Abstract

We used two 800 nm laser pulses propagating in the opposite directions, to drive the emission of high-order vacuum ultra-violet harmonics off of the surface of an MgO (100) single crystal. We demonstrated the advantages that our approach provides compared to a single beam geometry, in both forward and backward emission.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
    [Crossref]
  2. O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
    [Crossref]
  3. T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
    [Crossref]
  4. G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
    [Crossref]
  5. Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13(4), 345–349 (2017).
    [Crossref]
  6. M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
    [Crossref]
  7. G. Vampa, Y. S. You, H. Liu, S. Ghimire, and D. A. Reis, “Observation of backward high-harmonic emission from solids,” Opt. Express 26(9), 12210 (2018).
    [Crossref]
  8. http://henke.lbl.gov/optical_constants/filter2.html
  9. S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
    [Crossref]
  10. R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
    [Crossref]
  11. R. Stephens and I. Malitson, “Index of refraction of magnesium oxide,” J. Res. Natl. Bur. Stand. 49(4), 249 (1952).
    [Crossref]
  12. Y. S. You, M. Wu, Y. Yin, A. Chew, X. Ren, S. Gholam-Mirzaei, D. A. Browne, M. Chini, Z. Chang, K. J. Schafer, M. B. Gaarde, and S. Ghimire, “Laser waveform control of extreme ultraviolet high harmonics from solids,” Opt. Lett. 42(9), 1816 (2017).
    [Crossref]
  13. D. M. Roessler and W. C. Walker, “Electronic Spectrum and Ultraviolet Optical Properties of Crystalline MgO,” Phys. Rev. 159(3), 733–738 (1967).
    [Crossref]
  14. D. M. Roessler and W. C. Walker, “Optical Constants of Magnesium Oxide and Lithium Fluoride in the Far Ultraviolet,” J. Opt. Soc. Am. 57(6), 835 (1967).
    [Crossref]
  15. R. W. Boyd, Nonlinear Optics (Academic, 2008), 3rd ed.
  16. K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
    [Crossref]

2018 (1)

2017 (4)

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13(4), 345–349 (2017).
[Crossref]

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Y. S. You, M. Wu, Y. Yin, A. Chew, X. Ren, S. Gholam-Mirzaei, D. A. Browne, M. Chini, Z. Chang, K. J. Schafer, M. B. Gaarde, and S. Ghimire, “Laser waveform control of extreme ultraviolet high harmonics from solids,” Opt. Lett. 42(9), 1816 (2017).
[Crossref]

K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
[Crossref]

2015 (2)

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

2014 (1)

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

2012 (1)

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

2011 (1)

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

1989 (1)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
[Crossref]

1967 (2)

D. M. Roessler and W. C. Walker, “Electronic Spectrum and Ultraviolet Optical Properties of Crystalline MgO,” Phys. Rev. 159(3), 733–738 (1967).
[Crossref]

D. M. Roessler and W. C. Walker, “Optical Constants of Magnesium Oxide and Lithium Fluoride in the Far Ultraviolet,” J. Opt. Soc. Am. 57(6), 835 (1967).
[Crossref]

1952 (1)

R. Stephens and I. Malitson, “Index of refraction of magnesium oxide,” J. Res. Natl. Bur. Stand. 49(4), 249 (1952).
[Crossref]

Adair, R.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
[Crossref]

Agostini, P.

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Boyd, R. W.

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

Brabec, T.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Browne, D. A.

Chang, Z.

Chase, L. L.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
[Crossref]

Chew, A.

Chini, M.

Corkum, P. B.

K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
[Crossref]

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Dichiara, A. D.

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Dimauro, L. F.

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Ding, X.

Fermann, M. E.

Gaarde, M. B.

Garg, M.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

Ghimire, S.

G. Vampa, Y. S. You, H. Liu, S. Ghimire, and D. A. Reis, “Observation of backward high-harmonic emission from solids,” Opt. Express 26(9), 12210 (2018).
[Crossref]

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13(4), 345–349 (2017).
[Crossref]

Y. S. You, M. Wu, Y. Yin, A. Chew, X. Ren, S. Gholam-Mirzaei, D. A. Browne, M. Chini, Z. Chang, K. J. Schafer, M. B. Gaarde, and S. Ghimire, “Laser waveform control of extreme ultraviolet high harmonics from solids,” Opt. Lett. 42(9), 1816 (2017).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Gholam-Mirzaei, S.

Golde, D.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Goulielmakis, E.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

Hammond, T. J.

K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Hassan, M. T.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

Hohenleutner, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Huber, R.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Huttner, U.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Johnston, K.

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Kira, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Koch, S. W.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Lange, C.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Langer, F.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Lee, K. F.

Légaré, F.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Liu, H.

Luu, T. T.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

Malitson, I.

R. Stephens and I. Malitson, “Index of refraction of magnesium oxide,” J. Res. Natl. Bur. Stand. 49(4), 249 (1952).
[Crossref]

McDonald, C. R.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Meier, T.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Mohammad, A.

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

Moulet, A.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

Naumov, A. Y.

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Ndabashimiye, G.

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

Payne, S. A.

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
[Crossref]

Reis, D. A.

G. Vampa, Y. S. You, H. Liu, S. Ghimire, and D. A. Reis, “Observation of backward high-harmonic emission from solids,” Opt. Express 26(9), 12210 (2018).
[Crossref]

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13(4), 345–349 (2017).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Ren, X.

Roessler, D. M.

D. M. Roessler and W. C. Walker, “Optical Constants of Magnesium Oxide and Lithium Fluoride in the Far Ultraviolet,” J. Opt. Soc. Am. 57(6), 835 (1967).
[Crossref]

D. M. Roessler and W. C. Walker, “Electronic Spectrum and Ultraviolet Optical Properties of Crystalline MgO,” Phys. Rev. 159(3), 733–738 (1967).
[Crossref]

Ropers, C.

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Schafer, K. J.

Schmidt, B. E.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Schubert, O.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Sistrunk, E.

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Sivis, M.

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Staudte, A.

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Stephens, R.

R. Stephens and I. Malitson, “Index of refraction of magnesium oxide,” J. Res. Natl. Bur. Stand. 49(4), 249 (1952).
[Crossref]

Szafruga, U. B.

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

Taucer, M.

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Thiré, N.

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Urbanek, B.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Vampa, G.

G. Vampa, Y. S. You, H. Liu, S. Ghimire, and D. A. Reis, “Observation of backward high-harmonic emission from solids,” Opt. Express 26(9), 12210 (2018).
[Crossref]

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

K. F. Lee, X. Ding, T. J. Hammond, M. E. Fermann, G. Vampa, and P. B. Corkum, “Harmonic generation in solids with direct fiber laser pumping,” Opt. Lett. 42(6), 1113–1116 (2017).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Villeneuve, D. M.

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Walker, W. C.

D. M. Roessler and W. C. Walker, “Optical Constants of Magnesium Oxide and Lithium Fluoride in the Far Ultraviolet,” J. Opt. Soc. Am. 57(6), 835 (1967).
[Crossref]

D. M. Roessler and W. C. Walker, “Electronic Spectrum and Ultraviolet Optical Properties of Crystalline MgO,” Phys. Rev. 159(3), 733–738 (1967).
[Crossref]

Wu, M.

Yin, Y.

You, Y. S.

Yu. Kruchinin, S.

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

J. Res. Natl. Bur. Stand. (1)

R. Stephens and I. Malitson, “Index of refraction of magnesium oxide,” J. Res. Natl. Bur. Stand. 49(4), 249 (1952).
[Crossref]

Nat. Photonics (1)

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Nat. Phys. (2)

Y. S. You, D. A. Reis, and S. Ghimire, “Anisotropic high-harmonic generation in bulk crystals,” Nat. Phys. 13(4), 345–349 (2017).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011).
[Crossref]

Nature (2)

T. T. Luu, M. Garg, S. Yu. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis, “Extreme ultraviolet high-harmonic spectroscopy of solids,” Nature 521(7553), 498–502 (2015).
[Crossref]

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, C. R. McDonald, T. Brabec, and P. B. Corkum, “Linking high harmonics from gases and solids,” Nature 522(7557), 462–464 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

D. M. Roessler and W. C. Walker, “Electronic Spectrum and Ultraviolet Optical Properties of Crystalline MgO,” Phys. Rev. 159(3), 733–738 (1967).
[Crossref]

Phys. Rev. A (1)

S. Ghimire, A. D. Dichiara, E. Sistrunk, G. Ndabashimiye, U. B. Szafruga, A. Mohammad, P. Agostini, L. F. Dimauro, and D. A. Reis, “Generation and propagation of high-order harmonics in crystals,” Phys. Rev. A 85(4), 043836 (2012).
[Crossref]

Phys. Rev. B (1)

R. Adair, L. L. Chase, and S. A. Payne, “Nonlinear refractive index of optical crystals,” Phys. Rev. B 39(5), 3337–3350 (1989).
[Crossref]

Science (1)

M. Sivis, M. Taucer, G. Vampa, K. Johnston, A. Staudte, A. Y. Naumov, D. M. Villeneuve, C. Ropers, and P. B. Corkum, “Tailored semiconductors for high-harmonic optoelectronics,” Science 357(6348), 303–306 (2017).
[Crossref]

Other (2)

http://henke.lbl.gov/optical_constants/filter2.html

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

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Figures (4)

Fig. 1.
Fig. 1. Vacuum section of the experimental setup. Two laser beams ($E_1$ and $E_2$) were focused with protected silver concave mirrors (CC, 1 m radius of curvature) onto a back surface of MgO sample at a nearly straight angle of 177$^{\circ }$ to each other. HHG radiation emitted from this surface hit a slit of an XUV spectrometer followed by a curved XUV grating dispersing the beam over a microchannel plate XUV detector (MCP). The slit and the grating were mounted on a motorized platform allowing to replace them with a grazing incidence gold mirror and to observe energy unresolved far-field profile of the HHG.
Fig. 2.
Fig. 2. HHG beam profiles, obtained with the XUV grating removed from the beam path in (a) forward and (b) backward emission geometries, taken at the same laser peak intensity of $I_{\mathrm {peak}}=1.66$ TW/cm$^{2}$. Large phase mismatch between the fundamental and the HHG resulted in a strong decrease in the harmonic brightness in the backward emission configuration, while the non-linear phase accumulated by the laser beam during its propagation through the 200 µm MgO crystal resulted in a higher beam divergence in the forward emission geometry. (c) Total harmonic yield with the both beams present, as a function of the relative delay between them.
Fig. 3.
Fig. 3. (a, b) Raw images from the detector of the XUV spectrometer, taken with (a) two counter-propagating pulses of the field intensities of $I_{1}=1.66$ TW/cm$^{2}$ and $I_{2}=11.9$ TW/cm$^{2}$ and (b) a single backward-propagating beam with a peak intensity of $I_{2}=25.5$ TW/cm$^{2}$. In both cases the peak field amplitude was 1.06 V/Å near the interface. (c, d) Far-field profile comparison between backward only (blue) and counter-propagating (red) geometry at optimal two pulse delay of harmonics orders (c) H9 and (d) H15. Peak intensities are the same as in (a, b). Horizontal bars indicate FWHM of the beams.
Fig. 4.
Fig. 4. (a) Comparison of the HH spectra generated with a single pulse of $I_{\mathrm {peak}}=25.5$ TW/cm$^{2}$ in a backward emission geometry (blue) and two counter-propagating pulses $I^{\mathrm {tr}}_{\mathrm {peak}}=1.66$ TW/cm$^{2}$, $I^{\mathrm {r}}_{\mathrm {refl}}=11.9$ TW/cm$^{2}$ (red). Both curves correspond to the same peak field strength of 1.06 V/Å at the interface. The signal intensity observed in the two pulse case is approximately 3 to 4 times higher. (b) Calculated (black dashed line) and observed (red circles) HHG efficiency increase in the counter-propagating geometry relative to the backward emission geometry, at the same peak field of 1.06 V/Å at the interface.

Equations (5)

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E ( t , x ) = E 1 ( t , x ) + E 2 ( t , x ) = E 1 0 e i ω n c x i ω t + E 2 0 e i ω n c x i ω t = E 0 ( x ) e i φ ( x ) e i ω t ,
δ λ = 2 π c / ω n ,
E ( t , x ) ( E 1 0 + E 2 0 ) e i ω n e f f c x i ω t ,
d E ν ( x , x , t ) = E ν e i ν ω n e f f c x e i ν ω n _ ( ν ω ) c ( x x ) d x .
I ν | 0 d x   e i ν ω n e f f c x e i ν ω n ( ν ω ) + i κ ( ν ω ) c x | 2 = c 2 / ( ω ν ) 2 ( n e f f n ( ω ν ) ) 2 + κ ( ω ν ) 2

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