The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
푸리에 급수 확장 방법은 광 도파관의 불연속성 문제에 접근하는 데 유용한 도구이며 광결정 도파관의 플로켓 모드를 분석하는 데 적용할 수 있습니다. 그러나 잘림 차수가 큰 Floquet 모드 계산은 반올림 오류로 인해 제한되는 것으로 알려져 있습니다. 본 논문은 원형 실린더로 형성된 XNUMX차원 광결정 도파관에서 전파되는 Floquet 모드의 새로운 공식을 제안합니다. 기존 방법과 동일하게 주기적인 경계조건을 도입하고, 필드는 푸리에 급수 확장으로 표현됩니다. 본 공식은 또한 원통형 파 확장을 도입하고 원통형 배열의 산란을 분석하는 데 사용되는 재귀 전이 매트릭스 알고리즘을 사용합니다. 이는 푸리에 급수 확장을 위해 큰 절단 차수를 사용하지 않고도 매우 높은 정확도를 얻을 수 있게 해줍니다. 제시된 공식은 수치 실험을 통해 검증되었습니다.
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부
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
부
@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},}
부
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 -