傳統的光子晶體光纖在製作完成後，難再利用外在因素調變其光學特性，因此有人提出在光子晶體光纖之空氣孔洞內填入液體，來達到可調式的光學特性。可是當有限的液體層數和有損耗之液體填充在整個空氣孔洞時，光纖的傳播損耗會變大。在本論文中，我們利用了一個有完美匹配層的有限差分頻域法，分析選擇性液體填充光子晶體光纖的傳播特性，並成功地獲得其傳導模態的傳播常數與傳播損耗。從模擬結果顯示，不管空氣孔洞層數是在內層還是外層，選擇性液體填充光子晶體光纖的傳播損耗皆能有效地被降低並且保持其可調的特性。此外，我們也利用選擇性液體填充的方法，設計了光纖色散相關元件，成功地得到一個在波長1.45μm 到1.65μm 範圍內，色散值D = 0 ± 1 ps/nm/km 的色散平坦光纖，以及在波長1.55μm 處，一個具有極大負色散值D = -3100 ps/nm/km 的色散補償光纖。
在實驗部份，我們利用顯微鏡、封孔光纖和對準技術，簡單的進行光子晶體光纖選擇性的封孔，再填注液體以製作出內圈液體填充光子晶體光纖與外層液體填充光子晶體光纖，並量測其傳播特性，把實驗量測結果跟模擬結果詳加比較並討論。

As the photonic crystal fibers (PCFs) are fabricated, it is hard to modulate their optical characteristics to function as tunable optical devices. To introduce tunable optical characteristics into the PCF structures, one can infiltrate liquids into the air holes of the PCFs to form the liquid-filled PCFs. However, the propagation losses become larger due to the
finite liquid-hole layers and the lossy liquids infused in all the air holes of the cladding. In this thesis, an efficient full-vector finite-difference frequency-domain (FDFD) mode solver cooperated with the PMLs is utilized to investigate the propagation characteristics of the selectively liquid-filled PCFs. The propagation constants and the propagation losses of the
guided modes on the selectively liquid-filled PCFs can be successfully obtained. From our numerical results, the propagation losses of both the internally liquid-filled PCFs and externally liquid-filled PCFs can be efficiently reduced by the outer or inner air-hole layers, and the useful tunablility characteristics for optical device applications can be maintained.
Besides, the dispersion-related devices based on the selectively liquid-filled PCFs are also investigated. It is demonstrated that a DFPCF with the flatten dispersion value D within 0 ± 1 ps/nm/km over λ = 1.45 μm to 1.65 μm or a DCPCF with a high negative dispersion value D = -3100 ps/nm/km at λ = 1.55 μm can be achieved by infiltrating the liquid into all air holes or specified air-hole layers.
In the experiment, a simple selectively blocking technique using the microscopy, the tool fiber and the alignment technique is employed to fabricate the internally and externally liquid-filled PCFs. The measurement of the optical characteristics of these selectively liquid-filled PCFs is carried out and compared with the simulation results.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 1
1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 1
1.2 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . .. . 12
2.1 Finite-Difference Frequency-Domain Mode Solver. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . 12
2.2 The Perfectly Matched Layer. . . . . . . . . . . . . . . . . . 17
2.3 Index Averaging Scheme . . . . . . . . . . . . . . . . . . . . . 22
3 Numerical Results for Selectively Liquid-Filled
Photonic Crystal Fibers . . . . . . . . . . . . . . . . . . . . . . . . .. 26
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 26
3.2 PCFs with Liquid Filled in Inner Air-Hole Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 27
3.3 PCFs with Liquid Filled in Outer Air-Hole Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Dispersion-Related Devices Based on Selectively Liquid-Filled PCFs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Fabrication and Spectral Characteristics of Selectively Liquid-Filled Photonic Crystal Fibers . . . 52
4.1 Selectively Blocking Technique . . . . . . . . . . . . . . . 52
4.2 Selectively Liquid-Filled PCFs . . . . . . . . . . . . . . . . 54
4.2.1 Vacuum Filling Setup . . . . . . . . . . . . . . . . . . . . . . 55
4.2.2 Experiment Setup and Results. . . . . . . . . . . . . . 56
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Bibliography . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . 79

[1] Alkeskjold, T. T., Jesper Lægsgaard and Anders Bjarklev, “All-optical modulation in dye-doped nematic liquid crystal photonic bandgap fibers,”
Opt. Express, vol. 12, pp. 5857–5871, 2004.
[2] Bétourné, A., V. Pureur, G. Bouwmans, Y. Quiquempois, L. Bigot, M. Perrin, and 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.
[3] Bierwirth, K., N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguides by a new finite difference method,” J.
Lightwave Technol., vol. 34, pp. 1104–1113, 1986.
[4] 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.
[5] Bouwmans, G., L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and M. Douay, “Fabrication and characterization of an allsolid 2D photonic
bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm,” Opt. Express, vol. 21, pp. 8452–8459, 2005.
[6] Brackett, C. A., “Dense wavelength division multiplexing networks: principles and applications,” IEEE Journal on Selected Areas in
Communications, vol. 8, pp. 948–964, 1990.
[7] Broderick, N. G. R., T. M. Monro, P. J. Bennett, and D. J. Richardson,
“Nonlinearity in holey optical fibers: measurement and future
opportunities,” Opt. Lett., vol. 24, pp. 1395–1397, 1999.
[8] Chang, C. C., H. P. Sardesai, and A. M. Weiner, “Dispersion-free fiber
transmission for femtosecond pulses by use of a dispersion-compensating
fiber and a programmable pulse shaper,” Opt. Lett., vol. 23, pp. 283–285,
1998.
[9] Chew, W.C., and W. H. Weedon, “A 3-D perfectly matched medium from
modified Maxwell’s equation with stretched coordinates,” Microwave
Optical Technol. Lett., vol. 7, pp. 599–604, 1994.
[10] Chiang, P. J., C. P. Yu, and H. C. Chang, “Robust calculation of
chromatic dispersion coefficients of optical fibers from numerically
determined effective indices using Chebyshev-Langrange interpolation
polynomials,” IEEE J. Lightwave Technol., vol. 24, pp. 4411–4416, 2006.
[11] Couny, F., F. Benabid, and P. S. Light, “Large-pitch kagome-structured
hollow-core photonic crystal fiber,” Opt. Lett., vol. 31, pp. 3574–3576,
2006.
[12] 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.
[13] 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.
[14] 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.
[15] 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.
[16] Ferrando, A., E. Silvestre, J.J. Miret, and P. Andr&#233;s, “Nearly zero
ultraflattened dispersion in photonic crystal fibers,” Opt. Lett., vol. 25, pp.
790–792, 2000.
[17] Ferrando, A., Enrique Silvestre, and Pedro Andr &#233; s, “Designing the
properties of dispersion-flattened photonic crystal fibers,” Opt. Express,
vol. 9, pp. 687–697, 2001.
[18] 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.
[19] Frigo, N. J ., P. P. Iannone, P. D. Magill, T. E. Darcie, M. M. Downs, B.
N. Desai, U. Koren, T. L. Koch, C. Dragone, H . M. Presby, and G. E. Bodeep, “A wavelength-division multiplexed passive optical network with cost-shared components,” IEEE Photon. Technol. Lett., vol. 6, pp. 1365–1367, 1994.
[20] G&#233;r&#244;me, F., J. L. Auguste, and J. M. Blondy, ”Design of dispersion-compensating fibers based on a dual-concentric-core photonic crystal fiber,” Opt. Lett., vol. 29, pp. 2725–2727, 2004.
[21] 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.
[22] Hadley, G. R., and R. E. Smith, “Full-vector waveguide modeling using an iterative finite-difference method with transparent boundary

conditions,” Journal of Lightwave Technol., vol. 13, pp. 465–469, 1995.
[23] Hansen, T. P., Jes Broeng, Stig E. B. Libori, Erik Knudsen, Anders Bjarklev, Jacob Riis Jensen, and Harald Simonsen, “Highly birefringent
index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett., vol. 13, pp. 588–590, 2001.
[24] Huang, Y., Yong Xu, and Amnon Yariv, “Fabrication of functional microstructured optical fibers through a selective-filling technique,” Appl. Phys. Lett., vol. 85, pp. 5182–5184, 2004.
[25] John, S., “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett., vol. 58, pp. 2486–2489, 1987.
[26] 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.
[27] Kakarantzas, G., T. A. Birks, and P. St. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett., vol. 27, pp. 1013–1015,
2002.
[28] Kim, K. S., and R. H. Stolen, “Measurement of the nonlinear index of silica-core and dispersion-shifted fibers,” Opt. Lett., vol. 19, pp. 257–259,
1994.
[29] 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.
[30] Knight, J. C., T.A. Birks, R.F. Cregan, P.St. J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fibre,” IEEE Electron Lett.,
vol. 34, pp. 1347–1348, 1998.

[31] 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.
[32] Knight, J. C., J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic
crystal fiber,” IEEE Photon. Technol. Lett., vol. 12, pp. 807–809, 2000.
[33] Koshiba, M., “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” Journal of Lightwave Technol., vol.
19, pp. 1970–1975, 2001.
[34] 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.
[35] Liu, Y., William B. Mattingly, David K. Smith, Claude E. Lacy, Jerrold A. Cline, and Evelyn M. De Liso, “Design and fabrication of locally
dispersion-flattened large effective area fibers,” European Conference on Optical Communication, ECOC 1998, vol. 1, pp. 37-38, 1998.
[36] Lim, J. H., Hyun S. Jang, and Kyung 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.
[37] L&#252;sse, P., P. Stuwe, J. Sch&#252;le, and H.-G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J.
Lightwave Technol., vol. 12, pp. 487–494, 1994.
[38] Mittra, R., and &#220;. Peke1, “A New Look at the Perfectly Matched Layer (PML) Concept for the Reflectionless Absorption of Electromagnetic
Waves,” IEEE Microwave and guided wave Lett., vol. 5, pp. 84–86, 1995.
[39] Mortensen, N. A. “Effective area of photonic crystal fibers,” Opt. Express, vol. 10, pp. 341–348, 2002.
[40] 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.
[41] Ni, Y., L. An, J. Peng, and C. Fan, “Dual-core photonic crystal fiber for dispersion compensation,” IEEE Photon. Technol. Lett., vol. 16, pp. 1516–1518, 2004.
[42] Noordegraaf, D., L. Scolari, J. L&#230;gsgaard, 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.
[43] Noordegraaf, D., L. Scolari, J. L&#230;gsgaard, T. T. Alkeskjold, G. Tartarini, E. Borelli, P. Bassi, J. Li, and S. T. Wu, “Avoided-crossing-based liquid-crystal photonic-bandgap notch filter,” Opt. Lett., vol. 33, pp.
986–988, 2008.
[44] Park, S. J., Chang-Hee Lee, Ki-Tae Jeong, Hyung-Jin Park, Jeong-Gyun Ahn, and Kil-Ho Song, “Fiber-to-the-home services based on wavelength-division-multiplexing passive optical network,” Journal of
Lightwave Technol., vol. 22, pp. 2582–2590, 2004.
[45] Poole, C. D., and C. R. Giles, “Polarization-dependent pulse compression and broadening due to polarization dispersion in dispersion-shifted fiber,”
Opt. Lett., vol. 13, pp. 155–157, 1988.
[46] Rappaport, C. M., “Perfectly matched absorbing boundary conditions based on anisotropic lossy mapping of space,” IEEE Microwave and
Guided Wave Lett., vol. 5, pp. 90–92, 1995.

[47] 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.
[48] Rindorf, L., Jesper B. Jensen, Martin Dufva, Lars Hagsholm Pedersen and Poul Erik H&#248;iby, and Ole Bang, “Photonic crystal fiber long-period
gratings for biochemical sensing,” Opt. Express, vol. 14, pp. 8224–8231, 2006.
[49] Saitoh, K., and M. Koshiba, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express, vol. 8, pp. 843–852, 2003.
[50] Scolari, L., Thomas Tanggaard Alkeskjold, Jesper Riishede, and Anders Bjarklev, “Continuously tunable devices based on electrical control of
dual-frequency liquid crystal filled photonic bandgap fibers,” Opt. Express, vol. 13, pp. 7483–7496, 2005.
[51] Song, B. S., S. Noda, T. Asano, and Y. Akahane, “Ultra-high Q photonic double-heterostructure nanocavity,” Nature Mater., vol. 4, pp. 207–210, 2005.
[52] Tamura, K. R., and M. Nakazawa, “Femtosecond soliton generation over a 32-nm wavelength range using a dispersion-flattened dispersion-decreasing fiber,” IEEE Photon. Technol. Lett., vol. 11, pp.
319–321, 1999.
[53] Thyagarajan, K., R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal,“A novel design of a dispersion compensating Fiber,” IEEE Photon.
Technol. Lett., vol. 8, pp. 1510–1512, 1996.
[54] Witkowska, A., K. Lai, S. G. Leon-Saval, W. J. Wadsworth, and T. A. Birks, “All-fiber anamorphic coreshape transitions,” Opt. Lett. vol. 31, pp. 2672–2674, 2006.
[55] 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.
[56] Yablonovitch, E., “Inhibited Spontaneous Emission in Solid-State Physics
Electronics,” Phys. Rev. Lett., vol. 58, pp. 2059–2062, 1987.
[57] Yang F. C., “Finite-difference time-domain method for modeling the photonic crystal fibers,” M.S. Thesis, Institute of Communication
Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan, June, 2007.
[58] Yee, K. S., “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas
and Propagation, vol. 3, pp. 302–307, 1966.
[59] Yu, C. P., and Hung-Chun 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.
[60] Yu, C. P., J. H. Liou, S. S. Huang, and H. C. Chang, “Tunable dual-core liquid-filled photonic crystal fibers for dispersion compensation,” Opt. Express, vol. 16, pp. 4443–4451, 2008.
[61] Zhang, R., J&#246;rn Teipel, and Harald Giessen, “Theoretical design of a
liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express, vol. 14, pp. 6800–6812, 2006.
[62] Zhu, Z., and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express, vol. 10, pp. 853–864, 2002.