Abstract

The force due to the transverse magnetic field of a laser beam drives an electron in the direction of laser propagation, thereby impeding the recollision mechanism for high-order harmonic generation. The longitudinal electric field component of a tightly focused Gaussian beam can sufficiently counteract the magnetic force to enhance the harmonic yield substantially. For tight focusing and a laser intensity of 1018Wcm2, it can raise the harmonic yield by several orders of magnitude.

© 2006 Optical Society of America

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  1. T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
    [CrossRef]
  2. Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006).
    [CrossRef]
  3. P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
    [CrossRef] [PubMed]
  4. M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, Phys. Rev. Lett. 85, 5082 (2000).
    [CrossRef] [PubMed]
  5. D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403(R) (2001).
  6. N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, J. Phys. B 34, L55 (2001).
    [CrossRef]
  7. V. D. Taranukhin, Laser Phys. 10, 330 (2000).
  8. J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
    [CrossRef]
  9. N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
    [CrossRef] [PubMed]
  10. B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
    [CrossRef]
  11. B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
    [CrossRef]
  12. A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
    [CrossRef] [PubMed]
  13. S. X. Hu and A. F. Starace, Phys. Rev. Lett. 88, 245003 (2002).
    [CrossRef] [PubMed]
  14. Y. I. Salamin, J. Phys. B 38, 4095 (2005).
    [CrossRef]
  15. B. Gottlieb, A. Lohr, W. Becker, and M. Kleber, Phys. Rev. A 54, R1022 (1996).
    [CrossRef] [PubMed]
  16. M. V. Ammosov, N. B. Delone, and V. P. Krainov, Sov. Phys. JETP 64, 1191 (1986).
  17. V. S. Popov, V. D. Mur, and B. M. Karnakov, Phys. Lett. A 250, 20 (1998).
    [CrossRef]

2006 (1)

Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006).
[CrossRef]

2005 (1)

Y. I. Salamin, J. Phys. B 38, 4095 (2005).
[CrossRef]

2004 (2)

N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
[CrossRef] [PubMed]

B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
[CrossRef]

2003 (1)

A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
[CrossRef] [PubMed]

2002 (1)

S. X. Hu and A. F. Starace, Phys. Rev. Lett. 88, 245003 (2002).
[CrossRef] [PubMed]

2001 (3)

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403(R) (2001).

N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, J. Phys. B 34, L55 (2001).
[CrossRef]

2000 (3)

V. D. Taranukhin, Laser Phys. 10, 330 (2000).

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, Phys. Rev. Lett. 85, 5082 (2000).
[CrossRef] [PubMed]

1998 (2)

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

V. S. Popov, V. D. Mur, and B. M. Karnakov, Phys. Lett. A 250, 20 (1998).
[CrossRef]

1996 (1)

B. Gottlieb, A. Lohr, W. Becker, and M. Kleber, Phys. Rev. A 54, R1022 (1996).
[CrossRef] [PubMed]

1993 (1)

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

1986 (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Sov. Phys. JETP 64, 1191 (1986).

Ammosov, M. V.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Sov. Phys. JETP 64, 1191 (1986).

Becker, W.

D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403(R) (2001).

B. Gottlieb, A. Lohr, W. Becker, and M. Kleber, Phys. Rev. A 54, R1022 (1996).
[CrossRef] [PubMed]

Brabec, T.

N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
[CrossRef] [PubMed]

M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, Phys. Rev. Lett. 85, 5082 (2000).
[CrossRef] [PubMed]

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Corkum, P. B.

N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
[CrossRef] [PubMed]

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

Delone, N. B.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Sov. Phys. JETP 64, 1191 (1986).

Ditmire, T.

A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
[CrossRef] [PubMed]

Gottlieb, B.

B. Gottlieb, A. Lohr, W. Becker, and M. Kleber, Phys. Rev. A 54, R1022 (1996).
[CrossRef] [PubMed]

Hatsagortsyan, K. Z.

Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006).
[CrossRef]

B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
[CrossRef]

Henrich, B.

B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
[CrossRef]

Hu, S.

D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403(R) (2001).

Hu, S. X.

Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006).
[CrossRef]

S. X. Hu and A. F. Starace, Phys. Rev. Lett. 88, 245003 (2002).
[CrossRef] [PubMed]

Joachain, C. J.

N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, J. Phys. B 34, L55 (2001).
[CrossRef]

Karnakov, B. M.

V. S. Popov, V. D. Mur, and B. M. Karnakov, Phys. Lett. A 250, 20 (1998).
[CrossRef]

Keitel, C. H.

Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006).
[CrossRef]

B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
[CrossRef]

M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, Phys. Rev. Lett. 85, 5082 (2000).
[CrossRef] [PubMed]

Kleber, M.

B. Gottlieb, A. Lohr, W. Becker, and M. Kleber, Phys. Rev. A 54, R1022 (1996).
[CrossRef] [PubMed]

Knight, P. L.

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Krainov, V. P.

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Sov. Phys. JETP 64, 1191 (1986).

Krausz, F.

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Kylstra, N. J.

N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, J. Phys. B 34, L55 (2001).
[CrossRef]

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Lohr, A.

B. Gottlieb, A. Lohr, W. Becker, and M. Kleber, Phys. Rev. A 54, R1022 (1996).
[CrossRef] [PubMed]

Maltsev, A.

A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
[CrossRef] [PubMed]

Milosevic, D. B.

D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403(R) (2001).

Milosevic, N.

N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
[CrossRef] [PubMed]

Mora, P.

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

Mur, V. D.

V. S. Popov, V. D. Mur, and B. M. Karnakov, Phys. Lett. A 250, 20 (1998).
[CrossRef]

Patel, A.

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Popov, V. S.

V. S. Popov, V. D. Mur, and B. M. Karnakov, Phys. Lett. A 250, 20 (1998).
[CrossRef]

Potvliege, R. M.

N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, J. Phys. B 34, L55 (2001).
[CrossRef]

Quesnel, B.

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

Roso, L.

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Salamin, Y. I.

Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006).
[CrossRef]

Y. I. Salamin, J. Phys. B 38, 4095 (2005).
[CrossRef]

Scrinzi, A.

M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, Phys. Rev. Lett. 85, 5082 (2000).
[CrossRef] [PubMed]

Starace, A. F.

S. X. Hu and A. F. Starace, Phys. Rev. Lett. 88, 245003 (2002).
[CrossRef] [PubMed]

Taranukhin, V. D.

V. D. Taranukhin, Laser Phys. 10, 330 (2000).

Vázquez de Aldana, J. R.

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Walser, M. W.

M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, Phys. Rev. Lett. 85, 5082 (2000).
[CrossRef] [PubMed]

Worthington, R. A.

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

J. Phys. B (2)

N. J. Kylstra, R. M. Potvliege, and C. J. Joachain, J. Phys. B 34, L55 (2001).
[CrossRef]

Y. I. Salamin, J. Phys. B 38, 4095 (2005).
[CrossRef]

Laser Phys. (1)

V. D. Taranukhin, Laser Phys. 10, 330 (2000).

Phys. Lett. A (1)

V. S. Popov, V. D. Mur, and B. M. Karnakov, Phys. Lett. A 250, 20 (1998).
[CrossRef]

Phys. Rep. (1)

Y. I. Salamin, S. X. Hu, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rep. 427, 41 (2006).
[CrossRef]

Phys. Rev. A (3)

D. B. Milosevic, S. Hu, and W. Becker, Phys. Rev. A 63, 011403(R) (2001).

J. R. Vázquez de Aldana, N. J. Kylstra, L. Roso, P. L. Knight, A. Patel, and R. A. Worthington, Phys. Rev. A 64, 013412 (2001).
[CrossRef]

B. Gottlieb, A. Lohr, W. Becker, and M. Kleber, Phys. Rev. A 54, R1022 (1996).
[CrossRef] [PubMed]

Phys. Rev. E (1)

B. Quesnel and P. Mora, Phys. Rev. E 58, 3719 (1998).
[CrossRef]

Phys. Rev. Lett. (6)

A. Maltsev and T. Ditmire, Phys. Rev. Lett. 90, 053002 (2003).
[CrossRef] [PubMed]

S. X. Hu and A. F. Starace, Phys. Rev. Lett. 88, 245003 (2002).
[CrossRef] [PubMed]

N. Milosevic, P. B. Corkum, and T. Brabec, Phys. Rev. Lett. 92, 013002 (2004).
[CrossRef] [PubMed]

B. Henrich, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 93, 013601 (2004).
[CrossRef]

P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993).
[CrossRef] [PubMed]

M. W. Walser, C. H. Keitel, A. Scrinzi, and T. Brabec, Phys. Rev. Lett. 85, 5082 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
[CrossRef]

Sov. Phys. JETP (1)

M. V. Ammosov, N. B. Delone, and V. P. Krainov, Sov. Phys. JETP 64, 1191 (1986).

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Figures (3)

Fig. 1
Fig. 1

Initial positions of electrons that return to their place of birth to within Δ x 1 and Δ z 50 1 (lower curve), Δ z + 50 1 (upper curve), and Δ z 1 (middle curve). For some initial positions the electron orbits are depicted. In the x direction, they are magnified by the factor indicated. Next to each orbit, the speed of the electron upon its return is given as a fraction of c. The laser parameters are λ = 0.8 μ m , I = 10 17 W cm 2 , and w 0 = 2 μ m (expansion parameter ϵ = 0.064 ), and the electron is born through ionization of Li 2 + .

Fig. 2
Fig. 2

(a) Single-atom harmonic emission rate R and order of harmonics radiated by electrons that start at positions x 0 x ( t = 0 ) = 14,010 , 13,010 , , 10 a.u. and z 0 z ( t = 0 ) = 1500 , 1501 , 1502 , 3900 a.u. , as shown in Fig. 1 and for the same parameters. The data points form 15 strings, each characterized by its value of x 0 and combining about 2400 values of z 0 . The strings start in the lower left of the figure with z 0 = 1500 . The direction of increasing z 0 is marked by arrows. The long arrow gives the direction of increasing x 0 . The open circles are for a beam with w 0 = 2 μ m , the black squares for w 0 = 20 μ m . (b) Harmonic yield from all electrons in (a).

Fig. 3
Fig. 3

Same as Fig. 2b, but for I = 10 18 W cm 2 and Be 3 + ( I p = 217.72 eV ) .

Equations (7)

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E x = E 0 1 + r z 2 exp ( r x 2 + r y 2 1 + r z 2 ) sin ϕ G + O ( ϵ 2 ) ,
E z = 2 E 0 ϵ r x 1 + r z 2 exp ( r x 2 + r y 2 1 r z 2 ) cos ϕ G ( 1 ) + O ( ϵ 3 ) ,
ϕ G = ω t k z + arctan r z r z ( r x 2 + r y 2 ) 1 + r z 2 ϕ 0 ,
d r d t = p γ , d p d t = E E C p × B ( γ c ) ,
Ψ 0 a ( 0 ) ( r ) = [ a ( 0 ) π ] 3 2 exp { ( x 2 + y 2 + z 2 ) [ 2 a ( 0 ) 2 ] } ,
Ψ t ( r ) = [ a ( t ) π ] 3 2 exp { ( x 2 + y 2 + [ z + Δ z ( t ) ] 2 ) [ 2 a ( t ) 2 ] } .
O ( t ) = [ 2 a ( t ) r 0 a ( t ) 2 + r 0 2 ] 3 2 exp { Δ z ( t ) 2 2 [ a ( t ) 2 + r 0 2 ] } .

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