中文提要：
對於等邊三角形結構的3x3光纖耦合器而言，根據純量耦合模態理論的分析結果顯示，當光由其中一個輸入埠輸入時，由於耦合器結構所具有的對稱性，其非輸入光之另外兩個埠的輸出功率將會相等。然而，數個學術論文的量測結果卻顯示出這兩個埠的輸出功率並不相等。本篇論文將提出一套適用於分析極化輸入光的功率耦合模型。經由這個模型的分析結果顯示出，當一極化光入射於其中一個埠時，另外兩個埠的輸出功率將不會相等，此現象與量測結果相符。

Abstract：
Scalar coupled mode theory predicts that the output powers at two nonlaunch fibers are identical for the equilateral 3x3 fiber couplers due to the geometrical symmetry, but several experimental results demonstrate that they are not equal. In this work, a power coupling model with considering the polarization property of input power is proposed for the equilateral 3x3 fiber couplers. Consistent with the measurement results, the model shows that when a polarized light is launched into one of the three fibers the output powers at the other two nonlaunch fibers are unequal.

目錄

第一章 序論………………………………………………………………………. 1
1.1 研究目的與背景………………………………………………………….. 1
1.2 論文大綱………………………………………………………………….. 2

第二章 表面積分法…………………………………………...………………….. 4
2.1 概述……………………………………………………………………….. 4
2.2 理論推演………………………………………………………………….. 4
2.3 數值程序…………………………………………………………………... 6

第三章 弱燒融式等邊三角形3x3光纖耦合器之三維模型…………………… 11
3.1 概述………………………………………………………………………... 11
3.2 導波模態之傳播常數與向量場型………………………………………... 11
3.2.1 正規化傳播常數與正規化頻率……………………………………. 12
3.2.2 正規化傳播常數與燒融程度………………………………………. 13
3.3 功率關係式的建立………………………………………………………... 13
3.4 模擬與量測的比較………………………………………………………... 18

第四章 對於各種極化輸入光之功率耦合特性分析…………………………….. 29
4.1 概述………………………………………………………………………... 29
4.2 線性極化入射光…………………………………………………………... 29
4.2.1功率耦合對入射光極化角的相依性……………………………….. 30
4.2.2功率耦合與燒融程度的相依性…………………………………….. 32
4.2.3功率耦合曲線與加熱區域長度的關係…………………………….. 33
4.3 橢圓極化入射光與圓形極化入射光……………………………………... 34
4.4 總結………………………………………………………………………... 36

第五章 結論……………………………………………………………………….. 53

附錄A 等邊三角形3x3光纖耦合器中電場與磁場的關係……………………. 54

附錄B 弱燒融式等邊三角形3x3光纖耦合器功率關係式的推導……………. 56

附錄C 以耦合模態方程式(coupled-mode equations)為基礎所推導的功率關係
式………………………………………………………………………….. 62

附錄D 等邊三角形3x3光纖耦合器的製作……………………………………. 65

參考文獻…………………………………………………………………………….. 70

參考文獻

[1] D. O. Culverhouse, T. A. Birks, S. G. Farwell, and P. St. J. Russel,“3x3 all-fiber routing switch,” IEEE Photon.Tech.Lett., vol. 9, pp. 333-335,1997.
[2] Y. H. Ja, “Analysis of optical fiber ring resonator using a collinear 3x3 fiber coupler” J. Quantum Electron., vol. 30, pp. 2639-2644, 1994.
[3] Y. H. Ja, “Analysis of four-port optical fiber ring and loop resonators using a 3x3 fiber coupler and degenerate two-wave mixing,” IEEE J. Quantum Electron., vol. 28, pp. 2749-2757, 1992.
[4] T. A. Birks, “Effect of twist in 3x3 fused tapered couplers,” Appl. Opt., vol. 31, pp. 3004-3014, 1992.
[5] C. C. Su, “A surface integral equations method for homogeneous optical fibers and coupled image lines of arbitrary cross sections,” IEEE Trans. Microwave Theory Tech., vol. MTT-33, pp. 1114-1120, 1985.
[6] M. Eisenmann, and E. Weidel, “Single-mode fused biconical couplers for wavelength division multiplexing with channel spacing between 100 and 300 nm,” J. Lightwave Technol., vol. 6, pp. 113-119, 1988.
[7] D. B. Mortimore, “Theory and fabrication of 4x4 single-mode fused optical fiber couplers,” Appl. Opt., vol 29, pp. 371-374, 1990.
[8] Y. H. Ja, “Performance parameters of a wavelength-division demultiplexer made with a single 3x3 coupler optical fiber ring or loop resonator,” J. Lightwave Technol., vol. 11, pp. 1337-1343, 1993.
[9] S. W. Yang, T. L. Wu, C.W. Wu, and H. C. Chang, “Numerical modeling of weakly fused fiber-optic polarization beamsplitters—part II: the three-dimensional electromagnetic model,” J. Lightwave Technol., vol. 16, pp. 691-696, 1998.
[10] Y. H. Chew, T. T. Tjhung, and F. V. C. Mendis, “Performance of single- and double-ring resonators using 3x3 optical-fiber coupler,” J. Lightwave Technol., vol. 11, pp. 1998-2008, 1993.
[11] A. J. Stevenson, and J. D. Love, “Vector modes of six-port couplers,” Electron. Lett., vol. 23, pp. 1011-1013, 1987.
[12] R. J. Black, L. Gagnon, R. C. Youngquist, R. H. Wentworth, “Modes of evanescent 3x3 couplers and three-core fibers,” Electron. Lett., vol. 22, pp. 1311-1313, 1986.
[13] H. S. Huang, and H. C. Chang, “Analysis of equilateral three-core fibers by circular harmonics expansion method,” J. Lightwave Technol., vol. 8, pp 945-952, 1990.
[14] T. L. Wu, and H. C. Chang, “Vectorial analysis of fiber-core effects in weakly fused couplers,” IEEE Photon.Tech.Lett., vol. 9, pp. 218-219, 1997.
[15] Y. H. Ja, “Avernier fiber double-ring resonator with a 3x3 fiber coupler and degenerate two-wave mixing,” IEEE Photon.Tech.Lett., vol. 4, pp. 743-745, 1992.
[16] Y. H. Ja, “Single-mode optical-fiber double-ring resonator with a planar 3x3 fiber coupler,” Opt. Lett., vol. 18, pp. 1502-1504, 1993.
[17] Y. H. Ja, “A single-mode optical fiber ring resomator using planar 3x3 fiber coupler and a sagnac loop,” J. Lightwave Technol., vol. 12, pp. 1348-1354, 1994.
[18] T. L. Wu, and H. C. Chang, “Rigorous analysis of form birefringence of fused fibre couplers,” Electron. Lett., vol. 30, pp. 998-999, 1994.
[19] K. Morishita, and K. Takashina, “Polarization properties of fused fiber couplers and polarizing beamsplitters,” J. Lightwave Technol., vol. 9, pp. 1503-1507, 1991.
[20] K. A. Murphy, M. F. Gunther, and A. M. Vengsarkar, “Variable-ratio polarization-insensitive, 3x3 fused biconical tapered couplers,” Electron. Lett., vol. 27, pp. 1336-1337, 1991.
[21] A. Niu, C. M. Fitzgerald, T. A. Birks, and C. D. Hussey, “1x3 linear array singlemode fibre couplers,” Electron. Lett., vol. 28, pp. 2330-2332, 1992.
[22] K. Okamoto, “Theoretical investigation of light coupling phenomena in wavelength-flattened couplers,” J. Lightwave Technol. Vol. 8, pp. 678-683, 1990.
[23] C. W. Wu, T. L. Wu, H. C. Chang, “A novel fabrication method for all-fiber, weakly fused, polarization beamsplitters,” IEEE Photon.Tech.Lett., vol. 7, pp. 786-788, 1995.
[24] T. L. Wu, and H. C. Chang, “Rigorous analysis of form birefringence of weakly fused fiber-optic couplers,” J. Lightwave Technol., vol. 13, pp. 687-691, 1995.
[25] S. W. Yang, and H. C. Chang, “Numerical modeling of weakly fused fiber-optic polarization beamsplitters—part I: accurate calculation of coupling coefficients and form birefringence,” J. Lightwave Technol., vol. 16, pp. 685-690, 1998.
[26] P. A. Davies, and G. Abd-el-Hamid, “Four-port fiber-optic ring resonator,” Electron. Lett., vol. 24, pp. 662-663, 1988.
[27] F. P, Payne, C. D. Hussey, and M. S. Yataki, “Polarisation analysis of strongly fused and weakly fused tapered couplers,” Electron. Lett., vol. 21, pp. 561-563, 1985.
[28] A. W. Snyder, and X. H. Zheng, “Fused couplers of arbitrary cross-section,” Electron. Lett., vol. 21, pp. 1079-1080, 1985.
[29] K. S. Chiang, “Analysis of fused couplers by the effective-index method,” Electron. Lett., vol. 22, pp. 1221-1222, 1986.
[30] X. H. Zheng, “Finite-element analysis for fused couplers,” Electron. Lett., vol. 22, pp. 804-805, 1986.
[31] L. F. Stokes, M. Chodorow, and H. J. Shaw, “All-single-mode fiber resonator,” Opt. Lett., vol. 7, pp. 288-290, 1982.
[32] R. A. Bergh, G. Kotler, and H. J. Shaw, “Single-mode fibre optic directional coupler,” Electron. Lett., vol. 16, pp. 260-261, 1980.
[33] A. W. Snyder, “Polarising beamsplitter from fused-taper couplers,” Electron. Lett., vol. 21, pp. 623-625, 1985.
[34] G. Abd-el-Hamid, and P. A. Davies, “Fibre-optic double ring resonator,” Electron. Lett., vol. 25, pp. 224-225, 1989.
[35] M. N. McLandrich, R. J. Orazi, and H. R. Marlin “Polarization independent narrow channel wavelength division multiplexing fiber couplers for 1.55 m,” J. Lightwave Technol., vol. 9, pp. 442-447, 1991.
[36] H. S. Huang, and H. C. Chang, “Guided vector modes of equilateral three-core fibres,” Electron. Lett., vol. 25, pp. 55-56, 1989.
[37] 吳宗霖, “融燒式光纖耦合器之三維電磁模擬,” 台灣大學博士論文,1995.
[38] 廖國助, “融燒式3x3光纖耦合器之理論分析,” 台灣大學博士論文,1995.
[39] 黃世年, “融燒式3x3光纖耦合器之電磁模態分析” 台灣大學博士論文,1999.