## Analytic scaling analysis of high harmonic generation conversion efficiency

Optics Express, Vol. 17, Issue 13, pp. 11217-11229 (2009)

http://dx.doi.org/10.1364/OE.17.011217

Acrobat PDF (356 KB)

### Abstract

Closed form expressions for the high harmonic generation (HHG) conversion efficiency are obtained for the plateau and cutoff regions. The presented formulas eliminate most of the computational complexity related to HHG simulations, and enable a detailed scaling analysis of HHG efficiency as a function of drive laser parameters and material properties. Moreover, in the total absence of any fitting procedure, the results show excellent agreement with experimental data reported in the literature. Thus, this paper opens new pathways for the global optimization problem of extreme ultraviolet (EUV) sources based on HHG.

© 2009 OSA

## 1. Introduction

1. Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science **278**(5338), 661–664 (1997). [CrossRef]

3. J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: source of coherent kiloelectronvolt X-rays,” Nature **433**(7026), 596–596 (2005). [CrossRef] [PubMed]

4. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science **320**(5883), 1614–1617 (2008). [CrossRef] [PubMed]

5. L.-H. Yu, M. Babzien, I. Ben-Zvi I, L. F. DiMauro, A. Doyuran, W. Graves, E. Johnson, S. Krinsky, R. Malone, I. Pogorelsky I, J. Skaritka, G. Rakowsky, L. Solomon, X. J. Wang, M. Woodle, V. Yakimenko V, S. G. Biedron, J. N. Galayda, E. Gluskin, J. Jagger, V. Sajaev V, and I. Vasserman I, “High-gain harmonic-generation free-electron laser,” Science **289**(5481), 932–934 (2000). [CrossRef] [PubMed]

6. E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science **302**(5642), 95–98 (2003). [CrossRef] [PubMed]

7. I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. **94**(24), 243901 (2005). [CrossRef]

8. R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. **94**(19), 193201 (2005). [CrossRef] [PubMed]

21. E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of strong optical field in soft X-ray region by using high-order harmonics,” IEEE J. Sel. Top. Quantum Electron. **10**(6), 1315–1328 (2004). [CrossRef]

6. E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science **302**(5642), 95–98 (2003). [CrossRef] [PubMed]

21. E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of strong optical field in soft X-ray region by using high-order harmonics,” IEEE J. Sel. Top. Quantum Electron. **10**(6), 1315–1328 (2004). [CrossRef]

23. M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-X-ray pulses,” Phys. Rev. Lett. **83**(4), 722–725 (1999). [CrossRef]

11. P. Salières, P. Antoine, A. de Bohan, and M. Lewenstein, “Temporal and spectral tailoring of high-order harmonics,” Phys. Rev. Lett. **81**(25), 5544–5547 (1998). [CrossRef]

## 2. Derivation

24. M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: Extreme nonlinear optics,” Phys. Rev. Lett. **83**(15), 2930–2933 (1999). [CrossRef]

*z*is the position coordinate along the propagation direction,

*t*is the retarded time appropriate for describing propagation at the speed of light in vacuum,

*P*is the polarization induced in the medium.

*N*means the number of optical cycles.

*ℏ*, the electron mass,

*e*, are set to unity, and the speed of light in vacuum equals the inverse fine structure constant

*ρ*as the density of atoms (number of atoms per atomic unit volume), Eq. (1) takes the formwhere

*σ*is the absorption cross section,

*x*is the dipole moment of a single atom, and

*z*, i.e. the changes in amplitude and phase of the driving pulse are small over the medium length

*L*. The results can also be applied to a weakly focused Gaussian beam for

*Ω*, is given by

*β*accounts for the depletion of the ground state amplitudes during each half period defined by

10. M. Lewenstein, Ph. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A **49**(3), 2117–2132 (1994). [CrossRef] [PubMed]

9. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. **71**(13), 1994–1997 (1993). [CrossRef] [PubMed]

10. M. Lewenstein, Ph. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A **49**(3), 2117–2132 (1994). [CrossRef] [PubMed]

*N*in the exponent of

*β*in Eq. (12). The last quarter of a cycle in the N-cycle pulse is neglected to keep the expression simple. Comparison with a full numerical simulation considering a Gaussian pulse at the end of the paper shows that this approximation even yields good results for a four-cycle non-flat-top pulses.

*Ω*. This condition is fulfilled twice during each half cycle and is referred as short and long trajectories. As

*Ω*increases approaching the cutoff frequency,

28. A. Gordon and F. X. Kärtner, “Scaling of keV HHG photon yield with drive wavelength,” Opt. Express **13**(8), 2941–2947 (2005). [CrossRef] [PubMed]

## 3. Discussion

*Ω*at the cutoff frequency and in the plateau region, respectively. In the following, our predicted efficiencies are compared with experimental data in the literature. Experimental data are chosen where the corresponding Keldysh parameter

7. I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. **94**(24), 243901 (2005). [CrossRef]

^{2}for 800 nm and

^{2}for 400 nm. The calculated efficiencies from Eq. (17) are shown in Fig. 3 and are indeed

16. J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. **98**(1), 013901 (2007). [CrossRef] [PubMed]

19. V. S. Yakovlev, M. Y. Ivanov, and F. Krausz, “Enhanced phase-matching for generation of soft X-ray harmonics and attosecond pulses in atomic gases,” Opt. Express **15**(23), 15351–15364 (2007). [CrossRef] [PubMed]

30. T. Popmintchev, M. C. Chen, O. Cohen, M. E. Grisham, J. J. Rocca, M. M. Murnane, and H. C. Kapteyn, “Extended phase matching of high harmonics driven by mid-infrared light,” Opt. Lett. **33**(18), 2128–2130 (2008). [CrossRef] [PubMed]

*σ*decreases, as shown in Fig. 1, compensating almost completely the reduction due to the front factor of

## 4. Conclusion

## Acknowledgments

## References and links

1. | Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science |

2. | Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. |

3. | J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: source of coherent kiloelectronvolt X-rays,” Nature |

4. | E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science |

5. | L.-H. Yu, M. Babzien, I. Ben-Zvi I, L. F. DiMauro, A. Doyuran, W. Graves, E. Johnson, S. Krinsky, R. Malone, I. Pogorelsky I, J. Skaritka, G. Rakowsky, L. Solomon, X. J. Wang, M. Woodle, V. Yakimenko V, S. G. Biedron, J. N. Galayda, E. Gluskin, J. Jagger, V. Sajaev V, and I. Vasserman I, “High-gain harmonic-generation free-electron laser,” Science |

6. | E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science |

7. | I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. |

8. | R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. |

9. | P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. |

10. | M. Lewenstein, Ph. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A |

11. | P. Salières, P. Antoine, A. de Bohan, and M. Lewenstein, “Temporal and spectral tailoring of high-order harmonics,” Phys. Rev. Lett. |

12. | N. H. Shon, A. Suda, and K. Midorikawa, “Generation and propagation of high-order harmonics in high-pressure gases,” Phys. Rev. A |

13. | M. B. Gaarde and K. J. Schafer, “Space-time considerations in the phase locking of high harmonics,” Phys. Rev. Lett. |

14. | E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A |

15. | G. Tempea and T. Brabec, “Optimization of high-harmonic generation,” Appl. Phys. B |

16. | J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. |

17. | P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. |

18. | C. Vozzi, F. Calegari, F. Frassetto, E. Benedetti, M. Nisoli, G. Sansone, L. Poletto, P. Villoresi, and S. Stagira, “Generation of high-order harmonics with a near-IR self-phase-stabilized parametric source,” Proceedings of Conference on Ultrafast Phenomena, FRI2.2 (2008). |

19. | V. S. Yakovlev, M. Y. Ivanov, and F. Krausz, “Enhanced phase-matching for generation of soft X-ray harmonics and attosecond pulses in atomic gases,” Opt. Express |

20. | A. Gordon, F. X. Kärtner, N. Rohringer, and R. Santra, “Role of many-electron dynamics in high harmonic generation,” Phys. Rev. Lett. |

21. | E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of strong optical field in soft X-ray region by using high-order harmonics,” IEEE J. Sel. Top. Quantum Electron. |

22. | E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: Model and experiment,” Phys. Rev. Lett. |

23. | M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-X-ray pulses,” Phys. Rev. Lett. |

24. | M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: Extreme nonlinear optics,” Phys. Rev. Lett. |

25. | M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varying electromagnetic-field,” Sov. Phys. JETP |

26. | A. Gordon and F. X. Kärtner, “Quantitative modeling of single atom high harmonic generation,” Phys. Rev. Lett. |

27. | R. Santra and A. Gordon, “Three-step model for high-harmonic generation in many-electron systems,” Phys. Rev. Lett. |

28. | A. Gordon and F. X. Kärtner, “Scaling of keV HHG photon yield with drive wavelength,” Opt. Express |

29. | Lawrence Berkeley National Laboratory, (http://henke.lbl.gov/optical_constants/). |

30. | T. Popmintchev, M. C. Chen, O. Cohen, M. E. Grisham, J. J. Rocca, M. M. Murnane, and H. C. Kapteyn, “Extended phase matching of high harmonics driven by mid-infrared light,” Opt. Lett. |

**OCIS Codes**

(260.7200) Physical optics : Ultraviolet, extreme

(020.2649) Atomic and molecular physics : Strong field laser physics

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: May 1, 2009

Revised Manuscript: May 29, 2009

Manuscript Accepted: May 30, 2009

Published: June 19, 2009

**Citation**

E. L. Falcão-Filho, V. M. Gkortsas, Ariel Gordon, and Franz X. Kärtner, "Analytic scaling analysis of high harmonic generation conversion efficiency," Opt. Express **17**, 11217-11229 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-13-11217

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### References

- Ch. Spielmann, N. H. Burnett, S. Sartania, R. Koppitsch, M. Schnürer, C. Kan, M. Lenzner, P. Wobrauschek, and F. Krausz, “Generation of coherent X-rays in the water window using 5-femtosecond laser pulses,” Science 278(5338), 661–664 (1997). [CrossRef]
- Z. Chang, A. Rundquist, H. Wang, M. M. Murnane, and H. C. Kapteyn, “Generation of coherent soft X rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79(16), 2967–2970 (1997). [CrossRef]
- J. Seres, E. Seres, A. J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, and F. Krausz, “Laser technology: source of coherent kiloelectronvolt X-rays,” Nature 433(7026), 596–596 (2005). [CrossRef] [PubMed]
- E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, “Single-cycle nonlinear optics,” Science 320(5883), 1614–1617 (2008). [CrossRef] [PubMed]
- L.-H. Yu, M. Babzien, I. Ben-Zvi, L. F. DiMauro, A. Doyuran, W. Graves, E. Johnson, S. Krinsky, R. Malone, I. Pogorelsky, J. Skaritka, G. Rakowsky, L. Solomon, X. J. Wang, M. Woodle, V. Yakimenko, S. G. Biedron, J. N. Galayda, E. Gluskin, J. Jagger, V. Sajaev, and I. Vasserman, “High-gain harmonic-generation free-electron laser,” Science 289(5481), 932–934 (2000). [CrossRef] [PubMed]
- E. A. Gibson, A. Paul, N. Wagner, R. Tobey, D. Gaudiosi, S. Backus, I. P. Christov, A. Aquila, E. M. Gullikson, D. T. Attwood, M. M. Murnane, and H. C. Kapteyn, “Coherent soft x-ray generation in the water window with quasi-phase matching,” Science 302(5642), 95–98 (2003). [CrossRef] [PubMed]
- I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. 94(24), 243901 (2005). [CrossRef]
- R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94(19), 193201 (2005). [CrossRef] [PubMed]
- P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71(13), 1994–1997 (1993). [CrossRef] [PubMed]
- M. Lewenstein, Ph. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49(3), 2117–2132 (1994). [CrossRef] [PubMed]
- P. Salières, P. Antoine, A. de Bohan, and M. Lewenstein, “Temporal and spectral tailoring of high-order harmonics,” Phys. Rev. Lett. 81(25), 5544–5547 (1998). [CrossRef]
- N. H. Shon, A. Suda, and K. Midorikawa, “Generation and propagation of high-order harmonics in high-pressure gases,” Phys. Rev. A 62(2), 023801 (2000). [CrossRef]
- M. B. Gaarde and K. J. Schafer, “Space-time considerations in the phase locking of high harmonics,” Phys. Rev. Lett. 89(21), 213901 (2002). [CrossRef] [PubMed]
- E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, “Nonadiabatic three-dimensional model of high-order harmonic generation in the few-optical-cycle regime,” Phys. Rev. A 61(6), 063801 (2000). [CrossRef]
- G. Tempea and T. Brabec, “Optimization of high-harmonic generation,” Appl. Phys. B 70, S197 (2000).
- J. Tate, T. Auguste, H. G. Muller, P. Salières, P. Agostini, and L. F. DiMauro, “Scaling of wave-packet dynamics in an intense midinfrared field,” Phys. Rev. Lett. 98(1), 013901 (2007). [CrossRef] [PubMed]
- P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nat. Phys. 4(5), 386–389 (2008). [CrossRef]
- C. Vozzi, F. Calegari, F. Frassetto, E. Benedetti, M. Nisoli, G. Sansone, L. Poletto, P. Villoresi, and S. Stagira, “Generation of high-order harmonics with a near-IR self-phase-stabilized parametric source,” Proceedings of Conference on Ultrafast Phenomena, FRI2.2 (2008).
- V. S. Yakovlev, M. Y. Ivanov, and F. Krausz, “Enhanced phase-matching for generation of soft X-ray harmonics and attosecond pulses in atomic gases,” Opt. Express 15(23), 15351–15364 (2007). [CrossRef] [PubMed]
- A. Gordon, F. X. Kärtner, N. Rohringer, and R. Santra, “Role of many-electron dynamics in high harmonic generation,” Phys. Rev. Lett. 96(22), 223902 (2006). [CrossRef] [PubMed]
- E. J. Takahashi, Y. Nabekawa, H. Mashiko, H. Hasegawa, A. Suda, and K. Midorikawa, “Generation of strong optical field in soft X-ray region by using high-order harmonics,” IEEE J. Sel. Top. Quantum Electron. 10(6), 1315–1328 (2004). [CrossRef]
- E. Constant, D. Garzella, P. Breger, E. Mével, Ch. Dorrer, C. Le Blanc, F. Salin, and P. Agostini, “Optimizing high harmonic generation in absorbing gases: Model and experiment,” Phys. Rev. Lett. 82(8), 1668–1671 (1999). [CrossRef]
- M. Schnürer, Z. Cheng, M. Hentschel, G. Tempea, P. Kálmán, T. Brabec, and F. Krausz, “Absorption-limited generation of coherent ultrashort soft-X-ray pulses,” Phys. Rev. Lett. 83(4), 722–725 (1999). [CrossRef]
- M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: Extreme nonlinear optics,” Phys. Rev. Lett. 83(15), 2930–2933 (1999). [CrossRef]
- M. V. Ammosov, N. B. Delone, and V. P. Krainov, “Tunnel ionization of complex atoms and atomic ions in a varying electromagnetic-field,” Sov. Phys. JETP 64, 1191–1194 (1986).
- A. Gordon and F. X. Kärtner, “Quantitative modeling of single atom high harmonic generation,” Phys. Rev. Lett. 95(22), 223901 (2005). [CrossRef] [PubMed]
- R. Santra and A. Gordon, “Three-step model for high-harmonic generation in many-electron systems,” Phys. Rev. Lett. 96(7), 073906 (2006). [CrossRef] [PubMed]
- A. Gordon and F. X. Kärtner, “Scaling of keV HHG photon yield with drive wavelength,” Opt. Express 13(8), 2941–2947 (2005). [CrossRef] [PubMed]
- Lawrence Berkeley National Laboratory, ( http://henke.lbl.gov/optical_constants/ ).
- T. Popmintchev, M. C. Chen, O. Cohen, M. E. Grisham, J. J. Rocca, M. M. Murnane, and H. C. Kapteyn, “Extended phase matching of high harmonics driven by mid-infrared light,” Opt. Lett. 33(18), 2128–2130 (2008). [CrossRef] [PubMed]

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