We solved one dimensional Schrodinger equation in a H_{2}^{+ }molecular environment by using 3 femtosecond homogeneous and nonhomogeneous laser fields. In homogeneous case, we found out that larger inter nuclear distances result in earlier ionization and also more instability in the wave packet. We deducted that the more the instability is, the more modulated the power spectrum will be. So, by choosing a fixed 1.96 atomic units inter nuclear distance, we investigated high harmonic generation in both linear and nonlinear nonhomogeneous laser pulses. We observed that in comparison with the linear case, in nonlinear one, the plateau possessed higher intensity harmonics. On the other hand, in this case, cutoff order occurred on higher frequency. By superposing several harmonics near cutoff region, we predicted the generation of a 73 attosecond pulse.

Type of Study: Research |
Subject:
Special

Received: 2018/08/21 | Revised: 2018/10/31 | Accepted: 2018/12/2 | Published: 2019/12/27

Received: 2018/08/21 | Revised: 2018/10/31 | Accepted: 2018/12/2 | Published: 2019/12/27

1. M. Hentschel, R. Kienberger, C. Spielmann, G. Reider, N. Milosevic, T. Brabec, P.B. Corkum, U. Heinzmann, M. Drescher, and F. Krausz, "Attosecond metrology," Nature , Vol. 414, pp. 509-513, 2001. [DOI:10.1038/35107000]

2. P. Tzallas, D. Charalambidis, N.A. Papadogiannis, K. Witte, and GD. Tsakiris, "Direct observation of attosecond light bunching," Nature, Vol. 426, pp. 267-271, 2003. [DOI:10.1038/nature02091]

3. G. Sansone, "Isolated Single-Cycle Attosecond Pulses," Science, Vol. 314, pp. 443-446, 2006. [DOI:10.1126/science.1132838]

4. E. Goulielmakis, "Single-Cycle Nonlinear Optics," Science, Vol. 320, pp. 1614 (1-20), 2008 . [DOI:10.1126/science.1157846]

5. T. Brabec and F. Krausz, "Intense few-cycle laser fields Frontiers of nonlinear optics," Rev. Mod. Phys. Vol. 72, pp. 545-591, 2000. [DOI:10.1103/RevModPhys.72.545]

6. C. Winterfeldt, C. Spielmann, and G. Gerber, "Optimal control of high-harmonic generation," Rev. Mod. Phys. Vol. 80, pp. 117-120, 2008. [DOI:10.1103/RevModPhys.80.117]

7. B. Mette, J. Gaarde, and K.J. Kenneth, "Amplitude and Phase Control of Attosecond Light Pulses," J. Phys. B, Vol. 41, pp. 31-36, 2008.

8. P. Corkum, "Plasma perspective on strong field multiphoton ionization," Phys. Rev. Lett. Vol. 71, pp.1994-1997, 1993. [DOI:10.1103/PhysRevLett.71.1994]

9. M. Lewenstein, P. Balcou, M.Y. Ivanov, A.L. Huillier, and P. B. Corkum, "Theory of high-harmonic generation by low-frequency laser fields," Phys. Rev. A, Vol. 49, pp. 2117-2132, 1994. [DOI:10.1103/PhysRevA.49.2117]

10. A.D. Bandrauk, S. Chelkowski, and S. Goudreau "Control of harmonic generation using two color femtosecond -attosecond laser fields," J. Mod. Opt. Vol. 52, pp. 411-428, 2005. [DOI:10.1080/09500340410001729582]

11. A.D. Bandrauk, S. Chelkowski, H. Yu, "Constant, Enhanced harmonic generation in extended molecular systems by two-color excitation," Phys. Rev. A, Vol. 56, pp. 2537-2540, 1997. [DOI:10.1103/PhysRevA.56.R2537]

12. A.D. Bandrauk, S. Barmaki, and G.L. Kamta, "Laser Phase Control of High-Order Harmonic Generation at Large Internuclear Distance The H+ − H2+ System," Phys. Rev. Lett. Vol. 98, pp. 013001 (1-4), 2007. [DOI:10.1103/PhysRevLett.98.013001]

13. Y. Chao, E. Haixiang, W. Yunhui, Q. Sh, Z. Yadong, and L. Ruifeng, "Intense attosecond pulse generated from a molecular harmonic plateau of H2+ in mid-infrared laser fields," Phys. Lett. Vol. 47, pp. 055601 (1-10), 2014. [DOI:10.1088/0953-4075/47/5/055601]

14. P.C. Li, I.L. Liu, and S.I. Chu, "Optimization of three-color laser field for the generation of single ultrashort attosecond pulse," Opt. Express, Vol. 19, pp. 23857-23866, 2011. [DOI:10.1364/OE.19.023857]

15. H. Sabzyan and H. Ebadi, "Evolution of the H2+ electron wavepacket under magnetic and electric fields of ultrashort intense laser pulse," J. Iran. Chem. Soc., Vol. 6, pp. 489-503, 2009. [DOI:10.1007/BF03246526]

16. M.F. Kling, "Control of Electron Localization in Molecular Dissociation," Science, Vol. 312, pp. 246-250, 2006. [DOI:10.1126/science.1126259]

17. A. Pic'on, A. Jaro'n-Becker, and A. Becker, "Enhancement of Vibrational Excitation and Dissociation of H2+ in Infrared Laser Pulses," Phys. Rev. Lett. Vol. 109 pp. 163002 (1-5), 2012. [DOI:10.1103/PhysRevLett.109.163002]

18. V.T. Platonenko, A.F. Sterjantov and V.V. Strelkov, "Decrease of high harmonic generation yield in the barrier-suppression regime," Laser Phys. Vol. 13, pp. 443-449, 2003.

19. Z. Chang, Fundamental of attosecond optics CRC Press Taylor and Francis, 2016. [DOI:10.1201/b10402]

20. H. Sabzyan and H. Ebadi, "Ionization of 1-D model of H2+ from different states in intense laser field," Iran. J. Sci. Technol. Vol. 33, pp. 87-102, 2009.

21. F. Hosseinzadeh, M. Qadiri Soofi, and S. Batebi, "Time frequency analysis of high harmonic generation," Int. J. Opt. Photon. Vol. 121, pp. 57-68, 2018. [DOI:10.29252/ijop.12.1.57]

22. T. Zuo, A.D. Bandrauk, "Charge-resonance-enhanced ionization of diatomic molecular ions by intense lasers," Phys. Rev. A, Vol. 52, pp. 2511-2514, 1995. [DOI:10.1103/PhysRevA.52.R2511]

23. T. Seideman, M. Yu, P.B. Corkum, "Role of Electron Localization in Intense-Field Molecular Ionization," Phys. Rev. Lett. Vol. 75, pp. 2819-2822, 1995. [DOI:10.1103/PhysRevLett.75.2819]

24. S. Chelkowski and A.D. Bandrauk, "Two-step Coulomb explosions of diatoms in intense laser fields," J. Phys. B, Vol. 28, pp. L723-L731, 1995. [DOI:10.1088/0953-4075/28/23/004]

25. A. Husakou, S.J. Im, and J. Herrmann, "Theory of plasmon-enhanced high-order harmonic generation in the vicinity of metal nanostructures in noble gases," Phys. Rev A. Vol. 83, pp. 043839 (1-5), 2011. [DOI:10.1103/PhysRevA.83.043839]

26. H. Zhong, J. Guo, and W. Feng, "Analogy of electromagnetically induced transparency in plasmonic nanodisk with a square ring resonator," Phys. Lett. A, Vol. 380, pp. 232-237, 2016. [DOI:10.1016/j.physleta.2015.10.035]

27. Sh. Xue, H. Du, and Y. Xi, "Photochemical Synthesis of Ultrafine Cubic Boron Nitride Nanoparticles under Ambient Conditions," Chin. Phys. B, Vol. 24, pp. 7051-7054, 2015. [DOI:10.1002/anie.201502023]

28. J.M. Reed, Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide, PhD Thesis, B.S. University of Central Florida, 2013.

29. S. Kim, J. Jin, and Y.-J. Kim, "High-harmonic generation by resonant plasmon field enhancement," Nature, Vol. 453, pp. 757-760, 2008. [DOI:10.1038/nature07012]

30. F. Hosseinzadeh, S. Batebi, and M.Q. Soofi, "Dramatic dwindling of the power spectrum of high order harmonics by shrinking of the gap size in bowtie nanostructures," J. Exp. Theoretical Phys. (JETP), Vol. 124, pp. 379-387, 2017. [DOI:10.1134/S1063776117020121]

31. J. Juan, X.M. Carrera, and T. Sh-I. Chu, "Creation and control of a single coherent attosecond xuv pulse by few-cycle intense laser pulses," Phys. Rev. A, Vol. 74, pp. 023404 (1-8), 2006. [DOI:10.1103/PhysRevA.74.023404]

32. B. Wang, L. He, F. Wang, H. Yuan, X. Zhu Lan, and P. Lui, "Atomic layer graphene as a saturable absorber for ultrafast pulsed lasers," Opt. Express, Vol. 25, pp. 1-25, 2017. [DOI:10.1364/OE.25.017777]

33. B. Rotenberg, R. Taieb, V. Veniard, and A. Maquet, "H2+ in intense laser field pulses ionization versus dissociation within moving nucleus simulations," J. Phys. B, Vol. 35, pp. L397-L402, 2002. [DOI:10.1088/0953-4075/35/17/103]

34. I. Yavuz, Y. Tikman, and Z. Altun, "High-order-harmonic generation from H2+ molecular ions near plasmon-enhanced laser fields," Phys. Rev. A, Vol. 92, pp. 023413 (1-7), 2015. [DOI:10.1103/PhysRevA.92.023413]