本論文使用全像干涉技術來製作液晶聚合物薄膜(holographic polymer-dispersed liquid crystal, HPDLC)準光子晶體，並研究其產生雷射之特性。本實驗架構分成三部分，第一部分為尋找最佳化參數，藉由雙道光干涉來形成全像光柵，同時利用He-Ne雷射光即時觀測樣品的繞射曲線，藉由繞射曲線來選擇各材料最佳化的濃度比例；第二部分為利用最佳化的濃度比例製作HPDLC準光子晶體，實驗上使用兩道同調光干涉並配合樣品旋轉八次和十二次，曝光結束後利用He-Ne雷射光來觀察樣品的遠場繞射，從樣品的遠場繞射可以驗證樣品分別具有八次和十二次的旋轉對稱性，並藉由布拉格定律(Bragg’s law)可得到樣品的倒晶格向量。另外，我們也可以從寫入光的波向量之線性組合來計算倒晶格向量理論值，計算結果與實驗量測相當符合；第三部分為準光子晶體雷射的測量，使用調Q Nd-YAG脈衝雷射作為激發光源，觀察樣品產生雷射的波段、雷射閥值及雷射方向。另一方面，我們也從布里淵區(Brillouin zone)邊界來推估慢光(slow light)的波長以及雷射的方向，實驗結果與理論分析相當符合。

In this thesis, lasing characteristics of photonic quasi-crystals (PQCs) based on holographic polymer-dispersed liquid crystals (HPDLCs) are investigated. There are mainly three parts in this thesis. Firstly, we use two mutually coherent laser beams to form a holographic grating; in the meantime, a He-Ne laser is used as a probe beam monitoring the dynamical diffraction. By changing the weight percentage of HPDLC composite, an optimized weight percentage is obtained. Secondary, an optimized two-beam interference with multi-exposures is utilized to fabricate two types of PQCs, one is 8-fold rotational symmetry and the other is 12-fold rotational symmetry. The symmetries and reciprocal lattice vectors of PQCs are confirmed from the Fraunhofer diffraction pattern and the Bragg’s diffraction. The experimental results agree well with the calculation based on the superposition of wavevectors of writing beams. Thirdly, a Q-switching Nd-YAG laser pulse is used as a pumping source to excite the laser-dye-doped PQCs, the measured wavelengths and the directions of lasing from the PQCs agree well with the theoretical values which are calculated from the boundary of the Brillouin zone.

[1] K. Sakoda, "Optical Properties of Photonics Crystals", 2th ed. (Springer, 2004).
[2] D. W. Prather, S. Shi, A. Sharkawy, J. Murakowski, and G. J. Schneider, "Photonic Crystals", (Wiley, 2009).
[3] J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, "Photonics Crystals Towards Nanoscale Photonic Devices", 2th ed. (Springer,2008).
[4] D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951-1953 (1984).
[5] A. Rostami and S. Matloub, Progress In Electromagnetics Research M 9, 65-78 (2009).
[6] Robert, and H. Chen, "Liquid Crystal Displays" (Wiley, 2011).
[7] Pochi Yeh, and Claire Gu, "Optics of Liquid Crystal Displays" (Wiley, 1999).
[8] S. Chandrasekhar, "Liquid Crystals", 2th ed. (Cambridge University Press, 1992).
[9] P. G. de Gebbes and J. Prost, 'The Physics of Liquid Crystals', 2th ed. (Oxford University Press, 1993).
[10] Heinz-Siegfried Kitzerow, Christian Bahr, and Christian Bahr, "Chirality in Liquid Crystals", (Springer, 2001).
[11] S. Chandrasekhar, B. K. Sadashiva, and K. A. Suresh, Pramana 9, 471-480 (1977).
[12] Deng-Ke Yang and Shin-Tson Wu, "Fundamentals of Liquid Crystal Devices" (Wiley 2006).
[13] M. Marinelli and F. Mercuri, Phys. Rev. E 61, 1616-1621 (2000).
[14] D. J. Griffiths, "Introduction to Electrodynamics", 3th ed. (Prentice Hall, 1999).
[15] M. Fox, "Optical Properties of Solids", 2th ed. (Oxford University Press, 2010).
[16] Amnon Yariv and Pochi Yeh, "Photonics Optical Electronics in Modern Communications", 6th ed. (Oxford University Press, 2007).
[17] C. Janglin, C. Wayne, and F. Mark, "Handbook of Visual Display Technology", (Springer, 2012).
[18] V. G. Chigrinov, "Liquid Crystal Devices: Physics and Applications" (Artech House 1999).
[19] T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, Annu. Rev. Mater. Sci. 30, 83-115 (2000).
[20] T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, R. L. Sutherland, D. L. Vezie, and W. W. Adams, Polymer 36, 2699-2708 (1995).
[21] M. J. Escuti, J. Qi, and G. P. Crawford, Optics Letters 28, 522-524 (2003).
[22] Suraj P. Gorkhali, Jum Qi, and Gregory P. Crawford, J. Opt. Soc. Am. B 23,149-158 (2006).
[23] L. Z. Cai, X. L. Yang, and Y. R. Wang, J. Opt. Soc. Am. A 19, 2238-2244 (2002).
[24] Joseph W. Goodman, "Introduction to Fourier Optics", 3th ed. (Roberts & Company Publishers, 2005).
[25] T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, R. Haaga, and W. W. Adams, Proc. SPIE 2651, 44-55 (1996).
[26] Y. J. Liu, and X. W. Sun, Advances in OptoElectronics 2008, 684349 (2008).
[27] Harald Ibach and Hans Lüth, "Solid-State Physics", 4th ed. (Springer 2009).
[28] Charles Kittel, "Introduction to Solid State Physics", 8th ed. (Wiley 2005).
[29] M. A. Kaliteevskia, S. Branda, R. A. Abrama, T. F. Kraussb, R. M. De La Rueb, and P. Millarb, Nanotechnology 11, 274-280 (2000).
[30] M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, Nature 404, 740-743 (2000).
[31] Ted Janssen, Nature materials 6, 925-926 (2007).
[32] Marian Florescu, Salvatore Torquato, and Paul J. Steinhardt, Phys. Rev. B 80,155112 (2009).
[33] O. Painter, R. K. Lee, A. Scherer, A. Yarive, J. D. O'brien, P. D. Dapkus, and I. Kim, Science 284, 1819-1821 (1999).
[34] Jonathan P. Dowling, Michael Scalora, Mark J. Bloemer, and Charles M. Bowden, J. Appl. Phys. 75, 1896-1899 (1994).
[35] Thomas Engel, Philip Reid, "Physical Chemistry", (Pearson Prentice Hall 2006).
[36] NOA81, http://www.norlandprod.com/adhesives/noa%2081.html
[37] Rose bengal, http://omlc.ogi.edu/spectra/PhotochemCAD/html/084.html
[38] DCM, http://omlc.ogi.edu/spectra/PhotochemCAD/html/038.html
[39] Ying Liu, Shou Liu, and Xiangsu Zhang, Applied Optics 45, 480-483 (2006).
[40] Jun Li, Chien-Hui Wen, Sebastian Gauza, Ruibo Lu, and Shin-Tson Wu, Journal of Display Technology 1, 51-61 (2005).
[41] R. L. Sutherland, L.V. Natarajan, V. P. Tondiglia, and T. J. Bunning, Chem.Matter. 5, 1533-1538 (1993).
[42] Andy Y. -G. Fuh, T. -C. Ko, M. -S. Tsai, C. -Y. Huang, and L. -C. Chien, J. Appl.Phys. 83, 679 (1998).
[43] S. T. Thornton, and J. B. Marion, "Classical dynamics of particles and systems", 5th ed. (Thomson, 2004).
[44] J. M. Lourtioz, H. Benisty, V. Berger, J. M. Gerard, D. Maystre, and A. Tchelnokov, "Photonics Crystals Towards Nanoscale Photonic Devices", 2th ed. (Springer 2008).