## Terahertz wave generation from hyper-Raman lines in two-level quantum systems driven by two-color lasers |

Optics Express, Vol. 21, Issue 18, pp. 21349-21356 (2013)

http://dx.doi.org/10.1364/OE.21.021349

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### Abstract

Based on spatial-temporal symmetry breaking mechanism, we propose a novel scheme for terahertz (THz) wave generation from hyper-Raman lines associated with the 0th harmonic (a particular even harmonic) in a two-level quantum system driven by two-color laser fields. With the help of analysis of quasi-energy, the frequency of THz wave can be tuned by changing the field amplitude of the driving laser. By optimizing the parameters of the laser fields, we are able to obtain arbitrary frequency radiation in the THz regime with appreciable strength (as strong as the typical harmonics). Our proposal can be realized in experiment in view of the recent experimental progress of even-harmonics generation by two-color laser fields.

© 2013 OSA

## 1. Introduction

1. M. Tonouchi, “Cutting-edge terahertz technology,” Nature Photon. **1**(2), 97–105 (2007). [CrossRef]

2. T. Otsuji, M. Hanabe, T. Nishimura, and E. Sano, “A grating-bicoupled plasma- wave photomixer with resonant-cavity enhanced structure,” Opt. Express **14**(11), 4815–4825 (2006). [CrossRef] [PubMed]

19. Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “High performance terahertz quantum cascade laser sources based on intracavity difference frequency generation,” Opt. Express **21**(1), 968–973 (2013). [CrossRef] [PubMed]

6. H. Ito, F. Nakajima, T. Furuta, and T. Ishibashi, “Continuous THz-wave generation using antenna-integrated uni-travelling-carrier photodiodes,” Semicond. Sci. Technol. **20**(7), S191–S198 (2005). [CrossRef]

12. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum Cascade Laser,” Science **264**(5158), 553–556 (1994). [CrossRef] [PubMed]

16. M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference- frequency generation,” Nature Photon. **1**(5), 288–292 (2007). [CrossRef]

20. K. J. Ahn, F. Milde, and A. Knorr, “Phonon-Wave-Induced Resonance Fluorescence in Semiconductor Nanostructures: Acoustoluminescence in the Terahertz Range,” Phys. Rev. Lett. **98**(2), 027401 (2007). [CrossRef] [PubMed]

21. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature (London) **457**(7226), 174–178 (2009). [CrossRef]

22. S. Q. Duan, W. Zhang, Y. Xie, W. D. Chu, and X. G. Zhao, “Terahertz radiation in semiconductor quantum dots driven by gigahertz waves: The role of tailoring the quasienergy spectrum,” Phys. Rev. B **80**(16), 161304(R) (2009). [CrossRef]

*nω*

_{0}, where

*ω*

_{0}is the fundamental frequency of the incident laser) [23

23. T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt. **40**(11), 2161–2171 (1993). [CrossRef]

24. S. F. Guo, S. Q. Duan, Y. Xie, W. D. Chu, and W. Zhang, “Tailoring the photon emission patterns in nanostructures,” New J. Phys. **13**(5), 053005 (2011). [CrossRef]

*kω*

_{0}(

*k*= 1, 2, 3,...). Using analysis of quasienergy and optimization of laser fields, we are able to obtain considerably intense THz radiation with desired frequency. With the help of our optimization method, it is quite likely that our proposal can be realized in experiment considering the recent experimental progress of even-harmonics generation by two-color laser.

## 2. Theoretical formulism

*G*(

*t*) =

*F*(

*t*)

**e**·

*μ*

**, the laser field**

_{12}**E**=

*F*(

*t*)

**e**,

*F*(

*t*) =

*F*(

*t*+

*T*),

*T*the period of the lasers,

**e**a unit vector.

*μ*

**= 〈1|**

_{12}*e*

**r**|2〉 is the dipole between state |1〉 and state |2〉. The energy spacing between the two states [with energies

*E*(

_{i}*i*= 1, 2)] is set as Δ

*E*=

*E*

_{1}−

*E*

_{2}.

25. L. M. Narducci, M. O. Scully, G.-L. Oppo, P. Ru, and J. R. Tredicce, “Spontaneous emission and absorption properties of a driven three-level system,” Phys. Rev. A **42**(3), 1630–1649 (1990). [CrossRef] [PubMed]

*H*is the Hamiltonian, the last term describes possible dissipative effects (such as spontaneous phonon emission) and we set

*h̄*= 1 in the following. We numerically calculate the photon emission spectra of the two-level quantum systems by solving the density matrix in Eq. (2) through Runge-Kutta method with the time step of 0.002/

*ω*

_{0}, total steps of 1200000 and the electron initially setting at the lower level. The average dipole can be calculated as

**D**(

*t*) = ∑

_{ij}*μ*

_{ij}*ρ*(

_{ij}*t*). We use Fourier transformation to obtain the emission spectrum

*S*(

*ν*) = |∫

*dt*

**exp**(−

*iνt*)

**D**(

*t*)|

^{2}. In the calculation we set

*h̄ω*

_{0}(

*ω*

_{0}the driving field frequency) as the unit of energy. We choose

*ω*

_{0}= 100

*THz*as an example, yet in general one can also use other frequency (much larger than THz) laser as will be discussed later. The two-level quantum systems can be realized in many systems, such as atoms, molecules, and semiconductor quantum dots. To demonstrate the basic physical mechanism, we study the optical process of the system with the typical parameters of a quantum dot: the energy spacing Δ

*E*= 10

*h̄ω*

_{0}, the dipole moment

*μ*

_{12}= 0.5

*e*·

*nm*, phonon emission coefficient Γ

*= 3.4 × 10*

_{ij}^{−3}

*ω*

_{0}.

24. S. F. Guo, S. Q. Duan, Y. Xie, W. D. Chu, and W. Zhang, “Tailoring the photon emission patterns in nanostructures,” New J. Phys. **13**(5), 053005 (2011). [CrossRef]

*θ*:

*t*→

*t*+

*T*/2 (

*T*= 2

*π/ω*

_{0}) combined with another operation Ω in spatial/spectrum domain, i.e.

*Q*= Ω ·

*θ*, such that the initial condition and the Hamiltonian (up to a sign) are invariant, and the dipole operator

*P̂*has a definite parity, then the emission spectrum contains no odd/even component if operator

*P̂*is even/odd. For our two-level quantum system driven by a monochromatic laser, i.e.

*E*(

*t*) =

*F*

_{1}

*cos*(

*ω*

_{0}

*t*), there exists one symmetric operation

*Q*

_{1}, which is the time shift

*θ*combined with spatial operation Ω

_{1}:

*c*

_{1}→ −

*c*

_{1}(here and in the following

*c*,

_{j}*j*= 1, 2, refers to the annihilation operator for state |

*j*〉), and the Hamiltonian is invariant and the dipole operator

*P̂*is odd. Then odd harmonics alone are generated because of the spatial-temporal symmetry. Other types of spatial-temporal symmetry may lead to many interesting emission patterns [24

24. S. F. Guo, S. Q. Duan, Y. Xie, W. D. Chu, and W. Zhang, “Tailoring the photon emission patterns in nanostructures,” New J. Phys. **13**(5), 053005 (2011). [CrossRef]

*ψ*(

_{α}*t*)〉 =

*e*

^{−iεαt}|

*ϕ*(

_{α}*t*)〉, where the Floquet state |

*ϕ*(

_{α}*t*)〉 = |

*ϕ*(

_{α}*t*+

*T*)〉 can be written in the form

*ψ*(

*t*)〉 =

*a*

_{1}|

*ψ*

_{1}〉 +

*a*

_{2}|

*ψ*

_{2}〉 =

*a*

_{1}

*e*

^{−iε1t}|

*ϕ*

_{1}〉 +

*a*

_{2}

*e*

^{−iε2t}|

*ϕ*

_{2}〉. Then we have

*n*−

*m*)

*ω*

_{0}and hyper-Raman lines with frequency (

*n*−

*m*)

*ω*

_{0}± (

*ε*

_{1}−

*ε*

_{2}).

*Q*= Ω ·

*θ*and the Floquet state |

*ϕ*(

_{α}*t*)〉 has a definite parity under Q, i.e.,

*Q*|

*ϕ*(

_{α}*t*)〉 = ±|

*ϕ*(

_{α}*t*)〉, then we have

*α*,

*β*= 1, 2) for

*n*−

*m*even/odd number and states

*α*,

*β*of same/different parity. Quite often the harmonics and the associated hyper-Raman lines appear simultaneously due to the same symmetry properties of the Floquet states. In the case with a monochromatic laser, we have odd harmonics and the associated hyper-Raman lines. While in other cases with symmetry broken, more harmonics and the associated hyper-Raman lines are generated.

## 3. Emission patterns

*ω*

_{0}. As seen in Fig. 1(b), there are odd harmonics as well as the associated hyper-Raman lines due to the spatial-temporal symmetry properties of the Floquet states as analyzed above. It is natural that, for the incident laser with frequency 2

*ω*

_{0}, the emission spectrum contains components with frequencies of 2

*ω*

_{0}, 6

*ω*

_{0}and 10

*ω*

_{0}...(odd orders of incident frequency 2

*ω*

_{0}) as shown in Fig. 1(c). One notices that there is no 0th hyper-Raman line in this case. If we use two-color lasers with frequencies

*ω*

_{0}and 2

*ω*

_{0}, interesting phenomena appear. As seen from Fig. 1(d), even harmonics and the associated hyper-Raman lines are generated by introducing the second laser field. Especially a low frequency radiation, 0th hyper-Raman radiation is generated. We would like to point out that the emission spectrum for the case with driving field

*F*(

*t*) =

*F*

_{1}cos(

*ω*

_{0}

*t*) +

*F*

_{2}cos(2

*ω*

_{0}

*t*) is not the supposition of those driven by

*F*

_{1}cos(

*ω*

_{0}

*t*) and

*F*

_{2}cos(2

*ω*

_{0}

*t*). For example, the harmonic 4

*ω*

_{0}in Fig. 1(d) neither appears in Fig. 1(b) nor in Fig. 1(c). It is also not the frequency summation or difference of the harmonics of systems driven by monochromatic incident laser with frequency

*ω*

_{0}and 2

*ω*

_{0}. In fact, the appearance of all even components (and the associated hyper-Raman lines) in Fig. 1(d) is the consequence of symmetry breaking.

*Q*

_{1}is broken by introducing the second laser with frequency 2

*kω*

_{0}(

*k*= 1, 2, 3...), and it is not broken by introducing the second laser with frequency (2

*k*− 1)

*ω*

_{0}(

*k*= 1, 2, 3...). These predictions are verified by our numerical results shown in Fig. 1(e) (the second laser of frequency 3

*ω*

_{0}) and Fig. 1(f) (the second laser of frequency 4

*ω*

_{0}). It is clear that the 0th hyper-Raman line does not appear in the cases with symmetry (see Figs. 1(b), 1(c), 1(e)). Interestingly, the second laser field with frequency 4

*ω*

_{0}leads to the appearance of 2

*n*th harmonics (even for

*n*= 1) and the associated hyper-Raman line (in particular the 0th hyper-Raman line) as predicted by our theory, since the second laser with frequency 4

*ω*

_{0}breaks the spatial-temporal symmetry generated by

*Q*

_{1}. Using this mechanism, we can explain the experimental results of observing even harmonics in helium or plasma plumes (containing nanoparticles, carbon nanotubes, etc) driven by a two-color laser [26

26. R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A **82**(5), 053831 (2010). [CrossRef]

27. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A **80**(3), 033845 (2009). [CrossRef]

**13**(5), 053005 (2011). [CrossRef]

28. O. V. Kibis, G. Ya. Slepyan, S. A. Maksimenko, and A. Hoffmann, “Matter Coupling to Strong Electromagnetic Fields in Two-Level Quantum Systems with Broken Inversion Symmetry,” Phys. Rev. Lett. **102**(2), 023601 (2009). [CrossRef] [PubMed]

## 4. Tuning of the frequency and intensity of THz wave

^{12}∼ 10

^{13}

*W/cm*

^{2}, which is lower than the typical driving field intensity (in the order of 10

^{14}

*W/cm*

^{2}∼ 10

^{15}

*W/cm*

^{2}) used in other methods for THz generation and/or HHG by two-color laser [8

8. X. Xie, J. Dai, and X.C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. **96**(7), 075005 (2006). [CrossRef] [PubMed]

11. J. Penano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E **81**(2), 026407 (2010). [CrossRef]

26. R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A **82**(5), 053831 (2010). [CrossRef]

27. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A **80**(3), 033845 (2009). [CrossRef]

29. I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. **94**(24), 243901 (2005). [CrossRef]

31. N. Ishii, A. Kosuge, T. Hayashi, T. Kanai, J. Itatani, S. Adachi, and S. Watanabe, “Quantum path selection in high-harmonic generation by a phase-locked two-color field,” Opt. express **16**(25), 20876–20883 (2008). [CrossRef] [PubMed]

*π/ω*

_{0})] as that used in Ref. [26

26. R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A **82**(5), 053831 (2010). [CrossRef]

27. R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A **80**(3), 033845 (2009). [CrossRef]

*ω*

_{0}∼ 50

*THz*– 500

*THz*, we may obtain the 0th hyper-Raman line with frequency

*ω*

_{0}∼ 1

*THz*– 10

*THz*. As shown in Fig. 1, the hyper-Raman lines are usually weaker than high order harmonics and are hard to be observed in experiment. Appropriate optimization may increase the possibility of observing hyper-Raman lines [23

23. T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt. **40**(11), 2161–2171 (1993). [CrossRef]

32. N. Moiseyev and M. Lein, “Non-Hermitian Quantum mechanics for high-order harmonic generation spectra,” J. Phys. Chem. A **107**(37), 7181–7188 (2003). [CrossRef]

*ω*

_{0}small to suppress the damping (of hyper-Raman lines) effect.

33. K. B. Nordstrom, K. Johnsen, S. J. Allen, A.-P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. **81**(2), 457–460 (1998). [CrossRef]

34. L. Plaja and L. Roso, “High-order harmonic generation in a two-level atom: effect of the multiphoton resonances tuned by the light shift,” J. Mod. Opt. **40**(5), 793–807 (1993). [CrossRef]

23. T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt. **40**(11), 2161–2171 (1993). [CrossRef]

35. A. D. Piazza and E. Fiordilino, “Why hyper-Raman lines are absent in high-order harmonic generation,” Phys. Rev. A **64**(1), 013802 (2001). [CrossRef]

43. H. Wang and X.G. Zhao, “Emission properties of electrons in two-level systems driven by DC - AC fields,” J. Phys.: Condens.Matter **8**(18), L285–L289 (1996). [CrossRef]

*eV*). It can be easily obtained from natural systems (such as atoms, molecules, and semiconductors) and artificial structures (such as quantum dots). Two-level model is an appropriate description of the systems in our parameter regimes [44

44. P. Huang, X.-T. Xie, X. Lu, J. Li, and X. Yang, “Carrier-envelope-phase-dependent effects of high-order harmonic generation in a strongly driven two-level atom,” Phys. Rev. A **79**(4), 043806 (2009). [CrossRef]

**13**(5), 053005 (2011). [CrossRef]

8. X. Xie, J. Dai, and X.C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. **96**(7), 075005 (2006). [CrossRef] [PubMed]

11. J. Penano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, “Terahertz generation in plasmas using two-color laser pulses,” Phys. Rev. E **81**(2), 026407 (2010). [CrossRef]

1. M. Tonouchi, “Cutting-edge terahertz technology,” Nature Photon. **1**(2), 97–105 (2007). [CrossRef]

**82**(5), 053831 (2010). [CrossRef]

**80**(3), 033845 (2009). [CrossRef]

29. I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. **94**(24), 243901 (2005). [CrossRef]

31. N. Ishii, A. Kosuge, T. Hayashi, T. Kanai, J. Itatani, S. Adachi, and S. Watanabe, “Quantum path selection in high-harmonic generation by a phase-locked two-color field,” Opt. express **16**(25), 20876–20883 (2008). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgments

## References and links

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19. | Q. Y. Lu, N. Bandyopadhyay, S. Slivken, Y. Bai, and M. Razeghi, “High performance terahertz quantum cascade laser sources based on intracavity difference frequency generation,” Opt. Express |

20. | K. J. Ahn, F. Milde, and A. Knorr, “Phonon-Wave-Induced Resonance Fluorescence in Semiconductor Nanostructures: Acoustoluminescence in the Terahertz Range,” Phys. Rev. Lett. |

21. | Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E. H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature (London) |

22. | S. Q. Duan, W. Zhang, Y. Xie, W. D. Chu, and X. G. Zhao, “Terahertz radiation in semiconductor quantum dots driven by gigahertz waves: The role of tailoring the quasienergy spectrum,” Phys. Rev. B |

23. | T. Millack and A. Maquet, “Hyper-Raman lines produced during high harmonic generation,” J. Mod. Opt. |

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25. | L. M. Narducci, M. O. Scully, G.-L. Oppo, P. Ru, and J. R. Tredicce, “Spontaneous emission and absorption properties of a driven three-level system,” Phys. Rev. A |

26. | R. A. Ganeev, H. Singhal, P. A. Naik, J. A. Chakera, H. S. Vora, R. A. Khan, and P. D. Gupta, “Systematic studies of two-color pump-induced high-order harmonic generation in plasma plumes,” Phys. Rev. A |

27. | R. A. Ganeev, H. Singhal, P. A. Naik, I. A. Kulagin, P. V. Redkin, J. A. Chakera, M. Tayyab, R. A. Khan, and P. D. Gupta, “Enhancement of high-order harmonic generation using a two-color pump in plasma plumes,” Phys. Rev. A |

28. | O. V. Kibis, G. Ya. Slepyan, S. A. Maksimenko, and A. Hoffmann, “Matter Coupling to Strong Electromagnetic Fields in Two-Level Quantum Systems with Broken Inversion Symmetry,” Phys. Rev. Lett. |

29. | I. J. Kim, C. M. Kim, H. T. Kim, G. H. Lee, Y. S. Lee, J. Y. Park, D. J. Cho, and C. H. Nam, “Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field,” Phys. Rev. Lett. |

30. | I. J. Kim, G. H. Lee, S. B. Park, Y. S. Lee, T. K. Kim, C. H. Namb, T. Mocek, and K. Jakubczak, “Generation of submicrojoule high harmonics using a long gas jet in a two-color laser field,” Appl. Phys. Lett. |

31. | N. Ishii, A. Kosuge, T. Hayashi, T. Kanai, J. Itatani, S. Adachi, and S. Watanabe, “Quantum path selection in high-harmonic generation by a phase-locked two-color field,” Opt. express |

32. | N. Moiseyev and M. Lein, “Non-Hermitian Quantum mechanics for high-order harmonic generation spectra,” J. Phys. Chem. A |

33. | K. B. Nordstrom, K. Johnsen, S. J. Allen, A.-P. Jauho, B. Birnir, J. Kono, T. Noda, H. Akiyama, and H. Sakaki, “Excitonic dynamical Franz-Keldysh Effect,” Phys. Rev. Lett. |

34. | L. Plaja and L. Roso, “High-order harmonic generation in a two-level atom: effect of the multiphoton resonances tuned by the light shift,” J. Mod. Opt. |

35. | A. D. Piazza and E. Fiordilino, “Why hyper-Raman lines are absent in high-order harmonic generation,” Phys. Rev. A |

36. | Z. Y. Zhou and J. M. Yuan, “Fine structures of the harmonic and hyper-Raman spectrum of the hydrogen atom in an intense high-frequency laser pulse,” Phys. Rev. A |

37. | Y. Dakhnovskii and H. Metiu, “Conditions leading to intense low-frequency generation and strong localization in two-level systems,” Phys. Rev. A |

38. | C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A |

39. | F. I. Gauthey, C. H. Keitel, P. L. Knight, and A. Maquet, “Role of initial coherence in the generation of harmonics and sidebands from a strongly driven two-level atom,” Phys. Rev. A |

40. | M. Frasca, “Theory of dressed states in quantum optics,” Phys. Rev. A |

41. | A. D. Piazza, E. Fiordilino, and M. H. Mittleman, “Analytical study of the spectrum emitted by a two-level atom driven by a strong laser pulse,” Phys. Rev. A |

42. | M. L. Pons, R. Taieb, and A. Maquet, “Importance of population transfers in high-order harmonic-generation spectra,” Phys. Rev. A |

43. | H. Wang and X.G. Zhao, “Emission properties of electrons in two-level systems driven by DC - AC fields,” J. Phys.: Condens.Matter |

44. | P. Huang, X.-T. Xie, X. Lu, J. Li, and X. Yang, “Carrier-envelope-phase-dependent effects of high-order harmonic generation in a strongly driven two-level atom,” Phys. Rev. A |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4180) Nonlinear optics : Multiphoton processes

(300.6495) Spectroscopy : Spectroscopy, teraherz

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: June 11, 2013

Revised Manuscript: August 23, 2013

Manuscript Accepted: August 24, 2013

Published: September 4, 2013

**Citation**

Wei Zhang, Shi-Fang Guo, Su-Qing Duan, and Xian-Geng Zhao, "Terahertz wave generation from hyper-Raman lines in two-level quantum systems driven by two-color lasers," Opt. Express **21**, 21349-21356 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-21349

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