Abstract

We investigate the ultrafast four-wave mixing (FWM) with two-color few-cycle ultrashort pulses propagating in a two-level polar molecule medium. It is found that the enhancement of FWM can be achieved even for low intensity pulses due to the effects of permanent dipole moments (PDM) in polar molecules. Moreover, the conversion efficiency of FWM can be controlled by the carrier-envelope phases (CEP) of two ultrashort pulses.

© 2006 Optical Society of America

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  1. O. G. Calderón, R. G.-Castrejón, and J. M. Guerra, "High harmonic generation induced by permanent dipole moments," IEEE J. Quantum Electron. 35, 47-53 (1999).
    [CrossRef]
  2. V. A. Kovarsky, B. S. Philipp, and E. V. Kovarsky, "The generation of short-wave UV light in cells under the action of ultrashort pulses of intense visible radiation," Phys. Lett. A 226, 321-322 (1997).
    [CrossRef]
  3. C. Hoerner, J. P. Lavine, and A. A. Villaeys, "Theoretical description of two-photon phase conjugation in polar molecules," Phys. Rev. A 48, 1564-1572 (1993).
    [CrossRef] [PubMed]
  4. B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755-5760 (1982).
    [CrossRef]
  5. S. Kočinac, Z. Ikonić, V. Milanović, "The influence of permanent dipole moments on second harmonic generation in asymmetric semiconductor quantum wells," Opt. Commun. 140, 89-92 (1997).
    [CrossRef]
  6. N. C. Kothari and T. Kobayashi, "Single beam two-photon optical bistability in a submicron size Fabry-Perot cavity," IEEE J. Quantum Electron. 20, 418-423 (1984).
    [CrossRef]
  7. L. Li and A. P. Alivisatos, "Origin and scaling of the permanent dipole moment in CdSe nanorods," Phys. Rev. Lett. 90, 097402-097405 (2003).
    [CrossRef] [PubMed]
  8. R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
    [CrossRef]
  9. R. Bavli and Y. B. Band, "Relationship between second-harmonic generation and electric-field-induced second-harmonic generation," Phys. Rev. A 43, 507-514 (1991).
    [CrossRef] [PubMed]
  10. R. Bavli and Y. B. Band, "Nonlinear absorption and dispersion in a two-level system with permanent dipole moments," Phys. Rev. A 43, 5039-5043 (1991).
    [CrossRef] [PubMed]
  11. J. P. Lavoine, C. Hoerner, and A. A. Villaeys, "Effects of permanent dipole moments in degenerate four-wave-mixing processes," Phys. Rev. A 44, 5947-5957 (1991).
    [CrossRef] [PubMed]
  12. T. Cusati, J. L. Paz, M. C. Salazar, and A. J. Hernández, "Intramolecular coupling study of the resonances in the four-wave-mixing signal," Phys. Lett. A 267, 18-23 (2000).
    [CrossRef]
  13. V. P. Gavrilenko and E. Oks, "A significant enhancement of high-order harmonic generation by using a dipole gas," J. Phys. B: At. Mol. Opt. Phys. 33, 1629-1643 (2000).
    [CrossRef]
  14. W. Yang, S. Gong, R. Li, and Z. Xu, "Coherent population accumulations of multiphoton transitions induced by an ultrashort pulse train in polar molecules," Phys. Rev. A (to be published).
    [PubMed]
  15. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
    [CrossRef] [PubMed]
  16. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
    [CrossRef] [PubMed]
  17. A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
    [CrossRef]
  18. I. P. Christov, "Phase-dependent ionization in the barrier suppression regime," Appl. Phys. B: Lasers Opt. 70, 459-462 (2000).
    [CrossRef]
  19. P. Dietrich, F. Krausz, and P. B. Corkum, "Determining the absolute carrier phase of a few-cycle laser pulse," Opt. Lett. 25, 16-18 (2000).
    [CrossRef]
  20. P. Salières, P. Antoine, A. de Bohan, and M. Lewenstein, "Temporal and spectral tailoring of high-order harmonics," Phys. Rev. Lett. 81, 5544-5547 (1998).
    [CrossRef]
  21. M. Mehendale, S. A. Mitchell, J.-P. Likforman, D. M. Villeneuve, and P. B. Corkum, "Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse," Opt. Lett. 25, 1672-1674 (2000).
    [CrossRef]
  22. M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
    [CrossRef] [PubMed]
  23. G. Lagmago Kamta and A. D. Bandrauk, "Phase dependence of enhanced ionization in asymmetric molecules," Phys. Rev. Lett. 94, 203003-203006 (2005).
    [CrossRef] [PubMed]
  24. G. Lagmago Kamta, A. D. Bandrauk and P. B. Corkum. "Asymmetry in the harmonic generation from nonsymmetric molecules," J. Phys. B: At. Mol. Opt. Phys. 38, L339-L346 (2005).
    [CrossRef]
  25. X. Song, S. Gong, S. Jin, and Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801-015804 (2004).
    [CrossRef]
  26. X. Song, S. Gong, S. Jin, and Z. Xu, "Two-color interference effects for ultrashort laser pulses propagating in a two-level medium," Phys. Lett. A 319, 150-156 (2003).
    [CrossRef]
  27. C. Serrat, "Coherent control of ultrafast optical four-wave mixing with two-color ω-3ω laser pulses," Phys. Rev. A 72, 023808-023810 (2005).
    [CrossRef]
  28. C. Serrat, "Ac Stark-mediated quantum control with femtosecond two-color laser pulses," Phys. Rev. A 72, 051803(R)-051806(R) (2005).
    [CrossRef]
  29. Y. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagation in three-level Λ-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
    [CrossRef]
  30. T. Cheng and A. Brown, "Carrier-envelope phase effects for a dipolar molecule interacting with two-color pump-probe laser pulses," Phys. Rev. A 70, 063411-063420 (2004).
    [CrossRef]
  31. A. Brown, "Two-color pulsed laser excitation of dipolar molecules: Absolute laser carrier-phase effects," Phys. Rev. A 66, 053404-053413 (2002).
    [CrossRef]
  32. L. W. Casperson, "Few-cycle pulses in two-level media," Phys. Rev. A 57, 609-621 (1998).
    [CrossRef]
  33. A. A. Zabolotskii, "Specific features of amplification of almost ultimately short pulses in media with a permanent dipole moment," Opt. Spectrosc. 95, 751-759 (2003).
    [CrossRef]
  34. A. I. Maĭmistov and J.-G. Caputo, "Extremely short electromagnetic pulses in a resonant medium with a permanent dipole moment," Opt. Spectrosc. 94, 245-250 (2003).
    [CrossRef]
  35. S. O. Elyutin, "Dynamics of an extremely short pulse in a Stark medium," J. Exp. Theor. Phys. 101, 11-21 (2005).
    [CrossRef]
  36. S. V. Sazonov and N. V. Ustinov, "Pulsed transparency of anisotropic media with Stark level splitting," Quantum Electron. 35, 701-704 (2005).
    [CrossRef]
  37. K. Zhao, H. Li, J. Liu, C. Wang, and Y. Luo, "Dipolar effects on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (pNA) molecules," J. Phys. B: At. Mol. Opt. Phys. 38, 4235-4245 (2005).
    [CrossRef]
  38. R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
    [CrossRef] [PubMed]
  39. M. Terauchi and T. Kobayashi, "Lasing and gain properties of a giant dipole molecule: 1-[p-(N, N-dimethylamino) phenyl]-4-(p-nitrophenyl)-1, 3-butadiene," Chem. Phys. Lett. 137, 319-323 (1987).
    [CrossRef]
  40. A. Brown and W. J. Meath, "On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules," J. Chem. Phys. 109, 9351-9365 (1998).
    [CrossRef]
  41. F. Gel’mukhanov, A. Baev, P. Macák, Y. Luo, and H. Ågren, "Dynamics of two-photon absorption by molecules and solutions," J. Opt. Soc. Am. B 19, 937-945 (2002).
    [CrossRef]

2006

Y. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagation in three-level Λ-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
[CrossRef]

2005

G. Lagmago Kamta and A. D. Bandrauk, "Phase dependence of enhanced ionization in asymmetric molecules," Phys. Rev. Lett. 94, 203003-203006 (2005).
[CrossRef] [PubMed]

G. Lagmago Kamta, A. D. Bandrauk and P. B. Corkum. "Asymmetry in the harmonic generation from nonsymmetric molecules," J. Phys. B: At. Mol. Opt. Phys. 38, L339-L346 (2005).
[CrossRef]

S. O. Elyutin, "Dynamics of an extremely short pulse in a Stark medium," J. Exp. Theor. Phys. 101, 11-21 (2005).
[CrossRef]

S. V. Sazonov and N. V. Ustinov, "Pulsed transparency of anisotropic media with Stark level splitting," Quantum Electron. 35, 701-704 (2005).
[CrossRef]

K. Zhao, H. Li, J. Liu, C. Wang, and Y. Luo, "Dipolar effects on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (pNA) molecules," J. Phys. B: At. Mol. Opt. Phys. 38, 4235-4245 (2005).
[CrossRef]

C. Serrat, "Coherent control of ultrafast optical four-wave mixing with two-color ω-3ω laser pulses," Phys. Rev. A 72, 023808-023810 (2005).
[CrossRef]

2004

X. Song, S. Gong, S. Jin, and Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801-015804 (2004).
[CrossRef]

T. Cheng and A. Brown, "Carrier-envelope phase effects for a dipolar molecule interacting with two-color pump-probe laser pulses," Phys. Rev. A 70, 063411-063420 (2004).
[CrossRef]

2003

X. Song, S. Gong, S. Jin, and Z. Xu, "Two-color interference effects for ultrashort laser pulses propagating in a two-level medium," Phys. Lett. A 319, 150-156 (2003).
[CrossRef]

A. A. Zabolotskii, "Specific features of amplification of almost ultimately short pulses in media with a permanent dipole moment," Opt. Spectrosc. 95, 751-759 (2003).
[CrossRef]

A. I. Maĭmistov and J.-G. Caputo, "Extremely short electromagnetic pulses in a resonant medium with a permanent dipole moment," Opt. Spectrosc. 94, 245-250 (2003).
[CrossRef]

L. Li and A. P. Alivisatos, "Origin and scaling of the permanent dipole moment in CdSe nanorods," Phys. Rev. Lett. 90, 097402-097405 (2003).
[CrossRef] [PubMed]

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef]

2002

R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
[CrossRef]

A. Brown, "Two-color pulsed laser excitation of dipolar molecules: Absolute laser carrier-phase effects," Phys. Rev. A 66, 053404-053413 (2002).
[CrossRef]

F. Gel’mukhanov, A. Baev, P. Macák, Y. Luo, and H. Ågren, "Dynamics of two-photon absorption by molecules and solutions," J. Opt. Soc. Am. B 19, 937-945 (2002).
[CrossRef]

2001

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

2000

I. P. Christov, "Phase-dependent ionization in the barrier suppression regime," Appl. Phys. B: Lasers Opt. 70, 459-462 (2000).
[CrossRef]

T. Cusati, J. L. Paz, M. C. Salazar, and A. J. Hernández, "Intramolecular coupling study of the resonances in the four-wave-mixing signal," Phys. Lett. A 267, 18-23 (2000).
[CrossRef]

V. P. Gavrilenko and E. Oks, "A significant enhancement of high-order harmonic generation by using a dipole gas," J. Phys. B: At. Mol. Opt. Phys. 33, 1629-1643 (2000).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

P. Dietrich, F. Krausz, and P. B. Corkum, "Determining the absolute carrier phase of a few-cycle laser pulse," Opt. Lett. 25, 16-18 (2000).
[CrossRef]

M. Mehendale, S. A. Mitchell, J.-P. Likforman, D. M. Villeneuve, and P. B. Corkum, "Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse," Opt. Lett. 25, 1672-1674 (2000).
[CrossRef]

1999

O. G. Calderón, R. G.-Castrejón, and J. M. Guerra, "High harmonic generation induced by permanent dipole moments," IEEE J. Quantum Electron. 35, 47-53 (1999).
[CrossRef]

1998

L. W. Casperson, "Few-cycle pulses in two-level media," Phys. Rev. A 57, 609-621 (1998).
[CrossRef]

A. Brown and W. J. Meath, "On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules," J. Chem. Phys. 109, 9351-9365 (1998).
[CrossRef]

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

1997

V. A. Kovarsky, B. S. Philipp, and E. V. Kovarsky, "The generation of short-wave UV light in cells under the action of ultrashort pulses of intense visible radiation," Phys. Lett. A 226, 321-322 (1997).
[CrossRef]

S. Kočinac, Z. Ikonić, V. Milanović, "The influence of permanent dipole moments on second harmonic generation in asymmetric semiconductor quantum wells," Opt. Commun. 140, 89-92 (1997).
[CrossRef]

1995

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

1993

C. Hoerner, J. P. Lavine, and A. A. Villaeys, "Theoretical description of two-photon phase conjugation in polar molecules," Phys. Rev. A 48, 1564-1572 (1993).
[CrossRef] [PubMed]

1991

R. Bavli and Y. B. Band, "Relationship between second-harmonic generation and electric-field-induced second-harmonic generation," Phys. Rev. A 43, 507-514 (1991).
[CrossRef] [PubMed]

R. Bavli and Y. B. Band, "Nonlinear absorption and dispersion in a two-level system with permanent dipole moments," Phys. Rev. A 43, 5039-5043 (1991).
[CrossRef] [PubMed]

J. P. Lavoine, C. Hoerner, and A. A. Villaeys, "Effects of permanent dipole moments in degenerate four-wave-mixing processes," Phys. Rev. A 44, 5947-5957 (1991).
[CrossRef] [PubMed]

1987

M. Terauchi and T. Kobayashi, "Lasing and gain properties of a giant dipole molecule: 1-[p-(N, N-dimethylamino) phenyl]-4-(p-nitrophenyl)-1, 3-butadiene," Chem. Phys. Lett. 137, 319-323 (1987).
[CrossRef]

1984

N. C. Kothari and T. Kobayashi, "Single beam two-photon optical bistability in a submicron size Fabry-Perot cavity," IEEE J. Quantum Electron. 20, 418-423 (1984).
[CrossRef]

1982

B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755-5760 (1982).
[CrossRef]

Ågren, H.

Alivisatos, A. P.

L. Li and A. P. Alivisatos, "Origin and scaling of the permanent dipole moment in CdSe nanorods," Phys. Rev. Lett. 90, 097402-097405 (2003).
[CrossRef] [PubMed]

Antoine, P.

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

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, "Ultrafast pulse interactions with two-level atoms," Phys. Rev. A 52, 3082-3094 (1995).
[CrossRef] [PubMed]

Baev, A.

Baltuška, A.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef]

Band, Y. B.

R. Bavli and Y. B. Band, "Nonlinear absorption and dispersion in a two-level system with permanent dipole moments," Phys. Rev. A 43, 5039-5043 (1991).
[CrossRef] [PubMed]

R. Bavli and Y. B. Band, "Relationship between second-harmonic generation and electric-field-induced second-harmonic generation," Phys. Rev. A 43, 507-514 (1991).
[CrossRef] [PubMed]

Bandrauk, A. D.

G. Lagmago Kamta, A. D. Bandrauk and P. B. Corkum. "Asymmetry in the harmonic generation from nonsymmetric molecules," J. Phys. B: At. Mol. Opt. Phys. 38, L339-L346 (2005).
[CrossRef]

G. Lagmago Kamta and A. D. Bandrauk, "Phase dependence of enhanced ionization in asymmetric molecules," Phys. Rev. Lett. 94, 203003-203006 (2005).
[CrossRef] [PubMed]

Bavli, R.

R. Bavli and Y. B. Band, "Relationship between second-harmonic generation and electric-field-induced second-harmonic generation," Phys. Rev. A 43, 507-514 (1991).
[CrossRef] [PubMed]

R. Bavli and Y. B. Band, "Nonlinear absorption and dispersion in a two-level system with permanent dipole moments," Phys. Rev. A 43, 5039-5043 (1991).
[CrossRef] [PubMed]

Brown, A.

T. Cheng and A. Brown, "Carrier-envelope phase effects for a dipolar molecule interacting with two-color pump-probe laser pulses," Phys. Rev. A 70, 063411-063420 (2004).
[CrossRef]

A. Brown, "Two-color pulsed laser excitation of dipolar molecules: Absolute laser carrier-phase effects," Phys. Rev. A 66, 053404-053413 (2002).
[CrossRef]

A. Brown and W. J. Meath, "On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules," J. Chem. Phys. 109, 9351-9365 (1998).
[CrossRef]

Calderón, O. G.

O. G. Calderón, R. G.-Castrejón, and J. M. Guerra, "High harmonic generation induced by permanent dipole moments," IEEE J. Quantum Electron. 35, 47-53 (1999).
[CrossRef]

Caputo, J.-G.

A. I. Maĭmistov and J.-G. Caputo, "Extremely short electromagnetic pulses in a resonant medium with a permanent dipole moment," Opt. Spectrosc. 94, 245-250 (2003).
[CrossRef]

Casperson, L. W.

L. W. Casperson, "Few-cycle pulses in two-level media," Phys. Rev. A 57, 609-621 (1998).
[CrossRef]

Cheng, T.

T. Cheng and A. Brown, "Carrier-envelope phase effects for a dipolar molecule interacting with two-color pump-probe laser pulses," Phys. Rev. A 70, 063411-063420 (2004).
[CrossRef]

Christov, I. P.

I. P. Christov, "Phase-dependent ionization in the barrier suppression regime," Appl. Phys. B: Lasers Opt. 70, 459-462 (2000).
[CrossRef]

Corkum, P. B.

G. Lagmago Kamta, A. D. Bandrauk and P. B. Corkum. "Asymmetry in the harmonic generation from nonsymmetric molecules," J. Phys. B: At. Mol. Opt. Phys. 38, L339-L346 (2005).
[CrossRef]

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

P. Dietrich, F. Krausz, and P. B. Corkum, "Determining the absolute carrier phase of a few-cycle laser pulse," Opt. Lett. 25, 16-18 (2000).
[CrossRef]

M. Mehendale, S. A. Mitchell, J.-P. Likforman, D. M. Villeneuve, and P. B. Corkum, "Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse," Opt. Lett. 25, 1672-1674 (2000).
[CrossRef]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Cusati, T.

T. Cusati, J. L. Paz, M. C. Salazar, and A. J. Hernández, "Intramolecular coupling study of the resonances in the four-wave-mixing signal," Phys. Lett. A 267, 18-23 (2000).
[CrossRef]

de Bohan, A.

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

De Silvestri, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Dick, B.

B. Dick and G. Hohlneicher, "Importance of initial and final states as intermediate states in two-photon spectroscopy of polar molecules," J. Chem. Phys. 76, 5755-5760 (1982).
[CrossRef]

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Dietrich, P.

Drescher, M.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

Elyutin, S. O.

S. O. Elyutin, "Dynamics of an extremely short pulse in a Stark medium," J. Exp. Theor. Phys. 101, 11-21 (2005).
[CrossRef]

Garcia, J. M.

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X. Song, S. Gong, S. Jin, and Z. Xu, "Two-color interference effects for ultrashort laser pulses propagating in a two-level medium," Phys. Lett. A 319, 150-156 (2003).
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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
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R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
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M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
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M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
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J. P. Lavoine, C. Hoerner, and A. A. Villaeys, "Effects of permanent dipole moments in degenerate four-wave-mixing processes," Phys. Rev. A 44, 5947-5957 (1991).
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Liu, J.

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K. Zhao, H. Li, J. Liu, C. Wang, and Y. Luo, "Dipolar effects on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (pNA) molecules," J. Phys. B: At. Mol. Opt. Phys. 38, 4235-4245 (2005).
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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
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V. P. Gavrilenko and E. Oks, "A significant enhancement of high-order harmonic generation by using a dipole gas," J. Phys. B: At. Mol. Opt. Phys. 33, 1629-1643 (2000).
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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
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T. Cusati, J. L. Paz, M. C. Salazar, and A. J. Hernández, "Intramolecular coupling study of the resonances in the four-wave-mixing signal," Phys. Lett. A 267, 18-23 (2000).
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R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
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V. A. Kovarsky, B. S. Philipp, and E. V. Kovarsky, "The generation of short-wave UV light in cells under the action of ultrashort pulses of intense visible radiation," Phys. Lett. A 226, 321-322 (1997).
[CrossRef]

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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

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M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

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T. Cusati, J. L. Paz, M. C. Salazar, and A. J. Hernández, "Intramolecular coupling study of the resonances in the four-wave-mixing signal," Phys. Lett. A 267, 18-23 (2000).
[CrossRef]

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P. Salières, P. Antoine, A. de Bohan, and M. Lewenstein, "Temporal and spectral tailoring of high-order harmonics," Phys. Rev. Lett. 81, 5544-5547 (1998).
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S. V. Sazonov and N. V. Ustinov, "Pulsed transparency of anisotropic media with Stark level splitting," Quantum Electron. 35, 701-704 (2005).
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R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
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Schoenfeld, W.

R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
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R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
[CrossRef]

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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef]

Serrat, C.

Y. Loiko and C. Serrat, "Coherent and phase-sensitive phenomena of ultrashort laser pulses propagation in three-level Λ-type systems studied with the finite-difference time-domain method," Phys. Rev. A 73, 063809 (2006).
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C. Serrat, "Coherent control of ultrafast optical four-wave mixing with two-color ω-3ω laser pulses," Phys. Rev. A 72, 023808-023810 (2005).
[CrossRef]

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X. Song, S. Gong, S. Jin, and Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801-015804 (2004).
[CrossRef]

X. Song, S. Gong, S. Jin, and Z. Xu, "Two-color interference effects for ultrashort laser pulses propagating in a two-level medium," Phys. Lett. A 319, 150-156 (2003).
[CrossRef]

Spielmann, C.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

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G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Tempea, G.

M. Drescher, M. Hentschel, R. Kienberger, G. Tempea, C. Spielmann, G. A. Reider, P. B. Corkum, and F. Krausz, "X-ray pulses approaching the attosecond frontier," Science 291, 1923-1927 (2001).
[CrossRef] [PubMed]

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M. Terauchi and T. Kobayashi, "Lasing and gain properties of a giant dipole molecule: 1-[p-(N, N-dimethylamino) phenyl]-4-(p-nitrophenyl)-1, 3-butadiene," Chem. Phys. Lett. 137, 319-323 (1987).
[CrossRef]

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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef]

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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef]

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S. V. Sazonov and N. V. Ustinov, "Pulsed transparency of anisotropic media with Stark level splitting," Quantum Electron. 35, 701-704 (2005).
[CrossRef]

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C. Hoerner, J. P. Lavine, and A. A. Villaeys, "Theoretical description of two-photon phase conjugation in polar molecules," Phys. Rev. A 48, 1564-1572 (1993).
[CrossRef] [PubMed]

J. P. Lavoine, C. Hoerner, and A. A. Villaeys, "Effects of permanent dipole moments in degenerate four-wave-mixing processes," Phys. Rev. A 44, 5947-5957 (1991).
[CrossRef] [PubMed]

Villeneuve, D. M.

Villoresi, P.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Walther, H.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, "Absolute-phase phenomena in photonionization with few-cycle laser pulses," Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Wang, C.

K. Zhao, H. Li, J. Liu, C. Wang, and Y. Luo, "Dipolar effects on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (pNA) molecules," J. Phys. B: At. Mol. Opt. Phys. 38, 4235-4245 (2005).
[CrossRef]

Warburton, R. J.

R. J. Warburton, C. Schulhauser, D. Haft, C. Schäflein, K. Karrai, J. M. Garcia, W. Schoenfeld, and P. M. Petroff, "Giant permanent dipole moments of excitions in semiconductor nanostructures," Phys. Rev. B 65, 113303-113306 (2002).
[CrossRef]

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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Xu, Z.

X. Song, S. Gong, S. Jin, and Z. Xu, "Formation of higher spectral components in a two-level medium driven by two-color ultrashort laser pulses," Phys. Rev. A 69, 015801-015804 (2004).
[CrossRef]

X. Song, S. Gong, S. Jin, and Z. Xu, "Two-color interference effects for ultrashort laser pulses propagating in a two-level medium," Phys. Lett. A 319, 150-156 (2003).
[CrossRef]

W. Yang, S. Gong, R. Li, and Z. Xu, "Coherent population accumulations of multiphoton transitions induced by an ultrashort pulse train in polar molecules," Phys. Rev. A (to be published).
[PubMed]

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A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef]

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W. Yang, S. Gong, R. Li, and Z. Xu, "Coherent population accumulations of multiphoton transitions induced by an ultrashort pulse train in polar molecules," Phys. Rev. A (to be published).
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Figures (3)

Fig. 1.
Fig. 1.

Schematic energy level diagram.

Fig. 2.
Fig. 2.

The spectra of two-color few-cycle ultrashort pulses at z=60μm. The peak intensity of the pulses is 3.71×1011 W/cm2. (a) represents the nondipolar molecule case of ϕ1 = ϕ2 =0. (b), (d) and (f) represent the polar molecule cases, (b) ϕ1 = ϕ2 =0, (d) ϕ1 =0 and ϕ2 =π/2, (f) ϕ1 = ϕ2 =π, and the corresponding input carrier of two-color few-cycle pulses (c), (e) and (g).

Fig. 3.
Fig. 3.

Plot of the dimensionless FWM intensity. The parameter values are same with those of Fig. 2.

Equations (7)

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H ̱ = H ̱ 0 + V ̱ = [ E 1 0 0 E 2 ] E ̱ ( t ) [ μ ̱ 11 μ ̱ 12 μ ̱ 21 μ ̱ 22 ] .
E ( t ) = E 0 sec h [ ( t t 0 ) τ p ] { cos [ ω l ( t t 0 ) + ϕ 1 ] + cos [ 2 ω l ( t t 0 ) + ϕ 2 ] } ,
ρ 21 t = i [ ω 0 ρ 21 + ( μ 21 ρ 22 μ 22 ρ 11 d ρ 21 ) E ( t ) ħ ] 1 T 1 ρ 21 ,
ρ 22 t = i ħ ( ρ 12 ρ 21 ) μ 21 E ( t ) 1 T 2 ρ 22 ,
ρ 11 t = i ħ ( ρ 21 ρ 12 ) μ 21 E ( t ) ,
H ( z , t ) t = 1 μ 0 E ( z , t ) z ,
E ( z , t ) t = 1 ε 0 H ( z , t ) z 1 ε 0 P ( z , t ) t ,

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