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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/29770完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張宏鈞(Hung-Chun Chang) | |
| dc.contributor.author | Yen-Hung Lin | en |
| dc.contributor.author | 林彥宏 | zh_TW |
| dc.date.accessioned | 2021-06-13T01:18:09Z | - |
| dc.date.available | 2007-07-23 | |
| dc.date.copyright | 2007-07-23 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-18 | |
| dc.identifier.citation | Bibliography
[1] Baba, T., N. Fukaya, and J. Yonekura, Observation of light propagation in photonic crystal optical waveguides with bends,' Electron. Lett., vol. 35, pp.654--655, 1999. [2] Barkou, S. E., J. Broeng, and A. Bjarklev, Silica-air photonic crystal ber design that permits waveguiding by a true photonic bandgap e ect,' Opt. Lett., vol. 24, pp. 46--48, 1999. [3] Benisty, H., Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,' J. Appl. Phys., vol. 79, pp. 7483--7492, 1996. [4] Bierwirth, K., N. Schulz, and F. Arndt, Finite-di erence analysis of rectangular dielectric waveguides by a new nite di erence method,' J. Lightwave Technol., vol. 34, pp. 1104--1113, 1986. [5] Birks, T. A., J. C. Knight, and P. St. J. Russell, Endlessly single-mode photonic crystal ber,' Opt. Lett., vol. 22, pp. 961--963, 1997. [6] Boroditsky, M., R. Coccioli, and E. Yablonovitch, Analysis of photonic crystals for light emitting diodes using the nite di erence time domain technique,' Proc. SPIE, vol. 3283, pp. 184--190, 1998. [7] Brechet, F., J. Marcou, D. Pagnoux, and P. Roy, Complete analysis of the characteristics of propagation into photonic crystal bers, by the nite element method,' Opt. Fiber Technol., vol. 6, pp. 181--191, 2000. [8] Cendes, Z. J., and P. Silvester, Numerical solution of dielectric loaded waveguides: I-Finite-Element analysis,' IEEE Trans. Microwave Theory Tech., vol. 18, pp. 1124--1131, 1970. [9] Coccioli, R., M. Boroditsky, K. W. Kim, Y. Rahmat-Samii, and E. Yablonovitch, Smallest possible electromagnetic mode volume in a dielectric cavity,' IEE Proc. Optoelec., vol. 145, pp. 391--397, 1998. [10] Cregan, R. F., B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Single-mode photonic band gap guidance of light in air,' Science, vol. 285, pp. 1537--1539, 1999. [11] D'Urso, B., O. Painter, J. O'Brien, T. Tombrello, A. Yariv, and A. Scherer Modal relectivity in nite-depth two-dimensional photonic-crystal microcavities,' J. Opt. Soc. Amer. B, vol. 15, pp. 1155--1159, 1997. [12] Fan, S., P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,' Appl. Phys. Lett., vol. 78, pp. 3294--3297, 1997. [13] Feiertag, G., W. Ehrfeld, H. Freimuth, H. Kolle, H. Lehr, M. Schmidt, M. M. Sigalas, C. M. Soukoulis, G. Kiriakidis, and T. Pedersen, 'Fabrication of photonic crystals by deep x-ray lithography,' Appl. Phys. Lett. vol. 71, pp. 1441--1443, 1997. [14] Ferrando, A., E. Silvestre, J. J. Miret, P. Andr es, and M. V. Andr es, Fullvector analysis of a realistic photonic crystal ber,' Opt. Lett., vol. 24, pp. 276--278, 1999. [15] Gander, M. J., R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and P. St. J. Russel, Experimental measurement of group velocity dispersion in photonic crystal bres,' Electron. Lett., vol. 35, pp. 63--65, 1999. [16] Gourley, P. L., J. R. Wendt, G. A. Vawter, T. M. Brennan, and B. E. Hammons Optical properties of two-dimensional photonic lattices fabricated as honeycomb nanostructures in compound semiconductors,' Appl. Phys. Lett., vol. 64, pp. 687--689, 1994. [17] Hadley, G. R., and R. E. Smith, Full-vector waveguide modeling using an iterative nite-di erence method with transparent boundary conditions,' J. Lightwave Technol., vol. 13, pp. 465--469, 1995. 1992. [18] Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystal: Molding the Flow of Light. Princeton University Press, Princeton, NJ, 1995. [19] Joannopoulos, J. D., P. R. Villeneuve, and S. Fan, Photonic crystals: putting a new twist on light,' Nature, vol. 386, pp. 143--149, 1997. [20] John, S., Strong localization of photons in certain disordered dielectric superlattices,' Phys. Rev. Lett., vol. 58, pp. 2486--2489, 1987. [21] Johnson, S. G., P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Guided modes in photonic crystal slabs,' Phys. Rev. B, vol. 60, pp. 5751--5758, 1999. [22] Johnson, S. G., S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Linear waveguides in photonic-crystal slabs,' Phys. Rev. B, vol. 62, pp. 8212--8222, 2000. [23] Kanskar, M., P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,' Appl. Phys. Lett., vol. 70, pp. 1438--1440, 1997. [24] Knight, J. C., T. A. Birks, P. St. J. Russel, and D. M. Atkin, All-silica single mode optical ber with photonic crystal cladding,' Opt. Lett., vol. 21, pp. 1547--1549, 1996. [25] Knight, J. C., J. Broeng, T. A. Birks, and P. St. J. Russell, Photonic band gap guidance in optical bers,' Science, vol. 282, pp. 1476--1478, 1998. [26] Koshiba, M., and K. Saitoh, Numerical veri cation of degeneracy in hexagonal photonic crystal bers,' IEEE Photon. Technol. Lett., vol. 13, pp. 1313--1315, 2001. [27] Lee, J. F., D. K. Sun, and Z. J. Cendes, Full-wave analysis of dielectric waveguides using tangential vector nite elememts,' IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1262--1271, 1991. [28] Leonard, S. W., Complete three-dimensional band gap in macroporous silicon photonic crystals,' Appl. Phys. Lett., vol. 81, pp. 2917--2919, 2002. [29] Li, Y. F., K. Iizuka, and J. W. Y. Lit, Equivalent-layer method for optical waveguides with a mutiple quantum well structure,' Opt. Lett., vol. 17, pp. 273--275, 1992. [30] Li, Z. Y., J. Wang, and B. T. Gu, Creation of partial band gaps in anisotropic photonic-band-gap structures,' Phy. Rev. B, vol. 58, pp. 3721--3729, 1998. [31] Li, Z. Y., and L. L. Lin, Photonic band structures solved by a plane-wavebased transfer-matrix method,' Phy. Rev. E, vol. 67, 046607, 2003. [32] Lin, S. Y., J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, A three-dimensional photonic crystal operating at infrared wavelengths,' Nature, vol. 394, pp. 251--253, 1998. [33] Lin, S. Y., J. G. Fleming, R. Lin, M. M. Sigalas, R. Biswas, and K. M. Ho, 'Complete three-dimensional photonic bandgap in a simple cubic structure,' J. Opt. Soc. Amer. B, vol. 18, pp. 32--35, 2001. [34] L usse, P., P. Stuwe, J. Sch ule, and H.-G. Unger, Analysis of vectorial mode fields in optical waveguides by a new nite di erence method,' J. Lightwave Technol., vol. 12, pp. 487--494, 1994. [35] Meade, R. D., A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, Novel applications of photonic band gap materials: Low-loss bends and high Q cavities,' Appl. Phys. Lett., vol. 75, pp. 4753--4755, 1994. [36] Mekis, A., J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, High transmission through sharp bends in photonic crystal waveguides,' Phys. Rev. Lett., vol. 77, pp. 3787{3790, 1996. [37] Mekis, A., S. Fan, and J. D. Joannopoulos, Bound states in photonic crystal waveguides and waveguide bends,' Phys. Rev. B, vol. 58, pp. 4809--4817, 1998. [38] Mizuguchi, J., Y. Tanaka, S. Tamura, and M. Notomi, Focusing of light in a three-dimensional cubic photonic crystal,' Phys. Rev. B, vol. 67, 075109, 2003. [39] Noda, S., N. Yamamoto, and A. Sasaki, New Realization Method for Three-Dimensional Photonic Crystal in Optical Wavelength Region,' Jpn. J. Appl. Phys., vol. 35, pp. 909--912, 1996. [40] Ohke, S., T. Umeda, and Y. Cho, Equivalent-layer method for optical waveguides with a mutiple quantum well structure: comment,' Opt. Lett., vol. 18, pp. 1870--1872, 1993. [41] Painter, O., R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brien, P. D. Dapkus, and I. Kim, Two-dimensional photonic band-gap defect mode laser,' Science, vol. 284, pp. 1919--1821, 1999. [42] Qiu, M., and S. He, A nonorthogonal nite-di erence time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metalic inclusions,' Appl. Phys., vol. 87, pp. 8268--8275, 2000. [43] Qiu, M., Analysis of guided modes in photonic crystal bers using the finite difference time-domain method,' Microwave and Optical Technol. Lett., vol. 30, pp. 327--330, 2001. [44] Rahman, B. M. A., and J. B. Davies, Finite-element analysis of optical and microwave waveguide problems,' IEEE. Trans. Microwvae Theory Tech., vol. 32, pp. 20--28, 1984. [45] Romanov, S. G., N. P. Johnson, A. V. Fokin, V. Y. Butko, H. M. Yates, M. E. Pemble, and C. M. S. Torres, Enhancement of the photonic gap of opal-based three-dimensional gratings,' Appl. Phys. Lett., vol. 70, pp. 2091--2093, 1997. [46] Saini, M., and E. K. Sharma, Equivalent refrective index of MQW waveguides,' IEEE J. Quantum Electron., vol. 32, pp.1383--1390, 1996. [47] S oz uer, H. S., and J. W. Haus, Photonic bands: simple-cubic lattic,' J. Opt. Soc. Amer. B, vol. 10, pp. 296--302, 1993. [48] Toyama, H., K. Yasumoto, and H. Jia, Electromagnetic scattering and guidance by two-dimensional photonic bandgap structures,' XXIIth General Assembly of the International Union of Radio Science Digest, Paper DB.P.2, Maastricht, the Netherlands, August 17--24, 2002. [49] Villeneuve, P., S. Fan, and J. D. Joannopoulos, Microcavities in phontonic crystals: mode symmetry, tunability, and coupling e ciency,' Phys. Rev. B, vol. 54, pp. 7837--7842, 1996. [50] Villeneuve, P., S. Fan, S. G. Johnson, and J. D. Joannopoulos, Three dimensional photon confinement in photonic crystals of low-dimensional periodicity,' IEE Proc. Optoelec., vol. 145, pp. 384--390, 1998. [51] Yablonovitch, E., Inhibited spontaneous emission in solid-state physics and electronics,' Phys. Rev. Lett., vol. 58, pp. 2059--2062, 1987. [52] Yee, K. S., Numerical solution of initial boundary value problems involving Maxwell's equations on isotropic media,' IEEE Trans. Antenna Propagat., vol. 14, pp. 302--307, 1966. [53] Yu, C. P., and H. C. Chang, Applications of the nite di erence mode solution method to photonic crystal structures,' Opt. Quamtum Electron., vol. 36, pp. 145--163, 2004. [54] Yu, C. P., and H. C. Chang, Compact nite-di erence frequency-domain method for the analysis of two-dimensional photonic crystals,' Opt. Express, vol. 12, pp. 1397--1408, 2004. [55] Zhu, Z., and T. G. Brown, Full-vectorial nite-di erence analysis of microstructured optical bers,' Opt. Express, vol. 10, pp. 853--864, 2002. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/29770 | - |
| dc.description.abstract | 摘要
本論文係採用以余氏網格為基礎所建立之三維有限差分頻域法來分析三維光子晶體元件的能帶結構。利用均勻網格及週期性的邊界條件，我們可以很容易地從馬克斯威爾旋度方程式，推導出三維光子晶體能帶結構的特徵矩陣方程式，並求出能帶結構圖。為了處理光子晶體結構中介質介面不連續的問題，我們利用折射率加權平均法以增進數值計算的精確性並加速數值計算的收斂性。 本研究中，我們先探討兩種三維結構的簡單立方光子晶體，包括球型結構與鷹架型結構。利用三維有限差分頻域法來獲得這兩種光子晶體的能帶結構，並將該數值結果與其他數值方法所獲得的結果相互比較與探討。另外，折射率加權平均法對數值結果的影響也會加以討論。我們也分析與探討有限厚度的三維光子晶體平板，成功地獲得此種光子晶體平板的能帶結構，並在能帶結構中以光錐表示非導波模態。為了減少計算的時間與計算器記憶體的使用量，我們在數值模擬中引入此三維光子晶體的鏡射對稱。利用這個概念，我們成功地獲得偶模態與奇模態的縱剖面模態輪廓圖，並與鏡射對稱條件相符合。此外，我們也分別計算了被支撐於空氣、介質材料與週期性結構的三維光子晶體平板，從其能帶結構圖中可以發現光子晶體能隙出現於光子晶體折射率與支撐背景折射率差異較大的時候。我們的三維有限差分頻域法的計算可以有效地獲得三維光子晶體結構圖，並可繼續應用於分析更多實際的結構。 | zh_TW |
| dc.description.abstract | An Yee-mesh-based three-dimensional (3-D) finite-difference frequency-domain (FDFD) method is proposed for the band structure analysis of 3-D photonic crystal (PC) devices.
With uniform meshes and periodic boundary conditions in the numerical implementation, it is easy to derive eigenvalue matrix equations from Maxwell's curl equations to obtain the band structures of the 3-D PCs. For dealing with the dielectric discontinuity in the PC structures, the index-averaging scheme is employed to improve the numerical accuracy and accelerate the numerical convergency. In this work, two kinds of 3-D simple-cubic PCs are first considered, including spheres structures and scaffold structures. The band structures of these two PCs are obtained by using our 3-D FDFD method. Comparsion of our results with those from other numerical methods is performed and discussed. The influence of the index-averaging scheme on the 3-D PCs analysis is also investigated. We also consider 3-D PC slabs with finite thickness. Their band structures can be successfully obtained with non-guided modes referred as light cone in the band diagrams. To reduce the computing time and memory, the mirror symmetry of 3-D PC slabs is introduced in the numerical simulations. The mode profiles of even and odd modes can be obtained and coincide with other numerical investigations. We also calculate the band structures of 3-D PC slabs suspended in air, dielectric materials, and periodic backgrounds, respectively. It is found that the phtonic bandgaps appear for larger index difference between the PC slabs and the background region. Our 3-D FDFD algorithm is demonstrated to be a useful numerical tool to find out the band diagrams of 3-D PC structures for more practical applications. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T01:18:09Z (GMT). No. of bitstreams: 1 ntu-96-R94941039-1.pdf: 2474456 bytes, checksum: 550345c96acbc3fe564d1bf53b00388e (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Contents
1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Formulation of the Finite-Dierence Frequency-Domain Method 7 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 The Bloch Function for 3-D Photonic Crystals and Periodic Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Formulae for 3-D Anisotropic Band Structures . . . . . . . . . . . . . 9 2.3.1 Central Dierence Scheme . . . . . . . . . . . . . . . . . . . . 9 2.3.2 The FDFD Method . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Improvements for the Dielectric Medium Interfaces . . . . . . . . . . 16 3 Band Structures of 3-D Simple Cubic Photonic Crystal Structures 23 3.1 3-D Simple Cubic Photonic Crystal: Sphere Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.1 Isotropic Materials . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.2 Anisotropic Materials . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 3-D Simple Cubic Photonic Crystal: Scaold Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4 Band Structures of 3-D Photonic Crystal Slabs 51 4.1 Computational Method for Band Structures of 3-D Photonic Crystal Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.2 Band Structures for PC Slabs Suspended in Air . . . . . . . . . . . . 54 4.3 Band Structures for PC Slabs with Solid Background . . . . . . . . . 56 4.4 Band Structures for PC Slabs with Periodic Background . . . . . . . 57 5 Conclusion 84 | |
| dc.language.iso | en | |
| dc.title | 以有限差分頻域法分析三維光子晶體的能帶結構 | zh_TW |
| dc.title | Band Structure Analysis of Three-Dimensional Photonic Crystal by the Finite-Difference Frequency-Domain Method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 江衍偉(Yean-Woei Kiang),彭隆瀚(Lung-Han Peng),楊宗哲(Tzong-Jer Yang) | |
| dc.subject.keyword | 光子晶體,有限差分頻域法,光子晶體能帶結構, | zh_TW |
| dc.subject.keyword | Photonic crystal,Finite-difference frequency-domain method,Photonic band structure, | en |
| dc.relation.page | 92 | |
| 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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