Abstract

We demonstrate non-perturbative 3rd (267 nm) and 5th (160 nm) harmonic generation in solids from a Ti:sapphire frequency comb (800 nm) at 108 MHz repetition rate. The experiments show that non-perturbative low harmonics are dominantly generated on the surface and on the interface between solids, and that they are not produced by bulk processes from the near-surface layer of the material. Measurements reveal that due to the lack of phase matching, the generated harmonics in bulk are suppressed by orders of magnitude compared to the signal generated on the surface. Our results pave the way for the development of all-solid-state high repetition rate harmonic sources for vacuum ultraviolet spectroscopy and high precision frequency comb metrology.

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

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References

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    [Crossref] [PubMed]
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    [Crossref]

2018 (4)

D. Bauer and K. K. Hansen, “High-harmonic generation in solids with and without topological edge states,” Phys. Rev. Lett. 120(17), 177401 (2018).
[Crossref] [PubMed]

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

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), 12210–12218 (2018).
[Crossref] [PubMed]

C. Beckerleg, T. J. Constant, I. Zeimpekis, S. M. Hornett, C. Craig, D. W. Hewak, and E. Hendry, “Cavity enhanced third harmonic generation in graphene,” Appl. Phys. Lett. 112(1), 011102 (2018).
[Crossref]

2017 (11)

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

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] [PubMed]

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

D. D. Hickstein, D. R. Carlson, A. Kowligy, M. Kirchner, S. R. Domingue, N. Nader, H. Timmers, A. Lind, G. G. Ycas, M. M. Murnane, H. C. Kapteyn, S. B. Papp, and S. A. Diddams, “High-harmonic generation in periodically poled waveguides,” Optica 4(12), 1538–1544 (2017).
[Crossref]

A. A. Lanin, E. A. Stepanov, A. B. Fedotov, and A. M. Zheltikov, “Mapping the electron band structure by intraband high-harmonic generation in solids,” Optica 4(5), 516–519 (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), 1816–1819 (2017).
[Crossref] [PubMed]

N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation,” Science 356(6339), 736–738 (2017).
[Crossref] [PubMed]

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[Crossref]

H. Kim, S. Han, Y. W. Kim, S. Kim, and S.-W. Kim, “Generation of coherent extreme-ultraviolet radiation from bulk sapphire crystal,” ACS Photonics 4(7), 1627–1632 (2017).
[Crossref]

G. Yi, H. Lee, J. Jiannan, B. J. Chun, S. Han, H. Kim, Y. W. Kim, D. Kim, S.-W. Kim, and Y.-J. Kim, “Nonlinear third harmonic generation at crystalline sapphires,” Opt. Express 25(21), 26002–26010 (2017).
[Crossref] [PubMed]

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] [PubMed]

2016 (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 (2016).
[Crossref]

G. Winkler, J. Fellinger, J. Seres, E. Seres, and T. Schumm, “Non-planar femtosecond enhancement cavity for VUV frequency comb applications,” Opt. Express 24(5), 5253–5262 (2016).
[Crossref] [PubMed]

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]

T. T. Luu and H. J. Worner, “High-order harmonic generation in solids: A unifying approach,” Phys. Rev. B 94(11), 115164 (2016).
[Crossref]

2015 (1)

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]

2014 (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]

N. Garejev, I. Grazuleviciute, D. Majus, G. Tamosauskas, V. Jukna, A. Couairon, and A. Dubietis, “Third- and fifth-harmonic generation in transparent solids with few-optical-cycle midinfrared pulses,” Phys. Rev. A 89(3), 033846 (2014).
[Crossref]

2012 (2)

M. C. Kohler, T. Pfeifer, K. Z. Hatsagortsyan, and C. H. Keitel, “Frontiers of atomic high-harmonic generation,” Adv. At. Mol. Opt. Phys. 61, 159–208 (2012).
[Crossref]

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

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]

2008 (1)

D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
[Crossref]

2005 (1)

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005).
[Crossref] [PubMed]

2001 (1)

A. H. Chin, O. G. Calderón, and J. Kono, “Extreme midinfrared nonlinear optics in semiconductors,” Phys. Rev. Lett. 86(15), 3292–3295 (2001).
[Crossref] [PubMed]

1995 (2)

T. Dekorsy, R. Ott, H. Kurz, and K. Köhler, “Bloch oscillations at room temperature,” Phys. Rev. B Condens. Matter 51(23), 17275–17278 (1995).
[Crossref] [PubMed]

T. Y. F. Tsang, “Optical third-harmonic generation at interfaces,” Phys. Rev. A 52(5), 4116–4125 (1995).
[Crossref] [PubMed]

1990 (1)

1977 (1)

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31(12), 822–825 (1977).
[Crossref]

Agostini, P.

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]

Allison, T. K.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

An, N.

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

Andrade, J. R. C.

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

Bastiaens, B.

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

Bauer, D.

D. Bauer and K. K. Hansen, “High-harmonic generation in solids with and without topological edge states,” Phys. Rev. Lett. 120(17), 177401 (2018).
[Crossref] [PubMed]

Beckerleg, C.

C. Beckerleg, T. J. Constant, I. Zeimpekis, S. M. Hornett, C. Craig, D. W. Hewak, and E. Hendry, “Cavity enhanced third harmonic generation in graphene,” Appl. Phys. Lett. 112(1), 011102 (2018).
[Crossref]

Berini, P.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

Boutu, W.

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

Browne, D. A.

Calderón, O. G.

A. H. Chin, O. G. Calderón, and J. Kono, “Extreme midinfrared nonlinear optics in semiconductors,” Phys. Rev. Lett. 86(15), 3292–3295 (2001).
[Crossref] [PubMed]

Carlson, D. R.

Chang, Z.

Chen, X.

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

Chew, A.

Chin, A. H.

A. H. Chin, O. G. Calderón, and J. Kono, “Extreme midinfrared nonlinear optics in semiconductors,” Phys. Rev. Lett. 86(15), 3292–3295 (2001).
[Crossref] [PubMed]

Chini, M.

Chun, B. J.

Cingöz, A.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

Constant, T. J.

C. Beckerleg, T. J. Constant, I. Zeimpekis, S. M. Hornett, C. Craig, D. W. Hewak, and E. Hendry, “Cavity enhanced third harmonic generation in graphene,” Appl. Phys. Lett. 112(1), 011102 (2018).
[Crossref]

Corkum, P. B.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

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] [PubMed]

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (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] [PubMed]

Couairon, A.

N. Garejev, I. Grazuleviciute, D. Majus, G. Tamosauskas, V. Jukna, A. Couairon, and A. Dubietis, “Third- and fifth-harmonic generation in transparent solids with few-optical-cycle midinfrared pulses,” Phys. Rev. A 89(3), 033846 (2014).
[Crossref]

Couture, C.

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[Crossref]

Craig, C.

C. Beckerleg, T. J. Constant, I. Zeimpekis, S. M. Hornett, C. Craig, D. W. Hewak, and E. Hendry, “Cavity enhanced third harmonic generation in graphene,” Appl. Phys. Lett. 112(1), 011102 (2018).
[Crossref]

Dekorsy, T.

T. Dekorsy, R. Ott, H. Kurz, and K. Köhler, “Bloch oscillations at room temperature,” Phys. Rev. B Condens. Matter 51(23), 17275–17278 (1995).
[Crossref] [PubMed]

Denecke, M. A.

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[Crossref]

Deng, X.

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

DiChiara, A. D.

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G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

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] [PubMed]

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]

Nicolas, R.

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

Olivieri, A.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

Ott, R.

T. Dekorsy, R. Ott, H. Kurz, and K. Köhler, “Bloch oscillations at room temperature,” Phys. Rev. B Condens. Matter 51(23), 17275–17278 (1995).
[Crossref] [PubMed]

Papp, S. B.

Pfeifer, T.

M. C. Kohler, T. Pfeifer, K. Z. Hatsagortsyan, and C. H. Keitel, “Frontiers of atomic high-harmonic generation,” Adv. At. Mol. Opt. Phys. 61, 159–208 (2012).
[Crossref]

Rauschenberger, J.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005).
[Crossref] [PubMed]

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), 12210–12218 (2018).
[Crossref] [PubMed]

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 (2016).
[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, 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, H.

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

Ren, X.

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] [PubMed]

Ruehl, A.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

Schafer, K. J.

Schmidt, B. E.

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[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]

Schuessler, H. A.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005).
[Crossref] [PubMed]

Schumm, T.

Segerink, F. B.

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

Selvi, H.

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[Crossref]

Seres, E.

Seres, J.

Shi, L.

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

Sistrunk, E.

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] [PubMed]

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] [PubMed]

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

Stepanov, E. A.

Tamaya, T.

N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation,” Science 356(6339), 736–738 (2017).
[Crossref] [PubMed]

Tamosauskas, G.

N. Garejev, I. Grazuleviciute, D. Majus, G. Tamosauskas, V. Jukna, A. Couairon, and A. Dubietis, “Third- and fifth-harmonic generation in transparent solids with few-optical-cycle midinfrared pulses,” Phys. Rev. A 89(3), 033846 (2014).
[Crossref]

Tanaka, K.

N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation,” Science 356(6339), 736–738 (2017).
[Crossref] [PubMed]

Taucer, M.

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (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] [PubMed]

Thire, N.

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[Crossref]

Timmers, H.

Tsang, T. Y. F.

T. Y. F. Tsang, “Optical third-harmonic generation at interfaces,” Phys. Rev. A 52(5), 4116–4125 (1995).
[Crossref] [PubMed]

Udem, T.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005).
[Crossref] [PubMed]

Unsuree, N.

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[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), 12210–12218 (2018).
[Crossref] [PubMed]

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] [PubMed]

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (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] [PubMed]

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

Villeneuve, D. M.

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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]

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] [PubMed]

Weber, M. J.

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31(12), 822–825 (1977).
[Crossref]

Winkler, G.

Worner, H. J.

T. T. Luu and H. J. Worner, “High-order harmonic generation in solids: A unifying approach,” Phys. Rev. B 94(11), 115164 (2016).
[Crossref]

Wu, M.

Ycas, G. G.

Ye, J.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

Yi, G.

Yin, Y.

Yoshikawa, N.

N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation,” Science 356(6339), 736–738 (2017).
[Crossref] [PubMed]

Yost, D. C.

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[Crossref] [PubMed]

You, Y. S.

Zeimpekis, I.

C. Beckerleg, T. J. Constant, I. Zeimpekis, S. M. Hornett, C. Craig, D. W. Hewak, and E. Hendry, “Cavity enhanced third harmonic generation in graphene,” Appl. Phys. Lett. 112(1), 011102 (2018).
[Crossref]

Zhao, X.

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

Zheltikov, A. M.

Zheng, Y.

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

ACS Photonics (1)

H. Kim, S. Han, Y. W. Kim, S. Kim, and S.-W. Kim, “Generation of coherent extreme-ultraviolet radiation from bulk sapphire crystal,” ACS Photonics 4(7), 1627–1632 (2017).
[Crossref]

Adv. At. Mol. Opt. Phys. (1)

M. C. Kohler, T. Pfeifer, K. Z. Hatsagortsyan, and C. H. Keitel, “Frontiers of atomic high-harmonic generation,” Adv. At. Mol. Opt. Phys. 61, 159–208 (2012).
[Crossref]

Appl. Phys. Lett. (3)

C. Beckerleg, T. J. Constant, I. Zeimpekis, S. M. Hornett, C. Craig, D. W. Hewak, and E. Hendry, “Cavity enhanced third harmonic generation in graphene,” Appl. Phys. Lett. 112(1), 011102 (2018).
[Crossref]

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31(12), 822–825 (1977).
[Crossref]

L. Shi, J. R. C. Andrade, H. Kim, S. Han, R. Nicolas, D. Franz, W. Boutu, T. Heidenblut, F. B. Segerink, B. Bastiaens, H. Merdji, S.-W. Kim, U. Morgner, and M. Kovacev, “Investigating the origin of third harmonic generation from diabolo optical antennas,” Appl. Phys. Lett. 111(17), 173102 (2017).
[Crossref]

J. Opt. Soc. Am. B (1)

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. (3)

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 (2016).
[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]

G. Vampa, B. G. Ghamsari, S. S. Mousavi, T. J. Hammond, A. Olivieri, E. Lisicka-Skrek, A. Y. 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)

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436(7048), 234–237 (2005).
[Crossref] [PubMed]

A. Cingöz, D. C. Yost, T. K. Allison, A. Ruehl, M. E. Fermann, I. Hartl, and J. Ye, “Direct frequency comb spectroscopy in the extreme ultraviolet,” Nature 482(7383), 68–71 (2012).
[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]

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]

Opt. Express (3)

Opt. Lett. (2)

Optica (2)

Phys. Rev. A (2)

N. Garejev, I. Grazuleviciute, D. Majus, G. Tamosauskas, V. Jukna, A. Couairon, and A. Dubietis, “Third- and fifth-harmonic generation in transparent solids with few-optical-cycle midinfrared pulses,” Phys. Rev. A 89(3), 033846 (2014).
[Crossref]

T. Y. F. Tsang, “Optical third-harmonic generation at interfaces,” Phys. Rev. A 52(5), 4116–4125 (1995).
[Crossref] [PubMed]

Phys. Rev. B (3)

T. T. Luu and H. J. Worner, “High-order harmonic generation in solids: A unifying approach,” Phys. Rev. B 94(11), 115164 (2016).
[Crossref]

D. Golde, T. Meier, and S. W. Koch, “High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations,” Phys. Rev. B 77(7), 075330 (2008).
[Crossref]

M. Taucer, T. J. Hammond, P. B. Corkum, G. Vampa, C. Couture, N. Thire, B. E. Schmidt, F. Legare, H. Selvi, N. Unsuree, B. Hamilton, T. J. Echtermeyer, and M. A. Denecke, “Nonperturbative harmonic generation in graphene from intense midinfrared pulsed light,” Phys. Rev. B 96(19), 195420 (2017).
[Crossref]

Phys. Rev. B Condens. Matter (1)

T. Dekorsy, R. Ott, H. Kurz, and K. Köhler, “Bloch oscillations at room temperature,” Phys. Rev. B Condens. Matter 51(23), 17275–17278 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

A. H. Chin, O. G. Calderón, and J. Kono, “Extreme midinfrared nonlinear optics in semiconductors,” Phys. Rev. Lett. 86(15), 3292–3295 (2001).
[Crossref] [PubMed]

D. Bauer and K. K. Hansen, “High-harmonic generation in solids with and without topological edge states,” Phys. Rev. Lett. 120(17), 177401 (2018).
[Crossref] [PubMed]

Sci. Rep. (1)

X. Zhao, Y. Zheng, N. An, H. Ren, X. Deng, and X. Chen, “Enhancement of UV second-harmonic radiation at nonlinear interfaces with discontinuous second-order susceptibilities,” Sci. Rep. 8(1), 6695 (2018).
[Crossref] [PubMed]

Science (2)

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] [PubMed]

N. Yoshikawa, T. Tamaya, and K. Tanaka, “High-harmonic generation in graphene enhanced by elliptically polarized light excitation,” Science 356(6339), 736–738 (2017).
[Crossref] [PubMed]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

E. R. Dobrovinskaya, L. A. Lytvynov, and V. Pishchik, Sapphire: material, manufacturing, applications (Springer Science + Business Media, LLC, 2009).

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Figures (4)

Fig. 1
Fig. 1 (a) Experimental setup. CM: chirped mirror; L1: BK7 lens, f = 10 mm; L2: MgF2 lens, f = 40 mm. (b) Magnified area around the crystal. (c) The beam profiles of the focused laser beam before, at, and after the focus measured by replacing the crystal with a CCD camera. (d) Measured spectra generated from GaN film at two laser intensities. “2×H3” and “2×H5” denote the second diffraction order (534/320 nm) of the third/fifth (H3/H5) harmonics (267/160 nm) on the spectrograph's grating.
Fig. 2
Fig. 2 (a) Measured spectra of 3rd and 5th harmonics from different fluoride crystals, generated on the back surface of the crystals at laser intensity of 1 TW/cm2. “2×H5” denotes the second diffraction order (320 nm) of H5 (160 nm) on the spectrograph's grating. (b) Measured harmonic intensity generated on the front surface depends on the laser intensity on the surface what dependence can be well approximate with a power function.
Fig. 3
Fig. 3 Z-scan for fluoride crystals. Measured focus position dependent intensity of the generated 3rd harmonic from (a) LiF 0.5 mm (violet) and MgF2 1.0 mm (red) crystals and the generated (c) 3rd harmonic and (e) 5th harmonic from CaF2 crystals with a thickness of 0.2 mm (blue) and 0.45 mm (green),. The calculated harmonic intensities are plotted with dashed black and red curves assuming surface harmonics, and with dashed gray curves assuming bulk harmonics. The panels at the right side (b,d,f) show the calculated fitting errors for the cases.
Fig. 4
Fig. 4 GaN on sapphire. (a) Generated 3rd and 5th harmonic signals from a thin GaN layer (5-µm-thick) on a sapphire substrate (430-µm-thick) as the focus position moves through the crystal (z-scan). The black dashed line shows the 3rd harmonic generated from a sapphire sample (~500-µm-thick) without GaN layer. The insets show the relative position of the focused laser beam with respect to the sample in two cases when maximum signals were generated. (b) Measured harmonic spectra of the sample consisting of a GaN layer and of the sapphire substrate alone both at z0 = 0 focus position. “2×H5” denotes the second diffraction order (320 nm) of H5 (160 nm) on the spectrograph's grating. (c) Measured spectra of 5th harmonic generated on the GaN surface [blue, upper-left inset in (a)], the GaN-sapphire interface [red, upper-right inset in (a)] and on the substrate back surface (black).

Tables (1)

Tables Icon

Table 1 Fitting parameters

Equations (4)

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I(z) { θ 2 z R 2 [ 1+ ( z z 0 ) 2 / z R 2 ] } 1 ,
I q I surface. q'
I q ( z 0 )= c 0 [ 1+ ( L z 0 ) 2 / z R 2 ] q ,
I q ( z 0 )= I q,meas ( z 0 ) c 1 [ 1+ ( z 1 z 0 ) 2 / z R1 2 ] 1 .