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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 16 — Aug. 7, 2006
  • pp: 7216–7223
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Enhancement of ultrafast four-wave mixing in a polar molecule medium

Weifeng Yang, Shangqing Gong, and Zhizhan Xu  »View Author Affiliations


Optics Express, Vol. 14, Issue 16, pp. 7216-7223 (2006)
http://dx.doi.org/10.1364/OE.14.007216


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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

1. Introduction

In fact, the effects of PDMs can be modified by the temporal shape of electric field. If only a few optical cycles are contained within the laser pulse envelope, the carrier-envelope phase (CEP) will dramatically affect the temporal shape of electric field [15–17

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]

]. Because intense laser-matter interactions depend on the electric field of the pulse, the CEP is important for a number of nonlinear processes [18–22

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

]. Recently, it has been reported that the enhanced ionization of the asymmetric molecule (HeH2+) is much stronger when the electric field at the peak of the few-cycle pulse is antiparallel to the PDMs than that when the field at the peak is parallel to the PDMs [23

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]

]. This result was confirmed by a stronger harmonic emission obtained when the electric field at the peak of the few-cycle pulse is antiparallel to the PDMs [24

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]

]. The corresponding physical picture of enhanced ionization in these phenomena can be illustrated in dressed state interpretation. The dressed ground state moving up to cross with excited states enhances the ionization mechanism, and this ionization mechanism is weaker for a 180° change in the CEP because of the ground state moving down and avoiding excited states [23

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

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]

].

Phase effects can also be capable of providing important control over the excitations of atoms or molecules when two-color pulses are applied. In nondipolar medium, studies have found that the higher spectral components depend crucially on the relative phase of the two-color few-cycle pulses: continuum and distinct peaks can be achieved through the control of the relative phase [25

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

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]

]. By controlling the relative phase of the two-color large area pulses (20π corresponds to a intensity of 1.8×1013 W/cm2), the ultrafast optical four-wave mixing (FWM) can be obtained in two-level systems [27

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]

], and the relative phase dominating the efficiency of the coupling to the anti-Stokes Raman component is determined by the sign of the total ac Stark shift [28

28. C. Serrat, “Ac Stark-mediated quantum control with femtosecond two-color laser pulses,” Phys. Rev. A 72, 051803(R)–051806(R) (2005). [CrossRef]

]. Very recently, coherent propagation effects in two- and three-level systems with two-color pulses were studied, it is shown that population transfer and frequency down-conversion are both relative-phase-sensitive [29

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]

]. In dipole systems, the interaction of a two-level polar molecule with two laser pulses, where one laser’s frequency is tuned to the energy level separation (pump laser) while the second laser’s frequency is much smaller compared to the energy level separation (probe laser), has been investigated. It was found that the excited state population can be greatly affected by the CEP of the probe laser [30

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

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

].

Recently, the spectral features of pulses propagating in dipole medium have attracted much attention of researchers [32–37

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

]. However, to our knowledge, there has been no investigation on two-color few-cycle ultrashort pulses controlling FWM during the course of propagation in dipole medium. In this work, we apply two-color few-cycle ultrashort laser pulses with ωl and 2ωl combination scenario in a polar molecule medium. It is found due to the effects of PDMs, that the enhancement of ultrafast FWM can be produced even without high field intensities, which can not occur in the nondipolar medium. Moreover, the conversion efficiency of FWM can be controlled by the combination of CEPs because the temporal shape of electric field is modified by the interference between the two-color few-cycle pulses, and when the oscillation peak antiparalleling to the PDMs reaches a maximum, the intensity of FWM generated wave can be enhanced more than 10 times.

This paper is organized as follows. In Sec. II, we present a theoretical model of the propagation of two-color few-cycle laser pulses with a two-level polar molecule medium. In Sec. III, we investigate the relationship between ultrafast FWM and the corresponding input electric field shapes with different combinations of CEPs in this model. Finally, we offer some conclusions in Sec. IV.

2. Theoretical model

The level scheme of the medium we investigate in this work is presented in Fig. 1. Consider a two-level polar molecule medium where |1> and |2> represent the ground and the excited states, with corresponding energies E1=12ħω0 and E2=12ħω0, respectively. ω 0 is the transition frequency between the two levels.

Fig. 1. Schematic energy level diagram.

The total Hamiltonian describing the interaction of the fields with the polar molecules is given by

H̱=H̱0+V̱=[E100E2]E̱(t)[μ̱11μ̱12μ̱21μ̱22].
(1)

Here μ_ ij are the dipole moment matrix elements. We assume that the laser fields are linearly polarized, and the transition moment μ_ 21 and permanent moments μ_ jj are taken to be aligned with the direction of polarization of the laser fields. The hyperbolic secant two-color pulses can be expressed as

E(t)=E0sech[(tt0)τp]{cos[ωl(tt0)+ϕ1]+cos[2ωl(tt0)+ϕ2]},
(2)

where E 0, ωl, τp and ϕi are the electric field amplitude, the fundamental laser field frequency, the durations and the CEPs of each pulse, respectively.

The time evolution of the system is governed by the usual density-matrix equations and the equations of the time dependent ρ21, ρ22 and ρ11 can be expressed as follows:

ρ21t=i[ω0ρ21+(μ21ρ22μ22ρ11dρ21)E(t)ħ]1T1ρ21,
(3)
ρ22t=iħ(ρ12ρ21)μ21E(t)1T2ρ22,
(4)
ρ11t=iħ(ρ21ρ12)μ21E(t),
(5)

where T1 and T2 are the dephasing time and the excited-state lifetime, respectively. d2211 is the difference in the PDMs between the ground and the excited levels. dE(t) represents the effect of quantum interference resulting from the effects of PDMs. We should note for polar molecules, that the enhancement of ultrafast FWM can be achieved even without high intensity pulses, which can not occur in nondipolar systems. With proper combination of the CEPs, the intensity of the FWM generated wave can be enhanced more than 10 times in the polar molecules. In fact, PDMs can enlarge the multiphoton transitions in one specific orientation. The CEPs of the two-color pulses can modify the temporal shape of electric field. Therefore, PDMs and the CEPs play very important roles in the ultrafast FWM as we will show later.

The electromagnetic radiation is treated classically and the Maxwell’s equations take the form

H(z,t)t=1μ0E(z,t)z,
(6)
E(z,t)t=1ε0H(z,t)z1ε0P(z,t)t,
(7)

We employ a standard finite-difference time-domain approach for solving the full-wave Maxwell equations and predictor-corrector method to solve the density-matrix equations without any standard approximation. The time and space increments, Δt and Δz, are chosen to ensure cΔt ≤ Δz [38

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]

].

3. Results and discussion

Figure 2 presents the spectra produced by the two-color few-cycle ultrashort pulses at the propagation distance of z=60 μm, and the corresponding temporal shapes of the synthesized electric fields of input two-color pulses. In order to investigate the effects of PDMs on nonlinear interactions, we assume that there exists a nondipolar molecule medium with the same parameters as the above molecular parameters except for d=0. The propagation spectrum in the nondipolar molecule medium is shown in Fig. 2(a). In comparison to the initial spectrum (dashed line), there is no change and higher spectral components can be hardly presented. When the effects of PDMs are considered, the situation can be changed fundamentally. Figures 2(b), 2(d) and 2(f) show the propagation spectra in the polar molecule medium (d=1.18×10 a.u.). It can be found due to the effects of PDMs, that higher spectral components are produced in which the two peaks at frequencies 5ωl and 3ωl are the FWM generated waves, i.e. the ultrafast FWM can be enhanced with low intensity pulses propagating in polar molecule medium.

In fact, the FWM conversion efficiency can be controlled by the CEP combinations of two-color few-cycle pulses because the CEPs can modulate the synthesized electric field shape. For ϕ1=ϕ2=0, it can be seen in Fig. 2(c) that the electric field at the peak paralleling to the direction of polarization (or PDMs) is obviously larger than that at the opposite direction. The FWM generated waves at 3ωl and 5ωl are both enhanced in the polar molecule medium than in the nondipolar molecule medium due to the effects of PDMs (shown in Figs. 2(a) and 2(b)). When one of the CEPs is changed (ϕ2=π/2), the magnitude of the electric field at opposite direction of the PDMs is enlarged, and the peak intensities at both directions are about same (shown in Fig. 2(e)). It can be seen in Fig. 2(d) that the spectral component at 4ωl and other higher components, which are productions of complete multiphoton excitations, are enhanced. Although the ultrafast FWM at 5ωl is a process of three-photon excitations, the magnitude of the FWM generated wave is about same with the spectral component at 4ωl which is produced by a two-photon process. However, it should be noted that the FWM at 3ωl is not enhanced. It is because that the FWM at 3ωl includes a non-excited process. Figure 2(g) shows the temporal shapes of the synthesized electric fields in the situation ϕ1=ϕ2=π. The electric field at the peak antiparalleling to the PDMs reaches a maximum, which is evidently stronger than that at the other direction. Figure 2(f) presents the spectrum induced by the input two-color pulses of Fig. 2(g). The generated waves at 4ωl and 5ωl are further enhanced. The two-photon and three-photon excited processes are greatly enlarged, which suppresses the enhancements of other higher order processes.

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

4. Conclusions

In summary, we have investigated the spectra of few-cycle two-color ultrashort pulses in the two-level polar molecule medium by solving the full-wave Maxwell’s equations and density-matrix equations. It was demonstrated due to the effects of PDMs, that the enhancement of ultrafast FWM can occur in the polar molecule medium even for low pulse intensities. Moreover, the conversion efficiency of FWM can be controlled by the combinations of CEPs of two-color few-cycle ultrashort pulses because the interference between the two pulses can substantially modify the temporal shape of electric field. Using proper combination of the CEPs, the FWM generated wave can be enhanced greatly. The procedure developed in this work is to achieve the coherent control of the nonlinear interactions in low intensity scheme, which might be helpful to control ultrafast multiphoton excitations during the course of propagation.

Acknowledgments

The work is supported by the National Natural Science Foundation of China (Grant Nos. 10234030 and 60478002) and the Natural Science Foundation of Shanghai (Grant Nos. 04JC14036 and 05DJ14003).

References and links

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, and 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.

Liang-shi Li and A. Paul 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]

OCIS Codes
(020.1670) Atomic and molecular physics : Coherent optical effects
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.7150) Ultrafast optics : Ultrafast spectroscopy

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 24, 2006
Revised Manuscript: July 11, 2006
Manuscript Accepted: July 13, 2006
Published: August 7, 2006

Citation
Weifeng Yang, Shangqing Gong, and Zhizhan Xu, "Enhancement of ultrafast four-wave mixing in a polar molecule medium," Opt. Express 14, 7216-7223 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-16-7216


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References

  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]

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