在本論文中，我們探討如何利用多色光超快雷射脈衝聚焦產生之空氣電漿誘發寬頻兆赫波輻射。這個現象可以用瞬時光電流模型來解釋，其中多色雷射脈衝之間的相位差、能量比例、以及脈衝總能量是影響兆赫波強度的重要因素。因為較為不對稱的電場分佈會得到較強的方向性瞬時電流，以雙色光激發兆赫波輻射時，相位差為0.5π時產生之兆赫波強度最強，而相位差為0時沒有兆赫波輸出。雙色光的最佳相位在不同的脈衝能量下變化不大。若以三色光誘發兆赫波輻射，其最佳相對相位差則會隨著脈衝能量變化，二階諧波與基頻光之最佳相位差落在0.4π至0.5π之間，而三階諧波與基頻光最佳相位差落在0.7π至π的範圍。
不同色光之脈衝能量比例會影響電場之不對稱性，並且產生兆赫波的最佳比例會隨著總脈衝能量而改變。實驗結果驗證了模擬中對二色光之能量比例與兆赫波輻射能量變化之趨勢的預測。此外，多色脈衝光之偏振態與兆赫波輻射強度以及偏振態的關係也在此工作中被探討。同時，模擬結果顯示以同旋光性之圓偏振二色光脈衝，可消除相對相位差對兆赫波輻射產生強度之影響，惟線性偏振之兆赫波之偏振角會隨著相對相位改變而旋轉。

In this thesis, we investigate how to generate broadband terahertz (THz) emission by multi-color laser-induced filament in ambient air. The generation process of coherent THz wave from a gas plasma induced by multi-color ultrafast pulses can be well-described by transient photocurrent model. The relative phases, power ratios between multi-color laser fields and total pump power are important factors that will affect the yield of output THz signal. Simulation of THz emission based on the transient photocurrent model is carried out in this work. Because the directional transient current induced by the asymmetry of the synthesized electric field is stronger, the THz yield is strongest when one employs 2-color pulses pumping with their relative phase equals to π⁄2 while there is no output when the phase is 0. In 3-color pumping cases, the optimized relative phase changes with the power ratio between 3–color pulses and the total pump power, while it remains still in 2-color cases.
The relation of the THz power and the pumping power ratio has been investigated in 2-color pumping in both simulation and experiments. The experiment results are in general agreement with the prediction of the simulation outcome. We also considered the influence of polarizations of pumping pulses on THz emission. Meanwhile, using 2-color pulses pumping with both right or left circularly polarization, the relative phase does not affect the radiation power of the THz waves but the polarization angle of the linearly polarized THz field. 

[1] Jefferson Lab, Terahertz radiation frequency range (2003) (http://wwwold.jlab.org/news/releases/2003/03felthz.html)
[2] Jared H. Strait, Paul A. George, Mark Levendorf, Martin Blood-Forsythe, Farhan Rana, and Jiwoong Park, “Measurements of the Carrier Dynamics and Terahertz Response of Oriented Germanium Nanowires using Optical-Pump Terahertz-Probe Spectroscopy,” Nano Lett., Vol. 9, No. 8, pp. 2967-2972, June 2009.
[3] Katsuhiro Ajito and Yuko Ueno, “THz Chemical Imaging for Biological Applications,” IEEE Transactions on Terahertz Science and Technology, Vol. 1, No. 1, pp. 293-300, September 2011
[4] B. B. Hu and M. C. Nuss, W E. Sleat, and W Sibbett, “Imaging with terahertz waves,” Opt. Lett., Vol. 20, No. 16, pp. 1716-1718, August 1995.
[5] A.G. Marklz, A. Roitberg and E.J. Heilweil, ”Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0THz” Chemical physics letters Vol.320 pp.42-48, 2000.
[6] R. Piesiewicz, T. Kleine-Ostmann, N.Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kürner,”Short-range ultra-broadband terahertz communications: concepts and perspectives” IEEE antennas and propagation magazine Vol.49 No.6 pp.24-39, December 2007.
[7] D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett., Vol. 45, No. 3, pp. 284-286, May 1984.
[8] A. Rice, Y. Jin, X. F. Ma, X.C. Zhang, D. Bliss et al., “Terahertz optical rectification from 110 zincblende crystals,” Appl. Phys. Lett., Vol. 64, No. 11, pp. 1324-1326, March 1994.
[9] X.C. Zhang, B. B. Hu, J. T. Darrow, and D. H. Auston, “Generation of femtosecond electromagnetic pulses from semiconductor surfaces,” Appl. Phys. Lett., Vol. 56, No. 11, pp. 1011-1013, March 1990.
[10] Rüdeger Köhler et al, “Terahertz semiconductor heterostructure laser,” NATURE, Vol. 417, No. 6885, pp. 156-159, May 2002.
[11] Q. Wu and X.C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett., Vol. 67, No. 24, pp. 3523-3525, December 1995.
[12] D. Frischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, “far-infrared time domain spectroscopy with terahertz beams of dielectrics and semiconductors” J. Opt. Soc. Am. B Vol.7 No.10, pp. 2006-2015, 1990.
[13] D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett., Vol. 25, No. 16, pp. 1210-1212, August 2000.
[14] Zhang X.C., Xu J., “THz Air Photonics”, Introduction to THz Wave Photonics. Springer, Boston, MA, 2010.
[15] Hamster, H., et al., “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction” Phys Rev Lett, Vol.71 No.17, pp. 2725-2728, October 1993.
[16] K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Exp., vol. 15, no. 8, pp. 4577–4584, 2007.
[17] H. Hamster, A. Sullivan, S. Gordon, and R.W. Falcone, Phys. Rev. E 49, 671 ,1994.
[18] T. Löffler, F. Jacob, and H. G. Roskos, “Generation of terahertz pulses by photoionization of electrically biased air,” Appl. Phys. Lett., Vol. 77, No. 3, pp. 453-455, July 2000.
[19] T. Löffler and H. G. Roskos, “Gas-pressure dependence of terahertz-pulse generation in a laser generated nitrogen plasma,” J. Appl. Phys., Vol. 91, No. 5, pp. 2611-2614, March 2002.
[20] Mark D. Thomson, Markus Kreß, Torsten Löffler, and Hartmut G. Rosk, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: From fundamentals to applications,” Laser & Photon. Rev., Vol. 1, No. 4, pp. 349-368, November 2007.
[21] Markus Kress, Torsten Löffler, Susanne Eden, Mark Thomson, and Hartmut G. Roskosr, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett., Vol. 29, No. 10, pp. 1120-1122, November, 2004.
[22] T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett., Vol. 30, No. 20, pp. 2805-2807, October 2005.
[23] Xu Xie, Jianming Dai, and X.-C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett., Vol. 96, art. 075005, February 2006.
[24] Klaus Reimann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys., Vol. 70, pp. 1597-1632, September 2007.
[25] K. Y. KIM, A. J. TAYLOR, J. H. GLOWNIA AND G. RODRIGUEZ, “Coherent control of terahertz supercontinuum generation in ultrafast laser–gas interactions,” nature photonics, Vol. 2, pp. 605-609, October 2008.
[26] Ki-Yong Kim, “Generation of coherent terahertz radiation in ultrafast laser-gas interactions,” Phys. Plasmas, Vol. 16, art. 056706 1-8, May 2009.
[27] I. Babushkin, W. Kuehn, C. Ko¨hler, S. Skupin, L. Bergé, K. Reimann, M.Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast Spatiotemporal Dynamics of Terahertz Generation by Ionizing Two-Color Femtosecond Pulses in Gases,” Phys. Rev. Lett., Vol. 105, art. 053903, July 2010.
[28] Yasuo Minami, Makoto Nakajima, and Tohru Suemoto, “Effect of preformed plasma on terahertz-wave emission from the plasma generated by two-color laser pulses,” Phys. Rev. A, Vol. 83, art. 023828, 1990.
[29] Jianming Dai, Nicholas Karpowicz, and X.-C. Zhang, “Coherent Polarization Control of TerahertzWaves Generated from Two-Color Laser-Induced Gas Plasma,” Phys. Rev. Lett., Vol. 103, art. 023001, July 2009.
[30] C.M. Chang, The studies of indium-tin-oxide nanostructures by broadband terahertz spectroscopy. Master dissertation, National Tsing Hua University, Hsinchu, 2012.
[31] T. I. Oh, Y. S. You, and K. Y. Kim, “Two-dimensional plasma current and optimized terahertz generation in two-color photoionization,” Opt. Express, Vol. 20, No. 18, pp. 19778-19786, August 2012.
[32] Yun-Shik Lee, “Principles of terahertz science and technology,” Chapter3, Springer, Berlin, 2009.
[33] J. Dai, N. Karpowicz, and X.-C. Zhang, “Coherent polarization control of THz waves generated from asymmetrically ionized gases,” Journal of Physics: Conference Series,276, 012003, 2011.