請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/29786完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 邱奕鵬(Yih-Peng Chiou) | |
| dc.contributor.author | Kai-Hung Chi | en |
| dc.contributor.author | 綦凱宏 | zh_TW |
| dc.date.accessioned | 2021-06-13T01:18:48Z | - |
| dc.date.available | 2010-07-26 | |
| dc.date.copyright | 2007-07-26 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-19 | |
| dc.identifier.citation | [1] E. Yalonovitch, “Photonic band-gap structure,” J. Opt. Soc. Am. B, Vol. 10, Issue 2, 283-295, 1993.
[2] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett., Vol. 58, 2486, 1987. [3] K. M. Ho, C. T. Chan, and C. M Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett., Vol. 65, No. 25, 3152-3155, 1990. [4] M. Plihal, and A. A. Maradudin, “Photonic band structure of twodimensional systems: The triangular lattice,” Phys. Rev. B, Vol. 44, No. 16, 8565-8571, 1991. [5] S. Guo and S. Albin, “Simple plane wave implementation for phtonic crystal calculation,” Opt. Exp., Vol. 11, No. 2, 167-175, 2003. [6] A. Taflove , Computational Electrodynamics - The Finite-Difference Time-Domain Method, 3rd. ed., Artech House, 2005. [7] M. Qiu and S. He, “A nonorthogonal finite-difference time-domain method for comprting the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys., Vol. 87, No. 12, 8268-8275, 2000. [8] C. P. Yu, and H. C. Chang, “Compact finite-difference frequencydomain method for the analysis of two-dimensional photonic crystal,” Opt. Exp., Vol. 12, 1397-1408, 2004. [9] S. Guo, F. Wu, and S. Albin, “Photonic band gap analysis using finite-difference frequency-domain method,” Opt. Exp., Vol. 12, No. 8, 1741-1746, 2004. [10] H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, and T. Tmamura, “Superprism phenomena in photonic crystals,” Phys. Rev. B, Vol 58, No. 16, 10096-10099, 1998. [11] D. N. Chigrin, S. Enoch, C. M. S. Torres and G. Tayeb, “Selfguiding in two-dimensional photonic crystal,” Opt. Exp., Vol. 11, No. 10, 1203-1211, 2003. [12] W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Technol. Lett., Vol. 7, 599-604, 1994. [13] R. Mittra and U. Pekel, “A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves,” IEEE Microwave Guided Wave Lett. Vol. 5, 84-86, 1995. [14] C. M. Rappaport, “Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space,” IEEE Microwave Guided Wave Lett. Vol. 5, 90-92, 1995. [15] R. Mittra and U. Pekel, “A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves,” IEEE Microwave Guided Wave Lett., Vol. 5, 84-86 1995. [16] E. D. Palik, Handbook of optical constants of solids, Academic Press. [17] C. Kittel, Introduction to solid state physics, 8th. ed., Wiley, 2005. [18] S. Shi, C Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A, Vol. 21, No. 9, 1769-1775, 2004. [19] S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos. “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B, Vol. 62, No. 12, 8212-8222, 2000. [20] A.Mekis, S. Fan, and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Phys. Rev. B, Vol. 58, 4809, 1998. [21] E.Waks and J. Vuckovic, “Coupled mode theory for photonic crystal cavity-waveguide interaction,” Opt Exp., Vol. 13, No. 13, 5064-5073, 2005. [22] M. Bayindir, B. Temelkuran, and E. Ozbay, “Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals,” Phys. Rev. B, Vol. 61, R11855. [23] H. A. Haus, Waves and fields in optoelectronics, Prentice-Hall. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/29786 | - |
| dc.description.abstract | 藉由將馬克士威方程式推導為一個利用已知頻率來求波向量的特徵值方程式後，利用不同的數值方法來替代此特徵值方程式中的運算子，便可以利用不同的數值方法來計算光子晶體的頻帶結構，論文中將會介紹將有限差分法和平面波展開法帶入此特徵值方程式的優點及運算結果。利用修改過後的平面波展開法，可以分析以色散性材料所製成的光子晶體，同時可以有效率的計算等頻率曲線，突破傳統平面波展開法無法直接計算色散性材料的限制，因此可以利用等效折射率的概念來設計平板光子晶體。而修改後之有限差分法除了同樣可以計算以色散性材料所製成的光子晶體外，藉由觀察所計算出波向量的虛數部分可以推測電磁波在光子晶體中的衰減情況，在有限差分法中也較容易加入完美匹配邊界，便可以計算有限的週期會帶給光子晶體波導多少的衰減，可利用計算出來的結果設計光子晶體波導。 | zh_TW |
| dc.description.abstract | An eigenvalue equation was derived from Maxwell equations. By this equation, eigenfrequencies are calculated with known wavevectors. Different numerical methods are used to solve the eigenvalue equation. In this thesis, plane-wave expansion method and finite-difference method are used to solve this eigenvalue equation. Photonic crystals made by dispersive and absorptive material can be analyzed directly by these methods, while conventional plane wave expanison method can not. Isofrequency curves and isofequency surfaces are calculated efficiently by these methods. Finite-difference method is also used to analyze the finite size photonic crystals by using perfect match layer rather than periodic boundary conditions. The loss caused by leakage in photonic crystal waveguides is estimated. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T01:18:48Z (GMT). No. of bitstreams: 1 ntu-96-R94941046-1.pdf: 4793934 bytes, checksum: f3afa8fa4bc2ecdb2e7c2fa04bd088a4 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | 1 導論 13
1.1 光子晶體簡介 . . . . . . . . . . . . . . . . . . . . 13 1.2 光子晶體基本原理 . . . . . . . . . . . . . . . . . . 16 1.3 傳統數值方法介紹 . . . . . . . . . . . . . . . . . . 19 2 理論與數值方法簡介 21 2.1 平面波展開法 . . . . . . . . . . . . . . . . . . . . 21 2.2 時域有限差分法 . . . . . . . . . . . . . . . . . . . 26 2.3 特徵值方程式 . . . . . . . . . . . . . . . . . . . . 32 2.4 修改後之平面波展開法 . . . . . . . . . . . . . . . . 39 2.5 修改後之有限差分法 . . . . . . . . . . . . . . . . . 49 3 光子晶體的頻帶結構及等頻率曲線 61 3.1 非色散性材料之光子晶體 . . . . . . . . . . . . . . . 61 3.2 色散性材料之光子晶體 . . . . . . . . . . . . . . . . 63 3.3 吸收性材料之光子晶體 . . . . . . . . . . . . . . . . 65 3.4 間距色散性及吸收性材料之光子晶體 . . . . . . . . . . 71 3.5 等頻率曲線 . . . . . . . . . . . . . . . . . . . . . 73 4 光子晶體元件 78 4.1 光子晶體波導 . . . . . . . . . . . . . . . . . . . . 78 4.2 平板光子晶體 . . . . . . . . . . . . . . . . . . . . 94 5 結論 97 | |
| dc.language.iso | zh-TW | |
| dc.subject | 有限週期 | zh_TW |
| dc.subject | 光子晶體 | zh_TW |
| dc.subject | 特徵值方程式 | zh_TW |
| dc.subject | 修改之平面波展開法 | zh_TW |
| dc.subject | 修改之有限差分法 | zh_TW |
| dc.subject | 色散性 | zh_TW |
| dc.subject | 吸收性 | zh_TW |
| dc.subject | modified planewave expansion method | en |
| dc.subject | absorptive | en |
| dc.subject | dispersive | en |
| dc.subject | modified finite-difference method | en |
| dc.subject | Photonic crystal | en |
| dc.subject | eigenvalue equaltion | en |
| dc.subject | finite size | en |
| dc.title | 利用修改之平面波展開法和頻域有限差分法來分析光子晶體 | zh_TW |
| dc.title | Modified Plane-Wave Expansion and Modified Finite-Difference Frequency-Domain Methods for the Analysis of Photonic Crystals | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 江衍偉,王子建 | |
| dc.subject.keyword | 光子晶體,特徵值方程式,修改之平面波展開法,修改之有限差分法,色散性,吸收性,有限週期, | zh_TW |
| dc.subject.keyword | Photonic crystal,eigenvalue equaltion,modified planewave expansion method,modified finite-difference method,dispersive,absorptive,finite size, | en |
| dc.relation.page | 100 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-19 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 光電工程學研究所 | zh_TW |
| 顯示於系所單位： | 光電工程學研究所 | |
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|---|---|---|---|
| ntu-96-1.pdf 未授權公開取用 | 4.68 MB | Adobe PDF |
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