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Non-collinear generation of angularly isolated circularly polarized high harmonics

An Erratum to this article was published on 29 January 2016

This article has been updated


We generate angularly isolated beams of circularly polarized extreme ultraviolet light through the first implementation of non-collinear high harmonic generation with circularly polarized driving lasers. This non-collinear technique offers numerous advantages over previous methods, including the generation of higher photon energies, the separation of the harmonics from the pump beam, the production of both left and right circularly polarized harmonics at the same wavelength and the capability of separating the harmonics without using a spectrometer. To confirm the circular polarization of the beams and to demonstrate the practicality of this new light source, we measure the magnetic circular dichroism of a 20 nm iron film. Furthermore, we explain the mechanisms of non-collinear high harmonic generation using analytical descriptions in both the photon and wave models. Advanced numerical simulations indicate that this non-collinear mixing enables the generation of isolated attosecond pulses with circular polarization.

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Figure 1: Non-collinear circularly polarized high harmonic generation (NCP-HHG).
Figure 2: NCP-HHG using two 800 nm pulses.
Figure 3: Photon and wave models of non-collinear HHG.
Figure 4: NCP-HHG driven by different frequency driving lasers (400 and 800 nm).
Figure 5: EUV MCD of an iron film.
Figure 6: Numerical simulations reveal additional capabilities of the NCP-HHG method.

Change history

  • 07 October 2015

    In the version of this Article originally published the arrows in Fig. 1b indicating the direction of circular polarization were incorrect and several equations contained typographical errors and should have contained tan functions. These errors have been corrected in all versions of the Article.

  • 15 December 2015

    In the version of this Article originally published the blue dashed line was mislabelled in the legend in Fig. 3d and the label should have read i Evert. This has now been corrected in the online versions of the Article.


  1. 1

    McPherson, A. et al. Studies of multiphoton production of vacuum-ultraviolet. J. Opt. Soc. Am. B 4, 595–601 (1987).

    ADS  Article  Google Scholar 

  2. 2

    Ferray, M. et al. Multiple-harmonic conversion of 1064 nm radiation in rare gases. J. Phys. B 21, L31–L35 (1988).

    Article  Google Scholar 

  3. 3

    Rundquist, A. et al. Phase-matched generation of coherent soft X-rays. Science 280, 1412–1415 (1998).

    ADS  Article  Google Scholar 

  4. 4

    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 

  5. 5

    Seaberg, M. D. et al. Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography. Optica 1, 39–44 (2014).

    ADS  Article  Google Scholar 

  6. 6

    Adams, D. E., Wood, C., Murnane, M. M. & Kapteyn, H. C. Tabletop high harmonics illuminate the nano-world. Laser Focus World (4 May 2015);

  7. 7

    Ravasio, A. et al. Single-shot diffractive imaging with a table-top femtosecond soft X-ray laser-harmonics source. Phys. Rev. Lett. 103, 028104 (2009).

    ADS  Article  Google Scholar 

  8. 8

    Miao, J., Ishikawa, T., Robinson, I. K. & Murnane, M. M. Diffractive imaging with coherent X-ray sources. Science 348, 530–535 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  9. 9

    Hoogeboom-Pot, K. M. et al. A new regime of nanoscale thermal transport: collective diffusion counteracts dissipation inefficiency. Proc. Natl Acad. Sci. USA 112, 4846–4851 (2014).

    ADS  Article  Google Scholar 

  10. 10

    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 

  11. 11

    Turgut, E. et al. Controlling the competition between optically induced ultrafast spin-flip scattering and spin transport in magnetic multilayers. Phys. Rev. Lett. 110, 197201 (2013).

    ADS  Article  Google Scholar 

  12. 12

    Miaja-Avila, L. et al. Direct measurement of core-level relaxation dynamics on a surface-adsorbate system. Phys. Rev. Lett. 101, 46101 (2008).

    ADS  Article  Google Scholar 

  13. 13

    Beaurepaire, E., Merle, J.-C., Daunois, A. & Bigot, J.-Y. Ultrafast spin dynamics in ferromagnetic nickel. Phys. Rev. Lett. 76, 4250–4253 (1996).

    ADS  Article  Google Scholar 

  14. 14

    Bigot, J.-Y., Vomir, M. & Beaurepaire, E. Coherent ultrafast magnetism induced by femtosecond laser pulses. Nature Phys. 5, 515–520 (2009).

    ADS  Article  Google Scholar 

  15. 15

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

    ADS  Article  Google Scholar 

  16. 16

    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 

  17. 17

    Lambert, G. et al. Towards enabling femtosecond helicity-dependent spectroscopy with high-harmonic sources. Nature Commun. 6, 6167 (2015).

    ADS  Article  Google Scholar 

  18. 18

    Ferré, A. et al. A table-top ultrashort light source in the extreme ultraviolet for circular dichroism experiments. Nature Photon. 9, 93–98 (2015).

    ADS  Article  Google Scholar 

  19. 19

    Yuan, K. J. & Bandrauk, A. D. Circularly polarized molecular high-order harmonic generation in H2+ with intense laser pulses and static fields. Phys. Rev. A 83, 063422 (2011).

    ADS  Article  Google Scholar 

  20. 20

    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 

  21. 21

    Fleischer, A., Kfir, O., Diskin, T., Sidorenko, P. & Cohen, O. Spin angular momentum and tunable polarization in high-harmonic generation. Nature Photon. 8, 543–549 (2014).

    ADS  Article  Google Scholar 

  22. 22

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

    ADS  Article  Google Scholar 

  23. 23

    Milošević, D. B., Becker, W. & Kopold, R. Generation of circularly polarized high-order harmonics by two-color coplanar field mixing. Phys. Rev. A 61, 063403 (2000).

    ADS  Article  Google Scholar 

  24. 24

    Kfir, O. et al. Generation of bright circularly-polarized extreme ultraviolet high harmonics for magnetic circular dichroism spectroscopy. Nature Photon. 9, 99–105 (2015).

    ADS  Article  Google Scholar 

  25. 25

    Fan, T. et al. Bright circularly polarized soft X-Ray high harmonics for X-Ray magnetic circular dichroism. CLEO 2015 Postdeadline Papers Digest JTh5C.1 (2015).

    Google Scholar 

  26. 26

    Milošević, D. Generation of elliptically polarized attosecond pulse trains. Opt. Lett. 40, 2381–2384 (2015).

    ADS  Article  Google Scholar 

  27. 27

    Vincenti, H. & Quéré, F. Attosecond lighthouses: how to use spatiotemporally coupled light fields to generate isolated attosecond pulses. Phys. Rev. Lett. 108, 113904 (2012).

    ADS  Article  Google Scholar 

  28. 28

    Quéré, F. et al. Applications of ultrafast wavefront rotation in highly nonlinear optics. J. Phys. B 47, 124004 (2014).

    ADS  Article  Google Scholar 

  29. 29

    Heyl, C. M. et al. Noncollinear optical gating. New J. Phys 16, 052001 (2014).

    ADS  Article  Google Scholar 

  30. 30

    Louisy, M. et al. Gating attosecond pulses in a noncollinear geometry. Optica 2, 563–566 (2015).

    ADS  Article  Google Scholar 

  31. 31

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

    ADS  Article  Google Scholar 

  32. 32

    Ivanov, M. & Pisanty, E. High-harmonic generation: taking control of polarization. Nature Photon. 8, 501–503 (2014).

    ADS  Article  Google Scholar 

  33. 33

    Pisanty, E., Sukiasyan, S. & Ivanov, M. Spin conservation in high-order-harmonic generation using bicircular fields. Phys. Rev. A 90, 043829 (2014).

    ADS  Article  Google Scholar 

  34. 34

    Mancuso, C. A. et al. Strong-field ionization with two-color circularly polarized laser fields. Phys. Rev. A 91, 031402(R) (2015).

    ADS  Article  Google Scholar 

  35. 35

    Durfee, C. G. et al. Phase matching of high-order harmonics in hollow waveguides. Phys. Rev. Lett. 83, 2187 (1999).

    ADS  Article  Google Scholar 

  36. 36

    Eichmann, H. et al. Polarization-dependent high-order two-color mixing. Phys. Rev. A 51, R3414–R3417 (1995).

    ADS  Article  Google Scholar 

  37. 37

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

    ADS  Article  Google Scholar 

  38. 38

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

    ADS  Article  Google Scholar 

  39. 39

    Höchst, H., Zhao, D. & Huber, D. L. M2,3 magnetic circular dichroism (MCD) measurements of Fe, Co and Ni using a newly developed quadruple reflection phase shifter. Surf. Sci. 352–354, 998–1002 (1996).

    ADS  Article  Google Scholar 

  40. 40

    Valencia, S. et al. Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni. New J. Phys. 8, 254 (2006).

    ADS  Article  Google Scholar 

  41. 41

    Yuan, K. J. & Bandrauk, A. D. Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media. Phys. Rev. Lett. 110, 023003 (2013).

    ADS  Article  Google Scholar 

  42. 42

    Yuan, K.-J. & Bandrauk, A. D. Attosecond-magnetic-field-pulse generation by coherent circular molecular electron wave packets. Phys. Rev. A 91, 042509 (2015).

    ADS  Article  Google Scholar 

  43. 43

    Popmintchev, T., Chen, M.-C., Arpin, P., Murnane, M. M. & Kapteyn, H. C. The attosecond nonlinear optics of bright coherent X-ray generation. Nature Photon. 4, 822–832 (2010).

    ADS  Article  Google Scholar 

  44. 44

    Ding, C. et al. High flux coherent super-continuum soft X-ray source driven by a single-stage, 10mJ, Ti:sapphire amplifier-pumped OPA. Opt. Express 22, 6194–6202 (2014).

    ADS  Article  Google Scholar 

  45. 45

    Popmintchev, D. et al. Ultrahigh-efficiency high harmonic generation driven by UV lasers. CLEO 2013 OSA Technical Digest QW1A.5 (2013).

  46. 46

    Ferrari, F. et al. High-energy isolated attosecond pulses generated by above-saturation few-cycle fields. Nature Photon. 4, 875–879 (2010).

    ADS  Article  Google Scholar 

  47. 47

    Oppeneer, P. M. Handbook of Magnetic Materials (Elsevier, 2001).

    Google Scholar 

  48. 48

    Stohr, J. & Siegmann, H. C. Magnetism: From Fundamentals to Nanoscale Dynamics (Springer, 2006).

    Google Scholar 

  49. 49

    Hernández-García, C. et al. High-order harmonic propagation in gases within the discrete dipole approximation. Phys. Rev. A 82, 033432 (2010).

    ADS  Article  Google Scholar 

  50. 50

    Pérez-Hernández, J. A., Roso, L. & Plaja, L. Harmonic generation beyond the strong-field approximation: the physics behind the short-wave-infrared scaling laws. Opt. Express 17, 9891–9903 (2009).

    ADS  Article  Google Scholar 

  51. 51

    Keldysh, L. V. Ionization in the field of a string electromagnetic wave. Sov. Phys. JETP 20, 1307–1314 (1965).

    Google Scholar 

  52. 52

    Faisal, F. H. M. Multiple absorption of laser photons by atoms. J. Phys. B 6, L89–L92 (1973).

    ADS  Article  Google Scholar 

  53. 53

    Reiss, H. R. Effect of an intense electromagnetic field on a weakly bound system. Phys. Rev. A 22, 1786–1813 (1980).

    ADS  Article  Google Scholar 

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This work was completed at JILA. D.H., J.E., T.F., K.D., H.C. and M.M. acknowledge support from the Department of Energy BES Award DE-FG02-99ER14982. M.M., H.K. and C.D. acknowledge support from the National Science Foundation’s Engineering Research Centre in Extreme Ultraviolet Science and Technology. C.D. acknowledges support from the Air Force Office of Scientific Research under MURI grant FA9550-10-1-0561. J.E. acknowledges support from the National Science Foundation Graduate Research Fellowship (DGE-1144083). C.H.-G. acknowledges support from a Marie Curie International Outgoing Fellowship within the EU Seventh Framework Programme for Research and Technological Development (2007–2013), under REA grant agreement no. 328334. C. H.-G. acknowledges support from Junta de Castilla y León (Project SA116U13) and MINECO (FIS2013-44174-P). A.J.-B. was supported by grants from theNational Science Foundation (grants nos. PHY-1125844 and PHY-1068706). This work made use of the Janus supercomputer, which is supported by the National Science Foundation (award no. CNS-0821794) and the University of Colorado, Boulder. P.G. acknowledges support from the Deutsche Forschungsgemeinschaft (grant no. GR 4234/1–1). R.K. acknowledges the Swedish Research Council (VR) for financial support. A.B. acknowledges support from the Department of Energy, Office of Basic Sciences.

Author information




C.D., D.H., F.D., M.M. and H.K. conceived the NCP-HHG experiment. P.G., R.K., D.Z. and C.G. designed the MCD experiment. J.S. fabricated and characterized the magnetic sample. D.H., F.D., J.E., K.D., P.G., R.K., D.Z., C.G. and T.F. conducted the experiments. C.H.-G., C.D., A.J.-B. and A.B. conducted and interpreted the numerical simulations of HHG, including propagation. D.H., C.D., F.D., P.G., M.M., H.K. and C.H.-G. wrote the manuscript.

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Correspondence to Daniel D. Hickstein.

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Hickstein, D., Dollar, F., Grychtol, P. et al. Non-collinear generation of angularly isolated circularly polarized high harmonics. Nature Photon 9, 743–750 (2015).

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