臺灣博碩士論文加值系統

本論文中，我們研究了光聲效應(photoacoustic effect)中，當光子入射到電致伸縮材料上引起受激布里淵散射(Stimulated Brillouin Scattering)以及相關電致伸縮效應(electrostrictive effect)的現象，即光強度與材料體積變化所引起之聲波強度間的關係。
在光場的入射和影響下，電致伸縮材料會產生與場強平方成正比的應變(strain)，從而引起材料震動產生聲波。入射光因此受聲波引起的折射率變化所影響，引發受激布里淵散射。透過推論聲壓波的運動方程式，可以導出一組聲波強度與時間、空間依賴的耦合方程式。
利用這組泵浦、散射光波與聲波相互作用的非線性耦合方程式，我們可以描述入射材料後的泵浦光與散射光的強度是如何相互作用，並且特別地影響感應聲波的振幅。透過參考現存的實驗結果，提供了一組數值模擬結果來驗證感應聲強函數的理論表達式之有效性。

In this thesis, we investigate the phenomenon of photons that are incident upon an electrostrictive material to cause stimulated Brillouin scattering and the related electrostrictive effect which is the relationship between the intensity of light and the intensity of the acoustic wave induced by the changes in volume in the photoacoustic effect.
Under the incidence and affection of an optical field, the electrostrictive material produces a strain which is proportional to the square of the field strength, causing the material vibrate and produce sound waves. The incident light is hence affected by the change of refractive index caused by the acoustic wave, which induces the stimulated Brillouin scattering. A set of coupling equations of sound intensity with time and space dependence can be derived by deducing the equation of motion for the acoustic pressure wave.
Using this three-wave interacting nonlinear coupling equation, we can depict the interaction of how the intensity of the incident and the scattered light interact and specifically affect the amplitude of the induced acoustic wave. With the referring to the existed experimental results, a set of numerical simulation results are provided to prove the validity of the theoretical expression of the induced sound intensity function.

摘　要
Abstract
誌　謝
目　錄
圖目錄
表目錄
第一章 緒論
1.1 前言
1.2 研究動機與目的
1.3 論文架構
第二章 光聲效應
2.1 非線性波動方程
2.1.1 Maxwell’s equations
2.1.2 非線性材料中的波動方程式
2.2 光聲效應
2.2.1電致伸縮效應
2.2.2布里淵散射
2.2.3光聲效應(Photoacoustic effect)
第三章 聲波方程式
3.1 純量光散射的熱力學理論
3.2 電致伸縮引起的受激布里淵散射
3.2.1 布里淵頻率
3.2.2 自動相位匹配的三波非線性耦合
第四章 聲波強度函數
4.1 光場幅度與相位變化
4.2 SBS閾值功率與有效增益長度
4.3 聲波振幅與光強度之關係
第五章 結論與未來展望
5.1 結論
5.2 未來展望
參考文獻

[1] G. Gautschi, “Piezoelectric Sensors.”Piezoelectric Sensorics, 73-91: Springer, 2002.
[2] D. Damjanovic, and R. Newnham, “Electrostrictive and Piezoelectric Materials for Actuator Applications.” Journal of intelligent material systems and structures 3, no. 2 1992: 190-208.
[3] J. Zheludev, and A. Fotchenkov, “Electrostriction of Linear Dielectrics.” Kristallografiya 3 1958: 308-14.
[4] F. Jona, and G. Shirane, Ferroelectric Crystals, Vol. 1: Pergamon, 1962.
[5] I. Zheludev, “Fundamentals of Ferroelectricity.” Moscow, Atomizdat, 1973.
[6] V. Laude, “Photon and Acoustic Phonon Coupling in Phoxonic Crystals.” Photonic Crystal Materials and Devices X, 2012.
[7] D. Royer, and E. Dieulesaint. Elastic Waves in Solids Ii: Generation, Acousto-Optic Interaction, Applications, Springer Science & Business Media, 1999.
[8] J. Xu, and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications, Vol. 12: Wiley-Interscience, 1992.
[9] D.F. Nelson, Electric, Optic, and Acoustic Interactions in Dielectrics, John Wiley & Sons, 1979.
[10] R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin Scattering and Coherent Generation of Intense Hypersonic Waves.” Physical Review Letters 12, no. 21 1964: 592.
[11] V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J.M. Dudley, and H. Maillotte, “Phononic Band-Gap Guidance of Acoustic Modes in Photonic Crystal Fibers.” Physical Review B 71, no. 4 2005: 045107.
[12] P. Dainese, P.S.J. Russell, N. Joly, J. Knight, G. Wiederhecker, H.L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin Scattering from Multi-Ghz-Guided Acoustic Phonons in Nanostructured Photonic Crystal Fibres.” Nature Physics 2, no. 6 2006: 388.
[13] R.W. Boyd, Nonlinear Optics, Academic press, 2003.
[14] I.L. Fabelinskii, Molecular Scattering of Light, Springer Science & Business Media, 2012.
[15] E.L. Buckland, and R.W. Boyd, “Electrostrictive Contribution to the Intensity-Dependent Refractive Index of Optical Fibers.” Optics letters 21, no. 15 1996: 1117-19.
[16] J.B. Khurgin, and R.S. Tucker, Slow Light: Science and Applications, CRC press, 2008.
[17] R.R. Syms, and J.R. Cozens, Optical Guided Waves and Devices, McGraw-Hill, 1992.
[18] E. Ippen, and R. Stolen, “Stimulated Brillouin Scattering in Optical Fibers.” Applied Physics Letters 21, no. 11 1972: 539-41.
[19] V.I. Kovalev, and R.G. Harrison, “Threshold for Stimulated Brillouin Scattering in Optical Fiber.” Optics Express 15, no. 26 2007: 17625-30.
[20] A. Agrawal, T.M. Benson, M. Richard, D. La Rue, and G.A. Wurtz. Recent Trends in Computational Photonics, Vol. 204: Springer, 2017.
[21] K. Shiraki, M. Ohashi, and M. Tateda, “Sbs Threshold of a Fiber with a Brillouin Frequency Shift Distribution.” Journal of Lightwave Technology 14, no. 1 1996: 50-57.
[22] K.S. Abedin, “Observation of Strong Stimulated Brillouin Scattering in Single-Mode as 2 Se 3 Chalcogenide Fiber.” Optics Express 13, no. 25 2005: 10266-71.
[23] D. Cotter, “Observation of Stimulated Brillouin Scattering in Low-Loss Silica Fibre at 1.3 um.” Electronics Letters 18, no. 12 1982: 495-96.
[24] E.K.M. El-Khamesy, “Performance Enhancement of an Optical Pulse Compression Unit Using Optical Fiber Nonlinearities.” Arab Academy for Science, 2008.
[25] N. Uesugi, M. Ikeda, and Y. Sasaki, “Maximum Single Frequency Input Power in a Long Optical Fibre Determined by Stimulated Brillouin Scattering.” Electronics Letters 17, no. 11 1981: 379-80.
[26] D.J. Griffiths, Introduction to Electrodynamics, Prentice Hall, 1962.