光子晶體是一種介電質週期性排列的人為設計元件，可經由不同的設計成為波導或是共振腔。其中二維光子晶體共振腔在近十年來有重大的突破與發展，從最簡單的H1 共振腔到Q 值被證實高達45000 的L3 共振腔都引起許多研究者的高度興趣。本論文即著手研究H1 與L3 共振腔的共振模態，藉由共振腔的調變瞭解兩者之間有何關連性存在。由理論分析與量測實驗的對應比較，掌握了各個模態的行為特性，也對Q 值的變化有了更深入的瞭解。

Photonic crystal is an artificial device which arranges its dielectric material periodically. We can fabricate it as a wave guide or cavity via different design ideas. Two- dimension photonic crystals had significant development in recently decade. Numerous researchers were interested in H1 cavities and L3 cavities which were demonstrated possessing high quality factor as 45000. My thesis investigates resonance modes of H1 cavities and L3 cavities. Via adjusting the geometry structures of these cavities, we can understand the correlation of cavity modes between H1 and L3 cavities. Comparing theory analysis and measurement experiment, we can know well about behaviors of these cavity modes. Furthermore, we realize the variation of quality factor more deeply.

[1] E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics
and Electronics”, Phys. Rev. Lett., 58, 2059 (1987).
[2] Sajeev John, “Strong localization of photons in certain disordered dielectric
superlattices”, Phys. Rev. Lett., 58, 2486 (1987).
[3] L. P. Biró, ”Role of photonic-crystal-type structures in the thermal regulation
of a lycaenid butterfly sister species pair”, Phys. Rev. E 67, 021907-1(2003).
[4] John D. Joannopoulos, “Photonic Crystal (Molding The Flow Of Light)”
second edition, Princeton University Press, (2008)
[5] S.O. Kasap, “Optoelectronics and Photonics Principle and Practices”,
Pearson Education Press, (2001)
[6] E. M. Purcell, “Spontaneous emission probabilities at radio Frequencies”,
Phys. Rev. 69, 681 (1946).
[7] D. Kleppner, “Inhibited spontaneous emission”, Phys. Rev. Lett. 47,
233–236 (1981).
[8] Qi, M. et al. , “A three-dimensional optical photonic crystal with designed
point defects”, Nature 429,538–542 (2004).
[9] Blanco, A. et al. , “Large-scale synthesis of a silicon photonic crystal with a
complete threedimensionalbandgap near 1.5 micrometres” ,Nature 405,
437–440 (2000).
[10] Noda, S. , “Full three-dimensional photonic bandgap crystals at
near-infrared wavelengths” , Science 289, 606–606 (2000).
[11] Wijnhoven, J. E. G. J. & Vos, W. L. , “Preparation of photonic crystals
made of air spheres in titania “, Science 281, 802–804 (1998).
[12] Gourley, “Optical properties of two-dimensional photonic lattices
fabricated as honeycomb nanostructures in compound semiconductors”,
Appl. Phys. Lett. 64, 687–689 (1994).
[13] Fan, S. H. , ” High extraction efficiency of spontaneous emission from
slabs of photonic crystals” , Phys. Rev. Lett. 78,3294–3297 (1997).
[14] 盧贊文、李柏璁 , “光通訊波長二維光子晶體雷射發展簡介” ,
物理雙月刊（廿七卷五期）2005 年10 月
[15] Loncar, M. , “Low-threshold photonic crystal laser”, Appl. Phys. Lett.
81, 2680–2682 (2002).
[16] Akahane, Y., Asano, T., Song, B. S. & Noda, S. , “Investigation of high-Q
channel drop filters using donor-type defects in two-dimensional photonic
crystal slabs” , Appl. Phys. Lett. 83,1512–1514 (2003).
[17] Painter, O. et al. , “Two-dimensional photonic band-gap defect mode
Laser”, Science 284, 1819–1821 (1999).
[18] Painter, O. et al. , “Polarization properties of dipolelike defect modes in
photonic crystal nanocavities”, Optics Letters Vol.27 No.5 (2002)
[19] Masayuki Shirane et al. , ” Mode identification of high-quality-factor
single-defect nanocavities in quantum dot-embedded photonic crystals”,
Jour. Appl. Phys. 101, 073107 (2007)
[20] Masahiro Nomura et al. , “Room temperature continuous-wave lasing
in photonic crystal nanocavity”, Optics Express Vol.14 No.13 (2006)
[21] Yoshihiro Akahane et al. , “High-Q photonic nanocavity in a
two-dimensional photonic crystal”, Nature 425 , 944 (2003)
[22] S. Strauf et al. , “Self-Tuned Quantum Dot Gain in Photonic Crystal
Lasers”, Phys. Rev. Lett. 96 , 127404 (2006)
[23] 張高德 ; “廣義光子晶體元件之研究與分析”; 國立中央大學,光
電科學研究所,博士論文 (2007年6月)
[24] M. Plihal and A. A. Maradudin, “Photonic band structure of two
dimensional systems: the triangular lattice”, Phys. Rev. B 44, 8565–8571
(1991)
[25] L. A. Coldren and S. W. Corzine , “Diode Lasers and Photonic Integrated
Circuits”, (Wiley, New York, 1995).
[26] 欒丕綱、陳啟昌, ”光子晶體-從蝴蝶翅膀到奈米光子學”, 五南圖
書出版股份有限公司 (2005年8月)
[27] Min Qiu , “A nonorthogonal finite-difference time-domain method for
computing the band structure of a two-dimensional photonic crystal
with dielectric and metallic inclusions” , J. Appl. Phys. 87, 8268 (2000);
[28] K. S. Yee, IEEE Trans. Antennas Propagat, 14, 302 (1966)
[29] 曾彥鈞, “高品質因子與低模態體積光子晶體微共振腔之設計與
製作”, 國立中央大學,光電科學研究所,碩士論文 (2007年6月)