A numerical technique for the determination of propagation characteristics of inhomogeneous planar optical waveguides

Meunier, J.-P.; Pigeon, Jérôme; Massot, Jean

doi:10.1007/bf00620236

Cited by 36 publications

(6 citation statements)

References 36 publications

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“…where (11) Here, is a basis function of order 1 and the prime denotes the first derivative with respect to . are the collocation points with the conditions , where is the Kronecker delta.…”

Section: Spectral Collocation Methods With Domain Decompositionmentioning

confidence: 99%

“…The spectral collocation method (SCM) [8] (i.e., the collocation method in [9] proposed by Sharma and Banerjee) and the Galerkin method [10] are the two most prevalent methods in series expansion. More recently, many researchers [11]- [15] have successfully implemented the Galerkin method with different orthogonal basis functions to investigate optical waveguides and optical fibers but few pursued SCM. Sharma and Banerjee [9], [16] first applied SCM with Hermite-Gauss (HG) basis functions in propagation characteristics of optical waveguiding structures for two kinds of problems as follows.…”

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confidence: 99%

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An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

Huang

Yang²

2003

J. Lightwave Technol.

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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. Index Terms-Discontinuous refractive index profiles, domain decomposition, optical waveguides, orthogonal basis function, scaling factor, spectral collocation method. I. INTRODUCTION R ECENTLY, there has been growing interest in developing integrated optics devices in optical communication systems. The fundamental operating principle and optimal design of optical devices such as modulators, switches, filters, fibers, and semiconductor lasers are often based on the comprehension of optical waveguide theory [1]. Hence, solving the optical waveguide problems is an essential way to clearly realize these devices. However, only a limited number of waveguides, which have simple geometry and specific refractive index profiles (RIPs), have analytic solutions [1], [2]. Consequently, employing

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“…where (11) Here, is a basis function of order 1 and the prime denotes the first derivative with respect to . are the collocation points with the conditions , where is the Kronecker delta.…”

Section: Spectral Collocation Methods With Domain Decompositionmentioning

confidence: 99%

mentioning

confidence: 99%

An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

Huang

Yang²

2003

J. Lightwave Technol.

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“…However, this approach, requiring a staircase approximation of the refractive index profile for inhomogeneous waveguides, becomes tedious and results in complicated transcendental dispersion equations, which cannot be easily solved. Other approaches such as the variational method, 20 perturbation method, 21 differential TMM, [22][23][24] and numerical methods such as the beam propagation method, 25 FEM, 26 and others 27,28 can be used for analyzing inhomogeneous waveguides.…”

Section: Introductionmentioning

confidence: 99%

Legendre polynomial expansion for analysis of linear one-dimensional inhomogeneous optical structures and photonic crystals

2006

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A Legendre polynomial expansion of electromagnetic fields for analysis of layers with an inhomogeneous refractive index profile is reported. The solution of Maxwell's equations subject to boundary conditions is sought in a complete space spanned by Legendre polynomials. Also, the permittivity profile is interpolated by polynomials. Different cases including computation of reflection-transmission coefficients of inhomogeneous layers, band-structure extraction of one-dimensional photonic crystals whose unit-cell refractive index profiles are inhomogeneous, and inhomogeneous planar waveguide analysis are investigated. The presented approach can be used to obtain the transfer matrix of an arbitrary inhomogeneous monolayer holistically, and approximation of the refractive index or permittivity profile by dividing into homogeneous sublayers is not needed. Comparisons with other well-known methods such as the transfer-matrix method, WKB, and effective index method are made. The presented approach, based on a nonharmonic expansion, is efficient, shows fast convergence, is versatile, and can be easily and systematically employed to analyze different inhomogeneous structures.

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“…The fundamental operating theory of various devices are concerned with the interactions between the modes of waveguides; therefore, accurate and efficient modal analysis is crucial and preferred for investigating the performances of these complicated components. Many comprehensive numerical techniques, for instance, finite-difference (FD) [1,2], finite-element (FE) [3,4], and series expansion (SE) [5][6][7][8][9] methods for studying modal characteristics have been presented and developed.…”

Section: Introductionmentioning

confidence: 99%

Modal analysis of dielectric optical waveguides based on Chebyshev polynomials

Huang

2005

Micro & Optical Tech Letters

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We propose an accurate and efficient numerical method to compute the modal characteristics of dielectric optical waveguides. The present method represents electric and/or magnetic fields by Chebyshev polynomials based on a multidomain spectral collocation scheme. Compared with analytical solutions and the published results using rigorous numerical methods, our results show excellent agreement. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 328–331, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20813

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A numerical technique for the determination of propagation characteristics of inhomogeneous planar optical waveguides

Cited by 36 publications

References 36 publications

An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

Legendre polynomial expansion for analysis of linear one-dimensional inhomogeneous optical structures and photonic crystals

Modal analysis of dielectric optical waveguides based on Chebyshev polynomials

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