A wide‐angle beam propagation method using a finite element scheme

Tsuji, Yasuhidé; Koshiba, Masanori; Tanabe, Tomohide

doi:10.1002/(sici)1520-6432(199701)80:1<18::aid-ecjb3>3.3.co;2-m

Cited by 3 publications

(8 citation statements)

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“…First, we test the paraxial formulation. The lowest order eigenmode is analyzed using the imaginary distance BPM [37]- [39], in which the effective index is calculated by the following equation [38]: (25) where . The effective-index error is defined as…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The BPM's developed during the last two decades can be roughly categorized in terms of the discretization in the transverse direction, i.e., fast Fourier transform (FFT-BPM) [3], finite-difference (FD-BPM) [4]- [10], finite-element (FE-BPM) [11]- [14], and method of lines (Mol-BPM) [15]. In the FFT-BPM only a uniform grid is valid, while in the other BPM's a nonuniform grid [16]- [25] is allowed to improve computational efficiency or describe a waveguide configuration accurately. For a longitudinally invariant waveguide, a nonuniform grid has been applied to the FD-BPM [16], [17], [20].…”

Section: Introductionmentioning

confidence: 99%

“…For a longitudinally invariant waveguide, a nonuniform grid has been applied to the FD-BPM [16], [17], [20]. In the case of a longitudinally variant waveguide, an adaptive grid has been introduced into the FD-BPM [18], [19], [21] and the FE-BPM [22], [24], [25].…”

Section: Introductionmentioning

confidence: 99%

“…As an application, taking advantage of the PSM, we introduce an adaptive grid [18], [19], [21], [22], [24], [25] into the multistep method for wide-angle beam propagation. A Lagrange interpolation technique is used to determine missing values between sampling points.…”

Section: Introductionmentioning

confidence: 99%

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Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Shibayama

Matsubara²,

Sekiguchi³

et al. 1999

J. Lightwave Technol.

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Abstract-Efficient nonuniform schemes, based on the generalized Douglas (GD) scheme, are developed for the finite-difference beam propagation method (FD-BPM). For a two-dimensional (2-D) problem, two methods are presented: a computational space method and a physical space method. In the former, the GD scheme is employed, after replacing a nonuniform grid in the physical space with a uniform one in the computational space. In the latter, the GD scheme is directly extended to a nonuniform grid in the physical space. We apply these two methods to paraxial and wide-angle FD-BPM's. The fourth-order accuracy is achieved in the transverse direction, provided that the grid growth factor between two adjacent grids is r = 1 + O(1x). For the paraxial BPM, the reduction in the truncation error is demonstrated through modal calculations of a graded-index waveguide using an imaginary distance procedure. For the wide-angle BPM, the propagating field in a tilted waveguide is analyzed to show the effectiveness of the present scheme. As an application of the physical space method, an adaptive grid is introduced into the multistep method.Index Terms-Finite-difference methods, optical beam propagation, optical waveguides.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Shibayama

Matsubara²,

Sekiguchi³

et al. 1999

J. Lightwave Technol.

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“…The configuration parameters of the coupled waveguides are taken to be the same as those investigated by the finite-element BPM [19], i.e., m, and m. The computation parameters are , except for ( m for ), and . Fig.…”

Section: Evaluation Of -Derivative Of the Refractive Indexmentioning

confidence: 99%

Norm-conserving finite-difference beam-propagation method for TM wave analysis in step-index optical waveguides

Yamauchi

Matsubara

Tsuda

et al. 2000

J. Lightwave Technol.

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Combined beam propagation and finite element method for bidirectional optical beam propagation analysis

Yoneta

Koshiba

Tsuji

1999

Electron. Comm. Jpn. Pt. II

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As a powerful and efficient algorithm for bidirectional beam propagation analysis, a combination of the beam propagation method (BPM) and the finite element method (FEM) is proposed. Since the FEM is applied only to regions with significant reflected waves, arbitrary waveguide structures can be treated. A perfectly matched layer boundary condition to avoid nonphysical reflections from computational window edges is introduced. To show the validity and usefulness of the approach proposed here, numerical examples for a semiconductor laser facet and a hemispherically‐ended optical waveguide connection are presented. © 1999 Scripta Technica, Electron Comm Jpn Pt 2, 82(10): 1–9, 1999

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A wide‐angle beam propagation method using a finite element scheme

Cited by 3 publications

References 0 publications

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Norm-conserving finite-difference beam-propagation method for TM wave analysis in step-index optical waveguides

Combined beam propagation and finite element method for bidirectional optical beam propagation analysis

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