高功率、高度同調的兆赫波可應用在厚實樣品影像學、環境遙測、與國家安全檢查等領域。現今常見的兆赫波(頻率1-3 THz)多是以非線性晶體激發光參量非線性效應所產生，多數的非線性晶體在兆赫波波段上有很強的吸收峰值，而本研究的目標在於了解非線性晶體的特性與研究所需的突破點，發展光參量共振腔克服兆赫波吸收，並且延伸產生的兆赫波頻譜從0.3至5.5 THz。
我們發現在光參量產生過程中，雷射輸出脈衝寬度可從560皮秒縮減至80皮秒（1皮秒　=　1兆分之一秒），此外，輸出脈衝的時間與頻譜具有特定的關連性，可以協助我們計算兆赫波的峰值功率或是用於產生超短脈衝。
我們製作了一個可共振兆赫波的非共線參量震盪器。兆赫波在鈮酸鈮晶體中的全反射，使得這個離軸震盪器得以同時產生並且共振idler wave，我們也產生了超寬頻的signal wave頻率梳，並推測出idler wave的頻率梳是介於0.3-5.5 THz。
在以前的報告中，自鈮酸鈮晶體產生的拉曼散射(SPS)的峰值增益在1.8 THz，而我們使用高功率短脈衝雷射(560皮秒)的情況下，實驗驗證超過1.8-THz的另一個峰值出現在4.6 THz。在雷射強度2.1 GW/cm2入射到長2公分的離軸兆赫波共振腔(OTPO)實驗，我們在入射雷射往外4.8度角探測到SPS signal wave光束，可以對應到4.6 THz的兆赫波產生。這部分的關鍵是OTPO的發明，克服了材料吸收並讓產生的兆赫波延著入射光束震盪，讓4.6 THz兆赫波得到SPS增益並且在光混頻過程中有最小的walk-off。

Widely-tunable and high-power coherent THz radiations are important for studies such as thick-sample imaging, remote sensing, and security checking. Coherent THz radiations generated from nonlinear crystal are typically between 1-3 THz, and are generated by a parametric process already well developed. Most nonlinear optical materials used useful for the parametric process have strong absorption in THz region. The primary contributions of this thesis was to overcome the nature of this difficulty, to design a generic THz oscillator and to improve the frequency tuning range of the THz parametric oscillator.
In order to understand the pulse width in a THz parametric process, we demonstrated pedestal-free laser pulse shortening from 560 to 80 ps through optical parametric generation. We discovered the spectral-temporal correlation in an optical parametric process and employed it to demonstrate the laser pulse shortening.
Based on a non-collinear phase matching scheme, we invented a highly efficient parametric oscillator, called the off-axis THz parametric oscillator (OTPO), which, for the first time, resonates a THz wave in a nonlinear crystal. The OTPO resonates the generated idler wave at THz frequencies due to THz-wave total internal reflections in a pump-filled lithium niobate crystal. Also, we generated an ultra-broad signal frequency comb and inferred a corresponding comb between 0.3-5.5 THz in the idler spectrum.
LN is known to have a stand-alone SPS gain peak at 2 THz and is mostly considered for generating radiation below 2.5 THz. We report another peak at 4.6 THz that overtakes that at 2-THz at high pump intensity. With 2.1-GW/cm2 pumping intensity in a 20-mm off-axis oscillator, the 4-THz SPS signal wave can emerges at a 4.8o angle from the axis of pump wave. The primary contribution to this discovery is the invention of the off-axis oscillator, in which the generated THz wave extract the SPS gain at 4 THz with minimized diffraction loss.
These researches have been polished in three refereed articles by two well respected journals, and the OTPO scheme has been awared to a US patent.

CHAPTER 1 INTRODUCTION 1
1.1 MOTIVATION 1
1.2 EXISTING RADIATION TECHNOLOGIES 1
1.3 OFF-AXIS TERAHERTZ PARAMETRIC OSCILLATOR 2
1.4 NOVELTY OF THIS STUDY 3
REFERENCE 5
CHAPTER 2 PARAMETRIC PROCESS 7
2.1 INTRODUCTION 7
2.2 STIMULATED POLARTION SCATTERING 8
2.3 PARAMETRIC PULSE SHORTENING 13
2.4 CONCLUSION 22
REFERENCE 24
CHAPTER 3 OFF-AXIS TERAHERTZ PARAMETRIC OSCILLATOR 26
3.1 INTRODUCTION 26
3.2 EXPERIMENTAL SETUP 28
3.3 RESULT AND DISCUSSION 29
3.4 CONCLUSION 34
REFERENCE 36
CHAPTER 4 THZ PARAMETRIC AMPLIFIER 39
4.1 INTRODUCTION 39
4.2 SEED LASER: EXTENDED CAVITY DIODE LASER 40
4.3 EXPERIMENTAL SETUP 40
4.4 RESULT AND DISCUSSION 42
4.5 CONCLUSION 47
REFERENCE 49
CHAPTER 5 DISCOVERY OF HIGH-GAIN STIMULATED POLARITON SCATTERING NEAR 4 THZ FROM LITHIUM NIOBATE 51
5.1 INTRODUCTION 51
5.2 EXPERIMENTAL SETUP 52
5.3 RESULT AND DISCUSSION 54
5.4 CONCLUSION 61
REFERENCE 62
CHAPTER 6 CONCLUSION 65

CH1
1. Tonouchi, M. “Cutting-edge terahertz technology” Nat. Photon. 1, 97–105 (2007).
2. B. Ferguson and X.-C. Zhang “Materials for terahertz science and technology” Nature Materials 1, 26–33 (2002).
3. Lee, Y. -S. Principles of Terahertz science and technology 108 (Springer, 2008).
4. Hafez, H. A. et al. “Intense terahertz radiation and their applications” Journal of Optics 18, 093004 (2016).
5. Vijayraghavan, K. et al. “Broadly tunable terahertz generation in mid-infrared quantum cascade lasers” Nature Commun. 4, 2021 (2013).
6. Ko¨hler, R. et al. “Terahertz semiconductor heterostructure laser” Nat. Photon. 417, 156–159 (2002).
7. Williams, B. S. “Terahertz quantum-cascade lasers” Nat. Photon. 1, 517–525 (2007).
8. Belkin, M. A. et al. “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K” Opt. Express 16, 3242–3248 (2008).
9. Burghoff, D. et al. “Terahertz laser frequency combs” Nat. Photon. 8, 462–467 (2014).
10. Rösch, M., Scalari, G., Beck, M. and Faist, J. “Octave-spanning semiconductor laser” Nat. Photon. 9, 42–47 (2015).
11. S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide,“Ultrabright continuously tunable terahertz-wave generation at room temperature”, Sci. Rep. 4, 5045 (2014).
12. S. Fathololoumi, et al., “Terahertz quantum cascade lasers operating up to ∼ 200 K with optimized oscillator strength and improved injection tunneling,” Optics Express 20, 3866 (2012).
13. G. N. Kulipanov, et al., “Research highlights from the novosibirsk 400 W average power THz FEL," Terahertz Science and Technology 1, 107 (2008).
14. M. Shalaby, and C. P. Hauri, "Demonstration of a low-frequency three-dimensional terahertz bullet with extreme brightness," Nat. Commun. 6, 5976 (2015).
15. H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, "Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3," Appl. Phys. Lett. 98, 091106 (2011).
16. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

CH2
1. Sussman, S. S. (1970). Tunable light scattering from transverse optical modes in lithium niobate (No. SU-MLR-1851). STANFORD UNIV CA MICROWAVE LAB.
2. Schwarz UT, Maier M. "Frequency dependence of phonon-polariton damping in lithium niobate" Phys Rev B, 53, 5074 (1996).
3. Schwarz UT, Maier M. "Damping mechanisms of phonon polaritons, exploited by stimulated Raman gain measurements", Phys Rev B, 58, 766 (1998).
4. Takida, Y. et al. "Terahertz-wave parametric gain of stimulated polariton scattering" Phys. Rev. A, 93, 043836 (2016).
5. T.D. Wang, Y. C. Huang, M. Y. Chuang, Y. H. Lin, C. H. Lee, Y. Y. Lin, F. Y. Lin, and G. Kitaeva, “Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain,” Opt. Express 21, 2452 (2013).
6. X. Wu, C. Zhou, W. R. Huang, F. Ahr, and F. Kärtner ”Temperature dependent refractive index and absorption coefficient of congruent lithium niobate crystals in the terahertz range”, Opt. Express 23, 29729 (2015).
7. F. Seifert, V. Petrov, and F. Noack,” Sub-100-fs optical parametric generator pumped by a high-repetition-rate Ti:sapphire regenerative amplifier system” Opt. Lett. 19, 837 (1994).
8. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, E. W. Van Stryland, and H. Vanherzeele,” Self-focusing and self-defocusing by cascaded second-order effects in KTP” Opt. Lett. 17, 28 (1992).
9. A. Fendt, W. kranitzky, A. Laubereau and W. Kaiser,” Efficient generation of tunable subpicosecond pulses in the infrared” Opt. Commun. 28, 142 (1979).
10. W. Kranitzky, K. Ding, A. Seilmeier, W. Kaiser,” Parametric generation of shortened, narrow-band picosecond pulses using a Yag-pump laser” Opt. Commun. 34, 483 (1980).
11. A. C. Chiang, T. D. Wang, Y. Y. Lin, C. W. Liu, Y. H. Chen, B. C. Wong, Y. C. Huang, J. T. Shy, Y. P. Lan, Y. F. Chen, and P. H. Tsao,” Pulsed Optical Parametric Generation, Amplification, and Oscillation in Monolithic Periodically Poled
12. Lithium Niobate Crystals” IEEE J. Quantum Electron. 40, 791 (2004).
13. Y. F. Kong, W. L. Zhang, X. J. Chen, J. J. Xu and G. Y. Zhang,” OH absorption spectra of pure lithium niobate crystals” J. Phys.: Condens. Matter 11, 2139 (1999).
14. 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 (2005).

CH3
1.M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett. 26, 418 (1975).
2. Masayoshi Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97 (2007).
3. S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4, 5045 (2014).
4. A. J. Lee and H. M. Pask, “Continuous wave, frequency-tunable terahertz laser radiation generated via stimulated polariton scattering,” Opt. Lett. 39, 442 (2014).
5. B. Sun, X. Bai, J. Liu, and J. Yao, “Investigation of a terahertz-wave parametric oscillator using LiTaO3 with the pump-wavelength tuning method,” Laser Physics, 24, 035402 (2014).
6. W. Wang, Z. Cong, X. Chen, X. Zhang, Z. Qin, G. Tang, N. Li, C. Wang, and Q. Lu, “Terahertz parametric oscillator based on KTiOPO4 crystal,” Opt. Lett. 39, 3706 (2014).
7. J. Zang, Z. Cong, X. Chen, X. Zhang, Z. Qin, Z. Liu, J. Lu, D. Wu, Q. Fu, S. Jiang, and S. Zhang, “Tunable KTA Stokes laser based on stimulated polariton scattering and its intracavity frequency doubling,” Opt. Express 24, 7558 (2016).
8. M. H. Wu, Y. C. Chiu, T. D. Wang, G. Zhao, A. Zukauskas, F. Laurell, and Y. C. Huang, “Terahertz parametric generation and amplification from potassium titanyl phosphate in comparison with lithium niobate and lithium tantalate,” Opt. Express 24, 25964 (2016).
9. J. M. Yarborough, S. S. Sussman, H. E. Purhoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15, 102 (1969).
10. 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).
11. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 24, 24577 (2011).
12. T.D. Wang, Y. C. Huang, M. Y. Chuang, Y. H. Lin, C. H. Lee, Y. Y. Lin, F. Y. Lin, and G. Kitaeva, “Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain,” Opt. Express 21, 2452 (2013).
13. H. Jang, G. Strömqvist, V. Pasiskevicius, and C. Canalias, “Control of forward stimulated polariton scattering in periodically-poled KTP crystals,” Opt. Express 21, 27277 (2013).
14. S. Tripathi, Y. Taira, S. Hayashi, K. Nawata, K. Murate, H. Minamide, and K. Kawase, “Terahertz wave parametric amplifier,” Opt. Express 39, 1649 (2014).
15. 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 (2005).
16. K. Kawase, J. Shikata, K. Imai, and H. Ito, “Transform-limited, narrow-linewidth, terahertz-wave parametric generator,”Appl. Phys. Lett. 78, 2819 (2001).
17. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
18. L. Pálfalvi, J. A. Fülöp, and J. Hebling, “Absorption-reduced waveguide structure for efficient terahertz generation,” Appl. Phys. Lett. 107, 233507 (2015).
19. U. T. Schwarz, and M. Maier, “Damping mechanisms of phonon polaritons, exploited by stimulated Raman gain measurements,” Phys. Rev. B 58, 766 (1998).
20. K. Ravi, M. Hemmer, G. Cirmi, F. Reichert, D. N. Schimpf, O. D. Mücke, and F. X. Kärtner, “Cascaded parametric amplification for highly efficient terahertz generation,” Opt. Lett. 41, 3806 (2016).
21. D. Burghoff, T. Y. Kao, N. Han, C. W. Chan, X. Cai, Y. Yang, D. J. Hayton, J. R. Gao, J. L. Reno and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8, 462 (2014).
22. K.Ravi, D.N.Schimpf, and F.X. Kärtner, “Pulse sequences for efficient multi-cycle terahertz generation in periodically poled lithium niobate,” Opt.Express 24, 25582 (2016).
23. M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9, 42 (2015).
24. J. Shikata, M. Sato, T. Taniuchi, H. Ito, and K. Kawase, “Enhancement of terahertz-wave output from LiNbO3 optical parametric oscillators by cryogenic cooling,” Opt. Lett. 24, 202 (1999).
25. P. Liu, W. Shi, D. Xu, X. Zhang, J. Yao, R. A. Norwood, and N. Peyghambarian, “High-power high-brightness Terahertz source based on nonlinear optical crystal fiber,” IEEE Journal of Selected Topics in Quantum Electronics 22, 8500105 (2016).

CH4
1. Masayoshi Tonouchi. Cutting-edge terahertz technology. Nature Photonics 1, 97–105 (2007).
2. Shen, Y.-C. et al. Detection and identification of explosives using terahertz pulsed spectroscopic imaging. Appl. Phys. Lett. 86, 241116 (2005).
3. Schmuttenmaer C. A. Exploring dynamics in the far-infrared with terahertz spectroscopy. Chem. Rev. 104, 1759–1780 (2004).
4. Kodo Kawase, Yuichi Ogawa and Yuuki Watanabe. Non-destructive terahertz imaging of illicit drugs using spectral fingerprints. Opt. Express. 11, 2549–2554 (2003).
5. Hayashi, S. et al. High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited]. Opt. Express. 20, 2881–2886 (2012).
6. Chiang, A. C. et al. Enhanced terahertz-wave parametric generation and oscillation in lithium niobate waveguides at terahertz frequencies. Opt. Lett. 30, 3392–3394 (2005).
7. Hebling, J. et al. Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts. Appl. Phys. B 78, 593–599 (2004)
8. Hebling, J. et al. Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities. J. Opt. Soc. Am. B, 25, B6–B19 (2008)
9. Hirori, H. et al. Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3. Appl. Phys. Lett. 98, 091106 (2011).
10. Huang, Y.-C. et al. Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide. Opt. Express 19, 24577–24582 (2011).
11. Wang, T.-D. et al. Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain. Opt. Express 19, 2452–2462 (2013).
12. Minamide, Hiroaki. et al. Kilowatt-peak Terahertz-wave generation and Sub-femtojoule Terahertz-wave pulse detection based on nonlinear optical wavelength-conversion at room temperature. J. Infrared Millim Terahertz Waves 35, 25–37 (2014).
13. K. Kawase, J. Shikata, K. Imai, and H. Ito, “Transform-limited, narrow-linewidth, terahertz-wave parametric generator,”Appl. Phys. Lett. 78, 2819 (2001).
14. S. Hayashi, H. Minamide, T. Ikari, Y. Ogawa, J. -i. Shikata, H. Ito, C. Otani, and K. Kawase,” Output power enhancement of a palmtop terahertz-wave parametric generator,” Appl. Optics, 46, 117 (2007).

CH5
1. M. Tonouchi, "Cutting-edge terahertz technology," Nat. Photonics 1, 97-105 (2007).
2. B. Ferguson and X. C. Zhang, "Materials for terahertz science and technology," Nat. Materials 1, 26-33 (2002).
3. H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki, "Intense terahertz radiation and their applications," Journal of Optics 18, 093004 (2016).
4. D. H. Auston, K. P. Cheung, and P. R. Smith, "Picosecond photoconducting Hertzian dipoles," Appl. Phys. Lett. 45, 284–286 (1984).
5. M. Shalaby, and C. P. Hauri, "Demonstration of a low-frequency three-dimensional terahertz bullet with extreme brightness," Nat. Commun. 6, 5976 (2015).
6. H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, "Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3," Appl. Phys. Lett. 98, 091106 (2011).
7. F. Blanchard, G. Sharma, X. Ropagnol, L. Razzari, R. Morandotti, and T. Ozaki, "Improved terahertz two-color plasma sources pumped by high intensity laser beam," Optics Express 17, 6044-6052 (2009).
8. M. Rösch, G. Scalari, M. Beck, and J. Faist, "Octave-spanning semiconductor laser," Nat. Photon. 9, 42–47 (2015).
9. G. N. Kulipanov, N. G. Gavrilov, B. A. Knyazev, E. I. Kolobanov, V. V. Kotenkov, V. V. Kubarev, A. N. Matveenko, L. E. Medvedev, S. V. Miginsky, L. A. Mironenko, V. K. Ovchar, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Serednyakov, O. A. Shevchenko, A. N. Skrinsky, V. G. Tcheskidov, N. A. Vinokurov, M. A. Demyanenko, D. G.Esaev, E. V. Naumova, V. Y. Prinz, V. P. Fedin, A. M.Gonchar, S. E. Peltek, A. K. Petrov, L. A. Merzhievsky, and V. S. Cherkassky, "Research highlights from the novosibirsk 400 W average power THz FEL," Terahertz Science and Technology 1, 107–125 (2008).
10. M. A. Piestrup, R. N. Fleming, and R. H. Pantell, "Continuously tunable submillimeter wave source," Appl. Phys. Lett. 26, 418–421 (1975).
11. W. Wang, Z. Cong, X. Chen, X. Zhang, Z. Qin, G. Tang, N. Li, C. Wang, and Q. Lu, "Terahertz parametric oscillator based on KTiOPO4 crystal," Opt. Lett. 39, 3706–3709 (2014).
12. M. H. Wu, Y. C. Chiu, T. D. Wang, G. Zhao, A. Zukauskas, F. Laurell, and Y. C. Huang, "Terahertz parametric generation and amplification from potassium titanyl phosphate in comparison with lithium niobate and lithium tantalite, " Opt. Express 24, 25964–25973 (2016).
13. W. Wang, Z. Cong, Z. Liu, X. Zhang, Z. Qin, G. Tang, N. Li, Y, Zhang, and Q. Lu, "THz-wave generation via stimulated polariton scattering in KTiOAsO4 crystal, " Opt. Express 22, 17092–17098 (2014).
14. J. Zang, Z. Cong, X. Chen, X. Zhang, Z. Qin, Z. Liu, J. Lu, D. Wu, Q. Fu, S. Jiang, and S. Zhang, "Tunable KTA Stokes laser based on stimulated polariton scattering and its intracavity frequency doubling," Opt. Express 24, 7558–7565 (2016).
15. Tiago A. Ortega, Helen M. Pask, David J. Spence, and Andrew J. Lee, " Stimulated polariton scattering in an intracavity RbTiOPO4 crystal generating frequency-tunable THz output," Opt. Express 24, 10254–10264 (2016).
16. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).
17. T. D. Wang, Y. C. Huang, M. Y. Chuang, Y. H. Lin, C. H Lee, Y. Y Lin, F. Y. Lin, and G. Kh. Kitaeva, "Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain," Opt. Express 21, 2452–2462 (2013).
18. S. S. Sussman, Tunable Light Scattering from Transverse Optical Modes in Lithium Niobate (Stanford Univ., 1970).
19. U. T. Schwarz, and M. Maier, "Frequency dependence of phonon-polariton damping in lithium niobate," Phys. Rev. B 53, 5074–5077 (1996).
20. U. T. Schwarz, and M. Maier, "Damping mechanisms of phonon polaritons, exploited by stimulated Raman gain measurements," Phys. Rev. B 58, 766–775 (1998).
21. Y. Takida, J. Shikata, K. Nawata, Y. Tokizane, Z. Han, M. Koyama, T. Notake, S. Hayashi, and H, Minamide, "Terahertz-wave parametric gain of stimulated polariton scattering," Phys. Rev. A 93, 043836 (2016).
22. Y. C. Huang, T. D. Wang, Y. H. Lin. C. H. Lee, M. Y. Chuang, Y. Y. Lin and F. Y. Lin, "Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide," Opt. Express 19, 24577–24582 (2011)