Abstract

We experimentally demonstrate backward emission of high-harmonics of a near-infrared laser from MgO and Si crystals in the direction of specular reflection. We show that the variation of the high-harmonic power with the angle of incidence can be predicted with nonlinear reflection coefficients derived originally for perturbative nonlinearities. A comparison of transmission and reflection geometries suggests that backward-propagating high-harmonics are an excellent reference to study nonlinear propagation of intense light in solids. Backward emission will enable phase matching of the high-harmonic beam and the integration of the functionalities of extended gas-phase high-harmonic beamlines into a single optical element. The potential to achieve phase matching paves the way to solid-state based high-harmonic sources with higher flux than the best transmission-based sources, where high-harmonics are strongly absorbed by the crystal itself.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (3)

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

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017).
[Crossref]

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

2016 (1)

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

2015 (4)

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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] [PubMed]

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

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6(1), 6611 (2015).
[Crossref] [PubMed]

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]

2013 (1)

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

2012 (2)

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]

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl. 24(4), 042006 (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]

2010 (1)

C. Thaury and F. Quéré, “High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms,” J. Phys. At. Mol. Opt. Phys. 43(21), 213001 (2010).
[Crossref]

1994 (1)

1988 (1)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[Crossref]

1987 (1)

P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, “Temperature dependence of the dielectric function and interband critical points in silicon,” Phys. Rev. B Condens. Matter 36(9), 4821–4830 (1987).
[Crossref] [PubMed]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[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]

Auguste, T.

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

Berini, P.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

Biegert, J.

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6(1), 6611 (2015).
[Crossref] [PubMed]

Bloembergen, N.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[Crossref]

Bonse, J.

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl. 24(4), 042006 (2012).
[Crossref]

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] [PubMed]

Browne, D. A.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

Cardona, M.

P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, “Temperature dependence of the dielectric function and interband critical points in silicon,” Phys. Rev. B Condens. Matter 36(9), 4821–4830 (1987).
[Crossref] [PubMed]

Chaloupka, J. L.

Corkum, P. B.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (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] [PubMed]

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

Cousin, S. L.

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6(1), 6611 (2015).
[Crossref] [PubMed]

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]

Ferray, M.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[Crossref]

Gaarde, M. B.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

Garg, M.

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

Garriga, M.

P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, “Temperature dependence of the dielectric function and interband critical points in silicon,” Phys. Rev. B Condens. Matter 36(9), 4821–4830 (1987).
[Crossref] [PubMed]

Ghamsari, B. G.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

Ghimire, S.

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

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017).
[Crossref]

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

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]

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

Hammond, T. J.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (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] [PubMed]

Hassan, M. T.

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

Heinz, T. F.

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017).
[Crossref]

Hemmer, M.

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6(1), 6611 (2015).
[Crossref] [PubMed]

Hergott, J.-F.

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

Hohenleutner, M.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

Höhm, S.

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl. 24(4), 042006 (2012).
[Crossref]

Huber, R.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

Kim, K. T.

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

Kira, M.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

Knorr, M.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

Koch, S. W.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

Kruchinin, S. Y.

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

Krüger, J.

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl. 24(4), 042006 (2012).
[Crossref]

L’Huillier, A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[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.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

Lautenschlager, P.

P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, “Temperature dependence of the dielectric function and interband critical points in silicon,” Phys. Rev. B Condens. Matter 36(9), 4821–4830 (1987).
[Crossref] [PubMed]

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] [PubMed]

Li, X. F.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[Crossref]

Li, Y.

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017).
[Crossref]

Lisicka-Skrek, E.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

Liu, H.

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017).
[Crossref]

Lompre, L. A.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[Crossref]

Luu, T. T.

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

Mainfray, G.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[Crossref]

Manus, C.

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[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] [PubMed]

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]

Meyerhofer, D. D.

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

Mousavi, S. S.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

Ndabashimiye, G.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

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]

Olivieri, A.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

Peatross, J.

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[Crossref]

Quéré, F.

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

C. Thaury and F. Quéré, “High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms,” J. Phys. At. Mol. Opt. Phys. 43(21), 213001 (2010).
[Crossref]

Reis, D.

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

Reis, D. A.

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017).
[Crossref]

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

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]

Rosenfeld, A.

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl. 24(4), 042006 (2012).
[Crossref]

Ruchon, T.

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

Schafer, K. J.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

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] [PubMed]

Schubert, O.

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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]

Silva, F.

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6(1), 6611 (2015).
[Crossref] [PubMed]

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]

Staudte, A.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[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]

Teichmann, S. M.

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6(1), 6611 (2015).
[Crossref] [PubMed]

Thaury, C.

C. Thaury and F. Quéré, “High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms,” J. Phys. At. Mol. Opt. Phys. 43(21), 213001 (2010).
[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] [PubMed]

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, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (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] [PubMed]

Villeneuve, D. M.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

Vina, L.

P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, “Temperature dependence of the dielectric function and interband critical points in silicon,” Phys. Rev. B Condens. Matter 36(9), 4821–4830 (1987).
[Crossref] [PubMed]

Wu, M.

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

You, Y. S.

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

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (2017).
[Crossref]

Yu Naumov, A.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

Zhang, C.

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

J. Laser Appl. (1)

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl. 24(4), 042006 (2012).
[Crossref]

J. Phys. At. Mol. Opt. Phys. (2)

M. Ferray, A. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfray, and C. Manus, “Multiple-harmonic conversion of 1064 nm radiation in rare gases,” J. Phys. At. Mol. Opt. Phys. 21(3), L31–L35 (1988).
[Crossref]

C. Thaury and F. Quéré, “High-order harmonic and attosecond pulse generation on plasma mirrors: basic mechanisms,” J. Phys. At. Mol. Opt. Phys. 43(21), 213001 (2010).
[Crossref]

Nat. Commun. (1)

F. Silva, S. M. Teichmann, S. L. Cousin, M. Hemmer, and J. Biegert, “Spatiotemporal isolation of attosecond soft X-ray pulses in the water window,” Nat. Commun. 6(1), 6611 (2015).
[Crossref] [PubMed]

Nat. Photonics (2)

K. T. Kim, C. Zhang, T. Ruchon, J.-F. Hergott, T. Auguste, D. M. Villeneuve, P. B. Corkum, and F. Quéré, “Photonic streaking of attosecond pulse trains,” Nat. Photonics 7(8), 651–656 (2013).
[Crossref]

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. (4)

H. Liu, Y. Li, Y. S. You, S. Ghimire, T. F. Heinz, and D. A. Reis, “High-harmonic generation from an atomically thin semiconductor,” Nat. Phys. 13(3), 262–265 (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]

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

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Yu Naumov, D. M. Villeneuve, A. Staudte, P. Berini, and P. B. Corkum, “Plasmon-enhanced high-harmonic generation from silicon,” Nat. Phys. 13(7), 659–662 (2017).
[Crossref]

Nature (4)

G. Ndabashimiye, S. Ghimire, M. Wu, D. A. Browne, K. J. Schafer, M. B. Gaarde, and D. A. Reis, “Solid-state harmonics beyond the atomic limit,” Nature 534(7608), 520–523 (2016).
[Crossref] [PubMed]

M. Hohenleutner, F. Langer, O. Schubert, M. Knorr, U. Huttner, S. W. Koch, M. Kira, and R. Huber, “Real-time observation of interfering crystal electrons in high-harmonic generation,” Nature 523(7562), 572–575 (2015).
[Crossref] [PubMed]

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] [PubMed]

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

Opt. Lett. (1)

Phys. Rev. (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128(2), 606–622 (1962).
[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 Condens. Matter (1)

P. Lautenschlager, M. Garriga, L. Vina, and M. Cardona, “Temperature dependence of the dielectric function and interband critical points in silicon,” Phys. Rev. B Condens. Matter 36(9), 4821–4830 (1987).
[Crossref] [PubMed]

Other (6)

D. Attwood, “Radiation and scattering and EUV and soft X-Ray wavelengths,” in Soft X-Rays and Extreme Ultraviolet Radiation (Cambridge University, 1999).

http://www.refractiveindex.info

G. Vampa, T. J. Hammond, N. Thiré, B. E. Schmidt, F. Légaré, D. D. Klug, and P. B. Corkum, “Generation of high harmonics from silicon,” ArXiv:1605.06345 (2016).

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Z. Chang, “Phase matching” in Fundamentals of Attosecond Optics (CRC, 2016).

T. F. Heinz, “Second order nonlinear optical effects at surfaces and interfaces” in Nonlinear Surface Electromagnetic Phenomena29 (1991).

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Figures (5)

Fig. 1
Fig. 1 High-harmonic spectra measured in the specular reflection direction, from (a) a (100)-oriented MgO crystal with 1.32 µm laser excitation and (b) a (100)-oriented Si crystal with 2.1 µm laser excitation. In (a), the driver is s-polarized (red and blue lines), or p-polarized (black line). The spectrum for p-polarization has been multiplied by 2 to account for the lower reflectivity of the grating. The estimated intensities of the driver are 23 and 33 TW/cm2 (corresponding to 90 and 130 µJ driving-pulse energy). Harmonic power is normalized to the 17th order at the highest intensity. The angle of incidence is 45°. In (b), the angle of incidence is 46°, the driving laser is p-polarized, and the vacuum intensity is 4.2 TW/cm2. The highest detected harmonic in the case of Si is limited by the detection range of the VIS-UV spectrometer used.
Fig. 2
Fig. 2 Schematics of the phase matching condition for the high harmonics in the direction of specular reflection. The wavevectors are defined as follows: k0 is the fundamental wave, k0|| is the component of k0 in the plane of the surface, km and km are the reflected and transmitted harmonic waves respectively, kNL is the nonlinear polarization and kNL|| is its component in the plane of the surface. α is the angle between kNL and the polarization of PNL. The linear and nonlinear media have indices n1 and n2 respectively. All angles are measured relative to the normal to the surface.
Fig. 3
Fig. 3 Harmonic power as a function of the angle of incidence, for generation in Si. The experiment (colored dots) agrees with the theoretical prediction (solid lines, vertically offset to match the experiment for an angle of incidence of 30°). The fundamental driver is p-polarized. The dashed vertical black line marks the Brewster’s angle for the fundamental (74°). The linear Brewster’s angle for the high harmonics varies between 74° - 80°.
Fig. 4
Fig. 4 Power of the high harmonics generated from Si as a function of the driving laser intensity, for a fixed angle of incidence of 30°. The dashed black line, scaling with I5, is a guide to the eye. The driving field is p-polarized.
Fig. 5
Fig. 5 Spatially (divergence in the vertical axis, in mrad) and spectrally (horizontal axis, in eV) resolved XUV emission from the MgO crystal measured in the reflected (a) and transmitted (b) beams. The transmitted power is relative to the reflected power. (c) Spatial profile spectrally integrated for energies > 19 eV, for the transmitted (red) and reflected (blue) harmonics.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E m (r) = r NL P NL
r NL,s = sin 2 θ t sin θ s [ sin( θ r + θ t )sin( θ s + θ t )sin θ r ] 1
  r NL,p = sin 2 θ t sin θ s sin( α+ θ t + θ s )× × [ ϵ r sin( θ r + θ t )sin( θ s + θ t )sin θ r cos( θ t θ r )] 1
n 2 ( m ω 0 )sin θ t = n 1 ( m ω 0 )sin θ i
n 2 ( ω 0 )sin θ s = n 1 ( ω 0 )sin θ i

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