Theoretical study of influence of laser pulse chirp on terahertz emission characteristics of gas induced by two-color laser field

Li Han-Nan; Peng Yan

doi:10.7498/aps.73.20231806

Abstract

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.

Keywords:

Authors and contacts

Terahertz Spectral and Imaging Technology Collaborative Innovation Center, Engineering Research Center of Optical Instruments and Systems of the Ministry of Education, Shanghai Key Laboratory of Modern Optical System, Terahertz Technology Innovation Research Institute, University of Shanghai for Science and Technology, Shanghai 200093, China

Corresponding author: Peng Yan, py@usst.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61988102, 62335012).

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References

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[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
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[11]	Wang K, Mittleman D M 2004 Nature 432 376 Google Scholar
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[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 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 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 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
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[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
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[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
[48]	Corkum P B 1993 Phys. Rev. Lett. 71 1994 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
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Cited By

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

Figure 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).

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 5 (a)无啁啾情况与基频波存在正啁啾情况下0 fs时刻附近电场; (b)两种情况下各自产生的电流

Figure 5. (a) Electric field near the 0 fs time when there is no chirp and the FW has a positive chirp; (b) the current generated in each case.

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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

Figure 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.

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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

Figure 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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图 8 太赫兹能量与啁啾量的关系, 图右侧为基频波中存在正啁啾情况, 左侧为基频波中存在负啁啾情况

Figure 8. Relationship between terahertz energy and chirp. On the right is a positive chirp in the FW, and on the left is a negative chirp in the FW.

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map

[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 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 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 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 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 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 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
[48]	Corkum P B 1993 Phys. Rev. Lett. 71 1994 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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Vol. 73, Issue 6 - 2024-03-20

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