Analysis for Scattering Problem of Directional Coupler for Slab Waveguides

Masaji TOMITA

Analysis for Scattering Problem of Directional Coupler for Slab Waveguides

Masaji TOMITA

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In this paper, scattering problem of the directional coupler for the slab waveguides are analyzed by the mode-matching method in the sense of least squares for the lowest order even TE mode incidence. It is considered that the analysis of this coupler for the slab waveguides presents the fundamental data to design the directional coupler for the three dimensional waveguides. This directional coupler is composed of three parallel slabs which are placed at equal space in the dielectric medium. Respective slabs are core regions of three respective waveguides. The periodic groove structure of finite extent is formed on the both surfaces of core region of the central waveguide among them. The power of incident TE mode is coupled to other two waveguides through periodic groove structure. The coupled TE mode propagates in the other waveguides to the same or opposite direction for the direction of incident mode which propagates in the waveguide having periodic structure when the Bragg condition is selected appropriately. The scattered field of each region of this directional coupler is described by the superpositions of the plane waves with bandlimited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. The first order approximate solutions of the integral equations are derived and the coupling efficiency and scattered fields are analyzed on the basis of those solutions in this paper.

Publication: IEICE TRANSACTIONS on Electronics Vol.E80-C No.11 pp.1482-1490

Publication Date: 1997/11/25

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Type of Manuscript: Special Section PAPER (Special Issue on Electromagnetic TheoryScattering and Diffraction)

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Masaji TOMITA, "Analysis for Scattering Problem of Directional Coupler for Slab Waveguides" in IEICE TRANSACTIONS on Electronics, vol. E80-C, no. 11, pp. 1482-1490, November 1997, doi: .
Abstract: In this paper, scattering problem of the directional coupler for the slab waveguides are analyzed by the mode-matching method in the sense of least squares for the lowest order even TE mode incidence. It is considered that the analysis of this coupler for the slab waveguides presents the fundamental data to design the directional coupler for the three dimensional waveguides. This directional coupler is composed of three parallel slabs which are placed at equal space in the dielectric medium. Respective slabs are core regions of three respective waveguides. The periodic groove structure of finite extent is formed on the both surfaces of core region of the central waveguide among them. The power of incident TE mode is coupled to other two waveguides through periodic groove structure. The coupled TE mode propagates in the other waveguides to the same or opposite direction for the direction of incident mode which propagates in the waveguide having periodic structure when the Bragg condition is selected appropriately. The scattered field of each region of this directional coupler is described by the superpositions of the plane waves with bandlimited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. The first order approximate solutions of the integral equations are derived and the coupling efficiency and scattered fields are analyzed on the basis of those solutions in this paper.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e80-c_11_1482/_p

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@ARTICLE{e80-c_11_1482,
author={Masaji TOMITA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Analysis for Scattering Problem of Directional Coupler for Slab Waveguides},
year={1997},
volume={E80-C},
number={11},
pages={1482-1490},
abstract={In this paper, scattering problem of the directional coupler for the slab waveguides are analyzed by the mode-matching method in the sense of least squares for the lowest order even TE mode incidence. It is considered that the analysis of this coupler for the slab waveguides presents the fundamental data to design the directional coupler for the three dimensional waveguides. This directional coupler is composed of three parallel slabs which are placed at equal space in the dielectric medium. Respective slabs are core regions of three respective waveguides. The periodic groove structure of finite extent is formed on the both surfaces of core region of the central waveguide among them. The power of incident TE mode is coupled to other two waveguides through periodic groove structure. The coupled TE mode propagates in the other waveguides to the same or opposite direction for the direction of incident mode which propagates in the waveguide having periodic structure when the Bragg condition is selected appropriately. The scattered field of each region of this directional coupler is described by the superpositions of the plane waves with bandlimited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. The first order approximate solutions of the integral equations are derived and the coupling efficiency and scattered fields are analyzed on the basis of those solutions in this paper.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Analysis for Scattering Problem of Directional Coupler for Slab Waveguides
T2 - IEICE TRANSACTIONS on Electronics
SP - 1482
EP - 1490
AU - Masaji TOMITA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E80-C
IS - 11
JA - IEICE TRANSACTIONS on Electronics
Y1 - November 1997
AB - In this paper, scattering problem of the directional coupler for the slab waveguides are analyzed by the mode-matching method in the sense of least squares for the lowest order even TE mode incidence. It is considered that the analysis of this coupler for the slab waveguides presents the fundamental data to design the directional coupler for the three dimensional waveguides. This directional coupler is composed of three parallel slabs which are placed at equal space in the dielectric medium. Respective slabs are core regions of three respective waveguides. The periodic groove structure of finite extent is formed on the both surfaces of core region of the central waveguide among them. The power of incident TE mode is coupled to other two waveguides through periodic groove structure. The coupled TE mode propagates in the other waveguides to the same or opposite direction for the direction of incident mode which propagates in the waveguide having periodic structure when the Bragg condition is selected appropriately. The scattered field of each region of this directional coupler is described by the superpositions of the plane waves with bandlimited spectra, respectively. These approximate wave functions are determined by the minimization of the mean-square boundary residual. This method results in the simultaneous Fredholm type integral equations of the second kind for these spectra. The first order approximate solutions of the integral equations are derived and the coupling efficiency and scattered fields are analyzed on the basis of those solutions in this paper.
ER -