Abstract

The second-order Raman bands of SrTiO3 are excited under two-color cross-beam configuration using femto-second laser pulses. Raman-inactive one-phonon waves are generated by the coherently excited large amplitude two-phonon wave. The one-phonon waves are observed as a train of visible light spots, the frequency steps of which are coincident with the frequencies of the one-phonon modes. In order to understand the mechanism, a model of three-wave interaction among one two-phonon wave and two one-phonon waves is proposed.

© 2006 Optical Society of America

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References

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  1. M. Gühr, M. Bargheer, and N. Schwentner, "Generation of coherent zone boundary phonons by impulsive excitationof molecules," Phys. Rev. Lett. 91, 085504 (2003).
    [CrossRef] [PubMed]
  2. S. Hunsche, K. Wienecke, T. Dekorsy and H. Kurz, "Impulsive softening of coherent phonons in tellurium," Phys. Rev. Lett. 75, 1815-1818 (1995).
    [CrossRef] [PubMed]
  3. X. Hu and F. Nori, "Squeezed phonon states: modulating quantum fluctuations of atomic displacements," Phys. Rev. Lett. 76, 2294-2297 (1996).
    [CrossRef] [PubMed]
  4. X. Hu and F. Nori, "Phonon squeezed states generated by second-order Raman scattering," Phys. Rev. Lett. 79, 4605-4608 (1997).
    [CrossRef]
  5. G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
    [CrossRef] [PubMed]
  6. A. Bartels, T. Dekorsy and H. Kurz, "Impulsive excitation of phonon-pair combination states by second-order Raman scattering," Phys. Rev. Lett. 84, 2981-2984 (2000).
    [CrossRef] [PubMed]
  7. J. Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, "Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit," Phys. Rev. Lett. 93, 107203 (2004).
    [CrossRef] [PubMed]
  8. J.-i. Takahashi, E. Matsubara, T. Arima and E. Hanamura, "Coherent multistep anti-Stokes and stimulated Raman scattering associated with third harmonics in YFeO3 crystals," Phys. Rev. B 68, 155102 (2003).
    [CrossRef]
  9. J.-i. Takahashi, Y. Kawabe and E. Hanamura, "Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon," Optics Express 12, 1185-1190 (2004).
    [CrossRef] [PubMed]
  10. Y. R. Shen, "A note on two-phonon coherent anti-Stokes Raman scattering," J. Raman Spectrosc. 10, 110-112 (1981).Q1
    [CrossRef]
  11. M. J. Colles and J. A. Giordmaine, "Generation and detection of large-k-vector phonons," Phys. Rev. Lett. 27, 670-674 (1971).
    [CrossRef]
  12. J.-i. Takahashi, K. Mano, and T. Yagi, "Raman lasing and cascaded coherent anti-Stokes Raman scattering of two-phonon Raman band," Opt. Lett. (in press).
  13. J.-i. Takahashi, K. Mano, and T. Yagi, "Solid-state anti-Stokes Raman shifter covering extremely broadband tunable range," Jpn. J. Appl. Phys. (in press).
    [PubMed]
  14. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge, 2000).
  15. W. G. Nilsen and J. G. Skinner, "Raman spectrum of strontium titanate," J. Chem. Phys. 48, 2240-2248 (1968).
    [CrossRef]
  16. W. G. Stirling, "Neutron inelastic scattering study of the lattice dynamics of strontium titanate: harmonic models," J. Phys. C: Solid State Phys. 5, 2711-2730 (1972).Q2
    [CrossRef]
  17. K. Inoue, N. Asai, and T. Sameshima, "Experimental study of the hyper-Raman scattering due to Raman inactive lattice vibration of SrTiO3," J. Phys. Soc. Jpn. 50, 1291-1300 (1981).
    [CrossRef]
  18. J. M. Ziman, Electrons and Phonons, (Oxford University Press, 1963) pp. 130.
  19. Y. R. Shen, The Principles of Nonlinear Optics, (John Wiley & Sons, New York, 1984) pp. 303.

2004 (2)

J. Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, "Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit," Phys. Rev. Lett. 93, 107203 (2004).
[CrossRef] [PubMed]

J.-i. Takahashi, Y. Kawabe and E. Hanamura, "Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon," Optics Express 12, 1185-1190 (2004).
[CrossRef] [PubMed]

2003 (2)

J.-i. Takahashi, E. Matsubara, T. Arima and E. Hanamura, "Coherent multistep anti-Stokes and stimulated Raman scattering associated with third harmonics in YFeO3 crystals," Phys. Rev. B 68, 155102 (2003).
[CrossRef]

M. Gühr, M. Bargheer, and N. Schwentner, "Generation of coherent zone boundary phonons by impulsive excitationof molecules," Phys. Rev. Lett. 91, 085504 (2003).
[CrossRef] [PubMed]

2000 (1)

A. Bartels, T. Dekorsy and H. Kurz, "Impulsive excitation of phonon-pair combination states by second-order Raman scattering," Phys. Rev. Lett. 84, 2981-2984 (2000).
[CrossRef] [PubMed]

1997 (2)

X. Hu and F. Nori, "Phonon squeezed states generated by second-order Raman scattering," Phys. Rev. Lett. 79, 4605-4608 (1997).
[CrossRef]

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

1996 (1)

X. Hu and F. Nori, "Squeezed phonon states: modulating quantum fluctuations of atomic displacements," Phys. Rev. Lett. 76, 2294-2297 (1996).
[CrossRef] [PubMed]

1995 (1)

S. Hunsche, K. Wienecke, T. Dekorsy and H. Kurz, "Impulsive softening of coherent phonons in tellurium," Phys. Rev. Lett. 75, 1815-1818 (1995).
[CrossRef] [PubMed]

1981 (2)

Y. R. Shen, "A note on two-phonon coherent anti-Stokes Raman scattering," J. Raman Spectrosc. 10, 110-112 (1981).Q1
[CrossRef]

K. Inoue, N. Asai, and T. Sameshima, "Experimental study of the hyper-Raman scattering due to Raman inactive lattice vibration of SrTiO3," J. Phys. Soc. Jpn. 50, 1291-1300 (1981).
[CrossRef]

1972 (1)

W. G. Stirling, "Neutron inelastic scattering study of the lattice dynamics of strontium titanate: harmonic models," J. Phys. C: Solid State Phys. 5, 2711-2730 (1972).Q2
[CrossRef]

1971 (1)

M. J. Colles and J. A. Giordmaine, "Generation and detection of large-k-vector phonons," Phys. Rev. Lett. 27, 670-674 (1971).
[CrossRef]

1968 (1)

W. G. Nilsen and J. G. Skinner, "Raman spectrum of strontium titanate," J. Chem. Phys. 48, 2240-2248 (1968).
[CrossRef]

Arima, T.

J.-i. Takahashi, E. Matsubara, T. Arima and E. Hanamura, "Coherent multistep anti-Stokes and stimulated Raman scattering associated with third harmonics in YFeO3 crystals," Phys. Rev. B 68, 155102 (2003).
[CrossRef]

Asai, N.

K. Inoue, N. Asai, and T. Sameshima, "Experimental study of the hyper-Raman scattering due to Raman inactive lattice vibration of SrTiO3," J. Phys. Soc. Jpn. 50, 1291-1300 (1981).
[CrossRef]

Bargheer, M.

M. Gühr, M. Bargheer, and N. Schwentner, "Generation of coherent zone boundary phonons by impulsive excitationof molecules," Phys. Rev. Lett. 91, 085504 (2003).
[CrossRef] [PubMed]

Bartels, A.

A. Bartels, T. Dekorsy and H. Kurz, "Impulsive excitation of phonon-pair combination states by second-order Raman scattering," Phys. Rev. Lett. 84, 2981-2984 (2000).
[CrossRef] [PubMed]

Bragas, A. V.

J. Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, "Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit," Phys. Rev. Lett. 93, 107203 (2004).
[CrossRef] [PubMed]

Colles, M. J.

M. J. Colles and J. A. Giordmaine, "Generation and detection of large-k-vector phonons," Phys. Rev. Lett. 27, 670-674 (1971).
[CrossRef]

Dekorsy, T.

A. Bartels, T. Dekorsy and H. Kurz, "Impulsive excitation of phonon-pair combination states by second-order Raman scattering," Phys. Rev. Lett. 84, 2981-2984 (2000).
[CrossRef] [PubMed]

S. Hunsche, K. Wienecke, T. Dekorsy and H. Kurz, "Impulsive softening of coherent phonons in tellurium," Phys. Rev. Lett. 75, 1815-1818 (1995).
[CrossRef] [PubMed]

Garrett, G. A.

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

Giordmaine, J. A.

M. J. Colles and J. A. Giordmaine, "Generation and detection of large-k-vector phonons," Phys. Rev. Lett. 27, 670-674 (1971).
[CrossRef]

Gühr, M.

M. Gühr, M. Bargheer, and N. Schwentner, "Generation of coherent zone boundary phonons by impulsive excitationof molecules," Phys. Rev. Lett. 91, 085504 (2003).
[CrossRef] [PubMed]

Hanamura, E.

J.-i. Takahashi, Y. Kawabe and E. Hanamura, "Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon," Optics Express 12, 1185-1190 (2004).
[CrossRef] [PubMed]

J.-i. Takahashi, E. Matsubara, T. Arima and E. Hanamura, "Coherent multistep anti-Stokes and stimulated Raman scattering associated with third harmonics in YFeO3 crystals," Phys. Rev. B 68, 155102 (2003).
[CrossRef]

Hu, X.

X. Hu and F. Nori, "Phonon squeezed states generated by second-order Raman scattering," Phys. Rev. Lett. 79, 4605-4608 (1997).
[CrossRef]

X. Hu and F. Nori, "Squeezed phonon states: modulating quantum fluctuations of atomic displacements," Phys. Rev. Lett. 76, 2294-2297 (1996).
[CrossRef] [PubMed]

Hunsche, S.

S. Hunsche, K. Wienecke, T. Dekorsy and H. Kurz, "Impulsive softening of coherent phonons in tellurium," Phys. Rev. Lett. 75, 1815-1818 (1995).
[CrossRef] [PubMed]

Inoue, K.

K. Inoue, N. Asai, and T. Sameshima, "Experimental study of the hyper-Raman scattering due to Raman inactive lattice vibration of SrTiO3," J. Phys. Soc. Jpn. 50, 1291-1300 (1981).
[CrossRef]

Kawabe, Y.

J.-i. Takahashi, Y. Kawabe and E. Hanamura, "Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon," Optics Express 12, 1185-1190 (2004).
[CrossRef] [PubMed]

Kurz, H.

A. Bartels, T. Dekorsy and H. Kurz, "Impulsive excitation of phonon-pair combination states by second-order Raman scattering," Phys. Rev. Lett. 84, 2981-2984 (2000).
[CrossRef] [PubMed]

S. Hunsche, K. Wienecke, T. Dekorsy and H. Kurz, "Impulsive softening of coherent phonons in tellurium," Phys. Rev. Lett. 75, 1815-1818 (1995).
[CrossRef] [PubMed]

Lockwood, D. J.

J. Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, "Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit," Phys. Rev. Lett. 93, 107203 (2004).
[CrossRef] [PubMed]

Mano, K.

J.-i. Takahashi, K. Mano, and T. Yagi, "Raman lasing and cascaded coherent anti-Stokes Raman scattering of two-phonon Raman band," Opt. Lett. (in press).

J.-i. Takahashi, K. Mano, and T. Yagi, "Solid-state anti-Stokes Raman shifter covering extremely broadband tunable range," Jpn. J. Appl. Phys. (in press).
[PubMed]

Matsubara, E.

J.-i. Takahashi, E. Matsubara, T. Arima and E. Hanamura, "Coherent multistep anti-Stokes and stimulated Raman scattering associated with third harmonics in YFeO3 crystals," Phys. Rev. B 68, 155102 (2003).
[CrossRef]

Merlin, R.

J. Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, "Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit," Phys. Rev. Lett. 93, 107203 (2004).
[CrossRef] [PubMed]

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

Nilsen, W. G.

W. G. Nilsen and J. G. Skinner, "Raman spectrum of strontium titanate," J. Chem. Phys. 48, 2240-2248 (1968).
[CrossRef]

Nori, F.

X. Hu and F. Nori, "Phonon squeezed states generated by second-order Raman scattering," Phys. Rev. Lett. 79, 4605-4608 (1997).
[CrossRef]

X. Hu and F. Nori, "Squeezed phonon states: modulating quantum fluctuations of atomic displacements," Phys. Rev. Lett. 76, 2294-2297 (1996).
[CrossRef] [PubMed]

Rojo, A. G.

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

Sameshima, T.

K. Inoue, N. Asai, and T. Sameshima, "Experimental study of the hyper-Raman scattering due to Raman inactive lattice vibration of SrTiO3," J. Phys. Soc. Jpn. 50, 1291-1300 (1981).
[CrossRef]

Schwentner, N.

M. Gühr, M. Bargheer, and N. Schwentner, "Generation of coherent zone boundary phonons by impulsive excitationof molecules," Phys. Rev. Lett. 91, 085504 (2003).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen, "A note on two-phonon coherent anti-Stokes Raman scattering," J. Raman Spectrosc. 10, 110-112 (1981).Q1
[CrossRef]

Skinner, J. G.

W. G. Nilsen and J. G. Skinner, "Raman spectrum of strontium titanate," J. Chem. Phys. 48, 2240-2248 (1968).
[CrossRef]

Sood, A. K.

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

Stirling, W. G.

W. G. Stirling, "Neutron inelastic scattering study of the lattice dynamics of strontium titanate: harmonic models," J. Phys. C: Solid State Phys. 5, 2711-2730 (1972).Q2
[CrossRef]

Takahashi, J.-i.

J.-i. Takahashi, Y. Kawabe and E. Hanamura, "Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon," Optics Express 12, 1185-1190 (2004).
[CrossRef] [PubMed]

J.-i. Takahashi, E. Matsubara, T. Arima and E. Hanamura, "Coherent multistep anti-Stokes and stimulated Raman scattering associated with third harmonics in YFeO3 crystals," Phys. Rev. B 68, 155102 (2003).
[CrossRef]

J.-i. Takahashi, K. Mano, and T. Yagi, "Raman lasing and cascaded coherent anti-Stokes Raman scattering of two-phonon Raman band," Opt. Lett. (in press).

J.-i. Takahashi, K. Mano, and T. Yagi, "Solid-state anti-Stokes Raman shifter covering extremely broadband tunable range," Jpn. J. Appl. Phys. (in press).
[PubMed]

Whitaker, J. F.

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

Wienecke, K.

S. Hunsche, K. Wienecke, T. Dekorsy and H. Kurz, "Impulsive softening of coherent phonons in tellurium," Phys. Rev. Lett. 75, 1815-1818 (1995).
[CrossRef] [PubMed]

Yagi, T.

J.-i. Takahashi, K. Mano, and T. Yagi, "Solid-state anti-Stokes Raman shifter covering extremely broadband tunable range," Jpn. J. Appl. Phys. (in press).
[PubMed]

J.-i. Takahashi, K. Mano, and T. Yagi, "Raman lasing and cascaded coherent anti-Stokes Raman scattering of two-phonon Raman band," Opt. Lett. (in press).

Zhao, J.

J. Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, "Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit," Phys. Rev. Lett. 93, 107203 (2004).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

W. G. Nilsen and J. G. Skinner, "Raman spectrum of strontium titanate," J. Chem. Phys. 48, 2240-2248 (1968).
[CrossRef]

J. Phys. C: Solid State Phys. (1)

W. G. Stirling, "Neutron inelastic scattering study of the lattice dynamics of strontium titanate: harmonic models," J. Phys. C: Solid State Phys. 5, 2711-2730 (1972).Q2
[CrossRef]

J. Phys. Soc. Jpn. (1)

K. Inoue, N. Asai, and T. Sameshima, "Experimental study of the hyper-Raman scattering due to Raman inactive lattice vibration of SrTiO3," J. Phys. Soc. Jpn. 50, 1291-1300 (1981).
[CrossRef]

J. Raman Spectrosc. (1)

Y. R. Shen, "A note on two-phonon coherent anti-Stokes Raman scattering," J. Raman Spectrosc. 10, 110-112 (1981).Q1
[CrossRef]

Jpn. J. Appl. Phys. (1)

J.-i. Takahashi, K. Mano, and T. Yagi, "Solid-state anti-Stokes Raman shifter covering extremely broadband tunable range," Jpn. J. Appl. Phys. (in press).
[PubMed]

Opt. Lett. (1)

J.-i. Takahashi, K. Mano, and T. Yagi, "Raman lasing and cascaded coherent anti-Stokes Raman scattering of two-phonon Raman band," Opt. Lett. (in press).

Optics Express (1)

J.-i. Takahashi, Y. Kawabe and E. Hanamura, "Generation of a broadband spectral comb with multiwave mixing by exchange of an impulsively stimulated phonon," Optics Express 12, 1185-1190 (2004).
[CrossRef] [PubMed]

Phys. Rev. B (1)

J.-i. Takahashi, E. Matsubara, T. Arima and E. Hanamura, "Coherent multistep anti-Stokes and stimulated Raman scattering associated with third harmonics in YFeO3 crystals," Phys. Rev. B 68, 155102 (2003).
[CrossRef]

Phys. Rev. Lett. (7)

A. Bartels, T. Dekorsy and H. Kurz, "Impulsive excitation of phonon-pair combination states by second-order Raman scattering," Phys. Rev. Lett. 84, 2981-2984 (2000).
[CrossRef] [PubMed]

J. Zhao, A. V. Bragas, D. J. Lockwood and R. Merlin, "Magnon squeezing in an antiferromagnet: reducing the spin noise below the standard quantum limit," Phys. Rev. Lett. 93, 107203 (2004).
[CrossRef] [PubMed]

M. Gühr, M. Bargheer, and N. Schwentner, "Generation of coherent zone boundary phonons by impulsive excitationof molecules," Phys. Rev. Lett. 91, 085504 (2003).
[CrossRef] [PubMed]

S. Hunsche, K. Wienecke, T. Dekorsy and H. Kurz, "Impulsive softening of coherent phonons in tellurium," Phys. Rev. Lett. 75, 1815-1818 (1995).
[CrossRef] [PubMed]

X. Hu and F. Nori, "Squeezed phonon states: modulating quantum fluctuations of atomic displacements," Phys. Rev. Lett. 76, 2294-2297 (1996).
[CrossRef] [PubMed]

X. Hu and F. Nori, "Phonon squeezed states generated by second-order Raman scattering," Phys. Rev. Lett. 79, 4605-4608 (1997).
[CrossRef]

M. J. Colles and J. A. Giordmaine, "Generation and detection of large-k-vector phonons," Phys. Rev. Lett. 27, 670-674 (1971).
[CrossRef]

Science (1)

G. A. Garrett, A. G. Rojo, A. K. Sood, J. F. Whitaker and R. Merlin, "Vacuum squeezing of solids: macroscopic quantum states driven by light pulses," Science 275, 1638-1640 (1997).
[CrossRef] [PubMed]

Other (3)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge, 2000).

J. M. Ziman, Electrons and Phonons, (Oxford University Press, 1963) pp. 130.

Y. R. Shen, The Principles of Nonlinear Optics, (John Wiley & Sons, New York, 1984) pp. 303.

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Figures (5)

Fig. 1.
Fig. 1.

The setup of the measurement. OPA : optical parametric amplifier system, m : mirror (only one of the symbols is marked), VND : variable ND filter, T : translational stage with a retroreflector, L : lens, M : spectrometer and PC, F : optical fiber, ND : ND filter, R : rotational stage, S : sample (SrTiO3), Ls : signal light (ω 1), Li : idler light (ω 2).

Fig. 2.
Fig. 2.

The photographs of the signals, where ω 1 = 7013 cm-1 and ω 2 = 5999 cm-1 ( ∆ω = 1014 cm-1). (a) P1 = 27 mW, P2 = 30, 20, 10, 5 mW and (b) P2 = 10 mW, P1 = 27, 25, 20, 15, 10, 5 mW from top to bottom, respectively. The two bright spots on the left-hand side are the ω 1 and the ω 2 light.

Fig. 3.
Fig. 3.

Power dependence of the higher-order signals. Part of higher-order signals are simultaneously picked-up by an optical fiber after collecting them using a lens. (a) The change of the scaled spectra against P1, where P2 is fixed to 1.3 mW. (b) The change of the peak intensities of the spectra in Fig. 3(a) (scaling factors of Fig. 3(a)). (c) The change of the scaled spectra against P1, where P2 is fixed to 1.0 mW. (d) The change of the peak intensities of the spectra in Fig. 3(c). Each spectrum in Fig. 3(a) and 3(c) is shifted upward by the value of P1 and P2, respectively. The frequencies of excitation light are 6596 and 5993 cm-1.

Fig. 4.
Fig. 4.

The angle resolved spectra. (a) ω 1 = 6648 cm-1 and ω 2 = 5988 cm-1 (∆ω= 660 cm-1). P1 = 2.0 mW, P2 = 0.3 mW. (b) ω 1 = 6819 cm-1 and ω 2 = 5804 cm-1 (∆ω= 1015 cm-1). P1 = 2.1 mW, P2 = 1.6 mW. Each spectrum is scaled so that the peak intensities are the same (see text). The angle is measured from the direction of ω 1 light. The vertical lines indicate the peak positions. ∆’s are their spacing.

Fig. 5.
Fig. 5.

The wavevector component of the peaks of the emitted light to the direction of the sample surface against their frequencies, where the frequency difference is 714 cm-1 (ω 1 = 6667 cm-1 and ω 2 = 5953 cm-1 , P1 = 3.0 mW, and P2 = 0.5 mW) . The large open circles indicate the incident light beams. The smooth line is a guide for the eye.

Tables (1)

Tables Icon

Table 1. Assignments of the observed phonon frequencies [15, 16, 17]. The values in the parenthesis are the frequencies at the zone center. The spectral widths of the incident light pulses are about 200 cm-1.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

H phonon NL = ħ K q , q b q , 1 b k 1 k 2 q , 2 b q , 1 b k 1 + k 2 + q , 2 .
b ˙ 1 = i Ω 1 b 1 + i Λ b 2 ,
b ˙ 2 = i Ω 2 b 2 + i Λ b 1 ,
ω 1,2 = Ω 1,2 ± i Λ 0 .
b ˙ 1 = i Ω 1 b 1 + b 2 ,
b ˙ 2 = i Ω 2 b 2 + b 1 ,
ω 1,2 = Ω 1,2 ± Λ 0 .

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