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Chin. Phys. B, 2021, Vol. 30(4): 043202    DOI: 10.1088/1674-1056/abd389
ATOMIC AND MOLECULAR PHYSICS Prev   Next  

Generation of non-integer high-order harmonics and significant enhancement of harmonic intensity

Chang-Long Xia(夏昌龙)1,2, Yue-Yue Lan(兰悦跃)1,2, and Xiang-Yang Miao(苗向阳)1,2,†
1 College of Physics and Information Engineering, Shanxi Normal University, Linfen 041004, China; 2 Key Laboratory of Spectral Measurement and Analysis of Shanxi Province, Shanxi Normal University, Linfen 041004, China
Abstract  High-order harmonics from helium atom in the orthogonally two-color (OTC) laser field are investigated by solving the two-dimensional time-dependent Schrödinger equation. Non-integer high-order harmonics are obtained in some ratio of frequencies of two components. Pure odd and even harmonics from atoms could be separated in two components by adjusting the ratio of frequencies in OTC scheme, and the resolution of harmonics is improved at the same time. The physical mechanism is explained by the periodicity of dipole. With the same intensity of the incident laser, the intensity of the high-order harmonics from the OTC field scheme is improved by three orders of magnitude compared to the monochromatic laser field scheme. A theoretical scheme is provided for experimentally achieving improving energy resolution and separation of pure odd and even harmonics in atoms. Also, we provide a means for improving harmonic intensity.
Keywords:  non-integer high-order harmonic generation      the orthogonally two-color laser field      the enhancement of harmonic intensity  
Received:  03 September 2020      Revised:  09 November 2020      Accepted manuscript online:  15 December 2020
PACS:  32.80.Rm (Multiphoton ionization and excitation to highly excited states)  
  42.65.Ky (Frequency conversion; harmonic generation, including higher-order harmonic generation)  
  42.65.Re (Ultrafast processes; optical pulse generation and pulse compression)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11974229 and 11504221), the Natural Science Foundation of Shanxi Province, China (Grant No. 201901D111288), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi, China (Grant No. 2019L0452), the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi Province, China.
Corresponding Authors:  Corresponding author. E-mail: sxxymiao@126.com   

Cite this article: 

Chang-Long Xia(夏昌龙), Yue-Yue Lan(兰悦跃), and Xiang-Yang Miao(苗向阳) Generation of non-integer high-order harmonics and significant enhancement of harmonic intensity 2021 Chin. Phys. B 30 043202

1 Han S, Ortmann L, Kim H, Kim Y W, Oka T, Chacon A, Doran B, Ciappina M, Lewenstein M, Kim S W, Kim S and Landsman A S 2019 Nat. Commun. 10 3272
2 Yu C, Hansen K K and Madsen L B 2019 Phys. Rev. A 99 063408
3 Zhang C P, Xia C L, Jia X F and Miao X Y 2016 Opt. Express 24 20297
4 Gemsheim S and Rost J M 2019 Phys. Rev. A 100 043408
5 Chappuis C, Bresteau D, Auguste T, Gobert O and Ruchon T 2019 Phys. Rev. A 99 033806
6 Ghimire S and Reis D A 2019 Nat. Phys. 15 10
7 Bian X B and Bandrauk A D 2014 Phys. Rev. Lett. 113 193901
8 Agostini P, Fabre F, Mainfray G and Petite G 1979 Phys. Rev. Lett. 42 1127
9 Fittinghoff D N, Bolton P R, Chang B and Kulander K C 1992 Phys. Rev. Lett. 69 2642
10 Frasinski L J, Codling K, Hatherly P, Barr J, Ross I N and Toner W T 1987 Phys. Rev. Lett. 58 2424
11 Xia C L and Liu X S 2013 Phys. Rev. A 87 043406
12 Zhong C L, Qiao B, Xu X R, Zhang Y X, Li X B, Zhang Y, Zhou C T, Zhu S P and He X T 2020 Phys. Rev. A 101 053814
13 Luo J, Hong W, Zhang Q, Li Yang and Lu P 2012 Opt. Express 20 21346
14 Sarantseva T S, Frolov M V, Manakov N L, Silaev A A, Romanov A A, Vvedenskii N V and Starace A F 2020 Phys. Rev. A 101 013402
15 Yuan K J and Bandrauk A D 2011 Phys. Rev. A 84 023410
16 Sarukura N, Hata K, Adachi T, Nodomi R, Watanabe M and Watanabe S 1991 Phys. Rev. A 43 1669
17 Kondo K, Sarukura N, Sajiki K and Watanabe S 1993 Phys. Rev. A 47 R2480
18 L'Huillier A and Balcou Ph 1993 Phys. Rev. Lett. 70 774
19 Macklin J J, Kmetec J D and Gordon C L 1993 Phys. Rev. Lett. 70 766
20 Krause J L, Schafer K J and Kulander K C 1992 Phys. Rev. Lett. 68 3535
21 L'Huillier A, Lewenstein M, Sali\`eres P, Balcou Ph, Ivanov M Yu, Larsson J and Wahlström 1993 Phys. Rev. A 48 R3433
22 Li Y, Sato T and Ishikawa K L 2019 Phys. Rev. A 99 043401
23 Corkum P B 1993 Phys. Rev. Lett. 71 1994
24 Lewenstein M, Balcou Ph, Ivanov M Yu, L'Huillier A and Corkum P B 1994 Phys. Rev. A 49 2117
25 Ferray M, L'Huillier A, Li X F, Lompré L A, Mainfray G and Manus C 1988 J. Phys. B: At. Mol. Opt. Phys. 21 L31
26 Li X F, L'Huillier A, Ferray M, Lompré L A and Mainfray G 1989 Phys. Rev. A 39 5751
27 Le A T, Morishita T and Lin C D 2008 Phys. Rev. A 78 023814
28 Pfeifer T, Spielmann C and Gerber G 2006 Rep. Prog. Phys. 69 443
29 Ben-Tal N, Moiseyev N and Beswick A 1993 J. Phys. B: At. Mol. Opt. Phys. 26 3017
30 Kim I J, Kim C M, Kim H T, Lee G H, Lee Y S, Park J Y, Cho D J and Nam C H 2005 Phys. Rev. Lett. 94 243901
31 Frolov M V, Manakov N L, Sarantseva T S, Silaev A A, Vvedenskii N V and Starace A F 2016 Phys. Rev. A 93 023430
32 Frolov M V, Manakov N L, Silaev A A and Vvedenskii N V 2010 Phys. Rev. A 81 063407
33 Zhai C Y, Shao R Z, Lan P F, Wang B, Zhang Y, Yuan H, Njoroge S M, He L and Lu P 2020 Phys. Rev. A 101 053407
34 Lara-Astiaso M, Silva R E F, Gubaydullin A, Rivi\`ere P, Meier C and Mart\'ín F 2016 Phys. Rev. Lett. 117 093003
35 Guo Y, Liu A, Wang J and Liu X 2019 Chin. Phys. B 28 094212
36 Zhu X, Zhang C, Gu M and Yao J 2014 Opt. Express 22 7947
37 Yuan K J and Bandrauk A D 2019 Phys. Rev. A 100 033420
38 Li M, Jiang W C, Xie H, Luo S, Zhou Y and Lu P 2018 Phys. Rev. A 97 023415
39 Heslar J, Telnov D A and Chu S I 2018 Phys. Rev. A 97 043419
40 Liu X, Zhu X, Li L, Li Y, Zhang Q, Lan P and Lu P 2016 Phys. Rev. A 94 033410
41 Hu H, Li N, Liu P, Li R and Xu Z 2017 Phys. Rev. Lett. 119 173201
42 Yang Y, Liu L and Zhao Z The 9th International Symposium on Ultrafast Phenomena and Terahertz Waves January 2018, OSA
43 Xu L and He F 2019 J. Opt. Soc. Am. B 36 840
44 Neufeld O, Podolsky D and Cohen O 2019 Nat. Commun. 10 405
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[1] MAO ZHI-QIANG, YANG LI, FAN CHENG-GAO, WANG NAN-LIN, YAO ZHEN, WANG YU, JI MING-RONG, ZHANG YU-HENG. STRUCTURE AND PROPERTIES OF THE La-DOPED Bi-2201 SYSTEM[J]. Acta Phys. Sin. (Overseas Edition), 1993, 2(8): 591 -603 .
[2] CHENG HUAN-SHENG, SHEN HAO, TANG JIA-YONG, YANG FU-JIA. THE STUDIES OF NON-RUTHERFORD BACKSCATTERING CROSS SECTIONS OF 4He FROM 16O[J]. Acta Phys. Sin. (Overseas Edition), 1993, 2(9): 641 -647 .
[3] D.B. GRAVES, WU HAN-MING, LI MING, R.K PORTEOUS. BEHAVIOR OF Ar PLASMA FORMED IN A HIGH DENSITY PLASMA SOURCE-AN ECR REACTOR[J]. Acta Phys. Sin. (Overseas Edition), 1994, 3(10): 746 -757 .
[4] WANG HAI-LONG, YANG XI-ZHEN, FENG SONG-LIN, ZHOU JIE. DETERMINATION OF CAPTURE BARRIERS OF DEFECTS FOR GaAs ALLOYS AND TRANSIENT PHOTO-RESISTIVITY SPECTROSCOPY[J]. Acta Phys. Sin. (Overseas Edition), 1996, 5(1): 1 -9 .
[5] WANG YONG-CHENG. SCHWARZSCHILD BLACK HOLE,VACUUM C METRIC WHEN m=0 AND RINDLER METRIC[J]. Acta Phys. Sin. (Overseas Edition), 1997, 6(9): 666 -670 .
[6] Fang Jin-qing, Chen Guan-rong, Hong Yi-guang, Qin Hua-shu. CONTROLLING HOPF BIFURCATIONS: CONTINUOUS-TIME SYSTEMS[J]. Acta Phys. Sin. (Overseas Edition), 1999, 8(6): 416 -422 .
[7] Wang Shu-Xia, Zhang Han, Liu Wen-Li, Han Sheng-Hao. Combinative energy, oxygen deficiency and superconductivity in LnBa2Cu3O7-x(Ln=Nd, Er, Sm)[J]. Chin. Phys., 2003, 12(11): 1291 -1295 .
[8] Jiang Li-Xia, Xia Zhao-Yang, Meng Ji-Bao, Chen Zhao-Jia, Luo Jian-Lin, Wang Nan-Lin. Low-temperature specific heat and resistance for the heavy-electron metals CeCu6-xMx (M=Ni,Zn)[J]. Chin. Phys., 2004, 13(12): 2130 -2135 .
[9] Bi Yong, Bo Yong, Li Rui-Ning, Cui Da-Fu, Xu Zu-Yan, Geng Ai-Cong, Sun Zhi-Pei, Yang Xiao-Dong, Peng Qin-Jun, Li Hui-Qing. 1.15kW continuous-wave generation by diode-side-pumped two-rod Nd:YAG laser[J]. Chin. Phys., 2005, 14(4): 771 -773 .
[10] Cheng Xin-Lu, Yang Xiang-Dong, Shao Ju-Xiang, He Bi. The evaluation of bond dissociation energies for NO2 scission in nitro compounds using density functional and complete basis set methods[J]. Chin. Phys., 2006, 15(2): 329 -333 .