-
With the rapid development of laser technology, it is possible to control optical waveforms by coherent superposition of electric fields with multiple color components, which creates conditions for generating the ultra-short isolated attosecond pulses (IAP). Based on the strong-field approximation theory, this work focuses on the IAP generated by the optimized multicolor field synthesized by two fundamental near-infrared lasers and their second harmonic fields. The results show that by applying frequency-doubled pulses to the near-infrared laser fields and optimizing the laser parameters, the emission properties of high order harmonics from single atom can be greatly improved, and the nearly attochirp-free harmonic emission can be realized within a certain energy range. As a result, shorter IAPs are obtained. With the consideration of the macroscopic propagation effect of gas, the IAP with a pulse width up to 40 as is generated under appropriate experimental conditions. Finally, the effects of gas pressure on the properties of the high-order harmonic and attosecond pulses are also investigated. This study provides useful theoretical guidance for generating ultra-short IAPs with near-infrared laser pulses in experiment.
-
Keywords:
- high-order harmonic generation /
- isolated attosecond pulse /
- optimization of laser waveform /
- macroscopic propagation
[1] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
Google Scholar
[2] Cousin S L, Silva F, Teichmann S, Hemmer M, Buades B, Biegert J 2014 Opt. Lett. 39 5383
Google Scholar
[3] Popmintchev T, Chen M C, Popmintchev D, Arpin P, Brown S, Alisauskas S, Kapteyn H C 2012 Science 336 1287
Google Scholar
[4] Takahashi E J, Kanai T, Ishikawa K L, Nabekawa Y, Midorikawa K 2008 Phys. Rev. Lett. 101 253901
Google Scholar
[5] Paul P M, Toma E S, Breger P 2001 Science 292 1689
Google Scholar
[6] Hentschel M, Kienberger R, Spielmann C 2001 Nature 414 509
Google Scholar
[7] Mashiko H, Gilbertson S, Li C, Khan S D, Shakya M M, Moon E, Chang Z 2008 Phys. Rev. Lett. 100 103906
Google Scholar
[8] Schafer K J, Yang B, DiMauro L F, Kulander K C 1993 Phys. Rev. Lett. 70 1599
Google Scholar
[9] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[10] Goulielmakis E, Schultze M, Hofstetter M, Yakovlev V S, Gagnon J, Uiberacker M, Aquita A L, Gullikson E M, Attwood D T, Kienberger R 2008 Science 320 1614
Google Scholar
[11] Ferrari F, Calegari F, Lucchini M, Vozzi C, Stagira S, Sansone G, Nisoli M 2010 Nat. Photonics 4 875
Google Scholar
[12] Vincenti H, Quéré F 2012 Phys. Rev. Lett. 108 113904
Google Scholar
[13] Kim K T, Zhang C, Ruchon T, Hergott J F, Auguste T, Villeneuve D M 2013 Nat. Photonics 7 651
Google Scholar
[14] 方少波, 魏志义 2019 光学学报 39 0126006
Google Scholar
Fang S B, Wei Z Y 2019 Acta Opt. Sin. 39 0126006
Google Scholar
[15] 杨煜东, 魏志义 2022 光子学报 51 0151109
Google Scholar
Yang Y D, Wei Z Y 2022 Acta Photonica Sinica 51 0151109
Google Scholar
[16] Corkum P B, Burnett N H, Ivanov M Y 1994 Opt. Lett. 19 1870
Google Scholar
[17] Li J, Ren X M, Yin Y C, Zhao K, Chew A, Cunningham E, Wang Y, Hu S Y, Wu Y, Chini M, Chang Z H 2017 Nat. Commun. 8 186
[18] Gaumnitz T, Jain A, Pertot Y, Huppert M, Jordan I, Ardana-Lamas F 2017 Opt. Express 25 27506
Google Scholar
[19] Wang X W, Wang L, Xiao F, Zhang D W, Lu Z H, Yuan J M, Zhao Z X 2020 Chin. Phys. Lett. 37 023201
Google Scholar
[20] 兰鹏飞, 陆培祥 2021 科学通报 66 847
Google Scholar
Lan P F, Lu P X 2021 Chin. Sci. Bull. 66 847
Google Scholar
[21] 袁浩, 曹华保, 王虎山, 刘鑫, 孙先伟, 王屹山, 赵卫, 付玉喜 2021 科学通报 66 878
Google Scholar
Yuan H, Cao H B, Wang H S, Liu X, Sun X W, Wang Y S, Zhao W, Fu Y X 2021 Chin. Sci. Bull. 66 878
Google Scholar
[22] Wang G L, Zhou L H, Zhao S F, Zhou X X 2016 Commun. Theor. Phys. 65 601
Google Scholar
[23] Jin C, Wang G L, Wei H, Le A T, Lin C D 2014 Nat. Commun. 5 4003
Google Scholar
[24] 曾志男, 李儒新, 谢新华, 徐至展 2004 53 4
Google Scholar
Zeng Z N, Li R X, Xie X H, Xu Z Z 2004 Acta Phys. Sin. 53 4
Google Scholar
[25] Zeng Z, Cheng Y, Song X, Li R, Xu Z 2007 Phys. Rev. Lett. 98 203901
Google Scholar
[26] Lan P, Lu P, Cao W, Li Y, Wang X 2007 Phys. Rev. A 76 011402
Google Scholar
[27] Sansone G, Poletto L, Nisoli M 2011 Nat. Photonics 5 655
Google Scholar
[28] Du H C, Wang X S, Hu B T 2011 Chin. Phys. B 20 084206
Google Scholar
[29] Ge X L, Xia C L, Liu X S 2012 Laser Phys. 22 1704
Google Scholar
[30] Qin Y F, Guo F M, Li S Y, Yang Y J, Chen G 2014 Chin. Phys. B 23 093205
Google Scholar
[31] 刘胜男, 陈高, 孟健 2012 61 14
Google Scholar
Liu S N, Chen G, Meng J 2012 Acta Phys. Sin. 61 14
Google Scholar
[32] Yang K, Du J X, Wang G L, Jiao Z H, Zhao S F, Zhou X X 2022 J. Opt. Soc. Am. B 39 3
Google Scholar
[33] Pan Y, Guo F, Jin C, Yang Y J, Ding D J 2019 Phys. Rev. A 99 033411
Google Scholar
[34] Wang J, Chen G, Li S Y, Ding D J, Chen J G, Guo F M, Yang Y J 2015 Phys. Rev. A 92 033848
Google Scholar
[35] Falcao-Filho E L, Lai C J, Hong K H, Gkortsas V M, Huang S W, Chen L J 2010 Appl. Phys. Lett. 97 061107
Google Scholar
[36] Hadrich S, Klenke A, Rothhardt J, Krebs M, Hoffmann A, Pronin O, Tunnermann A 2014 Nat. Photonics 8 779
Google Scholar
[37] Jin C, Le A T, Lin C D 2011 Phys. Rev. A 83 023411
Google Scholar
[38] Colosimo P, Doumy G, Blaga C I, Wheeler J, Dimauro L F 2008 Nat. Phys. 4 386
Google Scholar
[39] 王国利, 董小敏, 赵松峰, 周效信 2016 科学通报 61 1808
Google Scholar
Wang G L, Dong X M, Zhao S F, Zhou X X 2016 Chin. Sci. Bull. 61 1808
Google Scholar
[40] Hong K H, Lai C J, Gkortsas V M, Huang S W, Moses J, Granados E, Kartner F X 2012 Phys. Rev. A 86 043412
Google Scholar
[41] Chipperfield L E, Robinson J S, Tisch J W G, Marangos J P 2009 Phys. Rev. Lett. 102 063003
Google Scholar
[42] Balogh E, Bódi B, Tosa V, Goulielmakis E, Varjú K, Dombi P 2014 Phys. Rev. A 90 023855
Google Scholar
[43] Lewenstein M, Balcou P, Ivanov M Y, Huillier L, Corkum P B 1994 Phys. Rev. A 49 2117
Google Scholar
[44] Lewenstein M, Salieres P, Huillier A L 1995 Phys. Rev. A 52 4747
Google Scholar
[45] Ammosov M V, Delone N B, Krainov V P 1986 Sov. Phys. JETP 64 1191
Google Scholar
[46] Tosa V, Kim H, Kim I, Nam C H 2005 Phys. Rev. A 71 063807
Google Scholar
[47] Gaarde M B, Tate J L, Schafer K J 2008 J. Phys. B: At. Mol. Opt. Phys. 41 132001
Google Scholar
[48] He L, Yuan G, Wang K, Hua W, Yu C, Jin C 2019 Photonics Res. 7 12
Google Scholar
[49] Wirth A, Hassan M Th. Grguras I, Gagnon J, Moulet A, Luu T T, Goulielmakis E 2011 Science 334 195
Google Scholar
[50] Yang Y, Mainz R E, Rossi G M, Scheiba F, Silva-Toledo M A, Keathley P D, Kartner F X 2021 Nat. Commun. 12 6641
Google Scholar
[51] 杜进旭, 王国利, 焦志宏, 赵松峰, 周效信 2021 科学通报 66 949
Google Scholar
Du J X, Wang G L, Jiao Z H, Zhao S F, Zhou X X 2021 Chin. Sci. Bull. 66 949
Google Scholar
[52] Jin C, Hong K H, Lin C D 2016 Sci. Rep. 6 38165
Google Scholar
[53] Xue B, Tamaru Y, Fu Y, Yuan H, Lan P F, Mucke O D, Suda A, Midorikawa K, Takahashi E J 2021 Ultrafast Science 1 13
Google Scholar
[54] Huang P, Fang S B, Gao Y T, Zhao K, Hou X, Wei Z Y 2019 Appl. Phys. Lett. 115 031102
Google Scholar
-
图 1 优化双色场(800 nm + 1200 nm)和三色场(800 nm + 1200 nm + 600 nm)产生的高次谐波和阿秒脉冲 (a)优化的激光波形; (b) 两种激光场产生的Ne原子高次谐波谱, 为了观察谐波谱的特征, 对双色场谐波谱做了平移处理, 并给出了谐波谱的乘因子; (c), (d) 双色场和三色场下分别叠加140—190 阶、140—200阶谐波获得的阿秒脉冲; (e), (f) 双色场和三色场产生的谐波所对应的时频分析, 已将数据归一化处理. o.c.表示800 nm激光脉冲的光学周期
Figure 1. The high-order harmonic spectra and attosecond pulses generated by optimized two- (800 nm + 1200 nm) and three-color (800 nm + 1200 nm + 600 nm) laser fields: (a) Optimized laser waveforms; (b) Ne harmonic spectra generated by two laser pluses, the harmonic spectrum of two-color field is shifted for easy observation, and the multiplied factors is indicated; (c), (d) attosecond pulses synthesized from harmonics H140–H190 and H140–H200, driven by two- and three-color fields, respectively; (e), (f) time-frequency analysis of the harmonic spectra generated by optimized two- and three-color field, the data have been normalized. o.c. is the optical cycle of 800 nm laser pulse
图 2 优化四色场(800 nm + 400 nm + 1200 nm + 600 nm)产生的高次谐波和阿秒脉冲 (a)激光波形; (b)高次谐波谱; (c)叠加120—190阶谐波所获得的阿秒脉冲; (d)谐波所对应的时频分析
Figure 2. The high-order harmonics and attosecond pulses generated by optimized four-color field (800 nm + 400 nm + 1200 nm + 600 nm):(a) Optimized laser waveform; (b) harmonic spectra; (c) attosecond pulses synthesized from harmonics H120-H190; (d) time-frequency analysis of the harmonics
图 3 优化四色场中电子动力学的经典分析
Figure 3. Classical analysis of electron dynamics in optimized four-color fields
图 4 优化四色场产生的宏观谐波和阿秒脉冲 (a), (b)分别在近场和远场(z = 500 mm)谐波辐射的空间分布; (c) 利用不同孔径r的圆孔在远场收集到的谐波; (d)叠加不同空间范围105—195阶谐波所获得的阿秒脉冲
Figure 4. The macroscopic harmonics and attosecond pulses generated by optimized four-color fields: (a), (b) The spatial distributions of harmonic emission in the near and far field, respectively; (c) harmonic spectra collected by a circular filter with different aperture r at the far field (z = 500 mm); (d) attosecond pulses synthesized by harmonics H105-H195 from different spatial range
图 5 优化四色场产生的远场谐波时空分布和小波时频分析 (a)位于远场z = 500 mm处105—195阶谐波发射时间随径向距离的依赖关系; (b)
$r=0—0.2$ mm空间范围谐波的时频分析Figure 5. Spatial distribution and time-frequency wavelet analysis of harmonics generated by optimized four-color fields: (a) The dependence of emission time of harmonics H105–H195 on their spatial distance at the far field z = 500 mm; (b) time-frequency analysis of harmonics from 0 to 0.2 mm
图 6 优化四色场在不同气体压强下产生的宏观谐波和阿秒脉冲 (a) 在20, 75和100 Torr不同气压下四色场产生的宏观谐波谱; (b), (c)在20 Torr和100 Torr气压下,
$ r < 0.2 $ mm空间范围远场谐波的时频分析; (d), (f) 两个压强下分别获得的阿秒脉冲Figure 6. The macroscopic harmonic and attosecond pulses generated by optimized four-color field at different gas pressures: (a) Macroscopic harmonic spectra at gas pressures of 20, 75 and 100 Torr; (b), (c) time-frequency analysis of harmonics from
$ r < 0.2 $ mm at 20 and 100 Torr pressures, respectively; (d), (e) the attosecond pulses synthesized from harmonics at two pressures, respectively表 1 激光总强度分别为
$ 8.0 I_{0}$ ,$7.5 I_{0}$ 和$7.0 I_{0}$ 时优化的双色场、三色场和四色场激光参数($I_{0}=1.0 \times $ $ 10^{14} \mathrm{\; W} / \mathrm{cm}^{2}$ )Table 1. Optimized laser parameters for two-, three- and four-color fields with total peak intensity of
$8.0 I_{0}$ ,$7.5 I_{0}$ and$7.0 I_{0}$ , respectively ($I_{0}=1.0 \times $ $ 10^{14} \mathrm{\; W} / \mathrm{cm}^{2}$ )参数 $I=8.0 I_{0}$ $I=7.5 I_{0}$ $I=7.0 I_{0}$ 双色场 三色场 四色场 $ I_{1} / I_{0} $ 5.056 1.991 0.943 $ I_{2}/ I_{0}$ 2.944 2.684 0.757 $ I_{3}/ I_{0}$ 2.825 1.577 $ I_{4}/ I_{0}$ 3.723 $\lambda_{1}$/nm 800.0 800.0 800.0 $\lambda_{2}$/nm 1200.0 1200.0 1200.0 $\lambda_{3}$/nm 600.0 600.0 $\lambda_{4}$/nm 400.0 $\tau_{1}$/fs 16.0 16.0 16.0 $\tau_{2}$/fs 16.0 16.0 19.0 $\tau_{3}$/fs 16.0 19.0 $\tau_{4}$/fs 16.0 $\delta_{1}$/fs 0.0 0.0 0.0 $\delta_{2}$/fs –0.136 0.026 –0.389 $\delta_{3}$/fs 0.092 0.328 $\delta_{4}$/fs 1.828 注: 斜体显示的是优化得到的值, 常规字体为优化中固定的参数. 
DownLoad: CSV
-
[1] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
Google Scholar
[2] Cousin S L, Silva F, Teichmann S, Hemmer M, Buades B, Biegert J 2014 Opt. Lett. 39 5383
Google Scholar
[3] Popmintchev T, Chen M C, Popmintchev D, Arpin P, Brown S, Alisauskas S, Kapteyn H C 2012 Science 336 1287
Google Scholar
[4] Takahashi E J, Kanai T, Ishikawa K L, Nabekawa Y, Midorikawa K 2008 Phys. Rev. Lett. 101 253901
Google Scholar
[5] Paul P M, Toma E S, Breger P 2001 Science 292 1689
Google Scholar
[6] Hentschel M, Kienberger R, Spielmann C 2001 Nature 414 509
Google Scholar
[7] Mashiko H, Gilbertson S, Li C, Khan S D, Shakya M M, Moon E, Chang Z 2008 Phys. Rev. Lett. 100 103906
Google Scholar
[8] Schafer K J, Yang B, DiMauro L F, Kulander K C 1993 Phys. Rev. Lett. 70 1599
Google Scholar
[9] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[10] Goulielmakis E, Schultze M, Hofstetter M, Yakovlev V S, Gagnon J, Uiberacker M, Aquita A L, Gullikson E M, Attwood D T, Kienberger R 2008 Science 320 1614
Google Scholar
[11] Ferrari F, Calegari F, Lucchini M, Vozzi C, Stagira S, Sansone G, Nisoli M 2010 Nat. Photonics 4 875
Google Scholar
[12] Vincenti H, Quéré F 2012 Phys. Rev. Lett. 108 113904
Google Scholar
[13] Kim K T, Zhang C, Ruchon T, Hergott J F, Auguste T, Villeneuve D M 2013 Nat. Photonics 7 651
Google Scholar
[14] 方少波, 魏志义 2019 光学学报 39 0126006
Google Scholar
Fang S B, Wei Z Y 2019 Acta Opt. Sin. 39 0126006
Google Scholar
[15] 杨煜东, 魏志义 2022 光子学报 51 0151109
Google Scholar
Yang Y D, Wei Z Y 2022 Acta Photonica Sinica 51 0151109
Google Scholar
[16] Corkum P B, Burnett N H, Ivanov M Y 1994 Opt. Lett. 19 1870
Google Scholar
[17] Li J, Ren X M, Yin Y C, Zhao K, Chew A, Cunningham E, Wang Y, Hu S Y, Wu Y, Chini M, Chang Z H 2017 Nat. Commun. 8 186
[18] Gaumnitz T, Jain A, Pertot Y, Huppert M, Jordan I, Ardana-Lamas F 2017 Opt. Express 25 27506
Google Scholar
[19] Wang X W, Wang L, Xiao F, Zhang D W, Lu Z H, Yuan J M, Zhao Z X 2020 Chin. Phys. Lett. 37 023201
Google Scholar
[20] 兰鹏飞, 陆培祥 2021 科学通报 66 847
Google Scholar
Lan P F, Lu P X 2021 Chin. Sci. Bull. 66 847
Google Scholar
[21] 袁浩, 曹华保, 王虎山, 刘鑫, 孙先伟, 王屹山, 赵卫, 付玉喜 2021 科学通报 66 878
Google Scholar
Yuan H, Cao H B, Wang H S, Liu X, Sun X W, Wang Y S, Zhao W, Fu Y X 2021 Chin. Sci. Bull. 66 878
Google Scholar
[22] Wang G L, Zhou L H, Zhao S F, Zhou X X 2016 Commun. Theor. Phys. 65 601
Google Scholar
[23] Jin C, Wang G L, Wei H, Le A T, Lin C D 2014 Nat. Commun. 5 4003
Google Scholar
[24] 曾志男, 李儒新, 谢新华, 徐至展 2004 53 4
Google Scholar
Zeng Z N, Li R X, Xie X H, Xu Z Z 2004 Acta Phys. Sin. 53 4
Google Scholar
[25] Zeng Z, Cheng Y, Song X, Li R, Xu Z 2007 Phys. Rev. Lett. 98 203901
Google Scholar
[26] Lan P, Lu P, Cao W, Li Y, Wang X 2007 Phys. Rev. A 76 011402
Google Scholar
[27] Sansone G, Poletto L, Nisoli M 2011 Nat. Photonics 5 655
Google Scholar
[28] Du H C, Wang X S, Hu B T 2011 Chin. Phys. B 20 084206
Google Scholar
[29] Ge X L, Xia C L, Liu X S 2012 Laser Phys. 22 1704
Google Scholar
[30] Qin Y F, Guo F M, Li S Y, Yang Y J, Chen G 2014 Chin. Phys. B 23 093205
Google Scholar
[31] 刘胜男, 陈高, 孟健 2012 61 14
Google Scholar
Liu S N, Chen G, Meng J 2012 Acta Phys. Sin. 61 14
Google Scholar
[32] Yang K, Du J X, Wang G L, Jiao Z H, Zhao S F, Zhou X X 2022 J. Opt. Soc. Am. B 39 3
Google Scholar
[33] Pan Y, Guo F, Jin C, Yang Y J, Ding D J 2019 Phys. Rev. A 99 033411
Google Scholar
[34] Wang J, Chen G, Li S Y, Ding D J, Chen J G, Guo F M, Yang Y J 2015 Phys. Rev. A 92 033848
Google Scholar
[35] Falcao-Filho E L, Lai C J, Hong K H, Gkortsas V M, Huang S W, Chen L J 2010 Appl. Phys. Lett. 97 061107
Google Scholar
[36] Hadrich S, Klenke A, Rothhardt J, Krebs M, Hoffmann A, Pronin O, Tunnermann A 2014 Nat. Photonics 8 779
Google Scholar
[37] Jin C, Le A T, Lin C D 2011 Phys. Rev. A 83 023411
Google Scholar
[38] Colosimo P, Doumy G, Blaga C I, Wheeler J, Dimauro L F 2008 Nat. Phys. 4 386
Google Scholar
[39] 王国利, 董小敏, 赵松峰, 周效信 2016 科学通报 61 1808
Google Scholar
Wang G L, Dong X M, Zhao S F, Zhou X X 2016 Chin. Sci. Bull. 61 1808
Google Scholar
[40] Hong K H, Lai C J, Gkortsas V M, Huang S W, Moses J, Granados E, Kartner F X 2012 Phys. Rev. A 86 043412
Google Scholar
[41] Chipperfield L E, Robinson J S, Tisch J W G, Marangos J P 2009 Phys. Rev. Lett. 102 063003
Google Scholar
[42] Balogh E, Bódi B, Tosa V, Goulielmakis E, Varjú K, Dombi P 2014 Phys. Rev. A 90 023855
Google Scholar
[43] Lewenstein M, Balcou P, Ivanov M Y, Huillier L, Corkum P B 1994 Phys. Rev. A 49 2117
Google Scholar
[44] Lewenstein M, Salieres P, Huillier A L 1995 Phys. Rev. A 52 4747
Google Scholar
[45] Ammosov M V, Delone N B, Krainov V P 1986 Sov. Phys. JETP 64 1191
Google Scholar
[46] Tosa V, Kim H, Kim I, Nam C H 2005 Phys. Rev. A 71 063807
Google Scholar
[47] Gaarde M B, Tate J L, Schafer K J 2008 J. Phys. B: At. Mol. Opt. Phys. 41 132001
Google Scholar
[48] He L, Yuan G, Wang K, Hua W, Yu C, Jin C 2019 Photonics Res. 7 12
Google Scholar
[49] Wirth A, Hassan M Th. Grguras I, Gagnon J, Moulet A, Luu T T, Goulielmakis E 2011 Science 334 195
Google Scholar
[50] Yang Y, Mainz R E, Rossi G M, Scheiba F, Silva-Toledo M A, Keathley P D, Kartner F X 2021 Nat. Commun. 12 6641
Google Scholar
[51] 杜进旭, 王国利, 焦志宏, 赵松峰, 周效信 2021 科学通报 66 949
Google Scholar
Du J X, Wang G L, Jiao Z H, Zhao S F, Zhou X X 2021 Chin. Sci. Bull. 66 949
Google Scholar
[52] Jin C, Hong K H, Lin C D 2016 Sci. Rep. 6 38165
Google Scholar
[53] Xue B, Tamaru Y, Fu Y, Yuan H, Lan P F, Mucke O D, Suda A, Midorikawa K, Takahashi E J 2021 Ultrafast Science 1 13
Google Scholar
[54] Huang P, Fang S B, Gao Y T, Zhao K, Hou X, Wei Z Y 2019 Appl. Phys. Lett. 115 031102
Google Scholar
DownLoad:
Catalog
Metrics
- Abstract views: 3985
- PDF Downloads: 126
- Cited By: 0
