Modulation of multiphoton resonant high-order harmonic spectra driven by two frequency-comb fields

doi:10.1088/1674-1056/27/5/053202

Abstract The frequency-comb structure in the extreme ultraviolet (XUV) and vacuum ultraviolet (VUV) regions can be realized by the high-order harmonic generation (HHG) process driven by frequency-comb fields, providing an alternative approach for the measurement of an unknown frequency in XUV or VUV. We consider the case of two driving frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental-and third-harmonics, respectively. The many-mode Floquet theorem (MMFT) is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the frequency-comb laser fields. Multiphoton transition paths involving both fundamental-and third-harmonic photons are opened due to the coupling of the third-harmonic frequency-comb field. The multiphoton transition paths are superpositioned when the carrier-envelope-phase shifts (CEPs) fulfill the matching condition. And the interference of the multiphoton transition paths can be controlled by tuning the relative envelope delay between the fields. We find that the quasienergy structure, as well as the multiphoton resonant high-order harmonic generation (HHG) spectra, driven by the two frequency-comb fields can be coherently controlled via the interference of multiphoton transition paths. It is also found that the spectral intensities of the generated harmonics can be modulated, and the modulation behavior is harmonic-sensitive.

Keywords: high-order harmonic generation two frequency-comb laser fields relative envelope delay

Received: 27 December 2017
Revised: 24 January 2018
Accepted manuscript online:

PACS:	32.80.Qk	(Coherent control of atomic interactions with photons)
	42.65.Ky	(Frequency conversion; harmonic generation, including higher-order harmonic generation)
	42.50.Hz	(Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.11504288,11374239,11534008,and 91536115) and the Fundamental Research Funds for the Central Universities,China.

Corresponding Authors: Di Zhao
E-mail: d.zhao@mail.xjtu.edu.cn

Cite this article:

Yuanyuan Zhao(赵媛媛), Di Zhao(赵迪), Chen-Wei Jiang(蒋臣威), Fu-li Li(李福利) Modulation of multiphoton resonant high-order harmonic spectra driven by two frequency-comb fields 2018 Chin. Phys. B 27 053202

[13]	Yost D C, Schibli T R, Ye J, Tate J L, Hostetter J, Gaarde M B and Schafer K J 2009 Nat. Phys. 5 815
[1]	L'Huillier A and Balcou P 1993 Phys. Rev. Lett. 70 774
[14]	Kandula D Z, Gohle C, Pinkert T J, Ubachs W and Eikema K S E 2010 Phys. Rev. Lett. 105 063001
[2]	Ravasio A, Gauthier D, Maia F R N C, et al. 2009 Phys. Rev. Lett. 103 028104
[15]	Peik E and Tamm Chr 2003 Europhys. Lett. 61 181
[3]	Winterfeldt C, Spielmann C and Gerber G 2008 Rev. Mod. Phys. 80 117
[16]	Takamoto M, Hong F L, Higashi R and Katori H 2005 Nature 435 321
[4]	Kapteyn H C, Murnane M M and Christov I P 2005 Physics Today 58 39
[17]	Gerginov V, Tanner C E, Diddams S A, Bartels A and Hollberg L 2005 Opt. Lett. 30 1734
[5]	Hentschel M 2001 Nature 414 509
[18]	Rellergert W G, DeMille D, Greco R R, Hehlen M P, Torgerson J R and Hudson E R 2010 Phys. Rev. Lett. 104 200802
[6]	Tzallas P 2003 Nature 426 267
[19]	Campbell C J, Radnaev A G and Kuzmich A 2011 Phys. Rev. Lett. 106 223001
[7]	Kienberger R 2004 Nature 427 817
[20]	Diddams S A, Udem Th, Bergquist J C, Curtis E A, Drullinger R E, Hollberg L, Itano W M, Lee W D, Oates C W, Vogel K R and Wineland D J 2001 Science 293 825
[8]	Nabekawa Y, Hasegawa H, Takahashi E J and Midorikawa K 2005 Phys. Rev. Lett. 94 043001
[21]	Stowe M C, Cruz F C, Marian A and Ye J 2006 Phys. Rev. Lett. 96 153001
[9]	Sansone G 2006 Science 314 443
[22]	Witte S, Zinkstok R Th, Ubachs W, Hogervorst W and Eikema K S E 2005 Science 307 400
[10]	Goulielmakis E 2008 Science 320 1614
[23]	Cingöz A, Yost D C, Allison Th K, Ruehl A, Fermann M E, Hartl I and Ye J 2012 Nature 482 68
[11]	Carrera J J, Son S K and Chu S I 2008 Phys. Rev. A 77 031401
[24]	Stalnaker J E, Coq Y Le, Fortier T M, Diddams S A, Oates C W and Hollberg L 2007 Phys. Rev. A 75 040502
[12]	Carrera J J and Chu S I 2009 Phys. Rev. A 79 063410
[25]	Holzwarth R, Udem Th, Hänsch T W, Knight J C, Wadsworth W J and Russell P St J 2000 Phys. Rev. Lett. 85 2264
[13]	Yost D C, Schibli T R, Ye J, Tate J L, Hostetter J, Gaarde M B and Schafer K J 2009 Nat. Phys. 5 815
[26]	Niering M, Holzwarth R, Reichert J, Pokasov P, Udem Th, Weitz M, Hänsch T W, Lemonde P, Santarelli G, Abgrall M, Laurent P, Salomon C and Clairon A 2000 Phys. Rev. Lett. 84 5496
[14]	Kandula D Z, Gohle C, Pinkert T J, Ubachs W and Eikema K S E 2010 Phys. Rev. Lett. 105 063001
[27]	Marian A, Stowe M C, Felinto D and Ye J 2005 Phys. Rev. Lett. 95 023001
[15]	Peik E and Tamm Chr 2003 Europhys. Lett. 61 181
[28]	Margolis H S, Barwood G P, Huang G, Klein H, Lea S N, Szymaniec K and Gill P 2004 Science 306 1355
[16]	Takamoto M, Hong F L, Higashi R and Katori H 2005 Nature 435 321
[29]	Herrmann M 2009 Phys. Rev. A 79 052505
[17]	Gerginov V, Tanner C E, Diddams S A, Bartels A and Hollberg L 2005 Opt. Lett. 30 1734
[30]	Mabuchi H, Ye J and Kimble H J 1999 Appl. Phys. B 68 1095
[18]	Rellergert W G, DeMille D, Greco R R, Hehlen M P, Torgerson J R and Hudson E R 2010 Phys. Rev. Lett. 104 200802
[31]	Eyler E E 2008 Euro. Phys. J. D 48 43
[19]	Campbell C J, Radnaev A G and Kuzmich A 2011 Phys. Rev. Lett. 106 223001
[32]	Son S K and Chu S I 2008 Phys. Rev. A 77 063406
[20]	Diddams S A, Udem Th, Bergquist J C, Curtis E A, Drullinger R E, Hollberg L, Itano W M, Lee W D, Oates C W, Vogel K R and Wineland D J 2001 Science 293 825
[33]	Zhao D, Li F L and Chu S I 2013 Phys. Rev. A 87 043407
[21]	Stowe M C, Cruz F C, Marian A and Ye J 2006 Phys. Rev. Lett. 96 153001
[34]	Pfeifer T, Gallmann L, Abel M J, Nagel P M, Neumark D M and Leone S R 2006 Phys. Rev. Lett. 97 163901
[22]	Witte S, Zinkstok R Th, Ubachs W, Hogervorst W and Eikema K S E 2005 Science 307 400
[35]	Hong W, Lu P, Lan P, Yang Z, Li Y and Liao Q 2008 Phys. Rev. A 77 033410
[23]	Cingöz A, Yost D C, Allison Th K, Ruehl A, Fermann M E, Hartl I and Ye J 2012 Nature 482 68
[36]	Zhang G T, Wu J, Xia C L and Liu X S 2009 Phys. Rev. A 80 055404
[24]	Stalnaker J E, Coq Y Le, Fortier T M, Diddams S A, Oates C W and Hollberg L 2007 Phys. Rev. A 75 040502
[37]	Song X, Zeng Z, Fu Y, Cai B, Li R, Cheng Y and Xu Z 2007 Phys. Rev. A 76 043830
[25]	Holzwarth R, Udem Th, Hänsch T W, Knight J C, Wadsworth W J and Russell P St J 2000 Phys. Rev. Lett. 85 2264
[38]	Wu J, Zhang G T, Xia C L and Liu X S 2010 Phys. Rev. A 82 013411
[26]	Niering M, Holzwarth R, Reichert J, Pokasov P, Udem Th, Weitz M, Hänsch T W, Lemonde P, Santarelli G, Abgrall M, Laurent P, Salomon C and Clairon A 2000 Phys. Rev. Lett. 84 5496
[39]	Zeng Z, Cheng Y, Song X, Li R and Xu Z 2007 Phys. Rev. Lett. 98 203901
[27]	Marian A, Stowe M C, Felinto D and Ye J 2005 Phys. Rev. Lett. 95 023001
[40]	Zhai Z and Liu X S 2008 J. Phys. B:At. Mol. Opt. Phys. 41 125602
[28]	Margolis H S, Barwood G P, Huang G, Klein H, Lea S N, Szymaniec K and Gill P 2004 Science 306 1355
[41]	Lan P, Lu P, Cao W, Li Y and Wang X 2007 Phys. Rev. A 76 011402
[29]	Herrmann M 2009 Phys. Rev. A 79 052505
[42]	Faria C F, Dörr M, Becker W and Sandner W 1999 Phys. Rev. A 60 1377
[30]	Mabuchi H, Ye J and Kimble H J 1999 Appl. Phys. B 68 1095
[43]	Li X X, Xu Z Z and Mao L Q 1997 Acta Phys. Sin. 6 197(in Chinese)
[31]	Eyler E E 2008 Euro. Phys. J. D 48 43
[44]	Ye X L, Zhou X X, Zhao S F and Li P C 2009 Acta Phys. Sin. 58 1579(in Chinese)
[32]	Son S K and Chu S I 2008 Phys. Rev. A 77 063406
[45]	Xiang Y, Niu Y and Gong S 2009 Phys. Rev. A 79 053419
[33]	Zhao D, Li F L and Chu S I 2013 Phys. Rev. A 87 043407
[46]	Carrera J J and Chu S I 2007 Phys. Rev. A 75 033807
[34]	Pfeifer T, Gallmann L, Abel M J, Nagel P M, Neumark D M and Leone S R 2006 Phys. Rev. Lett. 97 163901
[47]	Xu J, Zeng B and Yu Y 2010 Phys. Rev. A 82 053822
[35]	Hong W, Lu P, Lan P, Yang Z, Li Y and Liao Q 2008 Phys. Rev. A 77 033410
[48]	Xiao J, Sun Z R, Wang Y F, Deng L, Zhang X Y, Chen G L, Zhang W P, Wang Z G, Xu Z Z and Li R X 2005 Chin. Phys. Lett. 22 873
[36]	Zhang G T, Wu J, Xia C L and Liu X S 2009 Phys. Rev. A 80 055404
[49]	Zhao D, Jiang C W and Li F L 2015 Phys. Rev. A 92 043413
[37]	Song X, Zeng Z, Fu Y, Cai B, Li R, Cheng Y and Xu Z 2007 Phys. Rev. A 76 043830
[50]	Chu S I and Telnov D A 2004 Phys. Rep. 390 1
[38]	Wu J, Zhang G T, Xia C L and Liu X S 2010 Phys. Rev. A 82 013411
[51]	Ho T S, Chu S I and Tietz J V 1983 Chem. Phys. Lett. 96 464
[39]	Zeng Z, Cheng Y, Song X, Li R and Xu Z 2007 Phys. Rev. Lett. 98 203901
[52]	Ho T S and Chu S I 1984 J. Phys. B 17 2101
[40]	Zhai Z and Liu X S 2008 J. Phys. B:At. Mol. Opt. Phys. 41 125602
[53]	Ho T S and Chu S I 1985 Phys. Rev. A 31 659
[41]	Lan P, Lu P, Cao W, Li Y and Wang X 2007 Phys. Rev. A 76 011402
[54]	Ho T S and Chu S I 1985 Phys. Rev. A 32 377
[42]	Faria C F, Dörr M, Becker W and Sandner W 1999 Phys. Rev. A 60 1377
[43]	Li X X, Xu Z Z and Mao L Q 1997 Acta Phys. Sin. 6 197(in Chinese)
[44]	Ye X L, Zhou X X, Zhao S F and Li P C 2009 Acta Phys. Sin. 58 1579(in Chinese)
[45]	Xiang Y, Niu Y and Gong S 2009 Phys. Rev. A 79 053419
[46]	Carrera J J and Chu S I 2007 Phys. Rev. A 75 033807
[47]	Xu J, Zeng B and Yu Y 2010 Phys. Rev. A 82 053822
[48]	Xiao J, Sun Z R, Wang Y F, Deng L, Zhang X Y, Chen G L, Zhang W P, Wang Z G, Xu Z Z and Li R X 2005 Chin. Phys. Lett. 22 873
[49]	Zhao D, Jiang C W and Li F L 2015 Phys. Rev. A 92 043413
[50]	Chu S I and Telnov D A 2004 Phys. Rep. 390 1
[51]	Ho T S, Chu S I and Tietz J V 1983 Chem. Phys. Lett. 96 464
[52]	Ho T S and Chu S I 1984 J. Phys. B 17 2101
[53]	Ho T S and Chu S I 1985 Phys. Rev. A 31 659
[54]	Ho T S and Chu S I 1985 Phys. Rev. A 32 377

[1]	Spectral shift of solid high-order harmonics from different channels in a combined laser field Dong-Dong Cao(曹冬冬), Xue-Fei Pan(潘雪飞), Jun Zhang(张军), and Xue-Shen Liu(刘学深). Chin. Phys. B, 2023, 32(3): 034204.
[2]	Phase-coherence dynamics of frequency-comb emission via high-order harmonic generation in few-cycle pulse trains Chang-Tong Liang(梁畅通), Jing-Jing Zhang(张晶晶), and Peng-Cheng Li(李鹏程). Chin. Phys. B, 2023, 32(3): 033201.
[3]	Effect of laser focus in two-color synthesized waveform on generation of soft x-ray high harmonics Yanbo Chen(陈炎波), Baochang Li(李保昌), Xuhong Li(李胥红), Xiangyu Tang(唐翔宇), Chi Zhang(张弛), and Cheng Jin(金成). Chin. Phys. B, 2023, 32(1): 014203.
[4]	High-order harmonic generation of the cyclo[18]carbon molecule irradiated by circularly polarized laser pulse Shu-Shan Zhou(周书山), Yu-Jun Yang(杨玉军), Yang Yang(杨扬), Ming-Yue Suo(索明月), Dong-Yuan Li(李东垣), Yue Qiao(乔月), Hai-Ying Yuan(袁海颖), Wen-Di Lan(蓝文迪), and Mu-Hong Hu(胡木宏). Chin. Phys. B, 2023, 32(1): 013201.
[5]	Probing subcycle spectral structures and dynamics of high-order harmonic generation in crystals Long Lin(林龙), Tong-Gang Jia(贾铜钢), Zhi-Bin Wang(王志斌), and Peng-Cheng Li(李鹏程). Chin. Phys. B, 2022, 31(9): 093202.
[6]	Tunable spectral shift of high-order harmonic generation in atoms using a sinusoidally phase-modulated pulse Yue Qiao(乔月), Jun Wang(王俊), Yan Yan(闫妍), Simeng Song(宋思蒙), Zhou Chen(陈洲), Aihua Liu(刘爱华), Jigen Chen(陈基根), Fuming Guo(郭福明), and Yujun Yang(杨玉军). Chin. Phys. B, 2022, 31(6): 064214.
[7]	Enhancement of isolated attosecond pulse generation by using long gas medium Yueying Liang(梁玥瑛), Xinkui He(贺新奎), Kun Zhao(赵昆), Hao Teng(滕浩), and Zhiyi Wei(魏志义). Chin. Phys. B, 2022, 31(4): 043302.
[8]	Orientation and ellipticity dependence of high-order harmonic generation in nanowires Fan Yang(杨帆), Yinghui Zheng(郑颖辉), Luyao Zhang(张路遥), Xiaochun Ge(葛晓春), and Zhinan Zeng(曾志男). Chin. Phys. B, 2022, 31(4): 044204.
[9]	Decoding the electron dynamics in high-order harmonic generation from asymmetric molecular ions in elliptically polarized laser fields Cai-Ping Zhang(张彩萍) and Xiang-Yang Miao(苗向阳). Chin. Phys. B, 2022, 31(4): 043301.
[10]	Multiple collisions in crystal high-order harmonic generation Dong Tang(唐栋) and Xue-Bin Bian(卞学滨). Chin. Phys. B, 2022, 31(12): 123202.
[11]	Generation of non-integer high-order harmonics and significant enhancement of harmonic intensity Chang-Long Xia(夏昌龙), Yue-Yue Lan(兰悦跃), and Xiang-Yang Miao(苗向阳). Chin. Phys. B, 2021, 30(4): 043202.
[12]	Minimum structure of high-harmonic spectrafrom aligned O₂ and N₂ molecules Bo Yan(闫博), Yi-Chen Wang(王一琛), Qing-Hua Gao(高庆华), Fang-Jing Cheng(程方晶), Qiu-Shuang Jing(景秋霜), Hong-Jing Liang(梁红静), and Ri Ma(马日). Chin. Phys. B, 2021, 30(11): 114213.
[13]	Role of potential on high-order harmonic generation from atoms irradiated by bichromatic counter-rotating circularly polarized laser fields Xu-Xu Shen(申许许), Jun Wang(王俊), Fu-Ming Guo(郭福明), Ji-Gen Chen(陈基根), Yun-Jun Yang(杨玉军). Chin. Phys. B, 2020, 29(8): 083201.
[14]	Multiphoton quantum dynamics of many-electron atomic and molecular systems in intense laser fields Peng-Cheng Li(李鹏程), Shih-I Chu. Chin. Phys. B, 2020, 29(8): 083202.
[15]	Semi-integer harmonic generation from an argon atom by bichromatic counter-rotating circularly polarized laser field Tong Qi(齐桐), Xiao-Xin Huo(霍晓鑫), Jun Zhang(张军), Xue-Shen Liu(刘学深). Chin. Phys. B, 2020, 29(5): 053201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Modulation of multiphoton resonant high-order harmonic spectra driven by two frequency-comb fields

Cite this article:

Online attention