis and assessment", J. Lightwave Technol., vol. 10, pp. 295-305, Mar. 1992.

C. H. Henry and B. H. Verbeek, "Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis", J. Lightwave Technol., vol. 7, pp. 308-313, Feb. 1989.

A. Weisshaar, J. Li, R. L. Gallawa and I. C. Goyal, "Vector and quasivector solutions for optical waveguide modes using efficient Galerkin's method with Hermite-Gauss basis functions", J. Lightwave Technol., vol. 13, pp. 1795-1800, Aug. 1995.

F. Causa and J. Sarma, "A versatile method for analyzing paraxial optical propagation in dielectric structures", J. Lightwave Technol., vol. 18, pp. 1445-1452, Oct. 2000.

Opt. Lett.

A. Sharma and S. Banerjee, "Method for propagation of total fields or beam through optical waveguides", Opt. Lett., vol. 14, pp. 94-96, Jan. 1989.

Other

S. G. Mikhlin and K. L. Smolitskiy, Approximate Methods for Solution of Differential and Integral Equations, New York: Elsevier, 1967, pp. 250-252.

J. P. Meunier, T. Pigeon and J. N. Massot, "A numerical technique for the determination of propagation characteristics of inhomogeneous planar optical waveguides", Opt. Quantum Electron., vol. 15, pp. 77-85, 1983.

A. W. Snyder and J. D. Love, Optical Waveguides Theory,: Chapman and Hall, 1983.

T. Tamir, Guides-Wave Optoelectronics, Berlin: Germany: Springer-Verlag, 1988.

W. P. Huang and C. L. Xu, "Simulation of three-dimensional optical waveguides by a full-vector beam propagation method", IEEE J. Quantum Electron., vol. 29, pp. 2639-2649, Oct. 1993.

M. S. Stern, "Semivectorial polarized finite difference method for optical waveguides with arbitrary index profiles", Proc. Inst. Elect. Eng. J., vol. 135, pp. 56-63, Feb. 1988.

M. S. Stern, "Semivectorial polarized H field solutions for dielectric waveguides with arbitrary index profiles", Proc. Inst. Elect. Eng. J., vol. 135, pp. 333-338, Oct. 1988.

B. M. A. Rahman and J. B. Davies, "Finite-element solution of integrated optical waveguides", J. Lightwave Technol., vol. LT-2, pp. 682-688, Oct. 1984.

J. P. Boyd, Chebyshev and Fourier Spectral Methods, New York: Springer-Verlag, 1989.

J. P. Meunier, J. pigeon and J. N. Massot, "A general approach to the numerical determination of modal propagation constants and field distribution of optical fibers", Opt. Quantum Electron., vol. 13, pp. 71-83, 1981.

A. Sharma and P. Bindal, "Variational analysis of diffused planar and channel waveguides and directional couplers", J. Opt. Soc. Amer. A, vol. 11, pp. 2244-2248, Aug. 1994.

D. Funaro, Polynomials Approximation of Differential Equations, Berlin: Germany: Springer-Verlag, 1992.

T. Tang, "The Hermite spectral method for Gauss-type functions", SIAM J. Sci. Comput., vol. 14, pp. 594-605, May 1993.

S. Banerjee and A. Sharma, "Propagation characteristics of optical waveguiding structure by direct solution of the Helmholtz equation for total fields", J.Opt. Soc. Amer. A, vol. 6, pp. 1884-1894, Dec. 1989.

F. Causa, J. Sarma and R. Balasubramanyam, "A new method for computing nonlinear carrier diffusion in semiconductor optical devices", IEEE Trans. Electron Devices, vol. 46, pp. 1135-1139, June 1999.

R. L. Gallawa, I. C. Goyal, Y. Tu and A. K. Ghatak, "Optical waveguide modes: An approximate solution using Galerkin's method with Hermite-Gauss basis functions", IEEE J. Quantum Electron., vol. 27, pp. 518-522, Mar. 1991 .

D. Marcuse, "Solution of vector wave equation for general dielectric waveguides by the Galerkin method", IEEE J. Quantum Electron., vol. 28, pp. 459-465, Feb. 1992.

C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral Methods in Fluid Dynamics, New York: Springer Verlag, 1988.

G. B. Hocker and W. K. Burns, "Modes in diffused optical waveguides of arbitrary index profile", IEEE J. Quantum Electron., vol. QE-11, pp. 270-276, June 1975.

G. B. Hocker, "Strip-loaded diffused optical waveguides", IEEE J. Quantum Electron., vol. QE-12, pp. 232-236, Apr. 1976 .

L. Wang and C. S. Hsiao, "A matrix method for studying TM modes of optical planar waveguides with arbitrary index profiles", IEEE J. Quantum Electron. , vol. 37, pp. 1654-1660, Dec. 2001.

E. M. Conwell, "Modes in optical waveguides formed by diffusion", Appl. Phys. Lett., vol. 23, pp. 328-329, Sept. 1973 .

A. Sharma and P. Bindal, "An accurate variational analysis of single-mode diffused channel waveguides", Opt. Quantum Electron., vol. 24, pp. 1359-1371, 1992.

S. J. Al-Bader and H. A. Jamid, "Guided wave characteristics of metal-clad graded-index planar optical waveguides: Analytical approach", IEEE J. Quantum Electron., vol. QE-23, pp. 539-544, May 1987.

M. Masuda, A. Tanji, Y. Ando and J. Koyama, "Propagation losses of guided modes in anoptical graded-index slab waveguides with metal-cladding", IEEE Trans. Microwave Theory Tech., vol. MTT-25, pp. .773-776, Sept. 1977.

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