Abstract

The use of counterpropagating laser pulses to suppress high harmonic generation (HHG) is investigated experimentally for pulses polarized parallel or perpendicular to the driving laser pulse. It is shown for the first time that perpendicularly polarized pulses can suppress HHG. The intensity of the counterpropagating pulse required for harmonic suppression is found to be much larger for perpendicular polarization than for parallel polarization, in good agreement with simple models of the harmonic suppression. These results have applications to quasi-phase-matching of HHG with trains of counterpropagating pulses.

© 2007 Optical Society of America

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  1. A. L'Huillier and P. Balcou, "High-order harmonic generation in rare gases with a 1 ps1053 nm laser," Phys. Rev. Lett. 70, 774-777 (1993).
    [CrossRef] [PubMed]
  2. N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, "Coherent soft x ray generation by the harmonics of an ultra-high-power KrF laser," Phys. Rev. A 43, 1669-1672 (1991).
    [CrossRef] [PubMed]
  3. A. L'Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in xenon at 1064 nm: the role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
    [CrossRef] [PubMed]
  4. A. L'Huillier, K. J. Schafer, and K. C. Kulander, "Theoretical aspects of intense field harmonic generation," J. Phys. B 24, 3315-3341 (1991).
    [CrossRef]
  5. E. Takahashi, Y. Nabekawa, M. Nurhuda, and K. Midorikawa, "Generation of high-energy high-order harmonics by use of a long interaction medium," J. Opt. Soc. Am. B 20, 158-165 (2003).
    [CrossRef]
  6. A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x rays," Science 280, 1412-1415 (1997).
    [CrossRef]
  7. C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
    [CrossRef]
  8. A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, "Quasi-phase-matched generation of coherent extreme-ultraviolet light," Nature 421, 51-54 (2003).
    [CrossRef] [PubMed]
  9. J. Peatross, S. Voronov, and I. Prokopovich, "Selective zoning of high harmonic emission using counterpropagating light," Opt. Express 1, 114-125 (1997).
    [CrossRef] [PubMed]
  10. S. Voronov, I. Kohl, J. B. Madsen, J. Simmons, N. Terry, J. Titensor, Q. Wang, and J. Peatross, "Control of laser high-harmonic generation with counterpropagating light," Phys. Rev. Lett. 87, 133902 (2001).
    [CrossRef] [PubMed]
  11. X. Zhang, A. L. Lytle, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi phase-matching and quantum path control of high harmonic generation using counterpropagating light," Nat. Phys. 3, 270-275 (2007).
    [CrossRef]
  12. M. Lewenstein, P. Salieres, and A. L'Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
    [CrossRef] [PubMed]
  13. J. Peatross, M. V. Federov, and K. C. Kulander, "Intensity-dependent phase-matching effects in harmonic generation," J. Opt. Soc. Am. B 12, 863-870 (1995).
    [CrossRef]
  14. P. Salieres, A. L'Huillier, and M. Lewenstein, "Coherence control of high-order harmonics," Phys. Rev. Lett. 74, 3776-3779 (1995).
    [CrossRef] [PubMed]
  15. H. J. Shin, D. G. Lee, Y. H. Cha, J. H. Kim, K. H. Hong, and C. H. Nam, "Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field," Phys. Rev. A 63, 053407 (2001).
    [CrossRef]
  16. P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
    [CrossRef] [PubMed]
  17. K. S. Budil, P. Salieres, M. D. Perry, and A. L'Huillier, "Influence of ellipticity on harmonic generation," Phys. Rev. A 48, R3437-R3440 (1993).
    [CrossRef] [PubMed]
  18. P. Dietrich, N. H. Burnett, M. Ivanov, and P. B. Corkum, "High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light," Phys. Rev. A 50, R3585-R3588 (1994).
    [CrossRef] [PubMed]
  19. Y. Liang, M. V. Ammosov, and S. L. Chin, "High-order harmonic generation in argon by elliptically polarized picosecond dye laser pulses," J. Phys. B 27, 1269-1276 (1994).
    [CrossRef]
  20. N. H. Burnett, C. Kan, and P. B. Corkum, "Ellipticity and polarization effects in harmonic generation in ionizing neon," Phys. Rev. A 51, R3418-R3421 (1995).
    [CrossRef] [PubMed]
  21. B. Dromey, M. Zepf, M. Landreman, K. O'Keeffe, T. Robinson, and S. Hooker, "Generation of a high contrast train of ultrashort pulses using a compact birefringent crystal array," Appl. Opt. 46, 5142-5146 (2007).
    [CrossRef] [PubMed]
  22. J. B. Madsen, L. A. Hancock, S. L. Voronov, and J. Peatross, "High-order harmonics generation in crossed laser beams," J. Opt. Soc. Am. B 20, 166-170 (2003).
    [CrossRef]
  23. M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64, 1191-1194 (1986).

2007 (2)

X. Zhang, A. L. Lytle, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi phase-matching and quantum path control of high harmonic generation using counterpropagating light," Nat. Phys. 3, 270-275 (2007).
[CrossRef]

B. Dromey, M. Zepf, M. Landreman, K. O'Keeffe, T. Robinson, and S. Hooker, "Generation of a high contrast train of ultrashort pulses using a compact birefringent crystal array," Appl. Opt. 46, 5142-5146 (2007).
[CrossRef] [PubMed]

2003 (3)

2001 (2)

S. Voronov, I. Kohl, J. B. Madsen, J. Simmons, N. Terry, J. Titensor, Q. Wang, and J. Peatross, "Control of laser high-harmonic generation with counterpropagating light," Phys. Rev. Lett. 87, 133902 (2001).
[CrossRef] [PubMed]

H. J. Shin, D. G. Lee, Y. H. Cha, J. H. Kim, K. H. Hong, and C. H. Nam, "Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field," Phys. Rev. A 63, 053407 (2001).
[CrossRef]

1999 (1)

C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

1997 (2)

J. Peatross, S. Voronov, and I. Prokopovich, "Selective zoning of high harmonic emission using counterpropagating light," Opt. Express 1, 114-125 (1997).
[CrossRef] [PubMed]

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x rays," Science 280, 1412-1415 (1997).
[CrossRef]

1995 (4)

M. Lewenstein, P. Salieres, and A. L'Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
[CrossRef] [PubMed]

J. Peatross, M. V. Federov, and K. C. Kulander, "Intensity-dependent phase-matching effects in harmonic generation," J. Opt. Soc. Am. B 12, 863-870 (1995).
[CrossRef]

P. Salieres, A. L'Huillier, and M. Lewenstein, "Coherence control of high-order harmonics," Phys. Rev. Lett. 74, 3776-3779 (1995).
[CrossRef] [PubMed]

N. H. Burnett, C. Kan, and P. B. Corkum, "Ellipticity and polarization effects in harmonic generation in ionizing neon," Phys. Rev. A 51, R3418-R3421 (1995).
[CrossRef] [PubMed]

1994 (2)

P. Dietrich, N. H. Burnett, M. Ivanov, and P. B. Corkum, "High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light," Phys. Rev. A 50, R3585-R3588 (1994).
[CrossRef] [PubMed]

Y. Liang, M. V. Ammosov, and S. L. Chin, "High-order harmonic generation in argon by elliptically polarized picosecond dye laser pulses," J. Phys. B 27, 1269-1276 (1994).
[CrossRef]

1993 (3)

P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

K. S. Budil, P. Salieres, M. D. Perry, and A. L'Huillier, "Influence of ellipticity on harmonic generation," Phys. Rev. A 48, R3437-R3440 (1993).
[CrossRef] [PubMed]

A. L'Huillier and P. Balcou, "High-order harmonic generation in rare gases with a 1 ps1053 nm laser," Phys. Rev. Lett. 70, 774-777 (1993).
[CrossRef] [PubMed]

1991 (3)

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, "Coherent soft x ray generation by the harmonics of an ultra-high-power KrF laser," Phys. Rev. A 43, 1669-1672 (1991).
[CrossRef] [PubMed]

A. L'Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in xenon at 1064 nm: the role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
[CrossRef] [PubMed]

A. L'Huillier, K. J. Schafer, and K. C. Kulander, "Theoretical aspects of intense field harmonic generation," J. Phys. B 24, 3315-3341 (1991).
[CrossRef]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64, 1191-1194 (1986).

Appl. Opt. (1)

J. Opt. Soc. Am. B (3)

J. Phys. B (2)

A. L'Huillier, K. J. Schafer, and K. C. Kulander, "Theoretical aspects of intense field harmonic generation," J. Phys. B 24, 3315-3341 (1991).
[CrossRef]

Y. Liang, M. V. Ammosov, and S. L. Chin, "High-order harmonic generation in argon by elliptically polarized picosecond dye laser pulses," J. Phys. B 27, 1269-1276 (1994).
[CrossRef]

Nat. Phys. (1)

X. Zhang, A. L. Lytle, H. C. Kapteyn, M. M. Murnane, and O. Cohen, "Quasi phase-matching and quantum path control of high harmonic generation using counterpropagating light," Nat. Phys. 3, 270-275 (2007).
[CrossRef]

Nature (1)

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, "Quasi-phase-matched generation of coherent extreme-ultraviolet light," Nature 421, 51-54 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. A (6)

N. Sarukura, K. Hata, T. Adachi, R. Nodomi, M. Watanabe, and S. Watanabe, "Coherent soft x ray generation by the harmonics of an ultra-high-power KrF laser," Phys. Rev. A 43, 1669-1672 (1991).
[CrossRef] [PubMed]

M. Lewenstein, P. Salieres, and A. L'Huillier, "Phase of the atomic polarization in high-order harmonic generation," Phys. Rev. A 52, 4747-4754 (1995).
[CrossRef] [PubMed]

H. J. Shin, D. G. Lee, Y. H. Cha, J. H. Kim, K. H. Hong, and C. H. Nam, "Nonadiabatic blueshift of high-order harmonics from Ar and Ne atoms in an intense femtosecond laser field," Phys. Rev. A 63, 053407 (2001).
[CrossRef]

K. S. Budil, P. Salieres, M. D. Perry, and A. L'Huillier, "Influence of ellipticity on harmonic generation," Phys. Rev. A 48, R3437-R3440 (1993).
[CrossRef] [PubMed]

P. Dietrich, N. H. Burnett, M. Ivanov, and P. B. Corkum, "High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light," Phys. Rev. A 50, R3585-R3588 (1994).
[CrossRef] [PubMed]

N. H. Burnett, C. Kan, and P. B. Corkum, "Ellipticity and polarization effects in harmonic generation in ionizing neon," Phys. Rev. A 51, R3418-R3421 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

C. G. Durfee III, A. R. Rundquist, S. Backus, C. Herne, M. M. Murnane, and H. C. Kapteyn, "Phase matching of high-order harmonics in hollow waveguides," Phys. Rev. Lett. 83, 2187-2190 (1999).
[CrossRef]

P. B. Corkum, "Plasma perspective on strong-field multiphoton ionization," Phys. Rev. Lett. 71, 1994-1997 (1993).
[CrossRef] [PubMed]

P. Salieres, A. L'Huillier, and M. Lewenstein, "Coherence control of high-order harmonics," Phys. Rev. Lett. 74, 3776-3779 (1995).
[CrossRef] [PubMed]

A. L'Huillier, K. J. Schafer, and K. C. Kulander, "High-order harmonic generation in xenon at 1064 nm: the role of phase matching," Phys. Rev. Lett. 66, 2200-2203 (1991).
[CrossRef] [PubMed]

A. L'Huillier and P. Balcou, "High-order harmonic generation in rare gases with a 1 ps1053 nm laser," Phys. Rev. Lett. 70, 774-777 (1993).
[CrossRef] [PubMed]

S. Voronov, I. Kohl, J. B. Madsen, J. Simmons, N. Terry, J. Titensor, Q. Wang, and J. Peatross, "Control of laser high-harmonic generation with counterpropagating light," Phys. Rev. Lett. 87, 133902 (2001).
[CrossRef] [PubMed]

Science (1)

A. Rundquist, C. G. Durfee III, Z. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, "Phase-matched generation of coherent soft x rays," Science 280, 1412-1415 (1997).
[CrossRef]

Sov. Phys. JETP (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, "Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field," Sov. Phys. JETP 64, 1191-1194 (1986).

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Figures (7)

Fig. 1
Fig. 1

Calculated harmonic phase modulation caused by modulation in the phase of the fundamental for harmonic orders q = 15 (red solid curve) and q = 31 (blue dotted curve) using Eq. (3). Intensity-dependent phase modulation using Eqs. (2, 6) is also shown (black dashed curve), assuming k = 2 π . Calculations assume a driver with 1 × 10 14 W cm 2 and a counterpropagating wave of 1 100 the driver intensity. Figure adapted from [10].

Fig. 2
Fig. 2

Ellipticity, ϵ ( z ) , as a function of z for a perpendicularly polarized counterpropagating beam with peak electric field amplitude equal to a fraction r of that of the main driving pulse using Eq. (12).

Fig. 3
Fig. 3

Calculated ratio, r 2 , of the intensity of the CPB to that of the driving laser required to suppress harmonic orders q = 21 and q = 29 . Curves are calculated from Eq. (15) using empirical A q values for argon.

Fig. 4
Fig. 4

Configuration of the compressor and target chambers used throughout the experiment. λ 2 , half-wave plate; T, gas cell target; B, beam dump.

Fig. 5
Fig. 5

(a) Variation of the high-harmonic spectrum as a function of shot number while the timing slide was moved to random locations. Each “shot” was a 30 s exposure during which 300 driving laser pulses were incident on the target. Counts are binned in the spatial dimension of the CCD. (b) Same spectra, arranged in order of timing slide position, showing reproducible extinction of HHG near a timing slide position of 127.6 mm .

Fig. 6
Fig. 6

Measured harmonic signal as a function of the ratio, r 2 , of the intensity in the CPB to that in the driver beam for various harmonic orders, q, and for both parallel and perpendicular polarizations.

Fig. 7
Fig. 7

Measured fraction of the intensity in the CPB to that of the driving pulse required for half-extinction of the harmonic signal for several different runs. Solid symbols show results obtained with a perpendicularly polarized CPB, open symbols correspond to a parallel polarized beam. The solid green curve shows the predicted dependence for perpendicular polarization using Eq. (15). The dashed orange curve gives the predicted behavior arising from phase modulation of the driver beam by the CPB, Eq. (7). The calculated behavior arising from intensity modulation of the fundamental, Eq. (5), is shown for the case of the long (dotted blue curve) and short (dotted–dashed black curve) trajectories being dominant. The experimental data indicate that in this case the short trajectory dominates.

Equations (15)

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E ( z , t ) = Re [ E d e i ( k z ω t ) + E CPB e i ( k z ω t ) ] = Re [ E t ( z ) e i ( k z ω t + ϕ ( z ) ) ] ,
E t ( z ) = E d 1 + ( E CPB E d ) 2 + 2 E CPB E d cos ( 2 k z ) ,
ϕ ( z ) = arctan ( E CPB E d sin ( 2 k z ) 1 + E CPB E d cos ( 2 k z ) ) .
Δ ϕ P = 2 arctan ( E CPB E d 1 ( E CPB E d ) 2 ) 2 ( E CPB E d ) ,
I CPB I d = ( E CPB E d ) 2 = ( π 2 q ) 2 .
ϕ q I = K e 2 2 ϵ 0 c m e ω 3 ,
Δ ϕ I 2 K e 2 ϵ 0 c m e ω 3 I CPB I d .
I d I CPB > 4 × 10 26 K 2 [ W cm 2 ] 2 .
E ( z , t ) = Re { E d exp [ i ( k z ω t ) ] ( 1 0 ) + r E d exp [ i ( k z ω t ) ] ( 0 1 ) } ,
e i ϕ [ ( u ν ) + i ϵ ( ν u ) ] ,
E ( z , t ) = Re { E d e i ω t e i ϕ ( z ) [ ( u ( z ) ν ( z ) ) + i ϵ ( z ) ( ν ( z ) u ( z ) ) ] } .
ϵ ( z ) = 1 + r 2 1 + r 4 + 2 r 2 cos ( 4 k z ) 2 r sin ( 2 k z ) r sin ( 2 k z ) ,
I q ( ϵ ) = I q ( 0 ) e A ( q ) ϵ 2 .
ξ = exp [ A ( q ) ϵ ( z ) 2 ] = exp ( A ( q ) ϵ ( z ) 2 2 ) ,
I q , CPB I q , no CPB = [ 4 λ 0 λ 4 exp ( A ( q ) ϵ ( z ) 2 2 ) d z ] 2 [ exp ( A ( q ) r 2 4 ) I 0 ( A ( q ) r 2 4 ) ] 2 exp ( A ( q ) 2 ) ,

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