光纖環在過去已被廣泛地研究討論，並且應用在法拉第感測器上。在本論文中，我們製作了光子晶體光纖環，並利用桑克迴路(Sagnac loop)，量測光子晶體光纖環的干涉頻譜。我們可以從干涉頻譜中得到光子晶體光纖環的雙折射數值，在波長1264.3 nm，可以得到其量測的結果為1.31×10^-5；我們並且量測了單模光纖環的雙折射數值，在波長959.27 nm，量測結果為1.49×10^-5。我們發現單模光纖環的雙折射數值與理論計算相符合。接著我們改變光子晶體光纖環的製作參數，發現當纏繞的圈數增加時，相位差增加，干涉條紋彼此的間距會縮小。而當所纏繞圓柱體直徑變大時，雙折射數值會隨著變小。此外，我們得到光子晶體光纖環的溫度靈敏度為64.55 pm/ oC，與單模光纖環的溫度靈敏度130 pm/oC相比，為更低的溫度敏感度，因此更適合應用於量測各種環境的變化。最後，我們利用此光子晶體光纖環進行曲率半徑、水深、正向位移的量測。當圓柱體受到側向位移而彎曲，干涉頻譜會往短波長移動，其彎曲的靈敏度為-3.732 nm/m^-1。我們接著將光子晶體光纖環置於不同水深，量測其干涉頻譜的變化。發現當光纖環以水平放入水中，干涉頻譜會往短波長移動並呈現指數型的變化；而當光纖環以垂直放入水中，其水深的靈敏度可以達到-11.658 nm/cm。最後，我們進行正向位移的量測，可以得到相當大靈敏度為903.9 nm/cm，其干涉條紋的相對深度不會隨著正向位移增加而改變。此光子晶體光纖環是非常適合當正向位移感測器使用。

Fiber coils had been widely investigated as optical current sensors for a long time. In this thesis we have fabricated the LMA-10 PCF coils. By using the Sagnac fiber loop, we can obtain the transmission spectrum of the PCF coils. The measured birefringence of the SMF coil and the PCF coil are 1.49×10^-5 at λ= 959.27 nm and 1.31×10^-5 at λ = 1264.3 nm, respectively. The birefringence of the SMF coil agrees well with the theoretical result.
The properties of PCF coils for variant fiber turns and cylinder sizes are discussed. As we increase the number of fiber turns, the fringe spacing becomes smaller due to the increasing phase difference. The birefringence of the PCF coil decreases with the increasing cylinder radius. Besides, we also measure the temperature sensitivities of the SMF coil and PCF coil to be 130 pm/oC and 64.55 pm/ oC, respectively.
We have also demonstrated the sensing properties of the PCF coils. By introducing a displacement along the cylinder, the bending on the PCF coil can be induced. The measured bending sensitivity is -3.732 nm/m^-1. In addition, the water depth sensing properties are obtained by horizontally and vertically immersing the PCF coils into the water. As we put the PCF coil horizontally into the water, the shift of the measured spectra shows a exponential relation to the water depth. As for the vertically immersed PCF coil, the linear water depth sensitivity is -11.658 nm/cm. Finally, we propose the transverse displacement sensor based on the PCF coil. The measured sensitivity to transverse displacement can be as large as 903.9 nm/cm.

1 Introduction 1
1.1 Photonic Crystal Fiber…………………………………..………1
1.2 Fiber Coil Sensor………………………………………………..2
1.3 Chapter Outline…………………………………………………4

2 Principle of Fiber Coils and
Sagnac Fiber Loop Interferometer 10
2.1 Overview……………………………………………..………….10
2.2 Principle of Fiber Coils…………………………….…………….10
2.3 Sagnac Fiber Loop Interferometer………………………………12

3 Measurement Results of Fiber Coils 19
3.1 Overview………………………………………………………19
3.2 Fabrication of PCF Coils and Measurement Setup………………19
3.3 Properties of Fiber turns…………………………………………20
3.4 Properties of Diameters………………………………………….22
3.5 Temperature Sensing Property………………………….………24
4 Sensing Sensitivities of PCF Coils 40
4.1 Overview…………………………………………….………….40
4.2 Bending Sensing Property………………………………………40
4.3 Water Depth Sensing Property…………………………………42
4.4 Transverse Displacement Sensing Property……………………43

5 Conclusions 64
Bibliography 66

[1] Bergh, R. A., H. C. Lefevre, and H. J. Shaw, “All-single-mode fiber-optic gyroscope with long-term stability,” Opt. Lett., vol. 6, pp. 502-504, 1981.
[2] Birks, T. A., J. C. Knight, and P. St. J. Russell, “Endless single-mode photonic crystal fiber,” Opt. Lett., vol. 22, pp. 961-963, 1997.
[3] Blake, J., P. Tantaswadi, and R. T. de Carvalho, “In-line Sagnac interferometer current sensor,” IEEE Trans. Power Delivery, vol. 11, pp. 116-121, 1996.
[4] Bohm, K., K. Petermann, and E. Weidel, “Sensitivity of a fiber-optic gyroscope to environmental magnetic fields,” Opt. Lett., vol. 7, pp. 180-182, 1982.
[5] Chu, P. L., and R. A. Sammut, “Analytical method for calculation of stresses and material birefringence in polarization-maintaining optical fiber,” J. of Lightwave Technol., vol. 2, pp. 650-662, 1984.
[6] 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.
[7] Dennis, W. P., J. Murakowski, S. Shi, S. Venkataraman, A. Sharkway, C. Chen, and D. Pustai, “High-efficiency coupling structure for a single-line-defect photonic-crystal waveguide,” Opt. Lett., vol. 27, pp. 1601-1603, 2002.
[8] Fan, S. H., P. R. Villeneuve., J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals.” Opt. Express, vol. 3, pp. 4-11, 1998.
[9] Fang, X., and R. O. Claus, “Polarization-independent all-fiber wavelength-divison multiplexer on a Sagnac interferometer,” Opt. Lett., vol. 20, pp. 2146-2148, 1995.
[10] Ferrando, A., E. Silvestre, P. Andrés, J. J. Miret, and M. V. Andrés, “Desinging the properties of dispersion flattened photonic crystal fibers,” Opt. Express, vol. 9, pp. 687-697, 2001.
[11] Folkenberg, J. R., M. D. Nielsen, N. A. Mortensen, C. Jakobsen, and H. R. Simonsen, “Polarization maintaining large mode area photonic crystal fiber,” Opt. Express, vol. 12, pp. 956-960, 2004.
[12] Freitas, J. M. D., “Recent developments in seismic seabed oil reservoir monitoring applications using fibre-optic sensing networks,” Meas. Sci. Technol., vol. 22, pp. 1-30, 2011.
[13] Frosio, G., and R. Dandliker, “Reciprocal reflection interferometer for a fiber-optic Faraday current sensor,” Appl. Opt., vol. 33, pp. 6111-6122, 1994.
[14] Gray, D. E., ed., American Institute of Physics Handbook, 3rd ed, McGraw-Hill, New York, 1972.
[15] Hansen, T. P., J. Broeng, E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett., vol. 13, pp. 588-590, 2001.
[16] Hocker, G. B., “Fiber-optic sensing of pressure and temperature,” Appl. Opt., vol. 18, pp. 1445-1448, 1979.
[17] John, S., “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett., vol. 58, pp. 2486-2489, 1987.
[18] Knight, J. C., J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science, vol. 282, pp. 1476-1478, 1998.
[19] Knight, J. C., T. A. Birks, P. St. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett., vol. 21, pp. 1547-1549, 1996.
[20] Kuchinsky, S., D. C. Allan, N. F. Borrelli, and J. C. Cotteverte, “3D localization in a channel waveguide in a photonic crystal with 2D periodicity,” Opt. Commun., vol.175, pp. 147-152, 2000.
[21] Larsen, T., A. Bjarklev, D. Hermann, and J. Broeng, “Optical devices based on liquid crystal photonic bandgap fibres,” Opt. Express, vol. 11, pp. 2589-2596, 2003.
[22] Ma, X., and P. L. Chu, “Design of temperature-compensated elliptical core birefringent fibers,” Opt. Comm., vol. 130, pp. 357-364, 1996.
[23] Macpherson, W. N., M. J. Gander, R. Mcbride, J. D. C. Jones, P. M. Blanchard, J. G. Burnett, A. H. Greenway, B. Mangan, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Remotely addressed optical fibre curvature sensor using multicore photonic crystal fibre,” Opt. Commun., vol. 193, pp. 97-104, 2001.
[24] Moeller, R. P., W. K. Burns, and N. J. Frigo, “Open-loop output and scale factor stability in a fiber-optic gyroscope,” J. of Lightwave Technol., vol. 7, pp. 262-269, 1989.
[25] Mortensen, N. A., M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, “Improved large-mode area endlessly single-mode photonic crystal fibers,” Opt. Lett., vol. 28, pp. 393-395, 2003.
[26] Noda, J., K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. of Lightwave Technol., vol. 4, pp. 1071-1088, 1986.
[27] Perciante, C. D., and J. A. Ferrari, “Cancellation of bending-induced birefringence in single-mode fibers: application to Faraday sensors,” Appl. Opt., vol. 45, pp. 1951-1956, 2006.
[28] Rashleigh, S. C., and R. Ulrich, “High birefringence in tension-coiled single-mode fibers,” Opt. Lett., vol. 5, pp. 354-356, 1980.
[29] Reeves, W. H., J. C. Knight, and P. St. J. Russell, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express, vol. 10, pp. 609-613, 2002.
[30] Rose, A. H., Z. B. Ren, and G. W. Day, “Twisting and annealing optical fiber for current sensors,” J. of Lightwave Technol., vol. 14, pp. 2492-2498, 1996.
[31] Shibata, N., K. Okamoto, K. Suzuki, and Y. Ishida, “Polarization-mode properties of elliptical-core fibers and stress-induced birefringent fibers,” J. Opt. Soc. Amer., vol. 73, pp. 1792-1798, 1983.
[32] Smith, A. M., “Birefringence induced by bends and twists in single-mode optical fiber,” Appl. Opt., vol. 19, pp. 2606-2611, 1980.
[33] Tanabe, T., K. Nishiguchi, A. Shinya, E. Kuramochi, H. Inokawa, M. Notomi, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Fukuda, H. Shinojima, and S. Itabashi, “Fast all-optical switching using ion-implanted silicon photonic crystal nanocavities,” Appl. Phys. Lett., vol. 90, pp. 1063-1066, 2007.
[34] Tang, D., A. H. Rose, G. W. Day, and S. M. Etzel, “Annealing of linear birefringence in single-mode fiber coils: application to optical fiber current sensors,” J. of Lightwave Technol., vol. 9, pp. 1031-1037, 1991.
[35] Ulrich, R., S. C. Rashleigh, and W. Eickhoff, “Bending-induced birefringence in single-mode fibers,” Opt. Lett., vol. 5, pp. 273-275, 1980.
[36] Wang, J., K. Zheng, J. Li, L. S. Liu, G. X. Chen, and S. S. Jian, “Research on tunable erbium-doped ring fiber laser based on a high-birefringence Sagnac loop: theory and experiment,” Acta Physica Sinica, vol. 58, pp. 7695-7700, 2009.
[37] Yablonovitch, E., “Inhibited spontaneous emission in solid-state physics electronics,” Phys. Rev. Lett., vol. 58, pp. 2059-2062, 1987.
[38] Yablonovitch, E., T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett., vol. 67, pp. 3380-3383, 1991.
[39] Zhao, C. L., X. Yang, C. Lu, W. Jin, and M. S. Demokan, “Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror,” IEEE Photon. Technol. Lett., vol. 16, pp. 2535-2537, 2004.
[40] Zu, P., C. C. Chan, Y. X. Jin, Y. F. Zhang, and X. Y. Dong, “Fabrication of a temperature-insensitive transverse mechanical load sensor by using a photonic crystal fiber-based Sagnac loop,” Meas. Sci. Technol., vol. 22, pp. 1-4, 2011.