OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26521–26527
« Show journal navigation

Enhanced harmonic emission from a polar molecule medium driven by few-cycle laser pulses

Chaojin Zhang, Jinping Yao, Jielei Ni, and Fadhil A. Umran  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 26521-26527 (2012)
http://dx.doi.org/10.1364/OE.20.026521


View Full Text Article

Acrobat PDF (1166 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate theoretically the enhancement of the low-order harmonic emission from a polar molecular medium. The results show that, by using a control laser field, the intensity of the spectral signals near fourth-order harmonics will increase over 25 times as a result of the four-wave mixing process. Moreover, the enhancement effects depend strongly on the carrier-envelope phase of the initial laser fields, which cannot be found in a symmetric system.

© 2012 OSA

The rapidly development of ultrafast laser technology, caused the pulse duration to be decreased to a few cycles, and this can be shown from the series of novel phenomena [1

1. T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000). [CrossRef]

8

8. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006). [CrossRef] [PubMed]

], such as the carrier-wave Rabi flopping [6

6. S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett. 81(16), 3363–3366 (1998). [CrossRef]

, 7

7. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Signatures of carrier-wave Rabi flopping in GaAs,” Phys. Rev. Lett. 87(5), 057401 (2001). [CrossRef] [PubMed]

], the enhancement of four-wave mixing [8

8. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006). [CrossRef] [PubMed]

], and so on. In this regime, the investigations on few-cycle laser pulses interaction with asymmetric systems have been attracted and interested in the recent years [8

8. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006). [CrossRef] [PubMed]

15

15. Y. Zhou, Q. Miao, and C. Wang, “Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules,” Chin. Phys. B 20(4), 044205 (2011). [CrossRef]

]. The information of the carrier-envelope phase (CEP) can be obtained by utilizing the pulse duration and intensity [11

11. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007). [CrossRef] [PubMed]

], or by using a static electric field [12

12. C. Van Vlack and S. Hughes, “Carrier-envelope-offset phase control of ultrafast optical rectification in resonantly excited semiconductors,” Phys. Rev. Lett. 98(16), 167404 (2007). [CrossRef] [PubMed]

]. The main reason of the phenomena results from the permanent dipole moment (PDM) of asymmetric system. It directly affects the Lorentz local field correction and transmitted spectra [14

14. W. Yang, X. Song, C. Zhang, and Z. Xu, “Carrier-envelope phase-dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments,” J. Phys. B 42(17), 175601 (2009). [CrossRef]

, 15

15. Y. Zhou, Q. Miao, and C. Wang, “Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules,” Chin. Phys. B 20(4), 044205 (2011). [CrossRef]

].

It has been well known in resonant extreme nonlinear optics regime, the harmonic spectra can be effectively controlled by waveform-shaped techniques which are realized by manipulating CEP of driving laser field [9

9. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002). [CrossRef] [PubMed]

12

12. C. Van Vlack and S. Hughes, “Carrier-envelope-offset phase control of ultrafast optical rectification in resonantly excited semiconductors,” Phys. Rev. Lett. 98(16), 167404 (2007). [CrossRef] [PubMed]

] or the synthesis of multi-color fields [16

16. G. Orlando, P. P. Corso, E. Fiordilino, and F. Persico, “A three-colour scheme to generate isolated attosecond pulses,” J. Phys. B 43(2), 025602 (2010). [CrossRef]

25

25. Y. Wang, H. Wu, Y. Chen, Z. Lu, C. Yu, Q. Shi, K. Deng, and R. Lu, “Isolated sub-10 attosecond pulse generation by a 6-fs driving pulse and a 5-fs subharmonic controlling pulse,” AIP Advances 2(2), 022102 (2012). [CrossRef]

]. In the presence of additional control laser field, the transmitted spectra have been significantly modified [16

16. G. Orlando, P. P. Corso, E. Fiordilino, and F. Persico, “A three-colour scheme to generate isolated attosecond pulses,” J. Phys. B 43(2), 025602 (2010). [CrossRef]

18

18. 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(1), 015801 (2004). [CrossRef]

]. In this paper, we study theoretically the results of the interaction of few-cycle laser pulses with a polar molecular medium. These result can be shown in this kind of medium, even-order harmonics are generated due to PDM effects and third-order harmonic emission is enhanced about 2 times even under the condition of single-color laser field, and after using a weak control laser field, the intensity of third-order harmonics is further improved. And the intensity near the fourth-order harmonic (resulted from the four-wave mixing) increases over 25 times in two-color field regime. Moreover, the spectral signal depends strongly on the initial CEP of the fundamental laser fields.

We consider that the interaction is between the few-cycle laser pulses and a polar molecular medium (para-nitroaniline (PNA)) [15

15. Y. Zhou, Q. Miao, and C. Wang, “Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules,” Chin. Phys. B 20(4), 044205 (2011). [CrossRef]

, 26

26. C. Wang, Y. Wang, Y. Su, and Y. Luo, “Solvent dependence of solvatochromic shifts and the first hyperpolarizability of para-nitroaniline: a nonmonotonic behavior,” J. Chem. Phys. 119(8), 4409–4412 (2003). [CrossRef]

]. When the laser field propagates along z direction, the Maxwell-Bloch equations can be written in the following forms [8

8. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006). [CrossRef] [PubMed]

, 16

16. G. Orlando, P. P. Corso, E. Fiordilino, and F. Persico, “A three-colour scheme to generate isolated attosecond pulses,” J. Phys. B 43(2), 025602 (2010). [CrossRef]

, 17

17. C. Zhang, Z. Wang, and Y. Li, “The shift dependent chirping effects and carrier-envelope phase of few-cycle laser pulses,” Phys. Lett. A 376(12-13), 1115–1117 (2012). [CrossRef]

]:
Hyt=1μ0Exz,Ext=1ε0Hyz1ε0Pxt,
(1)
ρ12t=i[ω12ρ12+Ex(unΔdρ12)]1τ1ρ12,
(2)
nt=i2uEx(ρ12ρ12*)1τ2n,
(3)
where Hy, μ0 and ε0 are magnetic field, permeability and permittivity of the free space, respectively.uis the dipole moment and Δd is the difference between the PDMs. ρ12 is the off-diagonal element of the density matrix, n = ρ2211 is the population difference between the excited and ground states, ħω12 (~3.85 eV) is the transition energy of the asymmetric system [15

15. Y. Zhou, Q. Miao, and C. Wang, “Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules,” Chin. Phys. B 20(4), 044205 (2011). [CrossRef]

]. Px = 2NμRe[ρ12] is the macroscopic nonlinear polarization which connects with the off-diagonal element of the density matrix in the medium. Usually, the dephasing time τ1 and the excited-state lifetime τ2 are set to be τ1 = τ2 = 1 ps [8

8. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006). [CrossRef] [PubMed]

, 15

15. Y. Zhou, Q. Miao, and C. Wang, “Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules,” Chin. Phys. B 20(4), 044205 (2011). [CrossRef]

]. The number density of medium is taken to be N = 8.0 × 1025 m−3. The full-wave Maxwell-Bloch equations are solved by employing Yee's finite-difference time-domain (FDTD) discretization scheme [27

27. C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004). [CrossRef] [PubMed]

34

34. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]

].

Interestingly, harmonic intensity significantly increases by using a synthesized laser field, which consists of the two laser fields at different wavelengths Eq (4). It can be shown in Fig. 2(a)
Fig. 2 (a) Transmitted spectra of the laser fields in the presence of the PDM effects. (b) Transmitted spectra of the two-color laser fields without considering the PDM effects.
, the intensity of third-order harmonics only slightly increases comparing with that in the case of single-color laser field. Suddenly the third-order harmonic emission shows an extremely significant enhancement and the spectral intensity harmonics at the frequency 4.2ω0 is improved by ~25 times. However, as shown in Fig. 2(b), the enhancement of harmonic emission at 4.2ω0 in the absence of PDM effects is almost negligible as compared to the case in the presence of the PDM effects. Thus, our work demonstrates an obvious relation between the second- and the third-order nonlinear susceptibilities, χ(2) and χ(3) respectively. When we used a media with permanent dipole moment, or alternatively a media which can be excited to excited states with an electronic density is not symmetrical, the values of χ(2) and χ(3) will be increased [37

37. Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, 1984).

], and the results of harmonic waves will be enhanced too.

The above analysis can be further proved by the signal of the reemitted field. The so-called reemitted field depends sensitively on the macroscopic coherent polarization Px(t), i.e., Eem(ω)∝FFT(∂Px/∂t) [11

11. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007). [CrossRef] [PubMed]

, 33

33. C. Zhang, W. Yang, X. Song, and Z. Xu, “Dependence of dynamic Lorentz frequency shift on carrier-envelope phase and including local field effects,” Opt. Express 17(24), 21754–21761 (2009). [CrossRef] [PubMed]

]. As indicated in Fig. 3(b), there is also a significant enhancement for the reemitted laser spectra at 3ω0 and 4.2ω0, which is consistent with the spectra of synthesized laser field (see red dashed line of Fig. 2(a)).

Finally, the enhancement of harmonic emission depends strongly on the CEP of the fundamental laser pulses Fig. 5(a)
Fig. 5 (a) Transmitted spectra versus the CEPs of the initial fundamental laser pulses. (b) Same as in Fig. 5(a) but for the PDM d = 0.
, then the intensity of third order harmonics will be changed with adjusting the CEP of the laser pulses, and cannot be obtained in symmetric system (Fig. 5(b)). Moreover, more obvious changing can be observed for the spectral signal at frequency 4.2ω0. In this work, due to the employment of a non-resonant two-color field with a weak control field, there will be the same harmonic emissions at the CEPs of ϕ = 0 and ϕ = π (see Fig. 5(a)). This means that the period of the CEP-dependent spectral signal is π, which is different from the Ref [8

8. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006). [CrossRef] [PubMed]

]. Hence, in our work the intensities of the harmonic emission can be more effectively controlled not only by using a weak control field but also by adjusting CEPs of fundamental laser field, which may provide more ways for experimental demonstration of this scheme.

In conclusion, we investigated a new method to enhance harmonic emission from the polar molecular system, by using a control laser field with consideration of PDM effects, therefore the intensity of harmonic emission at 4.2ω0 was improved by ~25 times due to the four-wave mixing process. Moreover, the harmonic enhancement depends strongly on the CEP of the fundamental laser field, and could provide a useful method to obtain the CEP information in the polar molecular system.

Acknowledgments

C. Zhang and J. Yao attribute equally to this work. The work is supported by National Basic Research Program of China (Grant No. 2011CB808102), National Natural Science Foundation of China (Grants No. 11134010, No. 60825406, No. 60921004, No. 61008061, No. 11204332, and No. 11104236) and Education Committee Foundation of Jiangsu Province (Grant No. 10KJB140012). C. Zhang gratefully acknowledges the support of K.C.Wong Education Foundation, China and Shanghai Postdoctoral Science Foundation funded project (2012M511145 and 12R21416700), and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

References and links

1.

T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000). [CrossRef]

2.

Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett. 103(4), 043904 (2009). [CrossRef] [PubMed]

3.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414(6860), 182–184 (2001). [CrossRef] [PubMed]

4.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett. 91(25), 253004 (2003). [CrossRef] [PubMed]

5.

X. Song, Z. Zeng, Y. Fu, B. Cai, R. Li, Y. Cheng, and Z. Xu, “Quantum path control in few-optical-cycle regime,” Phys. Rev. A 76(4), 043830 (2007). [CrossRef]

6.

S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett. 81(16), 3363–3366 (1998). [CrossRef]

7.

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Signatures of carrier-wave Rabi flopping in GaAs,” Phys. Rev. Lett. 87(5), 057401 (2001). [CrossRef] [PubMed]

8.

W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express 14(16), 7216–7223 (2006). [CrossRef] [PubMed]

9.

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002). [CrossRef] [PubMed]

10.

C. Lemell, X. M. Tong, F. Krausz, and J. Burgdörfer, “Electron emission from metal surfaces by ultrashort pulses: determination of the carrier-envelope phase,” Phys. Rev. Lett. 90(7), 076403 (2003). [CrossRef] [PubMed]

11.

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007). [CrossRef] [PubMed]

12.

C. Van Vlack and S. Hughes, “Carrier-envelope-offset phase control of ultrafast optical rectification in resonantly excited semiconductors,” Phys. Rev. Lett. 98(16), 167404 (2007). [CrossRef] [PubMed]

13.

C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express 16(3), 1487–1496 (2008). [CrossRef] [PubMed]

14.

W. Yang, X. Song, C. Zhang, and Z. Xu, “Carrier-envelope phase-dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments,” J. Phys. B 42(17), 175601 (2009). [CrossRef]

15.

Y. Zhou, Q. Miao, and C. Wang, “Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules,” Chin. Phys. B 20(4), 044205 (2011). [CrossRef]

16.

G. Orlando, P. P. Corso, E. Fiordilino, and F. Persico, “A three-colour scheme to generate isolated attosecond pulses,” J. Phys. B 43(2), 025602 (2010). [CrossRef]

17.

C. Zhang, Z. Wang, and Y. Li, “The shift dependent chirping effects and carrier-envelope phase of few-cycle laser pulses,” Phys. Lett. A 376(12-13), 1115–1117 (2012). [CrossRef]

18.

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(1), 015801 (2004). [CrossRef]

19.

Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett. 98(20), 203901 (2007). [CrossRef] [PubMed]

20.

A. D. Bandrauk, S. Chelkowski, H. Yu, and E. Constant, “Enhanced harmonic generation in extended molecular systems by two-color excitation,” Phys. Rev. A 56(4), R2537–R2540 (1997). [CrossRef]

21.

C. Zhang, J. Yao, and J. Ni, “Generation of isolated attosecond pulses of sub-atomic-time durations with multi-cycle chirped polarization gating pulses,” Opt. Express 20(22), 24642–24649 (2012). [CrossRef]

22.

R. Lu, H. He, Y. Guo, and K. Han, “Theoretical study of single attosecond pulse generation with a three-colour laser field,” J. Phys. B 42(22), 225601 (2009). [CrossRef]

23.

C. Zhang, J. Yao, J. Ni, G. Li, Y. Cheng, and Z. Xu, “Control of bandwidth and central wavelength of an enhanced extreme ultraviolet spectrum generated in shaped laser field,” Opt. Express 20(15), 16544–16551 (2012). [CrossRef]

24.

Y. Oishi, M. Kaku, A. Suda, F. Kannari, and K. Midorikawa, “Generation of extreme ultraviolet continuum radiation driven by a sub-10-fs two-color field,” Opt. Express 14(16), 7230–7237 (2006). [CrossRef] [PubMed]

25.

Y. Wang, H. Wu, Y. Chen, Z. Lu, C. Yu, Q. Shi, K. Deng, and R. Lu, “Isolated sub-10 attosecond pulse generation by a 6-fs driving pulse and a 5-fs subharmonic controlling pulse,” AIP Advances 2(2), 022102 (2012). [CrossRef]

26.

C. Wang, Y. Wang, Y. Su, and Y. Luo, “Solvent dependence of solvatochromic shifts and the first hyperpolarizability of para-nitroaniline: a nonmonotonic behavior,” J. Chem. Phys. 119(8), 4409–4412 (2003). [CrossRef]

27.

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004). [CrossRef] [PubMed]

28.

X. Song, W. Yang, Z. Zeng, R. Li, and Z. Xu, “Unipolar half-cycle pulse generation in asymmetrical media with a periodic subwavelength structure,” Phys. Rev. A 82(5), 053821 (2010). [CrossRef]

29.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995). [CrossRef] [PubMed]

30.

W. Yang, X. Song, R. Li, and Z. Xu, “Generation of intense extreme supercontinuum radiation via resonant propagation effects,” Phys. Rev. A 78(2), 023836 (2008). [CrossRef]

31.

V. P. Kalosha and J. Herrmann, “Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,” Phys. Rev. Lett. 83(3), 544–547 (1999). [CrossRef]

32.

J. Xiao, Z. Wang, and Z. Xu, “Area evolution of a few-cycle pulse laser in a two-level-atom medium,” Phys. Rev. A 65(3), 031402 (2002). [CrossRef]

33.

C. Zhang, W. Yang, X. Song, and Z. Xu, “Dependence of dynamic Lorentz frequency shift on carrier-envelope phase and including local field effects,” Opt. Express 17(24), 21754–21761 (2009). [CrossRef] [PubMed]

34.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]

35.

E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L'Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-color laser fields,” New J. Phys. 10(8), 083041 (2008). [CrossRef]

36.

T. Shao, G. Zhao, B. Wen, and H. Yang, “Theoretical exploration of laser-parameter effects on the generation of an isolated attosecond pulse from two-color high-order harmonic generation,” Phys. Rev. A 82(6), 063838 (2010). [CrossRef]

37.

Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, 1984).

OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.2250) Ultrafast optics : Femtosecond phenomena
(320.7150) Ultrafast optics : Ultrafast spectroscopy

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 13, 2012
Revised Manuscript: October 24, 2012
Manuscript Accepted: October 28, 2012
Published: November 12, 2012

Citation
Chaojin Zhang, Jinping Yao, Jielei Ni, and Fadhil A. Umran, "Enhanced harmonic emission from a polar molecule medium driven by few-cycle laser pulses," Opt. Express 20, 26521-26527 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-26521


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys.72(2), 545–591 (2000). [CrossRef]
  2. Y. Zheng, Z. Zeng, P. Zou, L. Zhang, X. Li, P. Liu, R. Li, and Z. Xu, “Dynamic chirp control and pulse compression for attosecond high-order harmonic emission,” Phys. Rev. Lett.103(4), 043904 (2009). [CrossRef] [PubMed]
  3. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. De Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature414(6860), 182–184 (2001). [CrossRef] [PubMed]
  4. G. G. Paulus, F. Lindner, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the phase of few-cycle laser pulses,” Phys. Rev. Lett.91(25), 253004 (2003). [CrossRef] [PubMed]
  5. X. Song, Z. Zeng, Y. Fu, B. Cai, R. Li, Y. Cheng, and Z. Xu, “Quantum path control in few-optical-cycle regime,” Phys. Rev. A76(4), 043830 (2007). [CrossRef]
  6. S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett.81(16), 3363–3366 (1998). [CrossRef]
  7. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Signatures of carrier-wave Rabi flopping in GaAs,” Phys. Rev. Lett.87(5), 057401 (2001). [CrossRef] [PubMed]
  8. W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express14(16), 7216–7223 (2006). [CrossRef] [PubMed]
  9. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett.89(12), 127401 (2002). [CrossRef] [PubMed]
  10. C. Lemell, X. M. Tong, F. Krausz, and J. Burgdörfer, “Electron emission from metal surfaces by ultrashort pulses: determination of the carrier-envelope phase,” Phys. Rev. Lett.90(7), 076403 (2003). [CrossRef] [PubMed]
  11. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett.99(13), 133602 (2007). [CrossRef] [PubMed]
  12. C. Van Vlack and S. Hughes, “Carrier-envelope-offset phase control of ultrafast optical rectification in resonantly excited semiconductors,” Phys. Rev. Lett.98(16), 167404 (2007). [CrossRef] [PubMed]
  13. C. Zhang, X. Song, W. Yang, and Z. Xu, “Carrier-envelope phase control of carrier-wave Rabi flopping in asymmetric semiparabolic quantum well,” Opt. Express16(3), 1487–1496 (2008). [CrossRef] [PubMed]
  14. W. Yang, X. Song, C. Zhang, and Z. Xu, “Carrier-envelope phase-dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments,” J. Phys. B42(17), 175601 (2009). [CrossRef]
  15. Y. Zhou, Q. Miao, and C. Wang, “Effect of Lorentz local field correction on propagation of ultrashort laser pulse in one-dimensional para-nitroaniline (PNA) molecules,” Chin. Phys. B20(4), 044205 (2011). [CrossRef]
  16. G. Orlando, P. P. Corso, E. Fiordilino, and F. Persico, “A three-colour scheme to generate isolated attosecond pulses,” J. Phys. B43(2), 025602 (2010). [CrossRef]
  17. C. Zhang, Z. Wang, and Y. Li, “The shift dependent chirping effects and carrier-envelope phase of few-cycle laser pulses,” Phys. Lett. A376(12-13), 1115–1117 (2012). [CrossRef]
  18. 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. A69(1), 015801 (2004). [CrossRef]
  19. Z. Zeng, Y. Cheng, X. Song, R. Li, and Z. Xu, “Generation of an extreme ultraviolet supercontinuum in a two-color laser field,” Phys. Rev. Lett.98(20), 203901 (2007). [CrossRef] [PubMed]
  20. A. D. Bandrauk, S. Chelkowski, H. Yu, and E. Constant, “Enhanced harmonic generation in extended molecular systems by two-color excitation,” Phys. Rev. A56(4), R2537–R2540 (1997). [CrossRef]
  21. C. Zhang, J. Yao, and J. Ni, “Generation of isolated attosecond pulses of sub-atomic-time durations with multi-cycle chirped polarization gating pulses,” Opt. Express20(22), 24642–24649 (2012). [CrossRef]
  22. R. Lu, H. He, Y. Guo, and K. Han, “Theoretical study of single attosecond pulse generation with a three-colour laser field,” J. Phys. B42(22), 225601 (2009). [CrossRef]
  23. C. Zhang, J. Yao, J. Ni, G. Li, Y. Cheng, and Z. Xu, “Control of bandwidth and central wavelength of an enhanced extreme ultraviolet spectrum generated in shaped laser field,” Opt. Express20(15), 16544–16551 (2012). [CrossRef]
  24. Y. Oishi, M. Kaku, A. Suda, F. Kannari, and K. Midorikawa, “Generation of extreme ultraviolet continuum radiation driven by a sub-10-fs two-color field,” Opt. Express14(16), 7230–7237 (2006). [CrossRef] [PubMed]
  25. Y. Wang, H. Wu, Y. Chen, Z. Lu, C. Yu, Q. Shi, K. Deng, and R. Lu, “Isolated sub-10 attosecond pulse generation by a 6-fs driving pulse and a 5-fs subharmonic controlling pulse,” AIP Advances2(2), 022102 (2012). [CrossRef]
  26. C. Wang, Y. Wang, Y. Su, and Y. Luo, “Solvent dependence of solvatochromic shifts and the first hyperpolarizability of para-nitroaniline: a nonmonotonic behavior,” J. Chem. Phys.119(8), 4409–4412 (2003). [CrossRef]
  27. C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett.92(4), 047402 (2004). [CrossRef] [PubMed]
  28. X. Song, W. Yang, Z. Zeng, R. Li, and Z. Xu, “Unipolar half-cycle pulse generation in asymmetrical media with a periodic subwavelength structure,” Phys. Rev. A82(5), 053821 (2010). [CrossRef]
  29. R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A52(4), 3082–3094 (1995). [CrossRef] [PubMed]
  30. W. Yang, X. Song, R. Li, and Z. Xu, “Generation of intense extreme supercontinuum radiation via resonant propagation effects,” Phys. Rev. A78(2), 023836 (2008). [CrossRef]
  31. V. P. Kalosha and J. Herrmann, “Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,” Phys. Rev. Lett.83(3), 544–547 (1999). [CrossRef]
  32. J. Xiao, Z. Wang, and Z. Xu, “Area evolution of a few-cycle pulse laser in a two-level-atom medium,” Phys. Rev. A65(3), 031402 (2002). [CrossRef]
  33. C. Zhang, W. Yang, X. Song, and Z. Xu, “Dependence of dynamic Lorentz frequency shift on carrier-envelope phase and including local field effects,” Opt. Express17(24), 21754–21761 (2009). [CrossRef] [PubMed]
  34. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966). [CrossRef]
  35. E. Mansten, J. M. Dahlström, P. Johnsson, M. Swoboda, A. L'Huillier, and J. Mauritsson, “Spectral shaping of attosecond pulses using two-color laser fields,” New J. Phys.10(8), 083041 (2008). [CrossRef]
  36. T. Shao, G. Zhao, B. Wen, and H. Yang, “Theoretical exploration of laser-parameter effects on the generation of an isolated attosecond pulse from two-color high-order harmonic generation,” Phys. Rev. A82(6), 063838 (2010). [CrossRef]
  37. Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, 1984).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited