摘要
在光子晶體光纖外圍週期性的空氣孔洞中填入液晶，便形成液晶光子晶體光纖。利用液晶的光電特性，可以製作以液晶光子晶體光纖為基礎的可調變光電元件。
本論文是利用有限差分頻域法，對液晶光子晶體光纖的光能帶圖和傳導模態進行模擬，並討論溫度和液晶分子的排列方式對液晶光子晶體光纖所造成的影響。當液晶分子的排列垂直光纖時，提高溫度可以觀察到光能隙的藍位移與分裂的現象。而當液晶的排列為平行光纖時，光能隙則隨溫度提高產生紅位移且分裂的現象消失。由模擬的結果可以發現，操作溫度每上升1oC，穿透頻譜將會產生2.7nm的移動。造成位移和分裂的現象主要的原因為液晶分子本身高度異向性的光學性質。此外，我們利用改變外在的電場強度，可以旋轉液晶分子的排列方向。由於所考慮的模態為混合模態，此項調變方式對光能隙的大小及位置影響極大，且光能隙分裂的現象比使用溫度調變更為明顯。
在實驗方面，利用真空吸引的方式，我們成功地製作出液晶光子晶體光纖。在溫度調變的量測中，隨著溫度的上升，穿透頻譜發生紅位移，這和模擬的結果一致。而在控制液晶分子的排列實驗中，當外加電場強度小於100伏特時，可傳遞的波長範圍幾乎不變。在100~300伏特時，液晶分子開始出現明顯旋轉的現象，使得穿透頻譜的形狀和位置出現明顯的變化並在1090nm處出現凹陷。而當電場上升到400伏特之後，頻譜的形狀相同且存在紅位移的現象。
我們的模擬及實驗結果，將可幫助設計與製作以液晶光子晶體光纖為基礎之可調式光電元件。

Filling the liquid crystals (LCs) into the air holes of the photonic crystal fibers (PCFs), we can obtain the liquid-crystal photonic crystal fibers (LCPCFs). Due to the tunable optical properties of the LCs, we can fabricate tunable optical devices based on the LCPCFs. In this thesis, we investigate the photonic bandgap (PBG) properties and find out the effective modal index curves of the LCPCFs by the finite-difference frequency-domain (FDFD) method. The effects of the operation temperature and the alignment of the LCs are discussed. When the alignment of the LC is in the transverse plane of the PCF, we can observe the blue shift and the splitting of the PBGs as we increase the operation temperature. As the LC is aligned along the PCF, the red shift occurs and the splitting disappears. The shift and the splitting of the PBGs are due to the high anisotropic property of the LCs. Besides, we can rotate the alignment of the LCs by the external electric field, and the effects of the alignment on the propagation properties of the LCPCFs are larger than those of the operation temperature.
In the experiment, we successfully fabricate the LCPCFs by using the vacuum method. In the measurement of the LCPCF at different operation temperatures,the red shift of the spectra can be observed with the increasing operation temperatures, which has a very good agreement with the simulation results. As we vary the alignment of the LCs with the external electric field, the transmission bands are almost the same as the voltage is less than 200V. During the range of 200V to 400V, the PBGs demonstrate obvious variations and the deep appears at 1050nm. When the external electric field is raised to 400V, the shapes of the spectra are almost the same and the red shift of the PBGs can be observed. The results of our simulation and the experiment measurement can help us to design and fabricate optical devices based on the LCPCFs.

Contents
1 Introduction 1
1.1 Background 1
1.2 Photonic Crystal fibers 1
1.3 Liquid Crystal Photonic Crystal Fibers 2
1.4 Chapter Outline 4

2 Finite-Difference Frequency-Domain Method 8
2.1 Formulae for Band Structures Analysis 8
2.2 Formulae for Modal Analysis 12
2.3 Index Averaging Method 13

3 Numerical Results 18
3.1 Liquid-Crystal Photonic Crystal Fibers 18
3.2 Optical Properties of LCPCFs at Different Temperatures 19
3.3 Optical Properties of LCPCFs for Variant LC Alignments 21

4 Experimental Results 47
4.1 Fabrication of LCPCFs 47
4.2 Transmission Spectra of LCPCFs 48

5 Conclusion 60

Bibliography 61

[1] Alkeskjold, T. T., and A. Bjarklev, “Electrically controlled broadband liquid
crystal photonic bandgap fiber polarimeter,” Opt. Lett., vol. 32, pp. 1707−1709,
2007.
[2] Alkeskjold, T. T., L. Scolari, D. Noordegraaf, J. Lægsgaard, J. Weirich, L. Wei,
G. Tartarini, P. Bassi, S. Gauza, S.-T. Wu, and A. Bjarklev, “Integrating liquid
crystal based optical devices in photonic crystal fibers,” Opt. Quantum Electron.,
vol. 39, pp. 1009−1019, 2007.
[3] Barkou, S. E., J. Broeng, and A. Bjarklev, “Silica-air photonic crystal fiber
design that permits waveguiding by a true photonic bandgap effect,” Opt. Lett.,
vol. 24, pp. 46−48, 1999.
[4] Benistry, H., “Modal analysis of optical guides with two-dimensional photonic
band-gap boundries,” J. Appl. Phys., vol. 79, pp. 7483−7492, 1996.
[5] 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.
[6] Brechet, F., J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the
characteristics of propagation into photonic crystal fibers, by the finite element
method,” Opt. Fiber Technol., vol. 6, pp. 181−191, 2000.
[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] 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] Du, J., Y. Liu, Z. Wang, B. Zou, B. Liu, and X. Dong1, “Electrically tunable
Sagnac filter based on a photonic bandgap fiber with liquid crystal infused,” Opt.
Lett., vol. 33, pp. 2215−2217, 2008.
[10] Ferrando, A., E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, “Full-vector
analysis of a realistic photonic crystal fiber,” Opt. Lett., vol. 24, pp. 276−278,
1999.
[11] Ferrando, A., E. Silvestre, J. J. Miret, and P. Andrés, “Nearly zero ultraflattened
dispersion in photonic crystal fibers,” Opt. Lett., vol. 25, pp. 790–792, 2000.
[12] Ferrando, A., E. Silvestre, P. Andrés, J. J. Miret, and M. V. Andrés, “Desinging
the properties of dispersionflattened photonic crystal fibers,” Opt. Express, vol. 9,
pp. 687–697, 2001.
[13] 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.
[14] Gu, W., J. Zhao, L. Cui, and J. Hou, “A full-vectorial FDFD analysis of photonic
crystal fibers,” Proc. SPIE, vol. 6150, 2006.
[15] Hansen, T. P., J. Broeng, S. 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] 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.
[17] Knight, J. C., J. Broeng, T. A. Birks, P. St. J. Russell, “Photonic band gap
guidance in optical fibers,” Science, vol. 282, pp. 1476–1478, 1998.
[18] 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.
[19] Koshiba, M., “Wavelength division multiplexing and demultiplexing with
photonic crystal Waveguide couplers,” Journal of Lightwave Technol., vol. 19,
pp. 1970–1975, 2001.
[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,”
Optics Communications 175, pp. 147–152, 2000.
[21] Li, J., and S.-T. Wu, “Infrared refractive indices of liquid crystals,” J. Appl.
Phys., vol. 97, pp. 073501−0735015, 2005.
[22] Mortensen, N. A., “Effective area of photonic crystal fibers,” Opt. Express, vol.
10, pp. 341–348, 2002.
[23] 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.
[24] Noordegraaf, D., L. Scolari, J. Lægsgaard, 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.
[25] Qiu, M., “Analysis of guided modes in photonic crystal fibers using the
finite-difference time-domain method,” Microwave Opt. Technol. Lett., vol. 30,
pp. 327-330, 2001.
[26] 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.
[27] 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.
[28] Sun, J. and C. C. Chan, “Effect of liquid crystal alignment on bandgap formation
in photonic bandgap fibers,” Opt. Lett., vol. 32, pp. 1989−1991, 2007.
[29] Wolinski, T. R., A. Czapla, S. Ertman, M. Tefelska, A. W. Domanski, Edward
N.-K., and R. D.˛Browski, “Tunable highly birefringent solid-core photonic
crystal fibers.” Opt. Quanum. Electron., vol. 39, pp. 1021−1032, 2007.
[30] Yu, C. P., and H. C. Chang, “Applications of the finite difference mode solution
method to photonic crystal structures,” Opt. Quantum Electron., vol. 36, pp.145–163, 2004.
[31] 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.