當外加電場沿著本研究中第一種週期性極化翻轉鈮酸鋰的晶軸z方向，此時在晶軸x方向會產生週期性的介電常數變化，這種元件被稱為週期性極化翻轉鈮酸鋰電光光柵，它的倒晶格向量可用來補償在光柵中的0皆非尋常入射光和1皆非尋常繞射光的波向量不匹配。我們在本文中發展一種理論模型，用來分析並且觀察一個有限腰寬的高斯光束;當它沿1皆布拉格角度入射週期性極化翻轉鈮酸鋰電光光柵時的布拉格繞射行為。這種理論模型可以根據入射光束的束腰，來評估體積光柵在光學系統中的表現。
當外加電場沿著我們第二種週期性極化翻轉鈮酸鋰的晶軸y方向，此時沿x軸方向傳播光的偏振方向可以被快速的調製，這種元件我們稱為偏振模態轉換器。在本文中我們整合兩個偏振模態轉換器與一個週期性極化翻轉鈮酸鋰光參量增益介質在同一個鈮酸鋰晶體上，用它來產生並且快速調製光參量震盪器的輸出頻譜。 第三種元件是將退火式質子交換波導製作在週期性極化翻轉鈮酸鋰晶體上，當外加電場沿著週期性極化翻轉鈮酸鋰的晶軸y方向，我們設計並且展示了一種有效率的主動式電光模態轉換器，它可以被用來轉換波導中的傳播模態與輻射模態。
本研究中所展示元件具有實際應用的潛力，當將它們與具有不同光學功能的週期性極化翻轉鈮酸鋰與非週期性極化翻轉鈮酸鋰結構結合在一塊鈮酸鋰晶體上，這些元件可在光纖通訊與電光可調式脈衝雷射系統上具有更多種的應用。

Under the influence of the electric field in the direction of crystallographic z axis of the periodically poled lithium niobate (PPLN), a periodically varying permittivity along the crystallographic x axis will be produced. Such a device is called EO PPLN grating which can cause the reciprocal vector to compensate the phase mismatch between the incident extraordinary beam and its first order Bragg diffracted extraordinary beam in the device. In this dissertation, we developed a theoretical model to investigate and analyze the Bragg diffraction behavior of a Gaussian beam that interacts with such a device. This model can also be used to evaluate the performance of volume gratings in an optical system.
For an electric field along the crystallographic y axis of the PPLN, the polarization state of the light which propagates along x axis in the PPLN can be modulated efficiently, and it has been explored and exploited to demonstrate efficient and fast polarization-mode converter (PMC). In this dissertation, we integrated two PPLN EO PMCs with a PPLN optical parametric gain medium in a monolithic LiNbO3 to achieve unique spectral manipulations in an optical parametric oscillator (OPO) system. With this kind of EO effect in, say an, annealed proton-exchanged PPLN waveguides, we report the design and experimental demonstration of electro-optically active TM-guided to TE-radiation mode converters.
The devices demonstrated in this research have the potential for practical application. To further integrate the devices with other PPLN or APPLN structure with different optical functions in a monolithic LiNbO3 crystal, such devices can find many applications in optical communications or an electro-optic Q-switched and wavelength-tunable laser system.

1. L. E. Myers,* R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce , “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3, ” J. Opt. Soc. Am. B. 12, 2012 (1995)
2. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918 (1962).
3. M. Yamada, M. Saitoh, and H. Ooki, “Electric-field induced cylindrical lens, switching and deflection devices composed of the inverted domains in LiNbO3 crystals,” Appl. Phys. Lett. 69, 3659 (1996).
4. M. Yamada, “Electrically induced Bragg-diffraction grating composed of periodically inverted domains in lithium niobate crystals and its application devices,” Rev. Sci. Instrum. 71, 4010 (2000).
5. Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen, “Electro-optic periodically poled lithium niobate Bragg modulator as a laser Q-switch,” Opt. Lett. 32, 545 (2007).
6. H. Gnewuch, C. N. Pannell, G. W. Ross, P. G. R. Smith, and H. Geiger, “Nanosecond response of Bragg deflectors in periodically poled LiNbO3,” IEEE Photon. Technol. Lett. 10, 1730 (1998).
7. J. A. Abernethy, C. B. E. Gawith, R. W. Eason, and P. G. R. Smith, “Demonstration and optical characteristics of electro-optic Bragg modulators in periodically poled lithium niobate in the near-infrared,” Appl. Phys. Lett. 81, 2514 (2002).
8. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
9. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proceedings of the IEEE 73, 894 (1985).
10. N. Kato, “A theoretical study of pendellosung fringes,” Act. Cryst. 14, 526 (1961).
11. B. Benlarbi, P. St. J. Russell, and L. Solymar, “Bragg diffraction of finite beams by thick gratings: two rival theories,” Appl. Phys. B 28, 63 (1982).
12. Yan-Qing Lu, Zhi-Liang Wan, Quan Wang, Yuan-Xin Xi, and Nai-Ben Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys.
Lett. 77, 3719 (2000).
13. C. Y. Huang, C. H. Lin, Y. H. Chen, and Y. C. Huang,“Electro-optic Ti:PPLN waveguide as efficient optical wavelength filter and polarization mode converter,” Opt. Express 15, 2548 (2007).
14. S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies ,” IEEE J. Quantum Electron. 15, 415 (1979).
15. B. Jacobsson, M. Tiihonen, V. Pasiskevicius, and F. Laurell, “Narrowband bulk Bragg grating optical parametric oscillator ,” Opt. Lett. 30, 2281 (2005).
16. 林昭宏, Integrated Periodically and Aperiodically Poled Lithium Niobate and Photonics and Laser Devices (Doctoral dissertation, National Central University, 2009).
17. D. Marcuse, “Electrooptic coupling between TE and TM modes in anisotropic slabs,” IEEE J. Quantum Electron. 11(9), 759 (1975).
18. H. F. Taylor, and A. Yariv, “Guided Wave Optics,” Proc. IEEE 62(8), 1044 (1974).
19. Y. Okamura, S. Yamamoto, and T. Makimoto, “Electro-optic guided-to-radiation mode conversion in Cu-diffused LiTaO 3 waveguide with periodic electrodes,” Appl. Phys. Lett. 32(3), 161 (1978).
20. 鄧聖龍, Guided-to-radiation polarization mode conversion in electro-optic PPLN APE waveguides (Master's thesis, National Central University, 2008).
21. L. Paul and R. C. Dale, Electromagnetic Fields and Waves (W. H. Freeman and Company, 1972), Chap.12.
22. M. Müller, E. Soergel, and K. Buse, “Light deflection from ferroelectric domain structures in congruent lithium tantalate crystals,” Appl. Opt. 14, 6344 (2004).
23. L. E. Myers, Quasi-Phasematched Optical Parametric Oscillators in Bulk Periodically Poled Lithium Niobate (Ph.D. Dissertation, Stanford University, 1995).
24. M. de Angelis, S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, S. Grilli, and M. Paturzo, “Evaluation of the internal field in lithium niobate ferroelectric domains by an interferometric method,” Appl. Phys. Lett. 85, 2785 (2004).
25. M. Müller, E. Soergel, K. Buse, and M. C. Wengler, “Light deflection from ferroelectric domain boundaries,” Appl. Phys. B 78, 367 (2004).
26. J. A. Fleck, Jr. and M. D. Feit, “Beam propagation in uniaxial anisotropic media,” J. Opt. Soc. Am. 73, 920 (1983).
27. L. E. Myers, G. D. Miller, R. C. Eckardt, M. M. Fejer, R. L.Byer, and W. R. Bosenberg,” Quasi-phase-matched 1.064-μm-pumped optical parametric oscillator in bulk periodically poled LiNbO3” Opt. Lett. 20, 52 (1995).
28. Y. H. Chen and Y. C. Huang, “Actively Q-switched Nd:YVO4 laser using an electro-optic periodically poled lithium niobate crystal as a laser Q-switch” Opt. Lett. 28, 1460 (2003).
29. M. L. Bortz, and M. M. Fejer, “Annealed proton-exchanged LiNbO 3 waveguides,” Opt. Lett. 16 (23), 1844–1846 (1991).
30. D. Marcuse, “Coupled-mode theory for anisotropic optical waveguides,” Bell Syst. Tech. J. 54 (6), 985–995 (1975).
31. N. Mabaya, P. E. Lagasse, and P. Vandenbulcke, “Finite element analysis of optical waveguides,” IEEE Trans. Microw. Theory Tech. 29 (6), 600–605 (1981).
32. K. S. Chiang, “Construction of refractive-index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. LT-3, 385 (1985).
33. R. Regener, and W. Sohler, “Loss in low-finesse Ti:LiNbO 3 optical waveguide resonators,” Appl. Phys. B 36 (3), 143–147 (1985).
34. S. Yamamoto, and Y. Okamura, “Guided-radiation mode interaction in off-axis propagation in anisotropic optical waveguides with application to direct-intensity modulators,” J. Appl. Phys. 50 (4), 2555–2564 (1979).
35. M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5 μm wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23(13), 1004–1006 (1998).
36. B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75, 2175 (1999).