臺灣博碩士論文加值系統

本篇論文的研究主要針對橢圓形氣孔結構光子晶體光纖作模態分析，利用向量邊界元素法來模擬與分析，計算出等效折射率及模態場形圖，並探討改變空氣孔洞半徑、空氣孔洞橢圓率比值及旋轉光子晶體結構的傳輸特性，並分析橢圓形氣孔結構光子晶體光纖隨波長改變的模態分佈及極化特性，在改變空氣孔洞半徑中，發現空氣孔洞越大，等效折射率越低，而在改變橢圓率比值的模擬中，發現橢圓率比值越大，等效折射率越高，從極化特性來看，雙折射現象與波長成正比關係；當空氣孔洞半徑越大，雙折射數值會隨波長越長而越小，此外，當空氣孔洞橢圓率比值越小，雙折射數值越大；在旋轉光子晶體結構90度後的極化分析中，發現雙折射現象比原本結構更加明顯許多，最高可達雙折射數值0.0008。

Through Vector Boundary Element Method, this thesis is analyzing and simulating elliptical-hole photonic crystal fiber. For the propagation modes, we change the air hole radius, elliptical ratio, wavelength, and turn the angle of air hole structure. In here, we analyze not only in the characteristics of mode also including polarization. As shown in the result, we will discuss the effective index of the EPCF, we knows inversely proportional to relationship of effective index and wavelength. At η=1.2, the effective index is the maximum value. Therefore, we will discuss the polarization of the EPCFs, the relationship between the birefringence and the wavelength is direct ration. By analyzing turn the angle of air hole’s 90-degrees-polarization, it’s found that the birefringence is clearly more obvious than its original structure. The highest birefringence rate is 0.0008.

致謝i
中文摘要ii
英文摘要iii
目錄iv
圖目錄vi
表目錄ix
第一章緒論1
1.1前言1
1.2研究動機2
1.3研究方法2
1.4論文架構概述3
第二章數值方法5
2.1向量邊界元素法5
2.2數值程序9
第三章模態結果分析13
3.1程式驗證13
3.2空氣孔洞半徑與波長改變情形19
3.3橢圓形空氣孔洞改變情形21
3.4橢圓形氣孔半徑改變情形29
3.5改變空氣孔洞排列結構31
第四章極化分析43
4.1極化基本介紹43
4.2改變空氣孔洞半徑之極化分析44
4.3改變橢圓形空氣孔洞之極化分析47
4.4改變空氣孔洞排列結構之極化分析48
第五章結論53
參考文獻54
圖目錄
圖1.1光子晶體示意圖(a)一維(b)二維(c)三維3
圖1.2傳統光纖示意圖4
圖1.3光子晶體光纖示意圖4
圖2.1波導結構12
圖2.2光子晶體光纖積分路徑示意圖12
圖3.1六邊形光子晶體光纖參數示意圖14
圖3.2FEM與VBEM改變空氣孔洞半徑兩者數據比較圖15
圖3.3在HE11模態時磁場實部的場形圖(向量圖)16
圖3.4在TM01模態時磁場實部的場形圖(向量圖)16
圖3.5在HE21模態時磁場實部的場形圖(向量圖)17
圖3.6在TE01模態時磁場實部的場形圖(向量圖)17
圖3.7改變空氣孔洞間距之等效折射率變化圖18
圖3.8改變波長及空氣孔洞半徑之等效折射率變化圖20
圖3.9隨著空氣孔洞半徑改變之等效折射率變化圖20
圖3.10橢圓形空氣孔洞結構之參數示意圖22
圖3.11改變橢圓形孔洞橢圓率之示意圖22
圖3.12水平橢圓結構在HE11模態時磁場實部的場形圖(向量圖)23
圖3.13水平橢圓結構在TM01模態時磁場實部的場形圖(向量圖)23
圖3.14水平橢圓結構在HE21模態時磁場實部的場形圖(向量圖)24
圖3.15水平橢圓結構在TE01模態時磁場實部的場形圖(向量圖)24
圖3.16垂直橢圓結構在HE11模態時磁場實部的場形圖(向量圖)25
圖3.17垂直橢圓結構在TM01模態時磁場實部的場形圖(向量圖)25
圖3.18垂直橢圓結構在HE21模態時磁場實部的場形圖(向量圖)26
圖3.19垂直橢圓結構在TE01模態時磁場實部的場形圖(向量圖)26
圖3.20橢圓形氣孔結構改變波長及橢圓率之變化圖27
圖3.21隨著橢圓率改變之等效折射率變化圖28
圖3.22水平橢圓結構改變孔洞半徑隨波長曲線變化圖29
圖3.23垂直橢圓結構改變孔洞半徑隨波長曲線變化圖30
圖3.24光子晶體結構旋轉角度示意圖31
圖3.25旋轉角度後之HE11模態時的向量場形圖32
圖3.26旋轉角度後之TM01模態時的向量場形圖32
圖3.27旋轉角度後之HE21模態時的向量場形圖33
圖3.28旋轉角度後之TE01模態時的向量場形圖33
圖3.29旋轉角度後之隨空氣孔洞間距的等效折射率變化圖34
圖3.30旋轉角度後之隨空氣孔洞半徑的等效折射率變化圖35
圖3.31旋轉角度後之改變空氣孔洞半徑比較圖36
圖3.32旋轉角度後水平橢圓結構之HE11模態時的向量場形圖37
圖3.33旋轉角度後水平橢圓結構之TM01模態時的向量場形圖38
圖3.34旋轉角度後水平橢圓結構之HE21模態時的向量場形圖38
圖3.35旋轉角度後水平橢圓結構之TE01模態時的向量場形圖39
圖3.36旋轉角度後垂直橢圓結構之HE11模態時的向量場形圖39
圖3.37旋轉角度後垂直橢圓結構之TM01模態時的向量場形圖40
圖3.38旋轉角度後垂直橢圓結構之HE21模態時的向量場形圖40
圖3.39旋轉角度後垂直橢圓結構之TE01模態時的向量場形圖41
圖3.40旋轉角度後橢圓率之等效折射率變化圖41
圖3.41原本結構與旋轉角度後之改變橢圓率比較圖42
圖4.1〖HE〗_11^x模態下的向量場形圖45
圖4.2〖HE〗_11^y模態下的向量場形圖45
圖4.3改變空氣孔洞半徑與波長之極化變化圖46
圖4.4橢圓形空氣孔洞與波長之極化變化圖47
圖4.5x-極化之旋轉結構比較示意圖48
圖4.6旋轉角度後〖HE〗_11^x模態下的向量場形圖49
圖4.7旋轉角度後〖HE〗_11^y模態下的向量場形圖49
圖4.8旋轉角度之改變空氣孔洞半徑與波長的極化變化圖50
圖4.9原本結構與旋轉角度後之改變空氣孔洞半徑的雙折射比較圖51
圖4.10旋轉角度之改變橢圓率的極化變化圖52
表目錄
表3.1光子晶體光纖結構參數(程式驗證)13
表3.2光子晶體光纖空氣孔洞間距變化結構參數15
表3.3光子晶體光纖結構參數19
表3.4橢圓形氣孔之光子晶體光纖結構參數21
表4.1光子晶體光纖結構參數46
表4.2x-極化與y-極化之等效折射率比較48

[1]E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Physical review letters, vol. 58, Number 20, pp. 2059-2062, May 1987.
[2]S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Physical review letters, vol. 58, Number 23, pp. 2486-2489, June 1987.
[3]P. Russell, “Photonic Crystal Fibers,” Science, vol. 299, pp. 358-362, January 2003.
[4]J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-sillica single-mode optical fiber with photonic crystal cladding,’’ Opt. Lett., vol. 21, pp.1547-1549. October 1996.
[5]D. Ouzounov, D. Homoelle, and W. Zipfel, “Dispersion measurements of microstructured fibers using femtosecond laser pulses,’’ Opt. Commun., vol. 192, pp.219-223, June1997.
[6]B. J. Eggleton, P.S. Westbrook, R.S. Windeler, S. Spalter, T.A. Strasser, “Grating resonances in all-sillica microstructured optical fiber,’’ Opt. Lett., vol. 24, pp.1460-1462. November 1999.
[7]J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguies,’’ Opt. Fiber Technol., vol. 5, pp. 305-330, July 1999.
[8]P. J. Bennett, T. M. Monro, and D. J. Richardson, “A robust, large air fill fraction holey fiber,” The Conference on Lasers and Electro-Optics (CLEO’99), vol. 1, pp.293,May 1999.
[9]T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey Optical Fiber: An Efficient Modal Model,” J. Lightwave Technol., vol. 17, pp. 1093-1102, June 1999.
[10]K. Saitoh and M. Koshiba, “Photonic bandgap fibers with high birefringence,” IEEE Photon. Technol. Lett., vol. 14, pp. 1291-1293, September 2002.
[11]I.P. Kaminow, V. Ramaswamy, “Single-Polarization optical fibers: slab model,” Appl Phys. Lett., 34(4), pp. 1071~1089, 1979.
[12]A. Ortigosa-Blanch, J.c. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, P.St. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett., vol 25, pp.1325-1327, Sep. 2000.
[13]X. Y. Wang, J. J. Lou, C. Lu, P. Shum, C.L. Zhao, P.Roy Chaudhuri, M. Yan, “Full-Vector Analysis of Photonic Crystal Fibers Using the Boundary Element Method,” ICICS-PCM., pp.1293, pp.1293-1297, December 2003.
[14]T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett., vol. 22, pp. 961-963, July 1997.
[15]M. J. Grander, R. McBride, J. D. C. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, and p. St. J. Russell, “Experimental measurement of group velocity in photonic crystal fibers,” Electron. Lett., vol. 35, pp. 63-64, January 1999.
[16]J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett., vol. 34, pp.1347-1348, June1998.
[17]N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearlity in holey optical fibers: Measurement and future opportunities,” Opt. Lett., vol. 24, pp. 1395-1397, October 1999.
[18]T. A. Birks, J. C. Knight, B. J. Mangan, and P. St. J. Russell, “photonic crystal fibers: An endless variety,” IEICE Trans. Electron., vol. E84-C, pp.585-592, May 2001.
[19]M. Koshiba, “Full-Vector Analysis of Photonic Crystal Fiber Using the Finite Element Method,” IEICE Trans. Electron., vol. E85-C, pp. 881-888, April 2002.
[20]T. Haswgawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Modeling and design optimization of hole-assisted lightguide fiber by full-vector finite element method,” in ECoC’01,3.324-325, April 2001.
[21]M. Koshiba and K. Saitoh, “Finite-element Analysis of Birefringence and Dispersion Properties in Actual and Idealized Holey-fiber Structures,” Appl. Opt., vol.42, pp. 6267-6275, November 2003.
[22]M. J. Steel, T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry amd degeneracy in microstructured optical fiber,” Opt.Lett., vol. 26, pp.488-490, April 2001.
[23]T. P. White, R. C. McPhedran, and C. M. de Sterke, “Confinement losses in microstructured optical fibers,” Optics Lett., vol. 26, NO. 21, pp.1660-1662, November 2001.
[24]趙嘉信 著, “Study of Photonic Crystal Fiber using Vector Boundary Element Method,” 國立中山大學博士論文，中華民國95年。
[25]許云瑄 著, “兆赫波光子晶體光纖之特性與分析‘‘,義守大學電機研究所碩士論文，中華民國100年。
[26]洪文英 著, “奈米化光子晶體光纖特性與模擬‘‘,義守大學電機研究所碩士論文，中華民國101年。
[27]N. Moritra, “ A method extending the boundary condition for analyzing guided modes of dielectric waveguides of arbitrary cross-sectional shape,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp. 6-12, January1982.
[28]W. Yang and A.Gopinath, “A boundary integral method for propagation problems in integrated optical structures,” IEEE Photon. Technol. Lett., vol. 7, pp. 777-779, July 1995.
[29]S. Y. Lin and C. C. Lee, “A full wave analysis of microstrips by the boundary element method,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1977-1983, November 1996.
[30]P. Cecchini, F. Bardati, and R. Ravanelli, “A general approach to edge singularity extraction near composed wedges in boundary-element method,” IEEE Tran. Microwave Thory Tech., vol. 49, pp. 730-733, April 2001.
[31]C. C. Su, “A surface integral equation method for homogeneous optical fibers and coupled image lines of arbitrary cross section,” IEEE Tran. Microwave Theory Tech., vol. MTT-33, pp. 1114-1120, November 1985.
[32]K. Saitoh, and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method, ” Opt. Fiber technol., vol. 6, pp. 181-191, Apr. 2000.
[33]T. L. Wu, C. H. Chao, “Photonic Crystal Fiber Analysis Through the Vector Boundary-Element Method: Effect of Elliptical Air Hole,” IEEE Photonics Technology Lett., vol. 16, NO. 1, pp. 126-128, January 2004.
[34]D. Chen and L. Shen, “Highly birefringent elliptical-hole photonic crystal fibers with double defect,”Journal of Lightwave Technology., vol. 25, NO. 9, pp.2700-2705, September 2007.
[35]J. S. Chiang, T. L. Wu, “Analysis of propagation characteristics for an octagonal photonic crystal fiber(O-PCF), ”Optics Communications., vol. 258, pp.170-176, Feb. 2006.
[36]吳曜東 著, “光纖原理與應用”全華科技圖書股份有限公司，中華民國86年。
[37]Y. F. Chau and C. Y. Lin, “Ultrahigh birefringence with ultralow confinement loss of photonic crystal fibers, ”Photonics and Optoelectronics., pp.1-4, 2010.