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随着太赫兹波研究的深入, 研究者们对可调控太赫兹源的需求不断增加. 如何获取可调控的太赫兹波一直是太赫兹科学领域的研究热点和关键问题之一. 本文通过建立双色激光诱导气体电离光丝产生太赫兹波及其后续传播过程的三维理论模型, 详细研究了双色泵浦激光的啁啾参数对飞秒激光场辐射产生太赫兹波的影响. 研究结果表明, 在激光脉宽为飞秒量级时, 以40 fs的情况为例, 当啁啾参数在与激光脉宽处于相同的飞秒量级尺度上时, 其对太赫兹波的振幅与频谱都产生显著影响. 在双色飞秒激光场中, 基频波和倍频波的啁啾各自起到不同的作用: 基频波的啁啾主要影响太赫兹波的时域波形, 而倍频波的啁啾则决定了太赫兹辐射的振幅大小、中心频率与频谱宽度. 研究表明, 激光啁啾作为一种可控的参数, 对所辐射的太赫兹波属性具有多重调制效果, 且相关啁啾的作用规律随双色激光的初始相位也呈现规律性变化. 这些结果为研究太赫兹辐射的产生与调控提供了新的思路与依据.With the development of terahertz (THz) wave research, the demand for controllable THz sources is increasing. How to obtain the regulated THz waves has been one of the research hotspots and key problem in the field of THz science. There have been researches in which the resulting THz wave is modulated by changing the wavelength, relative phase, energy, or chirp of the laser produced by a two-color laser. In this work, we establish a three-dimensional theoretical model of THz wave generation and subsequent propagation induced by two-color laser. And we investigate the influence of chirp modulation of different laser on THz wave by chirp modulation of the fundamental wave (FW) and the second harmonic wave (SHW) of two-color laser, including THz wave amplitude, THz wave center frequency and spectrum width, and analyze the physical mechanism of related phenomena. At the same time, the effects of different orders of magnitudes of laser chirp parameters (femtosecond and picosecond) and initial phase of laser pulse on THz wave parameters are also studied. The results are shown below. 1) In the two-color laser, the chirp of FW mainly affects the shape of THz wave when the initial phase is unchanged. The chirp modulation of SHW can cause the amplitude of THz wave to change significantly, and affect the center frequency and spectrum width of THz waves. 2) In the case of laser pulse width of femtosecond order, 40 fs is taken as an example. When the chirp parameter is of femtosecond magnitude, the chirp parameter has a great influence on the THz wave generation efficiency of two-color laser filament. At the picosecond magnitude, the chirp parameter has a weak effect on the THz wave energy and mainly affects the phase of the THz wave. 3) The initial phase of the two-color laser can aid in chirp modulation of THz wave to optimize the energy generated. 4) The initial phase of two-color laser can assist in the process of chirped laser modulation of terahertz waves to optimize the energy generated. Our research shows that the chirp modulation, as a controllable parameter, has multiple regulation effect on the properties of radiated THz waves. The related research results provide a new idea and basis for studying the generation and regulation of THz waves.
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Keywords:
- terahertz radiation /
- two-color laser pulses /
- chirp /
- modulation
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图 1 不同啁啾情况下的(a), (d), (g)双色激光合成电场与电子密度、(b), (e), (h)太赫兹波形以及(c), (f), (i)太赫兹频谱 (a)—(c)无啁啾情况; (d)—(f)仅基频波中存在正啁啾的情况; (g)—(i)仅倍频波中存在正啁啾的情况下
Fig. 1. (a), (d), (g) Two-color laser synthetic electric field and electron density, (b), (e), (h) terahertz waveform and (c), (f), (i) terahertz spectrum of two-color laser with different chirps: (a)–(c) There is no chirp; (d)–(f) there is a positive chirp in the fundamental wave (FW); (g)–(i) there is a positive chirp in the second harmonic wave (SHW).
图 2 负啁啾情况下的(a), (d)双色激光合成电场与电子密度、(b), (e)太赫兹波形以及(c), (f)太赫兹频谱 (a)—(c)在基频波中存在负啁啾的情况; (d)—(f)在倍频波中存在负啁啾的情况
Fig. 2. (a), (d) Synthesized electric field and electron density, (b), (e) terahertz waveform and (c), (f) terahertz spectrum of two-color laser with negative chirps: (a)–(c) There is a negative chirp in the FW; (d)–(f) there is a negative chirp in the SHW.
图 3 双色激光中同时存在啁啾情况下的(a), (d)双色激光合成电场与电子密度、(b), (e)太赫兹波形以及(c), (f)太赫兹频谱 (a)—(c)同时存在正啁啾的情况; (d)—(f)同时存在负啁啾的情况
Fig. 3. (a), (d) Two-color laser synthetic electric field and electron density, (b), (e) terahertz waveform and (c), (f) terahertz spectrum of two-color laser with chirp exist simultaneously in the case of chirp in two-color laser at the same time: (a)—(c) There are positive chirps in two-color laser; (d)—(f) there are negative chirps in two-color laser.
图 4 双色激光中存在相反啁啾情况下的(a), (d)双色激光合成电场与电子密度、(b), (e)太赫兹波形以及(c), (f)太赫兹频谱 (a)—(c)在基频波中存在正啁啾, 倍频波中存在负啁啾的情况; (d)—(f)在基频波中存在负啁啾, 倍频波中存在正啁啾的情况
Fig. 4. (a), (d) Two-color laser synthetic electric field and electron density, (b), (e) terahertz waveform and (c), (f) terahertz spectrum of two-color laser with opposite chirp: (a)–(c) There is positive chirp in FW and negative chirp in SHW; (d)–(f) there is negative chirp in FW and positive chirp in SHW.
图 6 (a)不同初始相位和啁啾调制情况下太赫兹能量的变化; 倍频波中存在正啁啾情况下, 太赫兹能量最大值时(初始相位0.4π)的(b)太赫兹时域图和(c)太赫兹频域图; 双色激光中同时存在正啁啾情况下, 太赫兹能量最大值时(初始相位0.6π)的(d)太赫兹时域图和(e)太赫兹频域图
Fig. 6. (a) Variation in THz energy under different initial phases and chirp modulation; (b) terahertz time domain diagram and (c) terahertz frequency domain diagram for the maximum terahertz energy with positive chirp in SHW (initial phase 0.4π); (d) terahertz time domain diagram and (e) terahertz frequency domain diagram for the maximum terahertz energy (initial phase 0.6π) with positive chirp in two-color laser.
图 7 (a)当啁啾参数τ为ps量级即τ = 1 ps时, 不同初始相位和啁啾调制情况下太赫兹能量的变化; 倍频波中存在正啁啾情况下, 太赫兹能量最大值时(初始相位0.4π)的(b)太赫兹时域图和(c)太赫兹频域图; 双色光中同时存在正啁啾情况下, 太赫兹能量最大值时(初始相位0.7π)的(d)太赫兹时域图和(e)太赫兹频域图
Fig. 7. (a) When the chirped parameter τ is of ps magnitude, that is, τ = 1 ps, the variation in THz energy under different initial phases and chirp modulation. (b) Terahertz time domain diagram and (c) terahertz frequency domain diagram for the maximum terahertz energy with positive chirp in SHW (initial phase 0.4π). (d) Terahertz time domain diagram and (e) terahertz frequency domain diagram for the maximum terahertz energy (initial phase 0.7π) with positive chirp in two-color laser.
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[1] Pallavi D, Karim A, Cecil S J, Robert H G 2014 Terahertz, RF, Millimeter, and Submillimeter-Wave Technology and Applications VII San Francisco, California, United States, February 1–6, 2014 p89850K
[2] Bianco F, Miseikis V, Convertino D, Xu J H, Castellano F, Beere H E, Ritchie D A, Vitiello M S, Tredicucci A, Coletti C 2015 Opt. Express 23 11632
Google Scholar
[3] Adam A J L, Planken P C M, Meloni S, Dik J 2009 Opt. Express 17 3407
Google Scholar
[4] Han C, Chen Y 2018 IEEE. Commun. Mag. 56 96
Google Scholar
[5] Hu X, Zhou L, Wu X, Peng Y 2023 Adv. Photonics Nexus 2 044002
Google Scholar
[6] Peng Y, Huang J, Luo J, Yang Z, Wang L, Wu X, Zang X, Yu C, Gu M, Hu Q, Zhang X, Zhu Y, Zhuang S 2021 Photoni X 2 12
Google Scholar
[7] Peng Y, Shi C, Zhu Y, Gu M, Zhuang S 2020 PhotoniX 1 12
Google Scholar
[8] Hassani A, Dupuis A, Skorobogatiy M 2008 J. Opt. Soc. Am. B 25 1771
Google Scholar
[9] 王磊, 肖芮文, 葛士军, 沈志雄, 吕鹏, 胡伟, 陆延青 2019 物理学报 68 084205
Google Scholar
Wang L, Xiao R W, Ge S J, Shen Z X, Lü P, Hu W, Lu Y Q 2019 Acta Phys. Sin. 68 084205
Google Scholar
[10] Ferguson B, Zhang X C 2002 Nat. Mater. 1 26
Google Scholar
[11] Wang K, Mittleman D M 2004 Nature 432 376
Google Scholar
[12] Ding J, Maestrini A, Gatilova L, Cavanna A, Shi S, Wu W 2017 J. Infrared, Millimeter, Terahertz Waves 38 1331
Google Scholar
[13] Wang B, Shan S Y, Wu X J, Wang C, Pandey C, Nie T X, Zhao W S, Li Y T, Miao J G, Wang L 2019 Appl. Phys. Lett. 115 121104
Google Scholar
[14] Guo F, Pandey C, Wang C, Nie T, Wen L, Zhao W, Miao J G, Wang L, Wu X 2020 OSA Continuum 3 893
Google Scholar
[15] Siegel P H 2002 IEEE Trans. Microwave Theory Tech. 50 910
Google Scholar
[16] Mandehgar M, Yang Y, Grischkowsky D 2013 Opt. Lett. 38 3437
Google Scholar
[17] Möller L, Federici J, Sinyukov A, Xie C, Lim H C, Giles R C 2008 Opt. Lett. 33 393
Google Scholar
[18] Tonouchi M 2007 Nat. Photonics 1 97
Google Scholar
[19] 闫志巾, 施卫 2021 物理学报 70 248704
Google Scholar
Yan Z J, Shi W 2021 Acta Phys. Sin. 70 248704
Google Scholar
[20] 谭智勇, 陈镇, 韩英军, 张戎, 黎华, 郭旭光, 曹俊诚 2012 物理学报 61 098701
Google Scholar
Tan Z Y, Chen Z, Han Y J, Zhang R, Li H, Guo X G, Cao J C 2012 Acta Phys. Sin. 61 098701
Google Scholar
[21] 周康, 黎华, 万文坚, 李子平, 曹俊诚 2019 物理学报 68 109501
Google Scholar
Zhou K, Li H, Wan W J, Li Z P, Cao J C 2019 Acta Phys. Sin. 68 109501
Google Scholar
[22] 张开春, 刘盛纲 2007 物理学报 56 5258
Google Scholar
Zhang K C, Liu S G 2007 Acta Phys. Sin. 56 5258
Google Scholar
[23] 刘川川, 郝飞翔, 殷月伟, 李晓光 2020 物理学报 69 127301
Google Scholar
Liu C C, Hao F X, Yin Y W, Li X G 2020 Acta Phys. Sin. 69 127301
Google Scholar
[24] Hamster H, Sullivan A, Gordon S, White W, Falcone R W 1993 Phys. Rev. Lett. 71 2725
Google Scholar
[25] Hamster H, Sullivan A, Gordon S, Falcone R W 1994 Phys. Rev. E 49 671
Google Scholar
[26] Cook D J, Hochstrasser R M 2000 Opt. Lett. 25 1210
Google Scholar
[27] Kress M, Löffler T, Eden S, Thomson M, Roskos H G 2004 Opt. Lett. 29 1120
Google Scholar
[28] Zheng L, Zhao Q, Liu S Z, Xing X J 2012 Acta Phys. Sin. 61 245202
Google Scholar
[29] Zhu J F, Ma Z F, Sun W J, Ding F, He Q, Zhou L, Ma Y G 2014 Appl. Phys. Lett. 105 021102
Google Scholar
[30] Nouman M T, Kim H-W, Woo J M, Hwang J H, Kim D, Jang J H 2016 Sci. Rep. 6 26452
Google Scholar
[31] Liu M, Hwang H Y, Tao H, Strikwerda A C, Fan K, Keiser G R, Sternbach A J, West K G, Kittiwatanakul S, Lu J, Wolf S A, Omenetto F G, Zhang X, Nelson K A, Averitt R D 2012 Nature 487 345
Google Scholar
[32] Zhang S, Chen X, Liu K, Li H, Xu Y, Jiang X, Xu Y, Wang Q, Cao T, Tian Z 2022 PhotoniX 3 7
Google Scholar
[33] Liu K, Koulouklidis A, Parazoglou D, Stelios, Zhang X C 2016 The 8th International Symposium on Ultrafast Phenomena and Terahertz Waves Chongqing, China, October 10–12, 2016 pIM2B.1
[34] Zhao J, Guo L, Chu W, Zeng B, Gao H, Cheng Y, Liu W 2015 Opt. Lett. 40 3838
Google Scholar
[35] He B, Nan J, Li M, Yuan S, Zeng H 2017 Opt. Lett. 42 967
Google Scholar
[36] Li M, Yuan S, Zeng H 2017 IEEE J. Sel. Top. Quantum Electron 23 1
[37] Li J, Wilson C B, Cheng R, Lohmann M, Kavand M, Yuan W, Aldosary M, Agladze N, Wei P, Sherwin M S, Shi J 2020 Nature 578 70
Google Scholar
[38] Qiu H, Wang L, Shen Z, Kato K, Sarukura N, Yoshimura M, Hu W, Lu Y, Nakajima M 2018 Appl. Phys. Express 11 092101
Google Scholar
[39] Wang W M, Sheng Z M, Wu H C, Chen M, Li C, Zhang J, Mima K 2008 Opt. Express 16 16999
Google Scholar
[40] Clerici M, Peccianti M, Schmidt B E, Caspani L, Shalaby M, Giguère M, Lotti A, Couairon A, Légaré F, Ozaki T, Faccio D, Morandotti R 2013 Phys. Rev. Lett. 110 253901
Google Scholar
[41] Zhang Z W, Liu Z F, Wang S X, Lu C H, Fan Z G, Kostin V A, Liu Y 2023 Appl. Phys. Lett. 123 031108
Google Scholar
[42] Nguyen A, González de Alaiza Martínez P, Déchard J, Thiele I, Babushkin I, Skupin S, Bergé L 2017 Opt. Express 25 4720
Google Scholar
[43] Nguyen A, Martínez P G D A, Thiele I, Skupin S, Bergé L 2018 New J. Phys. 20 033026
Google Scholar
[44] Roskos H G, Thomson M D, Kreß M, Löffler T 2007 Laser Photonics Rev. 1 349
Google Scholar
[45] Wang S F, Xiao H C, Peng Y 2020 J. Opt. Soc. Am. B 37 3325
Google Scholar
[46] Xiao H C, Wang S F, Peng Y, Mittleman D M, Zhao J Y, Jin Z M, Zhu Y M, Zhuang S L 2021 Phys. Rev. A 104 013517
Google Scholar
[47] Li P C, Zhou X X, Wang G L, Zhao Z X 2009 Phys. Rev. A 80 053825
Google Scholar
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Google Scholar
[49] Rae S C, Burnett K 1992 Phys. Rev. A 46 1084
Google Scholar
[50] Andreeva V A, Kosareva O G, Panov N A, Shipilo D E, Solyankin P M, Esaulkov M N, González de Alaiza Martínez P, Shkurinov A P, Makarov V A, Bergé L, Chin S L 2016 Phys. Rev. Lett. 116 063902
Google Scholar
[51] Kim K Y, Taylor A J, Glownia J H, Rodriguez G 2008 Nat. Photonics 2 605
Google Scholar
[52] Constant E, Garzella D, Breger P, Mével E, Dorrer C, Le Blanc C, Salin F, Agostini P 1999 Phys. Rev. Lett. 82 1668
Google Scholar
[53] Wang T J, Chen Y, Marceau C, Théberge F, Châteauneuf M, Dubois J, Chin S L 2009 Appl. Phys. Lett. 95 131108
Google Scholar
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