## Dependence of dynamic Lorentz frequency shift on carrier-envelope phase and including local field effects

Optics Express, Vol. 17, Issue 24, pp. 21754-21761 (2009)

http://dx.doi.org/10.1364/OE.17.021754

Acrobat PDF (173 KB)

### Abstract

We investigate the local field effects in a ZnO dense medium. Our results show due to the local-field effects, the Lorentz shifts can be found in the reflected spectra driven by the few-cycle laser pulse. Moreover, the dynamic Lorentz shifts depend sensitively on the carrier-envelope phase (CEP) of the few-cycle laser pulse, which provides a useful means to obtain the CEP information by the frequency shifts.

© 2009 OSA

## 1. Introduction

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

9. 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]

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

3. 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]

4. 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]

10. 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**(5466), 635–639 (
2000). [CrossRef] [PubMed]

12. 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]

5. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, “Carrier-wave Rabi flopping: role of the carrier-envelope phase,” Opt. Lett. **29**(18), 2160–2162 (
2004). [CrossRef] [PubMed]

7. T. Tritschler, O. D. Mücke, M. Wegener, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett. **90**(21), 217404 (
2003). [CrossRef] [PubMed]

13. 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]

17. C. Zhang, W. Yang, X. Song, and Z. Xu, “Phase control of higher spectral components in the presence of a static electric field,” J. Phys. B **42**(5), 055602 (
2009). [CrossRef]

7. T. Tritschler, O. D. Mücke, M. Wegener, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett. **90**(21), 217404 (
2003). [CrossRef] [PubMed]

14. 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]

15. 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]

16. C. Zhang, W. Yang, X. Song, and Z. Xu, “Carrier-envelope phase dependence of the spectra of reflected few-cycle laser pulses in the presence of a static electric field,” Phys. Rev. A **79**(4), 043823 (
2009). [CrossRef]

17. C. Zhang, W. Yang, X. Song, and Z. Xu, “Phase control of higher spectral components in the presence of a static electric field,” J. Phys. B **42**(5), 055602 (
2009). [CrossRef]

22. C. M. Bowden and J. P. Dowling, “Near-dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A **47**(2), 1247–1251 (
1993). [CrossRef] [PubMed]

32. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A **40**(5), 2446–2451 (
1989). [CrossRef] [PubMed]

22. C. M. Bowden and J. P. Dowling, “Near-dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A **47**(2), 1247–1251 (
1993). [CrossRef] [PubMed]

23. M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and A. I. Zaitsev, “Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local-field effects,” Phys. Rev. A **43**(7), 3845–3853 (
1991). [CrossRef] [PubMed]

26. J. T. Manassah and B. Gross, “The dynamical lorentz shift in an extended optically dense superradiant amplifier,” Opt. Express **1**(6), 141–151 (
1997). [CrossRef] [PubMed]

32. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A **40**(5), 2446–2451 (
1989). [CrossRef] [PubMed]

26. J. T. Manassah and B. Gross, “The dynamical lorentz shift in an extended optically dense superradiant amplifier,” Opt. Express **1**(6), 141–151 (
1997). [CrossRef] [PubMed]

27. M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. **68**(7), 911–914 (
1992). [CrossRef] [PubMed]

29. H. Van Kampen, V. A. Sautenkov, C. J. C. Smeets, E. R. Eliel, and J. P. Woerdman, “Measurement of the excitation dependence of the Lorentz local-field shift,” Phys. Rev. A **59**(1), 271–274 (
1999). [CrossRef]

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

4. 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]

8. C. Van Vlack and S. Hughes, “Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase,” Opt. Lett. **32**(2), 187–189 (
2007). [CrossRef] [PubMed]

## 2. Theory

**81**(16), 3363–3366 (
1998). [CrossRef]

4. 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]

30. M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express **1**(6), 152–159 (
1997). [CrossRef] [PubMed]

*z*= 12 μm, and partially reflects backward. The backward reflected pulse is detected at

*z*= 3 μm. Taking the initial laser field propagating along

*z*direction, and polarized along

*x*direction, the Maxwell equations are the following form:where

8. C. Van Vlack and S. Hughes, “Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase,” Opt. Lett. **32**(2), 187–189 (
2007). [CrossRef] [PubMed]

22. C. M. Bowden and J. P. Dowling, “Near-dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A **47**(2), 1247–1251 (
1993). [CrossRef] [PubMed]

23. M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and A. I. Zaitsev, “Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local-field effects,” Phys. Rev. A **43**(7), 3845–3853 (
1991). [CrossRef] [PubMed]

7. T. Tritschler, O. D. Mücke, M. Wegener, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett. **90**(21), 217404 (
2003). [CrossRef] [PubMed]

8. C. Van Vlack and S. Hughes, “Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase,” Opt. Lett. **32**(2), 187–189 (
2007). [CrossRef] [PubMed]

33. 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]

38. 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]

39. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. **EMC-23**(4), 377–382 (
1981). [CrossRef]

40. A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. **23**(8), 623–630 (
1975). [CrossRef]

*z*direction iswhere

*φ*is the initial CEP, and

**81**(16), 3363–3366 (
1998). [CrossRef]

**32**(2), 187–189 (
2007). [CrossRef] [PubMed]

## 3. Results and discussions

15. 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]

42. 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]

*δ*depend crucially on the CEP of few-cycle laser pulses. By analysis, the underlying physical mechanism for the phenomenon can be explained with the field strength. As presented in Ref [43

43. 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**(21), 9351–9365 (
1998). [CrossRef]

*N*. As shown in Fig. 6 , due to the LFE, the characteristics of the dynamic Lorentz shift depending on the CEP of few-cycle laser pulses also occur. Our results may provide a potential method to gain the information about the CEP of few-cycle laser pulses by measuring the dynamic Lorentz shifts.

## 4. Conclusions

## Acknowledgments

## References and links

1. | T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. |

2. | S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett. |

3. | O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Signatures of carrier-wave Rabi flopping in GaAs,” Phys. Rev. Lett. |

4. | V. P. Kalosha and J. Herrmann, “Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,” Phys. Rev. Lett. |

5. | O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, “Carrier-wave Rabi flopping: role of the carrier-envelope phase,” Opt. Lett. |

6. | 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. |

7. | T. Tritschler, O. D. Mücke, M. Wegener, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett. |

8. | C. Van Vlack and S. Hughes, “Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase,” Opt. Lett. |

9. | 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 |

10. | 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 |

11. | 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 |

12. | W. Yang, X. Song, R. Li, and Z. Xu, “Generation of intense extreme supercontinuum radiation via resonant propagation effects,” Phys. Rev. A |

13. | 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. |

14. | C. Van Vlack and S. Hughes, “Carrier-envelope-offset phase control of ultrafast optical rectification in resonantly excited semiconductors,” Phys. Rev. Lett. |

15. | 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. |

16. | C. Zhang, W. Yang, X. Song, and Z. Xu, “Carrier-envelope phase dependence of the spectra of reflected few-cycle laser pulses in the presence of a static electric field,” Phys. Rev. A |

17. | C. Zhang, W. Yang, X. Song, and Z. Xu, “Phase control of higher spectral components in the presence of a static electric field,” J. Phys. B |

18. | R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms,” Phys. Rep. |

19. | K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. |

20. | D. S. Chemla and D. A. B. Miller, “Mechanism for enhanced optical nonlinearities and bistability by combined dielectric-electronic confinement in semiconductor microcrystallites,” Opt. Lett. |

21. | M. E. Crenshaw, “Comparison of quantum and classical local-field effects on two-level atoms in a dielectric,” Phys. Rev. A |

22. | C. M. Bowden and J. P. Dowling, “Near-dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A |

23. | M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and A. I. Zaitsev, “Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local-field effects,” Phys. Rev. A |

24. | E. Paspalakis, A. Kalini, and A. F. Terzis, “Local field effects in excitonic population transfer in a driven quantum dot system,” Phys. Rev. B |

25. | D. V. Novitsky, “Compression of an intensive light pulse in photonic-band-gap structures with a dense resonant medium,” Phys. Rev. A |

26. | J. T. Manassah and B. Gross, “The dynamical lorentz shift in an extended optically dense superradiant amplifier,” Opt. Express |

27. | M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. |

28. | J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. |

29. | H. Van Kampen, V. A. Sautenkov, C. J. C. Smeets, E. R. Eliel, and J. P. Woerdman, “Measurement of the excitation dependence of the Lorentz local-field shift,” Phys. Rev. A |

30. | M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express |

31. | R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A |

32. | R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A |

33. | K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. |

34. | R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A |

35. | 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 |

36. | X. Song, S. Gong, and Z. Xu, “Propagation of a few-cycle laser pulse in a V-type three-level system,” Opt. Spectrosc. |

37. | W. Yang, S. Gong, and Z. Xu, “Enhancement of ultrafast four-wave mixing in a polar molecule medium,” Opt. Express |

38. | J. Xiao, Z. Wang, and Z. Xu, “Area evolution of a few-cycle pulse laser in a two-level-atom medium,” Phys. Rev. A |

39. | G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. |

40. | A. Taflove and M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microw. Theory Tech. |

41. | K. Xia, S. Gong, C. Liu, X. Song, and Y. Niu, “Near dipole-dipole effects on the propagation of few-cycle pulse in a dense two-level medium,” Opt. Express |

42. | 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. |

43. | 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. |

**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:**

Ultrafast Optics

**History**

Original Manuscript: September 21, 2009

Revised Manuscript: October 30, 2009

Manuscript Accepted: November 2, 2009

Published: November 12, 2009

**Citation**

Chaojin Zhang, Weifeng Yang, Xiaohong Song, and Zhizhan Xu, "Dependence of dynamic Lorentz frequency shift on carrier-envelope phase and including local field effects," Opt. Express **17**, 21754-21761 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21754

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### References

- T. Brabec and F. Krausz, “Intense few-cycle laser field: frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000). [CrossRef]
- S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett. 81(16), 3363–3366 (1998). [CrossRef]
- 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]
- 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]
- O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, “Carrier-wave Rabi flopping: role of the carrier-envelope phase,” Opt. Lett. 29(18), 2160–2162 (2004). [CrossRef] [PubMed]
- 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]
- T. Tritschler, O. D. Mücke, M. Wegener, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett. 90(21), 217404 (2003). [CrossRef] [PubMed]
- C. Van Vlack and S. Hughes, “Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase,” Opt. Lett. 32(2), 187–189 (2007). [CrossRef] [PubMed]
- 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]
- 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(5466), 635–639 (2000). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- 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]
- C. Zhang, W. Yang, X. Song, and Z. Xu, “Carrier-envelope phase dependence of the spectra of reflected few-cycle laser pulses in the presence of a static electric field,” Phys. Rev. A 79(4), 043823 (2009). [CrossRef]
- C. Zhang, W. Yang, X. Song, and Z. Xu, “Phase control of higher spectral components in the presence of a static electric field,” J. Phys. B 42(5), 055602 (2009). [CrossRef]
- R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Frequency shifts in emission and absorption by resonant systems of two-level atoms,” Phys. Rep. 7(3), 101–179 (1973). [CrossRef]
- K. J. Boller, A. Imamolu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef] [PubMed]
- D. S. Chemla and D. A. B. Miller, “Mechanism for enhanced optical nonlinearities and bistability by combined dielectric-electronic confinement in semiconductor microcrystallites,” Opt. Lett. 11(8), 522–524 (1986). [CrossRef] [PubMed]
- M. E. Crenshaw, “Comparison of quantum and classical local-field effects on two-level atoms in a dielectric,” Phys. Rev. A 78(5), 053827 (2008). [CrossRef]
- C. M. Bowden and J. P. Dowling, “Near-dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47(2), 1247–1251 (1993). [CrossRef] [PubMed]
- M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and A. I. Zaitsev, “Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local-field effects,” Phys. Rev. A 43(7), 3845–3853 (1991). [CrossRef] [PubMed]
- E. Paspalakis, A. Kalini, and A. F. Terzis, “Local field effects in excitonic population transfer in a driven quantum dot system,” Phys. Rev. B 73(7), 073305 (2006). [CrossRef]
- D. V. Novitsky, “Compression of an intensive light pulse in photonic-band-gap structures with a dense resonant medium,” Phys. Rev. A 79(2), 023828 (2009). [CrossRef]
- J. T. Manassah and B. Gross, “The dynamical lorentz shift in an extended optically dense superradiant amplifier,” Opt. Express 1(6), 141–151 (1997). [CrossRef] [PubMed]
- M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switching in a dense medium of two-level atoms,” Phys. Rev. Lett. 68(7), 911–914 (1992). [CrossRef] [PubMed]
- J. J. Maki, M. S. Malcuit, J. E. Sipe, and R. W. Boyd, “Linear and nonlinear optical measurements of the Lorentz local field,” Phys. Rev. Lett. 67(8), 972–975 (1991). [CrossRef] [PubMed]
- H. Van Kampen, V. A. Sautenkov, C. J. C. Smeets, E. R. Eliel, and J. P. Woerdman, “Measurement of the excitation dependence of the Lorentz local-field shift,” Phys. Rev. A 59(1), 271–274 (1999). [CrossRef]
- M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express 1(6), 152–159 (1997). [CrossRef] [PubMed]
- R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effects of the dynamic Lorentz shift on four-wave parametric interactions in a strongly driven two-level system,” Phys. Rev. A 42(1), 494–497 (1990). [CrossRef] [PubMed]
- R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Effect of local-field correction on a strongly pumped resonance,” Phys. Rev. A 40(5), 2446–2451 (1989). [CrossRef] [PubMed]
- 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]
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