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The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it can apply to analyze the Floquet-modes of photonic crystal waveguides. However, it has known that the Floquet-mode calculation with large truncation order is limited because of the roundoff errors. This paper proposes a novel formulation of the Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. We introduce a periodic boundary condition as same with the conventional method, and the fields are expressed in the Fourier series expansions. The present formulation also introduces the cylindrical-wave expansions and uses the recursive transition-matrix algorithm, which is used to analyze the scattering from cylinder array. This makes us possible to obtain very high accuracy without the use of large truncation order for Fourier series expansion. The presented formulation is validated by numerical experiments.

- Publication
- IEICE TRANSACTIONS on Electronics Vol.E93-C No.1 pp.24-31

- Publication Date
- 2010/01/01

- Publicized

- Online ISSN
- 1745-1353

- DOI
- 10.1587/transele.E93.C.24

- Type of Manuscript
- Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application)

- Category

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Koki WATANABE, Yoshimasa NAKATAKE, "Floquet-Mode Analysis of Two-Dimensional Photonic Crystal Waveguides Formed by Circular Cylinders Using Periodic Boundary Conditions" in IEICE TRANSACTIONS on Electronics,
vol. E93-C, no. 1, pp. 24-31, January 2010, doi: 10.1587/transele.E93.C.24.

Abstract: The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it can apply to analyze the Floquet-modes of photonic crystal waveguides. However, it has known that the Floquet-mode calculation with large truncation order is limited because of the roundoff errors. This paper proposes a novel formulation of the Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. We introduce a periodic boundary condition as same with the conventional method, and the fields are expressed in the Fourier series expansions. The present formulation also introduces the cylindrical-wave expansions and uses the recursive transition-matrix algorithm, which is used to analyze the scattering from cylinder array. This makes us possible to obtain very high accuracy without the use of large truncation order for Fourier series expansion. The presented formulation is validated by numerical experiments.

URL: https://global.ieice.org/en_transactions/electronics/10.1587/transele.E93.C.24/_p

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@ARTICLE{e93-c_1_24,

author={Koki WATANABE, Yoshimasa NAKATAKE, },

journal={IEICE TRANSACTIONS on Electronics},

title={Floquet-Mode Analysis of Two-Dimensional Photonic Crystal Waveguides Formed by Circular Cylinders Using Periodic Boundary Conditions},

year={2010},

volume={E93-C},

number={1},

pages={24-31},

abstract={The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it can apply to analyze the Floquet-modes of photonic crystal waveguides. However, it has known that the Floquet-mode calculation with large truncation order is limited because of the roundoff errors. This paper proposes a novel formulation of the Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. We introduce a periodic boundary condition as same with the conventional method, and the fields are expressed in the Fourier series expansions. The present formulation also introduces the cylindrical-wave expansions and uses the recursive transition-matrix algorithm, which is used to analyze the scattering from cylinder array. This makes us possible to obtain very high accuracy without the use of large truncation order for Fourier series expansion. The presented formulation is validated by numerical experiments.},

keywords={},

doi={10.1587/transele.E93.C.24},

ISSN={1745-1353},

month={January},}

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TY - JOUR

TI - Floquet-Mode Analysis of Two-Dimensional Photonic Crystal Waveguides Formed by Circular Cylinders Using Periodic Boundary Conditions

T2 - IEICE TRANSACTIONS on Electronics

SP - 24

EP - 31

AU - Koki WATANABE

AU - Yoshimasa NAKATAKE

PY - 2010

DO - 10.1587/transele.E93.C.24

JO - IEICE TRANSACTIONS on Electronics

SN - 1745-1353

VL - E93-C

IS - 1

JA - IEICE TRANSACTIONS on Electronics

Y1 - January 2010

AB - The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it can apply to analyze the Floquet-modes of photonic crystal waveguides. However, it has known that the Floquet-mode calculation with large truncation order is limited because of the roundoff errors. This paper proposes a novel formulation of the Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. We introduce a periodic boundary condition as same with the conventional method, and the fields are expressed in the Fourier series expansions. The present formulation also introduces the cylindrical-wave expansions and uses the recursive transition-matrix algorithm, which is used to analyze the scattering from cylinder array. This makes us possible to obtain very high accuracy without the use of large truncation order for Fourier series expansion. The presented formulation is validated by numerical experiments.

ER -