Abstract

The high-order harmonic generation (HHG) in silver, gold, and zinc plasma plumes irradiated by orthogonally polarized two-color field is studied theoretically and experimentally. We find an increase of the HHG efficiency in comparison with the single-color case, which essentially depends on the plasma species and harmonic order. An increase of more than an order of magnitude is observed for silver plasma, whereas for gold and zinc it is lower; these results are reproduced in our calculations that include both propagation and microscopic response studies. We show that the widely used theoretical approach assuming the 1s ground state of the generating particle fails to reproduce the experimental results; the agreement is achieved in our theory using the actual quantum numbers of the outer electron of the generating particles. Moreover, our theoretical studies highlight the redistribution of the electronic density in the continuum wave packet as an important aspect of the HHG enhancement in the two-color orthogonally polarized fields with comparable intensities: in the single-color field the electronic trajectories with almost zero return energy are the most populated ones; in the two-color case the total field maximum can be shifted in time so that the trajectories with high return energies (in particular, the cut-off trajectory) become the most populated ones.

© 2016 Optical Society of America

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  1. T. T. Liu, T. Kanai, T. Sekikawa, and S. Watanabe, “Significant enhancement of high-order harmonics below 10nm in a two-color laser field,” Phys. Rev. A 73(6), 063823 (2006).
    [Crossref]
  2. N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).
  3. X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
    [Crossref]
  4. J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
    [Crossref] [PubMed]
  5. 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] [PubMed]
  6. C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
    [Crossref]
  7. D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
    [Crossref]
  8. L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
    [Crossref] [PubMed]
  9. L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
    [Crossref] [PubMed]
  10. H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).
  11. S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A 52(3), 2262–2278 (1995).
    [Crossref] [PubMed]
  12. W. Becker, B. N. Chichkov, and B. Wellegehausen, “Schemes for the generation of circularly polarized high-order harmonics by two-color mixing,” Phys. Rev. A 60(2), 1721–1722 (1999).
    [Crossref]
  13. D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A 61(6), 063403 (2000).
    [Crossref]
  14. Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
    [Crossref] [PubMed]
  15. M. Murakami, O. Korobkin, and M. Horbatsch, “High-harmonic generation from hydrogen atoms driven by two-color mutually orthogonal laser fields,” Phys. Rev. A 88(6), 063419 (2013).
    [Crossref]
  16. D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
    [Crossref]
  17. J. Henkel and M. Lein, “Analysis of electron trajectories with two-color strong-field ionization,” Phys. Rev. A 92(1), 013422 (2015).
    [Crossref]
  18. J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
    [Crossref] [PubMed]
  19. T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett. 31(7), 975–977 (2006).
    [Crossref] [PubMed]
  20. P. V. Ignatovich, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation by bichromatic field,” Laser Phys. 9(4), 570–574 (1999).
  21. K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer, “Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects,” Phys. Rev. A 74(5), 053412 (2006).
    [Crossref]
  22. C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115(4), 043901 (2015).
    [Crossref] [PubMed]
  23. B. Schütte, P. Weber, K. Kovács, E. Balogh, B. Major, V. Tosa, S. Han, M. J. J. Vrakking, K. Varjú, and A. Rouzée, “Bright attosecond soft X-ray pulse trains by transient phase-matching in two-color high-order harmonic generation,” Opt. Express 23(26), 33947–33955 (2015).
    [Crossref] [PubMed]
  24. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
    [Crossref]
  25. R. A. Ganeev, M. Suzuki, and H. Kuroda, “High-order harmonic generation in Ag, Sn, fullerene, and graphene nanoparticle-contained plasmas using two-color mid-infrared pulses,” Eur. Phys. J. D 70(1), 21 (2016).
    [Crossref]
  26. M. Rubenchik, M. D. Feit, M. D. Perry, and J. T. Larsen, “Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing,” Appl. Surf. Sci. 127–129, 193–198 (1998).
    [Crossref]
  27. 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]
  28. P. Lan, E. J. Takahashi, and K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81(6), 061802 (2010).
  29. R. A. Ganeev, M. Baba, M. Suzuki, and H. Kuroda, “High-order harmonic generation from silver plasma,” Phys. Lett. A 339(1–2), 103–109 (2005).
    [Crossref]
  30. A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “On the possibility of the generation of high harmonics with photon energies greater than 10 keV upon interaction of intense mid-IR radiation with neutral gases,” Quantum Electron. 44(5), 470–477 (2014).
    [Crossref]
  31. A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “Multi-keV ultrahigh-order harmonics produced in gases with subrelativistically intense mid-IR laser pulses,” J. Opt. Soc. Am. B 32(12), 2478–2487 (2015).
    [Crossref]
  32. M. Lewenstein, P. 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]
  33. V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
    [Crossref]
  34. V. V. Strelkov, “Theory of high-order harmonic generation and attosecond pulse emission by a low-frequency elliptically polarized laser field,” Phys. Rev. A 74(1), 013405 (2006).
    [Crossref]

2016 (1)

R. A. Ganeev, M. Suzuki, and H. Kuroda, “High-order harmonic generation in Ag, Sn, fullerene, and graphene nanoparticle-contained plasmas using two-color mid-infrared pulses,” Eur. Phys. J. D 70(1), 21 (2016).
[Crossref]

2015 (5)

C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115(4), 043901 (2015).
[Crossref] [PubMed]

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “Multi-keV ultrahigh-order harmonics produced in gases with subrelativistically intense mid-IR laser pulses,” J. Opt. Soc. Am. B 32(12), 2478–2487 (2015).
[Crossref]

B. Schütte, P. Weber, K. Kovács, E. Balogh, B. Major, V. Tosa, S. Han, M. J. J. Vrakking, K. Varjú, and A. Rouzée, “Bright attosecond soft X-ray pulse trains by transient phase-matching in two-color high-order harmonic generation,” Opt. Express 23(26), 33947–33955 (2015).
[Crossref] [PubMed]

J. Henkel and M. Lein, “Analysis of electron trajectories with two-color strong-field ionization,” Phys. Rev. A 92(1), 013422 (2015).
[Crossref]

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

2014 (2)

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “On the possibility of the generation of high harmonics with photon energies greater than 10 keV upon interaction of intense mid-IR radiation with neutral gases,” Quantum Electron. 44(5), 470–477 (2014).
[Crossref]

2013 (1)

M. Murakami, O. Korobkin, and M. Horbatsch, “High-harmonic generation from hydrogen atoms driven by two-color mutually orthogonal laser fields,” Phys. Rev. A 88(6), 063419 (2013).
[Crossref]

2012 (1)

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
[Crossref]

2011 (1)

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

2010 (3)

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
[Crossref] [PubMed]

P. Lan, E. J. Takahashi, and K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81(6), 061802 (2010).

2009 (2)

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

2008 (1)

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

2007 (2)

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
[Crossref] [PubMed]

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]

2006 (5)

K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer, “Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects,” Phys. Rev. A 74(5), 053412 (2006).
[Crossref]

V. V. Strelkov, “Theory of high-order harmonic generation and attosecond pulse emission by a low-frequency elliptically polarized laser field,” Phys. Rev. A 74(1), 013405 (2006).
[Crossref]

T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Single attosecond pulse generation in the multicycle-driver regime by adding a weak second-harmonic field,” Opt. Lett. 31(7), 975–977 (2006).
[Crossref] [PubMed]

T. T. Liu, T. Kanai, T. Sekikawa, and S. Watanabe, “Significant enhancement of high-order harmonics below 10nm in a two-color laser field,” Phys. Rev. A 73(6), 063823 (2006).
[Crossref]

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[Crossref] [PubMed]

2005 (3)

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] [PubMed]

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

R. A. Ganeev, M. Baba, M. Suzuki, and H. Kuroda, “High-order harmonic generation from silver plasma,” Phys. Lett. A 339(1–2), 103–109 (2005).
[Crossref]

2000 (1)

D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A 61(6), 063403 (2000).
[Crossref]

1999 (2)

W. Becker, B. N. Chichkov, and B. Wellegehausen, “Schemes for the generation of circularly polarized high-order harmonics by two-color mixing,” Phys. Rev. A 60(2), 1721–1722 (1999).
[Crossref]

P. V. Ignatovich, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation by bichromatic field,” Laser Phys. 9(4), 570–574 (1999).

1998 (1)

M. Rubenchik, M. D. Feit, M. D. Perry, and J. T. Larsen, “Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing,” Appl. Surf. Sci. 127–129, 193–198 (1998).
[Crossref]

1995 (2)

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A 52(3), 2262–2278 (1995).
[Crossref] [PubMed]

1994 (1)

M. Lewenstein, P. 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]

Abel, M. J.

Agostini, P.

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]

Auguste, T.

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]

Baba, M.

R. A. Ganeev, M. Baba, M. Suzuki, and H. Kuroda, “High-order harmonic generation from silver plasma,” Phys. Lett. A 339(1–2), 103–109 (2005).
[Crossref]

Balcou, P.

M. Lewenstein, P. 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]

Balogh, E.

Becker, W.

D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A 61(6), 063403 (2000).
[Crossref]

W. Becker, B. N. Chichkov, and B. Wellegehausen, “Schemes for the generation of circularly polarized high-order harmonics by two-color mixing,” Phys. Rev. A 60(2), 1721–1722 (1999).
[Crossref]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A 52(3), 2262–2278 (1995).
[Crossref] [PubMed]

Benis, E. P.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Brugnera, L.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
[Crossref] [PubMed]

Burgdörfer, J.

K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer, “Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects,” Phys. Rev. A 74(5), 053412 (2006).
[Crossref]

Chakera, J. A.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Charalambidis, D.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Cheng, Y.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
[Crossref] [PubMed]

Chichkov, B. N.

W. Becker, B. N. Chichkov, and B. Wellegehausen, “Schemes for the generation of circularly polarized high-order harmonics by two-color mixing,” Phys. Rev. A 60(2), 1721–1722 (1999).
[Crossref]

Cho, D. J.

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] [PubMed]

Conde, A. P.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Corkum, P. B.

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

M. Lewenstein, P. 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]

Dahlström, J. M.

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

DiMauro, L. F.

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]

Dudovich, N.

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

Egbert, A.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

Eichmann, H.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

Emelin, M. Yu.

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “Multi-keV ultrahigh-order harmonics produced in gases with subrelativistically intense mid-IR laser pulses,” J. Opt. Soc. Am. B 32(12), 2478–2487 (2015).
[Crossref]

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “On the possibility of the generation of high harmonics with photon energies greater than 10 keV upon interaction of intense mid-IR radiation with neutral gases,” Quantum Electron. 44(5), 470–477 (2014).
[Crossref]

Emelina, A. S.

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “Multi-keV ultrahigh-order harmonics produced in gases with subrelativistically intense mid-IR laser pulses,” J. Opt. Soc. Am. B 32(12), 2478–2487 (2015).
[Crossref]

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “On the possibility of the generation of high harmonics with photon energies greater than 10 keV upon interaction of intense mid-IR radiation with neutral gases,” Quantum Electron. 44(5), 470–477 (2014).
[Crossref]

Feit, M. D.

M. Rubenchik, M. D. Feit, M. D. Perry, and J. T. Larsen, “Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing,” Appl. Surf. Sci. 127–129, 193–198 (1998).
[Crossref]

Frank, F.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
[Crossref] [PubMed]

Froud, C.

Gaarde, M. B.

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[Crossref] [PubMed]

Gallmann, L.

Ganeev, R. A.

R. A. Ganeev, M. Suzuki, and H. Kuroda, “High-order harmonic generation in Ag, Sn, fullerene, and graphene nanoparticle-contained plasmas using two-color mid-infrared pulses,” Eur. Phys. J. D 70(1), 21 (2016).
[Crossref]

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

R. A. Ganeev, M. Baba, M. Suzuki, and H. Kuroda, “High-order harmonic generation from silver plasma,” Phys. Lett. A 339(1–2), 103–109 (2005).
[Crossref]

Geng, J.-W.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

Gong, Q.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

Gonoskov, A. A.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
[Crossref]

Gonoskov, I. A.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
[Crossref]

Gupta, P. D.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Gustafsson, E.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[Crossref] [PubMed]

Han, S.

He, X.

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

Henkel, J.

J. Henkel and M. Lein, “Analysis of electron trajectories with two-color strong-field ionization,” Phys. Rev. A 92(1), 013422 (2015).
[Crossref]

Heyl, C. M.

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

Hoffmann, D. J.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
[Crossref] [PubMed]

Hong, K.-H.

C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115(4), 043901 (2015).
[Crossref] [PubMed]

Horbatsch, M.

M. Murakami, O. Korobkin, and M. Horbatsch, “High-harmonic generation from hydrogen atoms driven by two-color mutually orthogonal laser fields,” Phys. Rev. A 88(6), 063419 (2013).
[Crossref]

Hutchison, C.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

Ignatovich, P. V.

P. V. Ignatovich, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation by bichromatic field,” Laser Phys. 9(4), 570–574 (1999).

Ivanov, M. Y.

M. Lewenstein, P. 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]

Jin, C.

C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115(4), 043901 (2015).
[Crossref] [PubMed]

Johnsson, P.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[Crossref] [PubMed]

Kanai, T.

T. T. Liu, T. Kanai, T. Sekikawa, and S. Watanabe, “Significant enhancement of high-order harmonics below 10nm in a two-color laser field,” Phys. Rev. A 73(6), 063823 (2006).
[Crossref]

Khan, R. A.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Khokhlova, M. A.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
[Crossref]

Kim, C. M.

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] [PubMed]

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

Kim, H. T.

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] [PubMed]

Kim, I. J.

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] [PubMed]

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

Kopold, R.

D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A 61(6), 063403 (2000).
[Crossref]

Korobkin, O.

M. Murakami, O. Korobkin, and M. Horbatsch, “High-harmonic generation from hydrogen atoms driven by two-color mutually orthogonal laser fields,” Phys. Rev. A 88(6), 063419 (2013).
[Crossref]

Kovács, K.

Kulagin, I. A.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Kuroda, H.

R. A. Ganeev, M. Suzuki, and H. Kuroda, “High-order harmonic generation in Ag, Sn, fullerene, and graphene nanoparticle-contained plasmas using two-color mid-infrared pulses,” Eur. Phys. J. D 70(1), 21 (2016).
[Crossref]

R. A. Ganeev, M. Baba, M. Suzuki, and H. Kuroda, “High-order harmonic generation from silver plasma,” Phys. Lett. A 339(1–2), 103–109 (2005).
[Crossref]

L’Huillier, A.

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[Crossref] [PubMed]

M. Lewenstein, P. 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]

Lan, P.

P. Lan, E. J. Takahashi, and K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81(6), 061802 (2010).

Larsen, J. T.

M. Rubenchik, M. D. Feit, M. D. Perry, and J. T. Larsen, “Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing,” Appl. Surf. Sci. 127–129, 193–198 (1998).
[Crossref]

Lee, G. H.

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] [PubMed]

Lee, Y. S.

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] [PubMed]

Lein, M.

J. Henkel and M. Lein, “Analysis of electron trajectories with two-color strong-field ionization,” Phys. Rev. A 92(1), 013422 (2015).
[Crossref]

Leone, S. R.

Lewenstein, M.

M. Lewenstein, P. 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]

Li, R.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
[Crossref] [PubMed]

Lin, C. D.

C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115(4), 043901 (2015).
[Crossref] [PubMed]

Liu, T. T.

T. T. Liu, T. Kanai, T. Sekikawa, and S. Watanabe, “Significant enhancement of high-order harmonics below 10nm in a two-color laser field,” Phys. Rev. A 73(6), 063823 (2006).
[Crossref]

Long, S.

S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A 52(3), 2262–2278 (1995).
[Crossref] [PubMed]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

Mairesse, Y.

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

Major, B.

Marangos, J. P.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
[Crossref] [PubMed]

Maravelias, G.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Mauritsson, J.

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[Crossref] [PubMed]

McIver, J. K.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A 52(3), 2262–2278 (1995).
[Crossref] [PubMed]

Midorikawa, K.

P. Lan, E. J. Takahashi, and K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81(6), 061802 (2010).

Miloševic, D. B.

D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A 61(6), 063403 (2000).
[Crossref]

Momma, C.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

Muller, H. G.

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]

Murakami, M.

M. Murakami, O. Korobkin, and M. Horbatsch, “High-harmonic generation from hydrogen atoms driven by two-color mutually orthogonal laser fields,” Phys. Rev. A 88(6), 063419 (2013).
[Crossref]

Naik, P. A.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Nam, C. H.

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

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] [PubMed]

Neumark, D. M.

Nikolopoulos, L. A. A.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Nolte, S.

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

Park, J. Y.

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] [PubMed]

Peng, L.-Y.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

Perry, M. D.

M. Rubenchik, M. D. Feit, M. D. Perry, and J. T. Larsen, “Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing,” Appl. Surf. Sci. 127–129, 193–198 (1998).
[Crossref]

Persson, A.

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

Persson, E.

K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer, “Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects,” Phys. Rev. A 74(5), 053412 (2006).
[Crossref]

Pfeifer, T.

Platonenko, V. T.

P. V. Ignatovich, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation by bichromatic field,” Laser Phys. 9(4), 570–574 (1999).

Rakowski, R.

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

Redkin, P. V.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Rouzée, A.

Rubenchik, M.

M. Rubenchik, M. D. Feit, M. D. Perry, and J. T. Larsen, “Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing,” Appl. Surf. Sci. 127–129, 193–198 (1998).
[Crossref]

Ryabikin, M. Yu.

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “Multi-keV ultrahigh-order harmonics produced in gases with subrelativistically intense mid-IR laser pulses,” J. Opt. Soc. Am. B 32(12), 2478–2487 (2015).
[Crossref]

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “On the possibility of the generation of high harmonics with photon energies greater than 10 keV upon interaction of intense mid-IR radiation with neutral gases,” Quantum Electron. 44(5), 470–477 (2014).
[Crossref]

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
[Crossref]

Salières, P.

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]

Schafer, K. J.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[Crossref] [PubMed]

Schiessl, K.

K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer, “Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects,” Phys. Rev. A 74(5), 053412 (2006).
[Crossref]

Schütte, B.

Scrinzi, A.

K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer, “Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects,” Phys. Rev. A 74(5), 053412 (2006).
[Crossref]

Sekikawa, T.

T. T. Liu, T. Kanai, T. Sekikawa, and S. Watanabe, “Significant enhancement of high-order harmonics below 10nm in a two-color laser field,” Phys. Rev. A 73(6), 063823 (2006).
[Crossref]

Siegel, T.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
[Crossref] [PubMed]

Singhal, H.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Skantzakis, E.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Song, X.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
[Crossref] [PubMed]

Springate, E.

Stein, G. J.

C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115(4), 043901 (2015).
[Crossref] [PubMed]

Strelkov, V. V.

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
[Crossref]

V. V. Strelkov, “Theory of high-order harmonic generation and attosecond pulse emission by a low-frequency elliptically polarized laser field,” Phys. Rev. A 74(1), 013405 (2006).
[Crossref]

P. V. Ignatovich, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation by bichromatic field,” Laser Phys. 9(4), 570–574 (1999).

Suzuki, M.

R. A. Ganeev, M. Suzuki, and H. Kuroda, “High-order harmonic generation in Ag, Sn, fullerene, and graphene nanoparticle-contained plasmas using two-color mid-infrared pulses,” Eur. Phys. J. D 70(1), 21 (2016).
[Crossref]

R. A. Ganeev, M. Baba, M. Suzuki, and H. Kuroda, “High-order harmonic generation from silver plasma,” Phys. Lett. A 339(1–2), 103–109 (2005).
[Crossref]

Takahashi, E. J.

P. Lan, E. J. Takahashi, and K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81(6), 061802 (2010).

Tate, J.

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]

Tate, J. L.

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

Tayyab, M.

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

Tisch, J. W. G.

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

L. Brugnera, F. Frank, D. J. Hoffmann, R. Torres, T. Siegel, J. G. Underwood, E. Springate, C. Froud, E. I. C. Turcu, J. W. G. Tisch, and J. P. Marangos, “Enhancement of high harmonics generated by field steering of electrons in a two-color orthogonally polarized laser field,” Opt. Lett. 35(23), 3994–3996 (2010).
[Crossref] [PubMed]

Torres, R.

Tosa, V.

Tsakiris, G. D.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Turcu, E. I. C.

Tzallas, P.

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Underwood, J. G.

Varjú, K.

Villeneuve, D. M.

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

Vrakking, M. J. J.

Watanabe, S.

T. T. Liu, T. Kanai, T. Sekikawa, and S. Watanabe, “Significant enhancement of high-order harmonics below 10nm in a two-color laser field,” Phys. Rev. A 73(6), 063823 (2006).
[Crossref]

Weber, P.

Wellegehausen, B.

W. Becker, B. N. Chichkov, and B. Wellegehausen, “Schemes for the generation of circularly polarized high-order harmonics by two-color mixing,” Phys. Rev. A 60(2), 1721–1722 (1999).
[Crossref]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

Xiao, X.-R.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

Xiong, W.-H.

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

Xu, Z.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
[Crossref] [PubMed]

Zaïr, A.

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

Zeng, Z.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
[Crossref] [PubMed]

Appl. Surf. Sci. (1)

M. Rubenchik, M. D. Feit, M. D. Perry, and J. T. Larsen, “Numerical simulation of ultra-short laser pulse energy deposition and bulk transport for material processing,” Appl. Surf. Sci. 127–129, 193–198 (1998).
[Crossref]

Eur. Phys. J. D (1)

R. A. Ganeev, M. Suzuki, and H. Kuroda, “High-order harmonic generation in Ag, Sn, fullerene, and graphene nanoparticle-contained plasmas using two-color mid-infrared pulses,” Eur. Phys. J. D 70(1), 21 (2016).
[Crossref]

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

Laser Phys. (1)

P. V. Ignatovich, V. T. Platonenko, and V. V. Strelkov, “High-order harmonic generation by bichromatic field,” Laser Phys. 9(4), 570–574 (1999).

New J. Phys. (1)

D. Charalambidis, P. Tzallas, E. P. Benis, E. Skantzakis, G. Maravelias, L. A. A. Nikolopoulos, A. P. Conde, and G. D. Tsakiris, “Exploring intense attosecond pulses,” New J. Phys. 10(2), 025018 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

R. A. Ganeev, M. Baba, M. Suzuki, and H. Kuroda, “High-order harmonic generation from silver plasma,” Phys. Lett. A 339(1–2), 103–109 (2005).
[Crossref]

Phys. Rev. A (17)

K. Schiessl, E. Persson, A. Scrinzi, and J. Burgdörfer, “Enhancement of high-order harmonic generation by a two-color field: Influence of propagation effects,” Phys. Rev. A 74(5), 053412 (2006).
[Crossref]

P. Lan, E. J. Takahashi, and K. Midorikawa, “Wavelength scaling of efficient high-order harmonic generation by two-color infrared laser fields,” Phys. Rev. A 81(6), 061802 (2010).

M. Lewenstein, P. 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]

V. V. Strelkov, M. A. Khokhlova, A. A. Gonoskov, I. A. Gonoskov, and M. Yu. Ryabikin, “High-order harmonic generation by atoms in an elliptically polarized laser field: Harmonic polarization properties and laser threshold ellipticity,” Phys. Rev. A 86(1), 013404 (2012).
[Crossref]

V. V. Strelkov, “Theory of high-order harmonic generation and attosecond pulse emission by a low-frequency elliptically polarized laser field,” Phys. Rev. A 74(1), 013405 (2006).
[Crossref]

C. M. Kim, I. J. Kim, and C. H. Nam, “Generation of a strong attosecond pulse train with an orthogonally polarized two-color laser field,” Phys. Rev. A 72(3), 033817 (2005).
[Crossref]

R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using two-color pump in plasma plumes,” Phys. Rev. A 80(3), 033845 (2009).
[Crossref]

M. Murakami, O. Korobkin, and M. Horbatsch, “High-harmonic generation from hydrogen atoms driven by two-color mutually orthogonal laser fields,” Phys. Rev. A 88(6), 063419 (2013).
[Crossref]

D. J. Hoffmann, C. Hutchison, A. Zaïr, and J. P. Marangos, “Control of temporal mapping and harmonic intensity modulation using two-color orthogonally polarized fields,” Phys. Rev. A 89(2), 023423 (2014).
[Crossref]

J. Henkel and M. Lein, “Analysis of electron trajectories with two-color strong-field ionization,” Phys. Rev. A 92(1), 013422 (2015).
[Crossref]

T. T. Liu, T. Kanai, T. Sekikawa, and S. Watanabe, “Significant enhancement of high-order harmonics below 10nm in a two-color laser field,” Phys. Rev. A 73(6), 063823 (2006).
[Crossref]

N. Dudovich, J. L. Tate, Y. Mairesse, D. M. Villeneuve, P. B. Corkum, and M. B. Gaarde, “Subcycle spatial mapping of recollision dynamics,” Phys. Rev. A 80(1), 011806 (2009).

X. He, J. M. Dahlström, R. Rakowski, C. M. Heyl, A. Persson, J. Mauritsson, and A. L’Huillier, “Interference effects in two-color high-order harmonic generation,” Phys. Rev. A 82(3), 033410 (2010).
[Crossref]

H. Eichmann, A. Egbert, S. Nolte, C. Momma, B. Wellegehausen, W. Becker, S. Long, and J. K. McIver, “Polarization-dependent high-order two-color mixing,” Phys. Rev. A 51(5), R3414 (1995).

S. Long, W. Becker, and J. K. McIver, “Model calculations of polarization-dependent two-color high-harmonic generation,” Phys. Rev. A 52(3), 2262–2278 (1995).
[Crossref] [PubMed]

W. Becker, B. N. Chichkov, and B. Wellegehausen, “Schemes for the generation of circularly polarized high-order harmonics by two-color mixing,” Phys. Rev. A 60(2), 1721–1722 (1999).
[Crossref]

D. B. Milošević, W. Becker, and R. Kopold, “Generation of circularly polarized high-order harmonics by two-color coplanar field mixing,” Phys. Rev. A 61(6), 063403 (2000).
[Crossref]

Phys. Rev. Lett. (7)

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007).
[Crossref] [PubMed]

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97(1), 013001 (2006).
[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] [PubMed]

J.-W. Geng, W.-H. Xiong, X.-R. Xiao, L.-Y. Peng, and Q. Gong, “Nonadiabatic electron dynamics in orthogonal two-color laser fields with comparable intensities,” Phys. Rev. Lett. 115(19), 193001 (2015).
[Crossref] [PubMed]

L. Brugnera, D. J. Hoffmann, T. Siegel, F. Frank, A. Zaïr, J. W. G. Tisch, and J. P. Marangos, “Trajectory selection in high harmonic generation by controlling the phase between orthogonal two-color fields,” Phys. Rev. Lett. 107(15), 153902 (2011).
[Crossref] [PubMed]

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]

C. Jin, G. J. Stein, K.-H. Hong, and C. D. Lin, “Generation of bright, spatially coherent soft X-ray high harmonics in a hollow waveguide using two-color synthesized laser pulses,” Phys. Rev. Lett. 115(4), 043901 (2015).
[Crossref] [PubMed]

Quantum Electron. (1)

A. S. Emelina, M. Yu. Emelin, and M. Yu. Ryabikin, “On the possibility of the generation of high harmonics with photon energies greater than 10 keV upon interaction of intense mid-IR radiation with neutral gases,” Quantum Electron. 44(5), 470–477 (2014).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for harmonic generation in metallic plasma.

Fig. 2
Fig. 2

HHG in (a) Ag, (b) Au, and (c) Zn plasmas using 1310 nm and 1310 nm + 655 nm pumps.

Fig. 3
Fig. 3

Spectra of a silver ion response: (a) with α = 1/3, φ = π/2 and various d(p) (see legend); (b) with φ = 0 and various α (see legend); (c) with φ = π/2 and various α (see legend). Results in (b) and (c) are obtained with the actual quantum numbers.

Fig. 4
Fig. 4

(a) Y-coordinate of the electron at the instant of its return to the parent ion in x-direction (solid line) and the y-width of the returning electron wavepacket (dashed line) as a function of ionization time. The calculations were made using formula proposed in [33, 34]; α = 1/3, φ = 1.4. (b) Time dependence of the absolute value of the total field and field components (see legend); α = 1/3, φ = 1.4. (c) Harmonic intensity vs. relative phase φ for several harmonics (see legend); α = 1/3.

Fig. 5
Fig. 5

The macroscopic signals of (a) H25 and (b) H35 as functions of the propagation distance in the single-color (dotted line) and two-color (solid lines) cases calculated for silver plasma. The signals for the two-color fields with I2ω = Iω/3 (α = 1/3) and I2ω = Iω (α = 1) are multiplied by 10−1 and 10−2, respectively.

Fig. 6
Fig. 6

The macroscopic spectrum calculated for (a)-(b) silver, (c) gold, and (d) zinc plasma in the single- and two-color cases for a given propagation distance L= L 21 coh . Results in (a) are obtained with α = 1/3 and various d(p) (see legend).

Fig. 7
Fig. 7

The gain in harmonic intensity in the TCP case compared to the SCP one for different plasmas.

Equations (17)

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

r( t )=i 0 dτ ( π ε+iτ/2 ) 3 2 d( p st A( tτ ) c ),E( tτ ) d * ( p st A( t ) c ) ×exp[ iS( p st ,t,τ ) 0 t W( t ) 2 d t 0 tτ W( t ) 2 d t ]+c.c.,
p st (t,τ)= 1 τ tτ t A(t') c dt'
{ E x (t)= E 1 (t)= E 0 exp[ ln(4) t 2 T 2 ]exp( iωt )+c.c. E y (t)= E 2 (t)= α E 0 exp[ ln(4) t 2 T 2 ]exp( i2ωt+iφ )+c.c.
d(p)= i l1 2 2l+3/2 ( l+1 )! γ l+3/2 π n ( nl1 )!( n+l )!( 2l+1 ) × p [ p l P l ( p z p ) m=0 nl1 ( 2γ ) m m!( 2l+1+m )!(nl1m)! d m d γ m γ ( γ 2 + p 2 ) l+2 ],
E 1 (z,t)= E 0 (z,t)exp[ iω(tz/c)+i φ 1 (z) ]+c.c.,
E 2 (z,t)= α E 0 (z,t)exp[ i2ω(tz/c)+i φ 2 (z) ]+c.c.,
t'=tδt,
E 1 (z,t')= E 0 (z,t)exp[ iω(t'z/c) ]+c.c.,
E 2 (z,t')= α E 0 (z,t)exp[ i2ω(t'z/c)+i φ 2 '(z) ]+c.c.,
φ 2 '= φ 2 2 φ 1 .
P(z,t')= Ω P Ω ( φ 2 ')exp[ iΩ(t'z/c) ] dΩ+c.c.,
P(z,t)= Ω P Ω [ φ 2 (z)2 φ 1 (z) ]exp[ iΩ(tz/c)+i Ω ω φ 1 (z) ] dΩ+c.c.
I Ω = N 2 | 0 L r Ω [ φ 2 (z)2 φ 1 (z) ]exp[ i Ω ω φ 1 (z) ] dz | 2 .
φ 1 (z)=zω( n 1 1)/c,
φ 2 (z,δ)=z2ω( n 2 1)/c+δ,
I ¯ Ω = 1 π 0 π dδ N 2 | 0 L r Ω [ φ 2 (z,δ)2 φ 1 (z) ]exp[ i Ω ω φ 1 (z) ] dz | 2 ,
n 1   1 = 4( n 2   1 ).

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