近幾年來，在光子晶體光纖上寫製長週期光纖光柵已被廣泛地討論及研究，利用長週期光纖光柵的頻譜特性，提出了許多應用在光通訊系統的光學元件，例如頻帶濾波器、干涉器或是環境的感測器等。在本論文中，我們提出了一個簡單的方法在光子晶體光纖上寫製長週期光纖光柵。首先利用真空吸引的方式將UV膠填入光子晶體光纖中，再透過光罩去照射紫外光，成功地製作出長週期光子晶體光纖光柵。藉由量測其穿透頻譜特性，我們在872 nm、1309 nm、1418 nm 發現數個損失峰，這表示在特定波長下，光纖中的基本纖心模態耦合到正向傳播的纖殼模態。我們並利用有限差分頻域法計算此結構之共振波長來和實驗結果進行比對，計算出來的共振波長是在875 nm、1319 nm、1415 nm，這跟我們實際量測出來的共振波長位置是很吻合的。此外，我們引進了光子晶體光纖的封孔技術來製作選擇性液體填充長週期光子晶體光纖光柵，由於液體層數的減少，我們成功地改善了該元件的傳播損耗。最後，我們調整外在環境的變數，例如溫度、曲率半徑、外在環境折射率、扭曲角度和張力，來觀察穿透頻譜損失峰的變化情形，計算並討論該元件對這些環境變數的靈敏度。我們發現將長週期光子晶體光纖光柵置於不同溫度環境中時，其共振波長會線性地隨著溫度增加而減少，並具有1.7 nm/°C的靈敏度。當我們改變外在環境折射率從1變化到1.377時，共振波長會有最大的位移量2 nm。然而，相較於其他長週期光子晶體光纖光柵，我們所製作的光纖光柵，由於光纖纖殼結構的完整性，使得對張力和曲率半徑的變化都顯得不明顯，這樣的特性對於當做一個環境溫度的感測器而言，是相當有幫助的。

A long period fiber grating (LPFG) is formed by inducing the periodic refractive index variation along a fiber. A lot of work has been done to fabricate the LPFGs in the photonic crystal fibers (PCFs) to function as all-fiber band-rejection filters, interferometers, and sensing applications.
In this thesis, we propose a novel LPFG based on the gel-filled PCF. The PCF filled with the UV gel was exposed to the high-intensity UV light through the mask. The periodic index variation is formed along the fiber in the cladding region, resulting in the LPFG. By measuring the propagation losses of our LPFG, three spectral dips in the transmission bands are observed at 872 nm, 1309 nm, and 1418 nm as the grating period is 600 μm, which indicates the mode coupling from the fundamental core mode to the higher order modes (HOMs) of the gel-filled PCFs. By using a full-vector finite-difference frequency-domain (FDFD) method, we numerically calculate the phase match condition for our LPFGs. The calculated resonant wavelengths are 875
nm, 1319 nm, and 1415 nm. Very good agreement between the measured resonant wavelengths and the numerical results is obtained. We also fabricate the selectively gel-filled LPFGs to reduce the propagation losses by utilizing a simple selectively blocking technique. In addition, we measure and discuss the sensing sensitivities of
the UV-induced LPFGs, including the temperature, strain, curvature, torsion, and surrounding refractive index (SRI) sensitivities. The measured sensitivity to temperature is 1.7 nm/°C from 25 °C to 45 °C. As the surrounding refractive index is increased to 1.377, the dip position has a maximum shift of 2 nm. Compared with other LPFGs, the UV-induced LPFGs are more insensitive to bending and strain due
to the complete cladding structure. This could benefit the stability of the temperature
sensors, based on our UV-induced LPFGs.

1 Introduction 1
1.1 Photonic Crystal Fiber . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Long-Period Fiber Grating . . . . . . . . . . . . . . . . . . . . . 3
1.3 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Coupling Theory and Fabrication of UV-Induced
Long-Period Fiber Grating 17
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Coupling Theory . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Vacuum Injection Method. . . . . . . . . . . . . . . . . . . . 19
2.4 Ultraviolet Exposure . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Experimental Results of UV-induced
Long-Period Fiber Grating 31
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Measurement Results of LPFGs . . . . . . . . . . . . . . . . . . 31
3.3 Fabrication of Selectively Gel-Filled LPFGs . . . . . . . . . . . . 34
3.4 Measurement Results of Selectively Gel-Filled LPFGs . . . . . . 36

4 Sensing Sensitivity of UV-Induced
Long-Period Fiber Grating 50
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 Temperature Sensing Property . . . . . . . . . . . . . . . . 50
4.3 Bending Sensing Property . . . . . . . . . . . . . . . . . . 52
4.4 Surrounding Refractive Index Sensing Property . . . . . . . . . . 53
4.5 Torsion Sensing Property . . . . . . . . . . . . . . . . . . . 54
4.6 Strain Sensing Property . . . . . . . . . . . . . . . . . . . . . . . 55

5 Conclusions 73
Bibliography 75

[1] Alkeskjold, T. T., J. Lægsgaard, and A. Bjarklev, “All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers,” Opt. Express, vol. 12, pp. 5857–5871, 2004.
[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] Bétourné, A., V. Pureur, G. Bouwmans, Y. Quiquempois, L. Bigot, M. Perrin, M. Douay, “Solid photonic bandgap fiber assisted by an extra air-clad structure for low-loss operation around 1.5 μm,” Opt. Express, vol. 15, pp. 316–324, 2007.
[4] 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.
[5] Choi, H. Y., K. S. Park, and B. H. Lee, “Photonic crystal fiber interferometer composed of a long period fiber grating and one point collapsing of air holes,” Opt. Lett., vol. 33, pp. 812–814, 2008.
[6] Dobb, H., K. Kalli, and D. J. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fibre,” Opt. Commun., vol. 260, pp. 184–191, 2006.
[7] Domachuk, P., H. C. Nguyen, B. J. Eggleton, M. Straub, and M. Gu, “Microfluidic tunable photonic bandgap device,” Appl. Phys. Lett., vol. 84, pp. 1838–1840, 2004.
[8] Du, F., Y. Q. Lu, and S. T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett., vol. 85, pp. 2181–2183, 2004.
[9] Eggleton, B. J., P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, “Grating resonances in air–silica microstructured optical fibers,” Opt. Lett., vol. 24, pp. 1460–1462, 1999.
[10] Eggleton, B. J., C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express, vol. 9, pp. 698–713, 2001.
[11] 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.
[12] 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.
[13] Gundu, K. M., M. Kolesik, J. V. Moloney, and K. S. Lee, “Ultra-flattened-dispersion selectively liquid-filled photonic crystal fibers,” Opt. Express, vol. 14, pp. 6870–6878, 2006.
[14] Guo, T., H. Tam, P. A. Krug, and J. Albert, “Reflective tilted fiber Bragg grating refractometer based on strong cladding to core recoupling,” Opt. Express, vol. 17, pp. 5736–5738, 2009.
[15] Han, Y. G., G. Kim, K. Lee, S. B. Lee, C. H. Jeong, C. H. Oh, and H. J. Kang, “Bending sensitivity of long-period fiber gratings inscribed in holey fibers depending on an axial rotation angle,” Opt. Express, vol. 15, pp. 12866–12871, 2007.
[16] He, Z., Y. Zhu, and H. Du, “Effect of macro-bending on resonant wavelength and intensity of long-period gratings in photonic crystal fiber,” Opt. Express, vol. 15, pp. 1804–1810, 2007.
[17] Hill, K. O., Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett., vol. 32, pp.647–649, 1978.
[18] Huang, Y., Yong Xu, and A. Yariv, “Fabrication of functional microstructured optical fibers through a selective-filling technique,” Appl. Phys. Lett., vol. 85, pp. 5182–5184, 2004.
[19] John, S., “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett., vol. 58, pp. 2486–2489, 1987.
[20] Knight, J. C., T. A. Birks, P. St. J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett., vol. 21, pp. 1547–1549, 1996.
[21] Knight, J. C., T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. Sandro, “Large mode area photonic crystal fibre,” IEEE Electron Lett., vol. 34, pp. 1347–1348, 1998.
[22] 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.
[23] 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.
[24] 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.
[25] Lim, J. H., and K. S. Lee, “Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure,” Opt. Lett., vol. 29, pp. 331–333, 2004.
[26] Lim, J. H., H. S. Jang, and K. S. Lee, “Mach–Zehnder interferometer formed in a photonic crystal fiber based on a pair of long-period fiber gratings,” Opt. Lett., vol. 29, pp. 346–348, 2004.
[27] Liou, J. H., “Fabrication and analysis of selectively liquid-filled photonic crystal fibers.” M.S Thesis, Institute of Communication Engineering, Nation Sun Yat-sen University, Kaohsiung, Taiwan, June, 2009.
[28] 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.
[29] Noordegraaf, D., L. Scolari, J. Lægsgaard, L. Rindorf, and T. T. Alkeskjold, “Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers,” Opt. Express, vol. 15, pp. 7901–7912, 2007.
[30] Park, B. H., J. Kim, T. J. Eom, B. H. Lee, and U. Paek, “Sensing Characteristics of long-period fiber gratings in photonic crystal fiber imprinted by CO2 laser,” Optical Fiber Communication Conference (OFC 2005), Anaheim, California March 6, 2005.
[31] Petrovic, J. S., H. Dobb, V. K. Mezentsev, K. Kalli, D. J. Webb, and I. Bennion, “Sensitivity of LPGs in PCFs fabricated by an electric arc to temperature, strain, and external refractive index,” J. of Lightwave Technol., vol. 25, pp. 1306–1312, 2007.
[32] 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.
[33] Rosa, L., F. Poli, M. Foroni, A. Cucinotta, and S. Selleri, “Polarization splitter based on a square-lattice photonic-crystal fiber,” Opt. Lett., vol. 31, pp. 441–443, 2006.
[34] Rindorf, L., and J. B. Jensen, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express, vol. 18, pp. 8224–8231, 2006.
[35] Shin, W., B. A. Yu, Y. L. Lee, Y. C. Noh, D. K. Ko, and J. Lee, “High strength coupling and low polarization-dependent long-period fiber gratings based on the helicoidal structure,” Optical Fiber Technol., vol. 14, pp. 323–327, 2008.
[36] Vengsarkar, A. M., P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber grating as band-rejection filters,” J. of Lightwave Technol., vol. 14, pp. 58–64, 1996.
[37] Wang, Y. P., L. Xiao, D. N. Wang, and W. Jin “Highly sensitive long-period fiber-grating strain sensor with low temperature sensitivity,” Opt. Lett., vol. 31, pp. 3414–3416, 2006.
[38] Wang, Y. P., L. Xiao, D. N. Wang, and W. Jin “In-fiber polarizer based on a long-period fiber grating written on photonic crystal fiber,” Opt. Lett., vol. 32, pp. 1035–1037, 2007.
[39] Wang, Y. P., W. Jin, J. Ju, H. L. Ho, L. Xiao, and D. Wang, “Long period gratings in air-core photonic bandgap fibers,” Opt. Express, vol. 16, pp. 2784–2790, 2008.
[40] Xiao, L., W. Jin, M. Demokan, H. Ho, Y. Hoo, and C. Zhao, “Fabrication of selective injection microstructured optical fibers with a conventional fusion splicer,” Opt. Express, vol. 13, pp. 9014–9022, 2005.
[41] Yablonovitch, E., “Inhibited spontaneous emission in solid-state physics electronics,” Phys. Rev. Lett., vol. 58, pp. 2059–2062, 1987.
[42] Yeom, D., P. Steinvurzel1, B. J. Eggleton, S. D. Lim, and B. Y. Kim, “Tunable acoustic gratings in solid-core photonic bandgap fiber,” Opt. Express, vol. 15, pp. 3513–3518, 2007.
[43] Yoshie, T., J. Vučković, and A. Scherer, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett., vol. 79, pp. 4289–4291, 2001.
[44] Yu, C. P., and H. C. Chang, “Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers,” Opt.Express, vol. 12, pp. 6165–6177, 2004.
[45] Yu, X., P. Shum, S. Fu, and L. Deng, “Torsion-sensitivity of mechanical long-period grating in photonic crystal fiber,” J. Opt. Adv. Mater., vol. 8, pp. 1247–1249, 2006.
[46] Zhang, R., J. Teipel, and H. Giessen, “Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express, vol. 14, pp. 6800–6812, 2006.
[47] Zhao, C. L., L. Xiao, J. Ju, M. S. Demokan, and W. Jin, “Strain and temperature characteristics of a long-period grating written in a photonic crystal fiber and its application as a temperature-insensitive strain sensor,” J. of Lightwave Technol., vol. 26, pp. 220–227, 2008.
[48] Zhu, Y., P. Shum, J. H. Chong, M. K. Rao, and C. Lu, “Deep-notch, ultra compact long-period grating in a large-mode-area photonic crystal fiber,” Opt. Lett., vol. 28, pp. 2467–2469, 2003.
[49] Zografopoulos, D. C., E. E. Kriezis, and T. D. Tsiboukis, “Photonic crystal-liquid crystal fibers for single-polarization or high-birefringence guidance,” Opt. Express, vol. 14, pp. 914–925, 2006.