兆赫波是近三十年來 (約自 1980 年代開始)，新興發展的一個研究領域。因其波長落在光學與電學頻譜之間的特殊性，使其難以有效率的產生。在非線性光學 (nonlinear optics) 與超快雷射 (ultra-fast laser) 的發展下，兆赫波已較以往容易產生，並在眾多的領域都有豐富的應用，如：醫學影像、基因分析、物質辨識、國防安全、光通訊、太空研究等。

本實驗中，利用非線性光差頻產生 (Difference Frequency Generation，DFG) 的機制，於鈮酸鋰晶體 (LiNbO3，Lithium Niobate，LN) 中產生兆赫波。在之前的文獻中認為，由於鈮酸鋰晶體對兆赫波的高吸收特性，晶體長度的增長對於兆赫波產生的強度應無實質幫助。但於吾等之理論分析中，兆赫波強度應與晶體長度成一正自然指數成長。為驗證此一分析結果，本實驗架構分為三大部分，第一部分為雷射源，其提供三道波長不同的光源，作為第二部分非線性光參數放大機制 (Optical Parametric Amplifier，OPA) 中的激發光和訊號光。第二部分為非線性光參數放大，目的在於放大第一部分的兩道連續波光源，成為脈衝雷射，以此作為第三部分的非線性光差頻產生機制的激發光與訊號光用以產生所需的閒光 (兆赫波)。第三部分為非線性光差頻產生機制，目的在於產生兆赫波。利用第二部分放大後的兩道相近波長雷射，當差頻落於兆赫波區段並滿足相位匹配條件時 (phase-matching condition)，在具有週期性極化反轉結構的鈮酸鋰晶體 (Periodical-Poled Lithium Niobate，PPLN) 中便可產生兆赫波。

第二與第三部分皆為非線性光學轉換機制，利用鈮酸鋰晶體的非線性特性，作為波長轉換的媒介。第三部分的鈮酸鋰晶體，具有不同長度但相同週期 (65 um) 的極化反轉結構。於第三部分兆赫波的產生為兩階段的實驗，第一階段為量測一維兆赫波波導晶體其不同結構長度與兆赫波強度之關係。於實驗中，兆赫波強度隨晶體長度呈正相關成長，直至晶體長度超過 11 mm 後呈現飽和。第二階段將第一階段中的一維兆赫波波導晶體改為二維兆赫波波導晶體，目的在於驗證二維兆赫波波導對於兆赫波是否有較佳的收集效果，可得到較強的兆赫波產生強度。在實驗中發現，與相同長度的一維兆赫波波導晶體作比較，兆赫波於二維兆赫波波導晶體中訊號增強約 1.67 倍。

吾等為探討實驗與理論分析間之差異，使用存在激發光消耗損耗 (pumping depletion loss) 與無激發光消耗損耗兩種理論模型，並配合分開衰減 (walk-off decay) 對等效激發光強度下降之影響，
模擬兆赫波訊號對晶體長度的關係。於存在激發光消耗損耗之理論模型中，使用非線性光差頻產生之三波耦合微分方程式，得到與實驗值相似的曲線，但曲線匹配下之參數不符合理論值。於無激發光消耗損耗之理論模型中，由三波耦合微分方程式簡化之兆赫波產生增益公式，使用合乎理論值之參數得到與實驗值趨勢近似之曲線，由於在激發光消耗損耗實驗尚未觀測到明顯的結果，且兩種理論模型之模擬結果皆可得到與實驗值近似之曲線，故由模擬方式並無法對系統中是否存在激發光消耗損耗有一個肯定的結論，期望未來可由實驗觀察了解並釐清此問題。

[1]
David.N.Nikogosyan,
Nonlinear Optical Crystals:A Complete Survey (Springer, New York, 2005)

[2]
C.Lee,
“Picosecond optoelectronic switching in GaAs”,
Appl. Phys. Lett. 30, 84 (1977)

[3]
F.Capasso, R.Colombelli, R.Paiella, C.Gmachl, A.Tredicucci, D.L.Sivco, A.Y.Cho,
“Far-infrared and ultra-high-speed quantum-cascade lasers”,
Opt. Photon. News, vol.12, no.5, p.40-46 (2001)

[4]
B.Ferguson, X.C.Zhang,
``Materials for terahertz science and technology,"
nature materials 1, 26-33 (2002)

[5]
L.Lefort, K.Puech, G.W.Ross, Y.P.Svirko, and D.C.Hanna,
``Optical parametric oscillation out to 6.3 um in periodically poled lithium niobate under strong idler absorption,”
Appl. Phy. Lett. 73, 1610–1612 (1998)

[6]
D.Grischkowsky, S.Keiding, M.van Exter, and C.Fattinger,
``Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,”
J. Opt. Soc. Am. B 7, 2006-2015 (1990)

[7]
M.Schall, H.Helm, and S.R.Keiding,
``Far Infrared Properties of Electro-Optic Crystals Measured by THz Time-Domain Spectroscopy,"
Int. J. Inf. Mill. Waves 20, 595-604 (1999)

[8]
J.Hebling, A.G.Stepanov, G.Almasi, B.Bartal, J.Kuhl,
``Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,”
Appl. Phys. B 78, 593–599 (2004)

[9]
S.S.Sussman,,
``Tunable light scattering from transverse optical modes in lithium niobate,”
Microwave Lab. Report No.1851, (Stanford University, Stanford, Calif., 1970).

[10]
D.H.Jundt,
``Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,"
Opt. Lett. 22, 1553-1555 (1997)

[11]
Robert W.Boyd,
Nonlinear Optics, 2nd ed. (Academic Press, INC., London, 2003), p.48.

[12]
M.Born and K.Huang,
Dynamic Theory of Crystal Lattice (Clarendon Press, Oxford, 1954)

[13]
A.C.Chiang, T.D.Wang, Y.Y.Lin, S.T.Lin, H.H.Lee, Y.C.Huang, and Y.H.Chen,
``Enhanced Terahertz-wave Parametric Generation and Oscillation in Lithium-Niobate Waveguides at Terahertz Frequencies,”
Opt. Lett 30, 3392-3394 (2005)

[14]
T.D.Wang, S.T.Lin, Y.Y.Lin, A.C.Chiang, and Y.C.Huang,
``Forward and backward Terahertz-wave difference-frequency generations from periodically poled lithium niobate,”
Opt. Express 16, 6471- (2008)

[15]
John Strong, and Paul W.Lawrence, Jr,
``Bolometer Theory,"
Applied Optics, vol. 7, no. 1, pp. 49-52, 1968.

[16]
A.Bonvalet, M.Joffre, J.Martin, A.Migus,
``Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,”
Appl. Phys. Lett. 67, 2907-2909 (1995)

[17]
J.A.Armstrong, N.Bloembergen, J.Ducuing, P.S.Pershan,
``Interactions between Light Waves in a Nonlinear Dielectric,”
Phys. Rev. 127, 1918 (1962)

[18]
M.M.Fejer, G.A.Magel, D.H.Jundt, R.L.Byer,
``Quasi phase matched second harmonic generation -- tuning and tolerances,”
IEEE J. Quan. Electron. 28, 2631-2654 (1992)

[19]
Y.S.Lee, T.Meade, V.Perlin, H.Winful, T.B.Norris,
``Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,”
Appl. Phys. Lett. 76, 2505 (2000)

[20]
Y.S.Lee, T.Meade, T.B.Norris, A.Galvanauskas,
``Tunable narrow-band terahertz generation from periodically poled lithium niobate,”
Appl. Phys. Lett. 78, 3583 (2001)

[21]
F.Y.Lin, H.L.Lu, T.D.Wang, Y.C.Huang,
``High-efficiency THz generation in optically contacted GaAs with near Brewster angle pumping,"
Opt. Express, vol. 15, no. 21, 13654-13659 (2007)

[22]
Huei-Lung Lu,
``High-efficiency THz generation in optically-contacted GaAs with near-Brewster angle pumping,"
國立清華大學光電所碩士論文 (2007)

[23]
D.M.Mittleman, R.H.~acobson, M.C.Nuss,
``T-ray imaging,”
IEEE J. Sel. Top. Quatum Eletron. 2, 689-692 (1996)

[24]
M.Walther, B.Fischer, M.Schall, H.Helm, P.Uhd Jepsen,
``Far-infrared vibrational spectra of all-trans, 9-cis and 13-cis retinal measured by THz time-domain spectroscopy,”
Chem. Phys. Lett. 332, 389-395 (2000)

[25]
A.G.Markelz, A.Roitberg, E.J.Heilweil,
``Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,”
Chem. Phys. Lett. 320, 42-48 (2000)

[26]
J.F.Federici, B.Schukin, F.Huang, D.Gray, R.Barat, F.Oliveira, D.Zimdars,
``THz imaging and sensing for security applications—explosives, weapons and drugs,”
Semicond.Sci.Technol 20, s266-s280 (2005)

[27]
D.Woolard,
``Terahertz electronic research for defense: Novel technology and science,”
11th Int. Space Terahertz Tech. Symp., Ann Arbor, MI, May 1-3, pp.22-38 (2000)

[28]
E.R.Brown,
``All-solid-state photomixing THz transmitter,”
Univ. California at LOS Angeles, Los Angeles, CA, DARPA proposal to BAA 99-15, Feb. (1999)

[29]
P.H.Siegel,
``Terahertz technology,”
IEEE Trans. Microwave Theory Technol. 50, 910-928 (2002)

[30]
T.D.Wang,
``High Efficiency THz-wave Generation from Nonlinear Frequency Mixing,”
國立清華大學光電所博士論文 (2009)

[31]
Y.C.Huang,
``Principles of Nonlinear Optics course reader,”
國立清華大學光電所非線性光學上課講義