Exact and variational Fourier transform methods for analysis of multilayered planar waveguides

Berry, G.; Burke, S.V.; Smartt, Christopher; Benson, T.M.; Kendall, P.C.

doi:10.1049/ip-opt:19951692

Cited by 9 publications

(25 citation statements)

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“…The single-mode waveguides in structures 1 and 2 were, respectively, studied by [4] and [16]. The modal indices of these two waveguides calculated by [4,16] are also given here for a comparison with the numerical results obtained using the commercial software BeamPROP and the proposed method. Note that the commercial software can find both types of semi-vectorial mode solutions (i.e.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Fourier operator transform method) outlined in [16]. The proposed method is also used to calculate the modal index n eff of this single-mode waveguide.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The proposed method is also used to calculate the modal index n eff of this single-mode waveguide. From Table 3 we can see the modal indices calculated by the proposed method, the software BeamPROP and [16] for the quasi-TE mode. It is clear that the calculated values of n eff for increasing N converge to a value quite close to that obtained by BeamPROP.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…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][2][3][4], finite element method [5][6][7][8], beam propagation method [9][10][11][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.…”

Section: Introductionmentioning

confidence: 99%

“…The accuracy of finding the modal index depends on the number of terms used in expanding the aforementioned refractive profile (as well as the modal field) into Fourier cosine series. It should be emphasized here that the proposed method is different from the discrete spectral index method [16], the generalized Fourier variational method [14,16] or the Fourier operator transform method [15,16]. In the discrete spectral index method, the field is expressed into a Fourier series in each region under the assumption of an effective rib waveguide.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Numerical Resultsmentioning

confidence: 99%

“…Fourier operator transform method) outlined in [16]. The proposed method is also used to calculate the modal index n eff of this single-mode waveguide.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%