Spectral index method applied to coupled rib waveguides

Burke, S.V.

doi:10.1049/el:19890411

Cited by 18 publications

(4 citation statements)

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“…Once is found, all the vectors H 1 , H 2 , H 3 and H 4 (see Equation (12)) can be determined. All the parameters g i , b i , i , d i , c i , and i (except one, which is assumed to be arbitrary) appearing in Equation (12) can be determined by using the boundary conditions stated in Equation (13). The field distribution of a quasi-TE mode can then be found.…”

Section: Kðþ àLðþmentioning

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%

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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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Section: Kðþ àLðþmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Hsiao

Chiang²,

Wang

et al. 2008

Journal of Modern Optics

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“…There has since been attempts at improving the method [5] and developing new methods to rapidly find the propagation constants of waveguides such as the weighted index method [6], perturbation methods [7] and variational methods [8]. As the EIM was originally intended for strip-wire waveguides, alternate methods for finding the propagation constants of other waveguide geometries such as ridge waveguides [9] were also developed, such as the spectral index method [10,11,12,13]. Most of these solutions were developed to circumvent the need for numerical calculations when determining the waveguiding properties of a component due to limited hardware at the time.…”

Section: Introductionmentioning

confidence: 99%

Inverse Effective Index Method for Two-Dimensional Simulations of Photonic Components

Høvik,

Aksnes

2024

IEEE Photonics J.

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The representation of three-dimensional integrated photonic structures in two-dimensional designs has been investigated through finite element analysis using COMSOL Multiphysics. The accuracy of the effective index method for various waveguide designs is studied. An alternative to the effective index method, here named the inverse effective index method, is derived in this paper. The results indicate that the commonly used effective index method has a deviation in propagation constant up to 17%, where the error is largest for low-confinement factor waveguides. The inverse effective index method vastly reduces this error to < 0.01% for low confinement-factor geometries. This enables an accurate simulation in two-dimensions while retaining the waveguiding properties of the third dimension. As with the effective index method, the inverse effective index method does not require proprietary software.

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“…Polarised fields are commonly assumed in both numerical and analytical methods and need no further explanation. The strongly confining nature of semiconductor-air boundaries has been exploited in the two dimensional case with great success to produce the SIM for characterising the modal properties of rib waveguides and rib waveguide couplers, [2][3], as well as to reduce the computational effort required for finite difference based mode solvers, [4]. This is a key feature of the method presented below as it is also noted that in many practical three dimensional rib waveguide based components, scattering is predominantly into the substrate underneath the guide and that it is unusual for any significant field to exist above it.…”

Section: Introductionmentioning

confidence: 99%

Generalized spectral index approach for the analysis of 3D structures

2001

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There is a clear demand in optoelectronic design for analysis techniques that provide accurate results with minimal computational effort. The Spectral Index Method (SIM) is well established as a very accurate yet rapid semianalytical technique for determining the modal properties of air-clad optical rib waveguides. The present work generalises the spectral index approach to the analysis of propagation in fully three-dimensional rib waveguide problems. The method is founded upon three practically observed features: fields are polarised, there is little penetration into the air cladding and continuous reflections are very weak with strong reflections occurring only at discrete boundaries. The new propagation algorithm retains the simplicity and computational advantages of the SIM.A full theoretical development of the methods will be presented, along with a discussion of the implementation and application to a typical practical problem illustrative of including taper-based spot-size converters. Comparisons with direct numerical methods show the new technique to be sufficiently accurate for the design of many optoelectronic components. Calculation times for the new method are significantly lower than those for purely numerical methods, making it well suited for use within an iterative design environment.

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Spectral index method applied to coupled rib waveguides

Cited by 18 publications

References 1 publication

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

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

Inverse Effective Index Method for Two-Dimensional Simulations of Photonic Components

Generalized spectral index approach for the analysis of 3D structures

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