An improved formulation of an optimizing Rayleigh-Ritz technique for closed dielectric waveguide analysis

Young, Ben

doi:10.1109/22.97484

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…An eigenvalue problem with a matrix for obtaining mode indices is thus of dimension N, where N is the number of Fourier series terms. Consequently, in solving for eigenmodes, this method is more efficient than that using 2-D Fourier series expansion [27]- [29], in the latter of which a matrix of dimension N Â M (with double series expansions) is required, with N and M being the numbers of Fourier series terms for x and y dimensions, respectively. On the other hand, the presented method here is also believed to be more efficient in computation than FDM or FEM, which requires a large grid number in many cases.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Numerical Full-Vectorial Mode Solver Based on Fourier Series Expansion Method

et al. 2014

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A new algorithm of full-vectorial eigenmode solver is presented, which is utilized to determine the modal index of dielectric optical waveguides. The approach is based on the Fourier cosine and sine series expansions of the magnetic field distributions and the refractive index profile. By substituting these series expansions in the wave equation, a pair of second-order differential matrix equations is obtained by collecting all the terms with the same spatial frequency. With boundary conditions used, a matrix equation with a dimension of ðN þ 1Þ by ðN þ 1Þ, where N is the number of terms for truncated series, is obtained, which can be easily solved by using the Newton-Raphson root-shooting algorithm. The presented scheme requires considerably less computational time and memory storage by only considering the finite terms of the Fourier cosine/ sinusoidal series. Calculated results by our proposed method are in good agreement with those obtained by BeamPROP and COMSOL and compare well with other available methods, demonstrating the accuracy and efficiency and also the applicability of our proposed method.

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Section: Introductionmentioning

confidence: 99%

An Efficient Numerical Full-Vectorial Mode Solver Based on Fourier Series Expansion Method

et al. 2014

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A semi-analytic method for solving rib-type waveguide problems

Hsiao

Chiang²,

Wang

et al. 2008

Journal of Modern Optics

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A semi-analytic method for solving rib-type waveguide problems, Journal of Modern Optics, 55:8, 1315-1329, A new semi-analytic method for solving optical rib-type waveguide problems is presented. In the method, the cross-section of a rib-type waveguide is divided into several regions. In each region, the refractive index profile and field distribution are expanded into Fourier cosine series, and then are substituted in the wave equation. A second-order differential matrix equation is then derived for each region, with a closed-form solution obtainable. With the boundary conditions used, an eigenmode equation for the rib waveguide can be derived and solved numerically to give the modal indices. Here, the presented method is used to deal with two rib waveguides in different geometric dimensions and/or compositions, respectively. Computational results show that the presented method is quite efficient, in terms of CPU time, in finding the modal indices accurately. The relative error in computing the modal index with the method is about 10 À5 -10 À6 . IntroductionFor more than a decade, considerable effort has been directed to computing the modes of optical rib waveguides, which form the important parts of photonic integrated circuits. Many kinds of numerical and semi-analytic methods were utilized for the computation of modal fields and the modal indices of rib-type waveguides. These include finite difference method [1-4], finite element method [5][6][7][8], beam propagation method [9-12] and many other semi-analytic methods [13][14][15][16]. Numerical methods based on finite element or finite difference basically discretize the transverse domain of an optical waveguide to induce an eigenvalue problem. A beam propagation algorithm was also introduced in the finite-difference discretization [10] or Fourier transform scheme [12] to determine the modal field and the modal index of a z-invariant structure. With the use of some

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An improved formulation of an optimizing Rayleigh-Ritz technique for closed dielectric waveguide analysis

Cited by 2 publications

References 11 publications

An Efficient Numerical Full-Vectorial Mode Solver Based on Fourier Series Expansion Method

An Efficient Numerical Full-Vectorial Mode Solver Based on Fourier Series Expansion Method

A semi-analytic method for solving rib-type waveguide problems

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