於本論文中，利用理論模型探討當飛秒雷射(Femtosecond laser)經過運行在近布拉格區(Near-Bragg region)的聲光偏轉器(Acousto-optic deflector)產生角度色散(Angular dispersion)問題。飛秒雷射為超短脈衝(Ultrashort-pulsed)，屬於寬頻譜光源(Broadband light source)，不同頻率的光在經過聲光偏轉器時會產生不同之偏轉角度，故有角度色散之問題。透過波動方程式(Maxwell’s equations)可以推導出一組耦合方程式能具體描述飛秒雷射的光在聲光偏轉器裡的動態(dynamics)，把耦合方程式經空間傅立葉轉換(Spatial Fourier transform)再用數值模擬出脈衝經過聲光偏轉器的角度變化。
利用反向傳輸聲波的聲光偏轉器可以讓原本經過一個聲光偏轉器產生的擴散效果消失就能解決角度色散問題，數值模擬可以證明理論模型的有效性。

In this thesis, a theoretical model is proposed to discuss the angular dispersion problem of a femtosecond laser using an acousto-optic deflectors operated under the near Bragg region. The ultra-pulsed laser has broadband optical spectrum and results in a problem of angular dispersion when a pulse passed through the acousto-optic deflector. Starting from the Maxwell’s equations, a set of coupled equations can be properly derived to describe the dynamics of a femtosecond laser light inside an acousto-optic deflector. Through these coupled equations, the angular dispersion phenomenon can be properly depicted. The coupled equations can be solved numerically with the spatial Fourier transformation.
The angular dispersion problem can be properly solved by using a counter propagating sound wave inside the acousto-optic deflector to offset the effect of spreading that caused by the interaction with the propagating sound wave inside the acousto-optic deflectors. Numerical simulations are provided to prove the validity of our theoretical model.

[1] R.W. Hellwarth, in Advances in Quantum Electronics (Columbia University Press, New York, 1961)
[2] J. R. Singer and S. Wang, in Advances in Quantum Electronics(Columbia University Press, New York, 1961).
[3] W. Koechner, Solid-state Laser Engineering, springer, 1996.
[4] R. L. Fork, B.I. Greene, and C.V. Shank, Generation of optical pulses shorter than 0.1 psec by colliding pulse mode locking Appl. Phys. Lett. 38, 671 (1981).
[5] F. J. McClung, R. W. Hellwarth, "Giant optical pulsations from ruby", J. Appl. Phys., vol. 33, pp. 828-829, Mar. 1962.
[6] P. Maine, et al. "Generation of ultrahigh peak power pulses by chirped pulse amplification." IEEE Journal of Quantum electronics 24.2 (1988): 398-403.
[7] E. Hecht, (1987). Optics (4th ed.). Addison Wesley. p. 337.
[8] B. E. A. Saleh and M. C. Tiech, Fundamentals of Photonics, New York, John Wiley, 1991.
[9] A. Yariv and A. P. Yeh, “Photonics: Optical Electronics in Modern Communications,” 6th Edition, Oxford University Press, New York, 2007. P.440.
[10] W. R. Klein, and Bill D. Cook. "Unified approach to ultrasonic light diffraction.＂ IEEE Transactions on sonics and ultrasonics14.3(1967):123-134.
[11] A. Korpel,"Acousto-optics—a review of fundamentals." Proceedings of the IEEE 69.1 (1981): 48-53.
[12] W. Koechner, Solid-state laser engineering. Vol. 1. Springer, 2013.
[13] L. Xinju, Laser technology. CRC Press, 2010. P.89.
[14] M. Roth, M. Tseitlin, and N. Angert. "Oxide crystals for electro-optic Q-switching of lasers." Glass physics and chemistry 31.1 (2005): 86-95.

[15] T. Taira, and T. Kobayashi. "Q-switching and frequency doubling of solid-state lasers by a single intracavity KTP crystal." IEEE journal of quantum electronics 30.3 (1994): 800-804.
[16] X. D. Wang,, et al. "Investigation of KTiOPO4 as an electro‐optic amplitude modulator." Applied physics letters 59.5 (1991): 519-521.
[17] M.Delgado-Pinar, et al. "Q-switching of an all-fiber laser by acousto-optic modulation of a fiber Bragg grating." Optics express 14.3 (2006): 1106-1112.
[18] W. A. Clarkson, and D. C. Hann,. "Acousto-optically induced unidirectional single mode operation of a Q-switched miniature Nd: YAG ring laser." Optics communications 81.6 (1991): 375-378.
[19] J. Zhou, G. Taft, C. Shi, H. C. Kapteyn, and M. Murnane, in Ultrafast Phenomena, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper MA2.
[20] F. Krauz, Ch. Spielmann, P. F. Curley, T. Brabec, S. M. J. Kelly, A. Stingl, R. Spizocs, E. Wintner, and A. J. Schmidt, in Ultrafast Phenomena, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper MAL
[21] D. Kuizenga, and A. Siegman. "FM and AM mode locking of the homogeneous laser-Part I: Theory." IEEE Journal of Quantum Electronics 6.11 (1970): 694-708.
[22] O. Svelto, "Principles of lasers." (1998): 1976.
[23] C. C. Wang, and C. W. Tarn, "Theoretical and experimental analysis of the near-Bragg acousto-optic effect." Optical Engineering 37.1 (1998): 208-214.
[24] A. E. Siegman, Lasers, Chap. 16, University Science Books, CA, 1986
[25] M. D. McNeil and T.-C. Poon, ‘‘Gaussian-beam profile shaping by
acousto-optic Bragg diffraction,’’ Appl. Opt. 33, 4508–4515 ~1994.
[26] B. A. Ngoi, et al. "Angular dispersion compensation for acousto-optic devices used for ultrashort-pulsed laser micromachining." Optics Express 9.4 (2001): 200-206.