A three-dimensional full vectorial beam propagation method for z-dependent structures

Kriezis, Emmanouil E.; Papagiannakis, A.G.

doi:10.1109/3.572165

Cited by 24 publications

(16 citation statements)

References 26 publications

(50 reference statements)

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“…The normalized transmission power of the fundamental mode is 0.281(converged value) at each port. This is in good agreement with results shown in [4]. We can see that the convergence speed is much faster for the QT/CuN elements than for the LT/QN elements, and computational cost is greatly reduced by using higher order QT/CuN elements.…”

Section: B Numerical Accuracy Of Field Interpolationsupporting

confidence: 81%

Study on High Precision and Stable Finite Element Beam Propagation Method Based on Incomplete Third Order Hybrid Edge/Nodal Element

Kawai

Iguchi

Tsuji

2018

J. Lightwave Technol.

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Abstract-It has been reported that the full vectorial finite element beam propagation method (FV-FE-BPM) is not always stable. In this paper, we propose a stabilized FV-FE-BPM using a linear filter to suppress unstable modes. Moreover, aiming for improving the computational accuracy of FV-FE-BPM for longitudinally varying optical waveguides, we employ incomplete third order hybrid edge/nodal elements to reduce interpolation error which occurs in finite element mesh update process at each propagation step. The validity and effectiveness of this approach are verified through several numerical examples of uniform waveguides and longitudinally varying waveguides.Index Terms-Beam propagation method (BPM), finite element method (FEM), hybrid edge/nodal element

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Section: B Numerical Accuracy Of Field Interpolationsupporting

confidence: 81%

Study on High Precision and Stable Finite Element Beam Propagation Method Based on Incomplete Third Order Hybrid Edge/Nodal Element

Kawai

Iguchi

Tsuji

2018

J. Lightwave Technol.

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“…Once f n and n are solved, H i y ðxÞ and henceforth the magnetic field can be found. The homogeneous solutions to (10)- (12) T n m n exp À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 À n p ðx À x 2 Þ for region 3 (21) where n ðQ n Þ, n ðR n Þ, and n ðT n Þ ðn ¼ 0; 1; . .…”

Section: Formulation Of the Proposed Methodsmentioning

confidence: 99%

“…This approach seems to have a problem of requiring large memory and CPU time. The vector beam propagation method (VBPM) [21] is a splitoperator method of combining the FFT, Pade' approximation with the alternating direction implicit (ADI) method, which has the operators of phase adjustment, polarization rotation, homogeneous propagation, and cross coupling to be decomposed and multiplied to avoid inversion of the cross-coupling terms existing in the full-vectorial equation, while being prone to large CPU time, instability, and convergence problems. Additionally, the noniterative fullvectorial beam propagation with ADI method longitudinally discretizes the waveguide structure by means of the Crank-Nicholson scheme.…”

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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“…The beam propagation method (BPM) is in its conception a numerical tool used in the study of optical guided-wave structures with small variations along a principal propagation direction or optical axis (Kriezis and Papagiannakis 1997). Exploitation of this feature, in the BPM framework, leads to a key structural reformulation of the vector wave equation, Eq.…”

Section: The Beam Propagation Methods In Plasmonicsmentioning

confidence: 99%

Computational techniques for the analysis and design of dielectric-loaded plasmonic circuitry

et al. 2011

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The finite element and the beam propagation method, two widely used methods in photonics, are utilized for the analysis of plasmonic components based on the dielectricloaded plasmonic waveguide. Two components are chosen as examples and are subsequently numerically investigated by employing the aforementioned methods, in order to demonstrate their applicability in plasmonics. Specifically, a microring resonator add-drop filter and a Mach-Zehnder interferometric switch are analyzed by means of the finite element and the beam propagation method, respectively. The formulation adopted is clearly presented in both cases and the case-dependent implementation details are thoroughly discussed.Keywords Dielectric-loaded plasmonic waveguide · Plasmonic components · Thermo-optic effect · Finite element method · Beam propagation method

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A three-dimensional full vectorial beam propagation method for z-dependent structures

Cited by 24 publications

References 26 publications

Study on High Precision and Stable Finite Element Beam Propagation Method Based on Incomplete Third Order Hybrid Edge/Nodal Element

Study on High Precision and Stable Finite Element Beam Propagation Method Based on Incomplete Third Order Hybrid Edge/Nodal Element

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

Computational techniques for the analysis and design of dielectric-loaded plasmonic circuitry

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