摘要

在本論文中， 我們使用四波混合的理論作為我們實驗的方法並且測量其 值。此次的樣品我們選用的是 或 PLZT (9.5/65/35). 或PLZT (9.5/65/35) 鐵電陶瓷材料現今被廣泛使用於電光元件上，主要是在於此材料有良好的鐵電特性、高穿透性及良好的光電效應等優點以及具有較大的 和 值。
我們將簡介四波混合的原理及應用，像是全像素、光源追蹤、相位偶合等。在本實驗中，我們嘗試藉由提供磊浦光以及外加電場來提高我們的訊號光光強。

Abstract

In the thesis, we used the theory of four wave mixing to be our method and calculated values. The sample we choosing was or PLZT (9.5/65/35). PLZT (9.5/65/35) ceramic has nowadays been used for electrooptic devices due to its interesting ferroelectric properties, high transparency, its well-performed electroooptic effects even in the form of non-single crystal and it has large and coefficients.
We will introduce the theory of four wave mixing and its application, likes holography, beam tracking, phase conjugation and so on. In the experiment, we try to increase the intensity of signal beam by applying pump beams and external dc field.

Table of Contents
Abstract……………………….……………………………………………...I
Table of Contents……..………………………………………………III
List of Figures………………………………….….……..…..……….. IV
Chapter 1 Introduction 1
1-1. Properties of fused silica glass……………………………………………1
1-2. The composition of PLZT………………………………………………...2
1-3. The Effect of Electric Field in PLZT……………………………………...3
1-4 The Effect of Temperature in PLZT……………………………………. . .4
1-5. Hysteresis………………………………………………………………....5
1-6. The Objective and Method of Study……………………………………...7

Chapter 2 Theoretical Analysis 8
2-1. The Origin of Nonlinear Optics…….…………………………….…...….8
2-2. Degenerate Four-Wave Mixing……………………………………….....10
2-3. Wave-equations for phase conjugation……….……………………....…11
2-4. Calculation for χ(3) Values…………............................................... ..…13

Chapter 3 Experimental Procedure 16
3-1. Sample Preparation………………………………………………………16
3-1-1. Sample Characteristics………………….……………………………16
3-1-2. Sample Preparations of PLZT………………………………………..17
3-2. Experimental Instrument…….…………………………………….….…18
3-3. Experimental Setup………...…………………………………….…..….19
3-4. Experimental Measurement……………………………………………..19

Chapter 4 Results and Discussion 21
4-1 Pumping beam in PLZT…………………………………………………21
4-1. Electric Field In PLZT…………………………………………………...22
4-3 Comparison for Different External Electric Field………………………..22
4-4. Hysteresis in PLZT…………………………………………………... …23
4-5. Calculation for values…………………………………………...…23
4-6. Comparison for ……………………………………………….. . ...24

Chapter 5 Conclusions and Future studies 25

References 26

List of Table

Table4.5.1 for PLZT samples at external electric fields………………….24

List of Figures

Figure 1-1. The Schematic representation of (a) ordered crystalline form and (b) random network or glassy form of SiO2.……………………… 30
Figure 1-2. (a) The basic structure of SiO2 or SiO?4 tetrahedron. (b) The distance and angle of an ideal SiO2 molecule.…. …………………………..31
Figure 1-3. The temperature and pressure of SiO2 phase diagram.……………..32
Figure 1-4. The perovskite unit cell of PLZT……………………….….33
Figure 1-5. The phase diagram of PLZT…………………………………………….34
Figure1-6. (a) Effective birefringence as a function of electric field and polarization. (b) For a 9/65/35 PLZT ceramic at room temperature. (c) The polarization values at stepwise increasing electric field were achieved as shown in the hysteresis loop………………………………………………………………….35
Figure1-7. (a) Hysteresis loop for polarization. (b) Domain microstructure without an applied field. (c) Domain growth in direction of an applied field………………………………………………………...36
Figure 1-8. The hysteresis loop and birefringence in different composition of PLZT……………………………..……………………………..37
Figure 2-1. Schematic of four wave-mixing………………………….………...38
Figure 3-1. The typical hot pressing setup for fabricating PLZT ceramics……..39
Figure 3-2. Experimental Setup…………………………………………………40
Figure 4-1. The lower curve is for signal intensity without pumping beam on the PLZT sample, V=0.The upper curve is for signal intensity with pumping beam on the PLZT sample, V=0…………………………..41
Figure 4-2. DFWM of PLZT (9.5/65/35) at 0.62mm thick under positive external electric field. The external electric field are 0V/mm, 800V/mm, 1000V/mm and 1200V/mm in the mode without using polarizers….42
Figure 4-3. DFWM of PLZT (9.5/65/35) at 0.62mm under positive external electric field. The external electric field are 0V/mm, 800V/mm, 1000V/mm, 1200V/mm in S-S mode, respectively…………………43
Figure 4-4. The DFWM hysteresis loop of PLZT………………………………44

References
[1] R. A. Myers, N. Mukherjee, and S. R. J. Brueck, “Large second-order nonlinearity in poled fused silica”, Optics Letters, Vol.16, p.1732, November (1991).
[2] A. Okada, K. Ishii, K. Mito, and K. Sasaki, “Second-order optical nonlinearity in corona-poled glass films”, Journal of Applied Physics, Vol.74, p.531, July (1993).
[3] A. Okada, K. Ishii, K. Mito, and K. Sasaki, “Phase-matched second-harmonic generation in novel corona poled glass waveguides”, Applied Physics Letters, Vol.60, p.2853, June (1992).
[4] R. A. Myers, “Large second-order nonlinearity in amorphous SiO2 using temperature/electric-field poling.” Dissertation, The University of New Mexico, (1995).
[5] M. Rothschild, D. J. Ehrlich, and D. C. Shaver, “Effects of excimer laser irradiation on the transmission, index of refraction, and density of ultraviolet grade fused silica”, Applied Physics Letters Vol.55, p.1276, (1989).
[6] J. S. Danel, M. Dufour and F. Michel, “Application of quartz micromachining to the realization of a pressure sensor”, IEEE International Frequency Control Symposium, p.581, (1993).
[7] 余樹楨, “晶體之結構與特性”, 渤海堂文化公司, (1987).
[8] L. L. Hencb and J. K. West, “Principles of electronic ceramics”, Chapter 6&10 (1986), A Wiley-Interscience Publication.
[9] K. H. Hardtl and D. Hennings, “Distribution of A-site and B-site acancies in (Pb, La)(Ti,Zr) ceramics”, Journal of the American ceramic society, Vol.55, pp230-231, May 1972.
[10] K. Betzler and D. Bauerle, “Second-harmonic generation in cubic PLZT ceramics”, Applied Physics, Vol.18, pp271-274 (1979).
[11] H. M. O`BYRAN, JR., “Phase relation in ”, Journal of the American ceramic society, Vol. 56, No7, p385 (1971).
[12] K. Carl and K. Geisen, “Dielectric and optical properties of a qusi
-ferroelectric PLZT ceramic”, Proceedings of IEEE, Vol.61, No. 7, p967 (1973).
[13] G. H. Heartling and C. E. Land, “Hot-pressed (Pb,La)(Zr,Ti) ferroelectric ceramics for electrooptic applications”, Journal of the American ceramic society, Vol. 54, No. 1, pp1-10 (1971).
[14] Yuhuan Xu , “Ferroelectric Materials and Their Applications” p7 (1991), North-Holland ;Sole distributors for the USA and Canada, Elsevier Science Pub. Co.
[15] E. T. Keve and A. D. Annis, “Studies of phases, phase transitions and properties of some PLZT ceramics”, Ferroelectrics, Vol.5, pp77-89 (1973).
[16] E. T. Keve and A. D. Annis, “Studies of Phase, Phase transitions and properties of some PLZT ceramics”, Ferroelectrics , Vol. 5, pp77-89 (1973)
[17] Hilary L. Hampsch and John M. Torkelson, “Second harmonic in corona poled, doped polymer films as a function of corona processing”, Journal of Applied Physics, 67, p1037 (1990).
[18] J. Wilson and J. F. B Hawkes, “Optoelectronics”, p104 (1989).
[19] 彭江得, 光電子技術基礎, 儒林圖書有限公司, p64 (1993).
[20] P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena”, Reviews of Modern Physics, 35, p23 (1963).
[21] K. Kato, “Second-harmonic and Sum-frequency generation in ”, IEEE Journal of Quantum Electronics, Vol. 30, pp881-883 (1994).
[22] W. P Risk, S. D. Lau, R. Fontana, L. Lane, and Ch. Nadler, “Type- second-harmonic generation waveguides”, Applied Physics Letter, Vol. 1993, pp1301-1303 (1993).
[23] N. Kagi, T. K. Chiang, M. E. Marchi and L. G. Kazovsky, “Fiber optical parametric amplifier operating near zero-disperation wavelength”, Electronic Letters, Vol. 31, pp1935-1937 (1995).
[24] Schiling G., Evnes. W. E., Schwentner. N., “Third harmonic international conference on indium phosphide related materials”, pp602-605 (1996).
[25] R. Normandin, and G. I. Stegeman, “Nondegenerate four-wave mixing in integrated optic”, Optics Letters, 4, p58 (1979).
[26] Xing-long Wu, Ming-sheng Zhang, and Feng Yan, “Raman spectroscopic studies of proton-exchanged crystal”, Journal of Applied Physics, 78, p1953 (1995).
[27] L. L. Kulyuk, D. A. Shutov, and E. E. Strumban, “Second -harmonic generation by interface: influence of the oxide layer”, 8 ,p1766 (1991).
[28] Charles Kittel, “Introduction to solid state physics 8th”, Wiley, (2005)