Finite element beam propagation method for nonlinear optical waveguides

Yasui, Takashi; Koshiba, Masanori; Niiyama, Akira; Tsuji, Yasuhidé

doi:10.1002/(sici)1520-6432(199904)82:4<47::aid-ecjb6>3.0.co;2-v

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…This equation cannot be solved explicitly due to the presence of the square root term. This difficulty can be overcome by way of Padé approximants which are applied to the square root term as follows [9]: (5) where and are polynomials in of order and for the numerator and the denominator, respectively. These polynomials are known as Padé ( ) approximants [8].…”

Section: Formulationmentioning

confidence: 99%

“…The most celebrated numerical tool for the simulation of longitudinally varying structures is the beam propagation method (BPM) [5]- [10]. Ordinary BPM analysis of nonlinear optical waveguides has been performed by solving the Helmholtz equation under the paraxial approximation [5]- [7].…”

Section: Introductionmentioning

confidence: 99%

“…Ordinary BPM analysis of nonlinear optical waveguides has been performed by solving the Helmholtz equation under the paraxial approximation [5]- [7]. In this case, the beam is assumed propagating almost parallel to the longitudinal axis.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improved wide-angle finite-difference beam propagation method for the analysis of nonlinear optical waveguides

Flamino¹,

Cesar²,

Borges³

2002

IEEE Trans. Magn.

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An improved wide-angle finite-difference beam propagation method (WA-FD-BPM) formulated in terms of complex Padé approximants is proposed to investigate nonlinear optical waveguides. The formalism utilizes the Crank-Nicholson scheme. An adaptive update of the reference index and an iterative algorithm in every propagation step are utilized to accelerate convergence. Stability problems relative to high-order approximants are also addressed in this work.Index Terms-BPM, Crank-Nicholson, finite difference, nonlinear waveguide, wide-angle.

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Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved wide-angle finite-difference beam propagation method for the analysis of nonlinear optical waveguides

Flamino¹,

Cesar²,

Borges³

2002

IEEE Trans. Magn.

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show abstract

“…Podem ser citados os acopladores direcionais [78], guias de onda com curvaturas [46], [71], guias de onda tridimensionais [54], [56], [61], [70], [76], [77], [79] guias de onda não-lineares [54], [55], [74] e guias de onda anisotrópicos [ 47], [51], [53], [60], [63], [72], [75], dentre outros. As primeiras formulações do BPM foram implementadas no .…”

Section: O Método De Propagação De Feixe 41 Introduçãounclassified

Análise de dispositivos com materiais magnetoópticos para aplicações em sistemas de comunicações ópticas

Gonçalves¹

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Optical communication networks have allowed a continuous increase of broadband services offer. The all-optical communication networks are becoming the most ambitious technological goal. Great efforts have been concentrated on the materiais and devices development and improvement to make it possible. Nonreciprocal devices, such as isolators and circulators constitute an imp01tant class of optical devices. lsolators are used in optical systems to avoid reflectio. n of light in lasers and amplifiers. Circulators are used in signal derivat ion schemes that use wavelength division multiplexing (WDM). The operation of these devices is based on the propetties of magnetooptic materiais. The purposes of this dissertation are to present the main features of the magnetooptic materiais as well as to analyze the eletromagnetic wave propagation in magnetooptic waveguides, exploring nonreciprocal features ofTM modes. Planar and three-dimensional waveguides are analysed in this present study. Therefore expressions of electromagnetic fie ld components and characteristic equations of the modes of interest in planar stmctures are obtained by using transfer matrix technique (TMT). The wave propagation analysis in planar magnetooptic waveguides is realized by using the finite-difference beam propagation method (FD-BPM) and Crank-Nicholson scheme (CN) applied to wave equation solution discretization. In arder to avoid electromagnetic wave reflect ion into computational window, the transparent boundary condition (TBC) is incorporated to the FD-BPM formalism. The effective index method (EIM) is used in the analysis ofthree-d imensional rib magnetooptic waveguides.

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Optics and optoelectronics: FEM and BEM analyses A bibliography (1998–1999)

Mackerle

2001

Finite Elements in Analysis and Design

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Finite element beam propagation method for nonlinear optical waveguides

Cited by 4 publications

References 14 publications

Improved wide-angle finite-difference beam propagation method for the analysis of nonlinear optical waveguides

Improved wide-angle finite-difference beam propagation method for the analysis of nonlinear optical waveguides

Análise de dispositivos com materiais magnetoópticos para aplicações em sistemas de comunicações ópticas

Optics and optoelectronics: FEM and BEM analyses A bibliography (1998–1999)

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