Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Spin angular momentum and tunable polarization in high-harmonic generation

Abstract

The roles of energy, momentum and orbital angular momentum conservation in high-harmonic generation were studied in the past. Here, we explore the role of spin angular momentum in high-harmonic generation by experimentally generating high harmonics of bichromatic elliptically polarized pump beams that interact with isotropic media. We explain qualitatively many observed intricate selection rules with a model that includes spin conservation in the conversion of many pump photons into a single photon. However, we also observe unequivocal deviations from this model, indicating that emission of an elliptically polarized high-energy photon is accompanied by an additional excitation (radiative or electronic). The presented results are also important for applications, because our system exhibits full control over the polarization of the harmonics, from circular through elliptical to linear polarization, without compromising the efficiency of the process. This work paves the way for a broad range of applications with high-harmonic generation, including ultrafast circular dichroism of molecules and magnetic materials.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Schematic of experimental set-up.
Figure 2: Experimental and numerical HHG spectra.
Figure 3: Experimental and numerical HHG polarization.
Figure 4: Spin conservation strong-field correction terms for different harmonic channels.

References

  1. Goulielmakis, E. et al. Real-time observation of valence electron motion. Nature 466, 739–744 (2010).

    ADS  Article  Google Scholar 

  2. Baker, S. et al. Probing proton dynamics in molecules on an attosecond time scale. Science 312, 424–427 (2006).

    ADS  Article  Google Scholar 

  3. Li, W. et al. Time-resolved dynamics in N2O4 probed using high harmonic generation. Science 322, 1207–1211 (2008).

    ADS  Article  Google Scholar 

  4. Wörner, H. J., Bertrand, J. B., Kartashov, D. V., Corkum, P. B. & Villeneuve, D. M. Following a chemical reaction using high-harmonic interferometry. Nature 466, 604–607 (2010).

    ADS  Article  Google Scholar 

  5. Cavalieri, A. L. et al. Attosecond spectroscopy in condensed matter. Nature 449, 1029–1032 (2007).

    ADS  Article  Google Scholar 

  6. Mathias. S. et al. Probing the timescale of the exchange interaction in a ferromagnetic alloy. Proc. Natl Acad. Sci. USA 109, 4792–4797 (2012).

    ADS  Article  Google Scholar 

  7. Salières, P. et al. Frequency-domain interferometry in the XUV with high-order harmonics. Phys. Rev. Lett. 83, 5483–5486 (1999).

    ADS  Article  Google Scholar 

  8. Seaberg, M. D. et al. Ultrahigh 22 nm resolution coherent diffractive imaging using a desktop 13 nm high harmonic source. Opt. Express 19, 22470–22479 (2011).

    ADS  Article  Google Scholar 

  9. Siemens, M. E. et al. Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams. Nature Mater. 9, 26–30 (2010).

    ADS  Article  Google Scholar 

  10. Corkum, P. B. Plasma perspective on strong field multiphoton ionization. Phys. Rev. Lett. 71, 1994–1997 (1993).

    ADS  Article  Google Scholar 

  11. Boyd, R. W. Nonlinear Optics 3rd edn (Academic, 2008).

    Google Scholar 

  12. Bloembergen, N. Conservation laws in nonlinear optics. J. Opt. Soc. Am. 70, 1429–1436 (1980).

    ADS  Article  Google Scholar 

  13. Eden, J. G. High-order harmonic generation and other intense optical field–matter interactions: review of recent experimental and theoretical advances. Prog. Quantum Electron. 28, 197–246 (2004).

    ADS  Article  Google Scholar 

  14. Perry, M. D. & Crane, J. K. High-order harmonic emission from mixed fields. Phys. Rev. A. 48, R4051–R4054 (1993).

    ADS  Article  Google Scholar 

  15. Bertrand, J. B. et al. Ultrahigh-order wave mixing in noncollinear high harmonic generation. Phys. Rev. Lett. 106, 023001 (2011).

    ADS  Article  Google Scholar 

  16. Gariepy G. et al. Conservation of Orbital Angular Momentum in High-Harmonic Generation. MSc thesis, Univ. Ottawa (2013).

  17. Lewenstein, M., Balcou, Ph., Ivanov, M. Yu., L'Huillier, A. & Corkum, P. B. Theory of high-harmonic generation by low-frequency laser fields. Phys. Rev. A 49, 2117–2132 (1994).

    ADS  Article  Google Scholar 

  18. Weihe, F. A. et al. Polarization of high-intensity high-harmonic generation. Phys. Rev. A 51, R3433–R3436 (1995).

    ADS  Article  Google Scholar 

  19. Strelkov, V. V., Gonoskov, A. A., Gonoskov, I. A. & Ryabikin, M. Yu. Origin for ellipticity of high-order harmonics generated in atomic gases and the sublaser-cycle evolution of harmonic polarization. Phys. Rev. Lett. 107, 043902 (2011).

    ADS  Article  Google Scholar 

  20. Antoine, P., Carré, B., L'Huiller, A. & Lewenstein, M. Polarization of high-order harmonics. Phys. Rev. A 55, 1314–1324 (1997).

    ADS  Article  Google Scholar 

  21. Zhou, X. et al. Elliptically polarized high-order harmonic emission from molecules in linearly polarized laser fields. Phys. Rev. Lett. 102, 073902 (2009).

    ADS  Article  Google Scholar 

  22. Mairesse, Y. et al. High harmonic spectroscopy of multichannel dynamics in strong-field ionization. Phys. Rev. Lett. 104, 213601 (2010).

    ADS  Article  Google Scholar 

  23. Dietrich, P., Burnett, N. H., Ivanov, M. & Corkum, P. B. High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light. Phys. Rev. A 50, R3585 (1994).

    ADS  Article  Google Scholar 

  24. Vodungbo, B. et al. Polarization control of high order harmonics in the EUV photon energy range. Opt. Express 19, 4346–4356 (2011).

    ADS  Article  Google Scholar 

  25. Alon, O. E., Averbukh, V. & Moiseyev, N. Selection rules for the high harmonic generation spectra. Phys. Rev. Lett. 80, 3743–3746 (1998).

    ADS  Article  Google Scholar 

  26. Husakou, A., Kelkensberg, F., Herrmann, J. & Vrakking, M. J. J. Polarization gating and circularly-polarized high harmonic generation using plasmonic enhancement in metal nanostructures. Opt. Express 19, 25346–25354 (2011).

    ADS  Article  Google Scholar 

  27. Yuan, K.-J. & Bandrauk, A. D. Generation of circularly polarized attosecond pulses by intense ultrashort laser pulses from extended asymmetric molecular ions. Phys. Rev. A 84, 023410 (2011).

    ADS  Article  Google Scholar 

  28. Fleischer, A. et al. Generation of high-order harmonics with controllable elliptical polarization. Opt. Lett. 38, 223–225 (2013).

    ADS  Article  Google Scholar 

  29. Ruiz, C., Hoffmann, D. J., Torres, R., Chipperfield, L. E. & Marangos, J. P. Control of the polarization of attosecond pulses using a two-color field. New J. Phys. 11, 113045 (2009).

    ADS  Article  Google Scholar 

  30. Long, S., Becker, W. & McIver, J. K. Model calculations of polarization-dependent two-color high-harmonic generation. Phys. Rev. A 52, 2262–2278 (1995).

    ADS  Article  Google Scholar 

  31. Eichmann, H. et al. Polarization-dependent high-order two-color mixing. Phys. Rev. A 51, R3414 (1995).

    ADS  Article  Google Scholar 

  32. Kfir, O. et al. Generation of phase-matched circularly-polarized extreme ultraviolet high harmonics for magnetic circular dichroism spectroscopy. http://arxiv.org/abs/1401.4101(2014).

  33. Boeglin, C. et al. Distinguishing the ultrafast dynamics of spin and orbital moments in solids. Nature 465, 458–461 (2010).

    ADS  Article  Google Scholar 

  34. Jahnke, T. et al. Circular dichroism in k-shell ionization from fixed-in-space CO and N2 molecules. Phys. Rev. Lett. 88, 073002 (2002).

    ADS  Article  Google Scholar 

  35. Wang, Y. & Gedik, N. Circular dichroism in angle-resolved photoemission spectroscopy of topological insulators. Phys. Status Solidi 7, 64–71 (2013).

    Google Scholar 

  36. Eckle, P. et al. Attosecond ionization and tunneling delay time measurements in helium. Science 322, 1525–1529 (2008).

    ADS  Article  Google Scholar 

  37. Fleischer, A. et al. Probing angular correlations in sequential double ionization. Phys. Rev. Lett. 107, 113003 (2011).

    ADS  Article  Google Scholar 

  38. Hernández-García, C. et al. Zeptosecond high harmonic keV X-ray waveforms driven by midinfrared laser pulses. Phys. Rev. Lett. 111, 033002 (2013).

    ADS  Article  Google Scholar 

  39. Milošević, D. B. & Becker, W. Attosecond pulse trains with unusual nonlinear polarization. Phys. Rev. A 62, 011403(R) 10.1103/PhysRevA.62.011403(2000).

    ADS  Article  Google Scholar 

  40. Milošević, D. B. & Sandner, W. Extreme-ultraviolet harmonic generation near 13 nm with a two-color elliptically polarized laser field. Opt. Lett. 25, 1532–1534 (2000).

    ADS  Article  Google Scholar 

  41. Lamberti, C. et al. Oxide/metal interface distance and epitaxial strain in the NiO/Ag(001) system. Phys. Rev. Lett. 91, 046101 (2003).

    ADS  Article  Google Scholar 

  42. Vondungbo, B. et al. Laser-induced ultrafast demagnetization in the presence of a nanoscale magnetic domain network. Nature Commun. 3, 999 (2012).

    ADS  Article  Google Scholar 

  43. Cinchetti, M. et al. Spin-flip processes and ultrafast magnetization dynamics in Co: unifying the microscopic and macroscopic view of femtosecond magnetism. Phys. Rev. Lett. 97, 177201 (2006).

    ADS  Article  Google Scholar 

  44. Stamm, C. et al. Femtosecond modification of electron localization and transfer of angular momentum in nickel. Nature Mater. 6, 740–743 (2007).

    ADS  Article  Google Scholar 

  45. Smirnova, O. et al. Attosecond circular dichroism spectroscopy of polyatomic molecules. Phys. Rev. Lett. 102, 063601 (2009).

    ADS  Article  Google Scholar 

  46. McFarland, B. K., Farrell, J. P., Bucksbaum, P. H. & Gühr, M. High harmonic generation from multiple orbitals in N2 . Science 322, 1232–1235 (2008).

    ADS  Article  Google Scholar 

  47. Xie, X. et al. Internal momentum state mapping using high harmonic radiation. Phys. Rev. Lett. 101, 033901 (2008).

    ADS  Article  Google Scholar 

  48. Barth, I., Manz, J., Shigeta, Y. & Yagi, K. Unidirectional electronic ring current driven by a few cycle circularly polarized laser pulse: quantum model simulations for Mg-porphyrin. J. Am. Chem. Soc. 128, 7043–7049 (2006).

    Article  Google Scholar 

  49. Kaminski, A. et al. Spontaneous breaking of time-reversal symmetry in the pseudogap state of a high-Tc superconductor. Nature 416, 610–613 (2002).

    ADS  Article  Google Scholar 

  50. Gao, J., Shen, F. & Eden, J. G. Quantum electrodynamic treatment of harmonic generation in intense optical fields. Phys. Rev. Lett. 81, 1833–1836 (1998).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The authors thank T. Yasniger, S. Avikzar, A. Anashkin and D. Cohen from the Technion for technical assistance. This work was support by ICore—the Israeli Excellence Center ‘Circle of Light’.

Author information

Authors and Affiliations

Authors

Contributions

A.F. and O.C. conceived the idea. A.F., O.K. and P.S. carried out experiments. A.F. and T.D. carried out the numerical analysis. All authors contributed to the analysis, interpretation and writing of the manuscript. O.C. supervised the project.

Corresponding authors

Correspondence to Avner Fleischer or Oren Cohen.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2572 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fleischer, A., Kfir, O., Diskin, T. et al. Spin angular momentum and tunable polarization in high-harmonic generation. Nature Photon 8, 543–549 (2014). https://doi.org/10.1038/nphoton.2014.108

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2014.108

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing