Abstract

We have measured the polarization of high harmonics of 785-nm Ti:sapphire radiation. The harmonics were generated in argon and nitrogen gas. When the driving field is elliptically polarized, there is, in general, an offset angle between the major axis of the driving field’s polarization ellipse and the polarization of the harmonics. The ellipticity of the harmonic polarization is also generally different from that of the driving field. There are substantial differences in behavior between the two gases, particularly for harmonics whose energies lie close to the ionization potential.

© 1996 Optical Society of America

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  1. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595 (1987).
    [CrossRef]
  2. A. L’Huillier, K. S. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315 (1991); A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, Boston, Mass., 1992), p. 139.
    [CrossRef]
  3. J. H. Eberly, Q. Su, and J. Javanainen, “High-order harmonic production in multiphoton ionization,” J. Opt. Soc. Am. B 6, 1289 (1989).
    [CrossRef]
  4. J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535 (1992).
    [CrossRef] [PubMed]
  5. P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993).
    [CrossRef] [PubMed]
  6. 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 (1986).
  7. D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1944).
    [CrossRef]
  8. P. L. DeVries, “Calculation of harmonic generation during the multiphoton ionization of the hydrogen atom,” J. Opt. Soc. Am. B 7, 517 (1990).
    [CrossRef]
  9. W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540 (1994).
    [CrossRef] [PubMed]
  10. M. Lewenstein, Ph. Balcou, M. Yu. Ivanov, A. L’Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low frequency laser fields,” Phys. Rev. A 49, 2117 (1994).
    [CrossRef] [PubMed]
  11. J. Squire, F. Salin, G. Mourou, and D. Harter, “100-fs pulse generation and amplification in Ti:Al2O3,” Opt. Lett. 16, 324 (1991).
    [CrossRef]
  12. F. S. Crawford, Waves: Berkeley Physics Course (McGraw-Hill, New York, 1968), Vol. 3, pp. 420–424.
  13. N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418 (1995); 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 48, R3585 (1994); K. S. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437 (1993); 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 (1994).
    [CrossRef] [PubMed]
  14. F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
    [CrossRef] [PubMed]

1995 (2)

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418 (1995); 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 48, R3585 (1994); K. S. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437 (1993); 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 (1994).
[CrossRef] [PubMed]

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

1994 (2)

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540 (1994).
[CrossRef] [PubMed]

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

1993 (1)

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

1992 (1)

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

1991 (2)

A. L’Huillier, K. S. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315 (1991); A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, Boston, Mass., 1992), p. 139.
[CrossRef]

J. Squire, F. Salin, G. Mourou, and D. Harter, “100-fs pulse generation and amplification in Ti:Al2O3,” Opt. Lett. 16, 324 (1991).
[CrossRef]

1990 (1)

1989 (1)

1987 (1)

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 (1986).

1944 (1)

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1944).
[CrossRef]

Ammosov, M. V.

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 (1986).

Balcou, Ph.

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

Becker, W.

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540 (1994).
[CrossRef] [PubMed]

Boyer, K.

Bucksbaum, P. H.

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1944).
[CrossRef]

Burnett, N. H.

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418 (1995); 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 48, R3585 (1994); K. S. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437 (1993); 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 (1994).
[CrossRef] [PubMed]

Corkum, P. B.

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418 (1995); 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 48, R3585 (1994); K. S. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437 (1993); 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 (1994).
[CrossRef] [PubMed]

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

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

Crawford, F. S.

F. S. Crawford, Waves: Berkeley Physics Course (McGraw-Hill, New York, 1968), Vol. 3, pp. 420–424.

Delone, N. B.

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 (1986).

DeVries, P. L.

Du, D.

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

Dutta, S. K.

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

Eberly, J. H.

Gibson, G.

Harter, D.

Ivanov, M. Yu.

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

Jara, H.

Javanainen, J.

Johann, U.

Kan, C.

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418 (1995); 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 48, R3585 (1994); K. S. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437 (1993); 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 (1994).
[CrossRef] [PubMed]

Korn, G.

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

Krainov, V. P.

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 (1986).

Krause, J. L.

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

Kulander, K. C.

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

A. L’Huillier, K. S. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315 (1991); A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, Boston, Mass., 1992), p. 139.
[CrossRef]

L’Huillier, A.

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

A. L’Huillier, K. S. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315 (1991); A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, Boston, Mass., 1992), p. 139.
[CrossRef]

Lewenstein, M.

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

Long, S.

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540 (1994).
[CrossRef] [PubMed]

Luk, T. S.

McIntyre, I.

McIver, J. K.

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540 (1994).
[CrossRef] [PubMed]

McPherson, A.

Mourou, G.

Muller, H. G.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1944).
[CrossRef]

Rhodes, C. K.

Salin, F.

Schafer, K. J.

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

Schafer, K. S.

A. L’Huillier, K. S. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315 (1991); A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, Boston, Mass., 1992), p. 139.
[CrossRef]

Schumacher, D. W.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1944).
[CrossRef]

Shkolnikov, P. L.

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

Squire, J.

Su, Q.

Weihe, F.

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1944).
[CrossRef]

Weihe, F. A.

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

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

J. Phys. B (1)

A. L’Huillier, K. S. Schafer, and K. C. Kulander, “Theoretical aspects of intense field harmonic generation,” J. Phys. B 24, 3315 (1991); A. L’Huillier, L. A. Lompre, G. Mainfray, and C. Manus, “High-order harmonic generation in rare gases,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic, Boston, Mass., 1992), p. 139.
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (4)

N. H. Burnett, C. Kan, and P. B. Corkum, “Ellipticity and polarization effects in harmonic generation in ionizing neon,” Phys. Rev. A 51, R3418 (1995); 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 48, R3585 (1994); K. S. Budil, P. Salieres, A. L’Huillier, T. Ditmire, and M. D. Perry, “Influence of ellipticity on harmonic generation,” Phys. Rev. A 48, R3437 (1993); 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 (1994).
[CrossRef] [PubMed]

F. A. Weihe, S. K. Dutta, G. Korn, D. Du, P. H. Bucksbaum, and P. L. Shkolnikov, “Polarization of high-intensity high-harmonic generation,” Phys. Rev. A 51, R3433 (1995).
[CrossRef] [PubMed]

W. Becker, S. Long, and J. K. McIver, “Modeling harmonic generation by a zero-range potential,” Phys. Rev. A 50, 1540 (1994).
[CrossRef] [PubMed]

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

Phys. Rev. Lett. (3)

J. L. Krause, K. J. Schafer, and K. C. Kulander, “High-order harmonic generation from atoms and ions in the high intensity regime,” Phys. Rev. Lett. 68, 3535 (1992).
[CrossRef] [PubMed]

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

D. W. Schumacher, F. Weihe, H. G. Muller, and P. H. Bucksbaum, “Phase dependence of intense field ionization: a study using two colors,” Phys. Rev. Lett. 73, 1344 (1944).
[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 (1986).

Other (1)

F. S. Crawford, Waves: Berkeley Physics Course (McGraw-Hill, New York, 1968), Vol. 3, pp. 420–424.

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Figures (8)

Fig. 1
Fig. 1

Experimental schematic. The linearly polarized incident beam enters from the right. Conversion to elliptical polarization is accomplished as follows. First, the linear polarization, which is originally horizontal, is rotated by a half-wave plate. Because the wave plate is not a perfect half-wave retarder, the polarization linearity is further improved by a thin-film polarizer that can be rotated so that it passes polarization along the new axis. Then the light passes through a fixed (i.e., nonrotating) quarter-wave plate whose axes are aligned with the original linear-polarization axis. This combination of optics produces elliptical polarization with the principal axes along the vertical and the horizontal, with any ellipticity. The polarization ellipse is then rotated 360° in small increments by another half-wave plate, after which the light is focused into the spectrometer. The focus is located at the entrance-slit position, where it intersects a thin gas target, as described in the text. The incident light and the harmonics are separated and are refocused by a spherical-surface grating. The grating can be rotated to deliver any diffracted harmonic to the exit slit, beyond which is a windowless photomultiplier tube (PMT) detector.

Fig. 2
Fig. 2

Fifteenth harmonic in 9 Torr of argon. Detected intensity versus rotation of driving-field polarization ellipse. Directions of the major axes of the incident-beam polarization ellipse are shown at the top. All the curves were generated under identical circumstances, except for the ellipticity ɛ of the incident field (shown in the upper right-hand corner of each plot). As the polarization ellipse of the incident light becomes more circular (|ɛ| → 1), the sinusoidal variation in the detected signal is shifted to the right. The filled squares represent data points; the solid curves are fits to the data.

Fig. 3
Fig. 3

Offset angle versus ellipticity for the seventh through the thirteenth harmonics in 9 Torr of argon. The harmonic order is shown toward the right-hand side of each plot. Note that the vertical scale changes sign for harmonic orders greater than 9.

Fig. 4
Fig. 4

Seventh harmonic in 9 Torr nitrogen. Detected intensity versus rotation of driving-field polarization ellipse. Unlike the case of argon, for this harmonic the measured shift of the signal variation is consistent with a zero offset angle.

Fig. 5
Fig. 5

Offset angle versus ellipticity for the seventh through the thirteenth harmonics in 9 Torr of nitrogen. The harmonic order is shown toward the right-hand side of each plot.

Fig. 6
Fig. 6

Eleventh harmonic in argon. On the left are intensity versus wave-plate rotation plots for different driving-field ellipticities ɛD. On the right is a plot of the extracted values of the ellipticity of the harmonic radiation ɛHHG versus ɛD.

Fig. 7
Fig. 7

Harmonic radiation ellipticity as a function of driving-field ellipticity for the seventh through the thirteenth harmonics in argon. The harmonic order appears toward the right-hand side of each plot.

Fig. 8
Fig. 8

Harmonic radiation ellipticity as a function of driving-field ellipticity for the seventh through the thirteenth harmonics in nitrogen. The harmonic order appears toward the right-hand side of each plot.

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