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High-order harmonic generation by aligned heteronuclear diatomic molecules in an orthogonally polarized two-color laser field

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Abstract

Using the molecular strong-field approximation, we investigate high-order harmonic generation by heteronuclear diatomic molecules exposed to an orthogonally polarized two-color laser field, which consists of two mutually orthogonal linearly polarized fields with frequencies \(r\omega \) and \(s\omega \). Here, r and s are integers and \(\omega \) is the fundamental frequency. The harmonic emission rate and the harmonic ellipticity can be controlled using the laser-field parameters, in particular the relative phase and the intensity ratio of the laser-field components. The value of the relative phase, for which the emission rate is optimal, and the position of the cutoff can be estimated using a classical model. Also, we analyze the harmonic emission rate and the harmonic ellipticity as functions of the molecular orientation, which can also be used as a control parameter. Two types of minima are present in the spectra, depending on r and s. For \(r+s\) even, interference minima are present in the spectra of the T-matrix component either parallel or perpendicular to the internuclear axis. Using quantum-orbit theory and the saddle-point method, we derive a condition for the interference minima, which relates the molecular orientation angle \(\theta _L\) and the harmonic order n. The corresponding curves in the (\(\theta _L\), n) plane well reproduce the minima of the numerically calculated spectra. For \(r+s\) odd, minima are present in the spectra for a particular molecular orientation angle. These minima are explained using the explicit form of the T-matrix element. A heteronuclear as opposed to a homonuclear molecule affords a larger region in the parameter space where both the harmonic ellipticity and the harmonic intensity vary smoothly and both are large.

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Data Availibility Statement

This manuscript has no associated data or the data will not be deposited [Authors’ comment: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.]

References

  1. P.B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)

    Article  ADS  Google Scholar 

  2. K.C. Kulander, K.J. Schafer, J.L. Krause, Super-intense laser-atom physics, in NATO Advanced Studies Institute, Series B: Physics. ed. by B. Piraux, A. L’Huillier, K. Rza̧żewski (Plenum, New York, 1993), p. 95

  3. T. Kanai, N. Minemoto, H. Sakai, Nature (London) 435, 470 (2005)

    Article  ADS  Google Scholar 

  4. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J.C. Kieffer, P.B. Corkum, D.M. Villeneuve, Nature (London) 432, 867 (2004)

    Article  ADS  Google Scholar 

  5. O. Smirnova, Y. Mairesse, S. Patchkovskii, N. Dudovich, D. Villeneuve, P. Corkum, M.Y. Ivanov, Nature (London) 460, 972 (2009)

    Article  ADS  Google Scholar 

  6. T. Das, B.B. Augstein, C. Figueira de Morisson Faria, Phys. Rev. A 88, 023404 (2013)

  7. C. Figueira de Morisson Faria, Phys. Rev. A 76, 043407 (2007)

    Article  ADS  Google Scholar 

  8. S. Odžak, E. Hasović, D.B. Milošević, Phys. Rev. A 93, 043413 (2016)

    Article  ADS  Google Scholar 

  9. D. Habibović, D.B. Milošević, Photonics 7, 110 (2020)

    Article  Google Scholar 

  10. S. Beaulieu, A. Comby, B. Fabre, D. Descamps, A. Ferre, G. Garcia, R. Geneaux, F. Legare, L. Nahon, S. Petit, T. Ruchon, B. Pons, V. Blanchet, Y. Mairesse, Faraday Discuss. 194, 325 (2016)

    Article  ADS  Google Scholar 

  11. L. Nahon, L. Nag, G.A. Garcia, I. Myrgorodska, U. Meierhenrich, S. Beaulieu, V. Wanie, V. Blanchet, R. Géneaux, I. Powis, Phys. Chem. Chem. Phys. 18, 12696 (2016)

    Article  Google Scholar 

  12. R. Hadidi, D.K. Bozanic, G.A. Garcia, L. Nahon, Adv. Phys. X 3, 1477530 (2018)

    Google Scholar 

  13. S. Beaulieu, A. Comby, D. Descamps, B. Fabre, G.A. Garcia, R. Géneaux, A.G. Harvey, F. Légaré, Z. Mašín, L. Nahon, A.F. Ordonez, S. Petit, B. Pons, Y. Mairesse, O. Smirnova, V. Blanchet, Nat. Phys. 14, 484 (2018)

    Article  Google Scholar 

  14. P.V. Demekhin, A.N. Artemyev, A. Kastner, T. Baumert, Phys. Rev. Lett. 121, 253201 (2018)

    Article  ADS  Google Scholar 

  15. U. Hergenhahn, E.E. Rennie, O. Kugeler, S. Marburger, T. Lischke, I. Powis, G. Garcia, J. Chem. Phys. 120, 4553 (2004)

    Article  ADS  Google Scholar 

  16. N. Böwering, T. Lischke, B. Schmidtke, N. Müller, T. Khalil, U. Heinzmann, Phys. Rev. Lett. 86, 1187 (2001)

    Article  ADS  Google Scholar 

  17. P. Fischer, D.H. Kim, W. Chao, J.A. Liddle, E.H. Anderson, D.T. Attwood, Mater. Today 9, 26 (2006)

    Article  Google Scholar 

  18. S. Eisebitt, J. Lüning, W.F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt, J. Stöhr, Nature (London) 432, 885 (2004)

    Article  ADS  Google Scholar 

  19. C. Boeglin, E. Beaurepaire, V. Halte, V. Lopez-Flores, C. Stamm, N. Pontius, H.A. Durr, J.Y. Bigot, Nature (London) 465, 458 (2010)

    Article  ADS  Google Scholar 

  20. O. Kfir, S. Zayko, C. Nolte, M. Sivis, M. Möller, B. Hebler, S.S.P.K. Arekapudi, D. Steil, S. Schäfer, M. Albrecht, O. Cohen, S. Mathias, C. Ropers, Sci. Adv. 3, eaao4641 (2017)

    Article  Google Scholar 

  21. J.L. Ellis, K.M. Dorney, D.D. Hickstein, N.J. Brooks, C. Gentry, C. Hernández-García, D. Zusin, J.M. Shaw, Q.L. Nguyen, C.A. Mancuso, G.S.M. Jansen, S. Witte, H.C. Kapteyn, M.M. Murnane, Optica 5, 479 (2018)

    Article  ADS  Google Scholar 

  22. T. Fan, P. Grychtol, R. Knut, C. Hernández-García, D.D. Hickstein, D. Zusin, C. Gentry, F.J. Dollar, C.A. Mancuso, C.W. Hogle, O. Kfir, D. Legut, K. Carva, J.L. Ellis, K.M. Dorney, C. Chen, O.G. Shpyrko, E.E. Fullerton, O. Cohen, P.M. Oppeneer, D.B. Milošević, A. Becker, A.A. Jaroń-Becker, T. Popmintchev, M.M. Murnane, H.C. Kapteyn, Proc. Natl. Acad. Sci. USA 112, 14206 (2015)

    Article  ADS  Google Scholar 

  23. D.B. Milošević, W. Becker, Phys. Rev. A 100, 031401(R) (2019)

    Article  ADS  Google Scholar 

  24. D.B. Milošević, W. Becker, J. Phys, J. Phys.: Conf. Ser. 1508, 012001 (2020)

    Google Scholar 

  25. D.B. Milošević, W. Becker, Phys. Rev. A 102, 023107 (2020)

    Article  ADS  Google Scholar 

  26. M.D. Perry, J.K. Crane, Phys. Rev. A 48, R4051 (1993)

    Article  ADS  Google Scholar 

  27. H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, J.K. McIver, Phys. Rev. A 51, R3414 (1995)

    Article  ADS  Google Scholar 

  28. I.J. Kim, C.M. Kim, H.T. Kim, G.H. Lee, Y.S. Lee, J.Y. Park, D.J. Cho, C.H. Nam, Phys. Rev. Lett. 94, 243901 (2005)

    Article  ADS  Google Scholar 

  29. L. Brugnera, D.J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J.W.G. Tisch, J.P. Marangos, Phys. Rev. Lett. 107, 153902 (2011)

    Article  ADS  Google Scholar 

  30. H. Niikura, H.J. Wörner, D.M. Villeneuve, P.B. Corkum, Phys. Rev. Lett. 107, 093004 (2011)

    Article  ADS  Google Scholar 

  31. G. Li, Y. Zheng, X. Ge, Z. Zeng, R. Li, Opt. Express 24, 18685 (2016)

    Article  ADS  Google Scholar 

  32. D. Shafir, H. Soifer, B.D. Bruner, M. Dagan, Y. Mairesse, S. Patchkovskii, M.Y. Ivanov, O. Smirnova, N. Dudovich, Nature (London) 485, 343 (2012)

    Article  ADS  Google Scholar 

  33. E. Bordo, O. Neufeld, O. Kfir, A. Fleischer, O. Cohen, Phys. Rev. A 100, 043419 (2019)

    Article  ADS  Google Scholar 

  34. M. Murakami, O. Korobkin, M. Horbatsch, Phys. Rev. A 88, 063419 (2013)

    Article  ADS  Google Scholar 

  35. M. Murakami, O. Korobkin, M. Horbatsch, Phys. Rev. A 95, 059909(E) (2017)

    Article  ADS  Google Scholar 

  36. L. Brugnera, F. Frank, D.J. Hoffmann, R. Torres, T. Siegel, J.G. Underwood, E. Springate, C. Froud, E.I.C. Turcu, J.W.G. Tisch, J.P. Marangos, Opt. Lett. 35, 3994 (2010)

    Article  ADS  Google Scholar 

  37. Y. Zheng, H. Diao, Z. Zeng, X. Ge, R. Li, Z. Xu, Phys. Rev. A 92, 033417 (2015)

    Article  ADS  Google Scholar 

  38. A.-S. Emelina, M. Emelin, R.A. Ganeev, M. Suzuki, H. Kuroda, V.V. Strelkov, Opt. Express 24, 13971 (2016)

    Article  ADS  Google Scholar 

  39. S. Watanabe, K. Kondo, Y. Nabekawa, A. Sagisaka, Y. Kobayashi, Phys. Rev. Lett. 73, 2692 (1994)

    Article  ADS  Google Scholar 

  40. K.-J. Yuan, C. Lefebvre, S. Chelkowski, H. Lu, A.D. Bandrauk, Phys. Rev. A 101, 023411 (2020)

    Article  ADS  Google Scholar 

  41. B. Zhang, M. Lein, Phys. Rev. A 100, 043401 (2019)

    Article  ADS  Google Scholar 

  42. O. Neufeld, D. Podolsky, O. Cohen, Nat. Commun. 10, 405 (2019)

    Article  ADS  Google Scholar 

  43. O. Neufeld, O. Cohen, Phys. Rev. Lett. 123, 103202 (2019)

    Article  ADS  Google Scholar 

  44. O. Neufeld, O. Cohen, Phys. Rev. Res. 2, 033037 (2020)

    Article  Google Scholar 

  45. A.J. Uzan, H. Soifer, O. Pedatzur, A. Clergerie, S. Larroque, B.D. Bruner, B. Pons, M. Ivanov, O. Smirnova, N. Dudovich, Nature Photon. 14, 188 (2020)

    Article  ADS  Google Scholar 

  46. A. Etches, M.B. Gaarde, L.B. Madsen, Phys. Rev. A 84, 023418 (2011)

    Article  ADS  Google Scholar 

  47. J. Heslar, D. Telnov, S.I. Chu, Phys. Rev. A 83, 043414 (2011)

    Article  ADS  Google Scholar 

  48. H. Hu, N. Li, P. Liu, R. Li, Z. Xu, Phys. Rev. Lett. 119, 173201 (2017)

    Article  ADS  Google Scholar 

  49. M. Qin, X. Zhu, Q. Zhang, W. Hong, P. Lu, Opt. Express 19, 25085 (2011)

    ADS  Google Scholar 

  50. N. Sun, X. Zhu, B. Wang, D. Wang, R. Shao, P. Lan, P. Lu, Phys. Rev. A 101, 053437 (2020)

    Article  ADS  Google Scholar 

  51. S. Yu, B. Zhang, Y. Li, S. Yang, Y. Chen, Phys. Rev. A 90, 053844 (2014)

    Article  ADS  Google Scholar 

  52. A. Etches, M.B. Gaarde, L.B. Madsen, Phys. Rev. A 86, 023818 (2012)

    Article  ADS  Google Scholar 

  53. Y. Chen, B. Zhang, Phys. Rev. A 84, 053402 (2011)

    Article  ADS  Google Scholar 

  54. B.B. Augstein, C. Figueira de Morisson Faria, J. Phys. B 44, 055601 (2011)

    Article  ADS  Google Scholar 

  55. H. Du, L. Luo, X. Wang, B. Hu, Phys. Rev. A 86, 013846 (2012)

    Article  ADS  Google Scholar 

  56. P.W. Atkins, R.S. Friedman, Molecular Quantum Mechanics, 3rd edn. (Oxford University Press, Oxford, 2001)

    Google Scholar 

  57. A. Etches, L.B. Madsen, J. Phys. B 43, 055602 (2010)

    Article  Google Scholar 

  58. D. Dimitrovski, C.P.J. Martiny, L.B. Madsen, Phys. Rev. A 82, 053404 (2010)

    Article  ADS  Google Scholar 

  59. B.A. Zon, E.I. Sholokhov, Zh Eksp, Zh. Eksp. Teor. Fiz. 70, 887 (1976)

    ADS  Google Scholar 

  60. B.A. Zon, E.I. Sholokhov, Sov. Phys. JETP 43, 461 (1976)

    ADS  Google Scholar 

  61. S. Odžak, D.B. Milošević, J. Opt. Soc. Am. B 29, 2147 (2012)

    Article  ADS  Google Scholar 

  62. X.S. Zhu, Q.B. Zhang, W.Y. Hong, P.X. Lu, C.L. Cocke, Phys. Rev. A 84, 043429 (2011)

    Article  ADS  Google Scholar 

  63. D.B. Milošević, F. Ehlotzky, Adv. At., Mol., Opt. Phys. 49, 373 (2003)

  64. T.F. Gallagher, Phys. Rev. Lett. 61, 2304 (1988)

    Article  ADS  Google Scholar 

  65. P.B. Corkum, N.H. Burnett, F. Brunel, Phys. Rev. Lett. 62, 1259 (1989)

    Article  ADS  Google Scholar 

  66. K.J. Schafer, B. Jang, L.F. DiMauro, K.C. Kulander, Phys. Rev. Lett. 70, 1599 (1993)

    Article  ADS  Google Scholar 

  67. N. Suárez, A. Chacón, J.A. Pérez-Hernández, J. Biegert, M. Lewenstein, M.F. Ciappina, Phys. Rev. A 95, 033415 (2017)

    Article  ADS  Google Scholar 

  68. B. Fetić, D.B. Milošević, Phys. Rev. A 99, 043426 (2019)

    Article  ADS  Google Scholar 

  69. D. Habibović, A. Gazibegović-Busuladžić, M. Busuladžić, A. Čerkić, D.B. Milošević, Phys. Rev. A 102, 023111 (2020)

    Article  ADS  Google Scholar 

  70. D.B. Milošević, J. Phys. B 33, 2479 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  71. R. Kopold, D.B. Milošević, W. Becker, Phys. Rev. Lett. 84, 3831 (2000)

    Article  ADS  Google Scholar 

  72. D.B. Milošević, D. Bauer, W. Becker, J. Mod. Opt. 53, 125 (2006)

    Article  ADS  Google Scholar 

  73. D.B. Milošević, Strong-field approximation and quantum orbits, in Computational Strong-Field Quantum Dynamics: Intense Light-Matter Interactions, ed. by D. Bauer (De Gruyter Textbook, Berlin, 2016)

    Google Scholar 

  74. S. Odžak, D.B. Milošević, J. Phys. B 44, 125602 (2011)

    Article  ADS  Google Scholar 

  75. D.B. Milošević, W. Becker, Phys. Rev. A 66, 063417 (2002)

    Article  ADS  Google Scholar 

  76. S. Odžak, D.B. Milošević, Phys. Rev. A 79, 023414 (2009)

    Article  ADS  Google Scholar 

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Acknowledgements

We gratefully acknowledge support by the Ministry for Education, Science and Youth Canton Sarajevo, Bosnia and Herzegovina, and the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Faculty of Science, University of Sarajevo, Zmaja od Bosne 35, 71000, Sarajevo, Bosnia and Herzegovina

    Dino Habibović & Dejan B. Milošević

  2. Max-Born-Institut for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Strasse 2a, 12489, Berlin, Germany

    Wilhelm Becker & Dejan B. Milošević

  3. National Research Nuclear University MEPhI, Kashirskoe Shosse 31, 115409, Moscow, Russia

    Wilhelm Becker

  4. Academy of Sciences and Arts of Bosnia and Herzegovina, Bistrik 7, 71000, Sarajevo, Bosnia and Herzegovina

    Dejan B. Milošević

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  1. Dino Habibović
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All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

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Correspondence to Dejan B. Milošević.

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Quantum Aspects of Attoscience - edited by Carla Figueira de Morisson Faria, Andrew Brown, David B. Cassidy.

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Habibović, D., Becker, W. & Milošević, D.B. High-order harmonic generation by aligned heteronuclear diatomic molecules in an orthogonally polarized two-color laser field. Eur. Phys. J. D 75, 122 (2021). https://doi.org/10.1140/epjd/s10053-021-00133-4

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