Abstract

Two-beam coupling, attributed to Raman gain, is observed in dielectrics using chirped femtosecond pulses. A time resolved pump-probe geometry is used to vary the frequency difference between pulses in the terahertz frequency band. Stimulated Raman scattering couples the pulses transferring energy from the higher to the lower frequency beam, resulting in a dispersion shaped curve as a function of the temporal delay, dependent on the product of the pump and probe irradiances. The observed signal gives the Raman gain in SiO2 and PbF2 for detunings up to 10 THz (approximately 300 cm-1) using mm-thick samples. This method may also be sensitive to the electronic motion responsible for bound-electronic nonlinear refractive index, which could yield the optical response time of bound electrons.

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References

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  1. N. Bloembergen, The stimulated Raman effect, Am. J. Phys. 35, 989 (1967).
    [CrossRef]
  2. W. Kaiser and M. Maier, Stimulated Rayleigh, Brillouin and Raman spectroscopy, in Laser Handbook, Vol. 2 edited by F. T. Arecchi and E. O. Schulz-DuBois, North-Holland, p. 1077, 1972.
  3. M. J. Weber, Handbook of Laser Science and Technology, Vol. 3, Optical Materials: Part 1, CRC Press Inc., p. 287-292(1986).
  4. F. M. Mitschke and L. F. Mollenauer, Discovery of the soliton self-frequency shift, Opt. Lett. 11, 659 (1986)
    [CrossRef] [PubMed]
  5. D. J. Dougherty, F. X. Kartner, H. A. Haus, and E. P. Ippen, Measurement of the Raman gain spectrum of optical fibers, Opt. Lett. 20, 31 (1995).
    [CrossRef] [PubMed]
  6. A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland and N. Bloembergen, Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering, J. Opt. Soc. Am. B, 14, 796 (1997).
    [CrossRef]
  7. J. P. Gordon, Theory of the soliton self-frequency shift, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  8. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, Raman response function of silica-core fibers, J. Opt. Soc. Am. B, 6, 1159 (1989).
    [CrossRef]

Other (8)

N. Bloembergen, The stimulated Raman effect, Am. J. Phys. 35, 989 (1967).
[CrossRef]

W. Kaiser and M. Maier, Stimulated Rayleigh, Brillouin and Raman spectroscopy, in Laser Handbook, Vol. 2 edited by F. T. Arecchi and E. O. Schulz-DuBois, North-Holland, p. 1077, 1972.

M. J. Weber, Handbook of Laser Science and Technology, Vol. 3, Optical Materials: Part 1, CRC Press Inc., p. 287-292(1986).

F. M. Mitschke and L. F. Mollenauer, Discovery of the soliton self-frequency shift, Opt. Lett. 11, 659 (1986)
[CrossRef] [PubMed]

D. J. Dougherty, F. X. Kartner, H. A. Haus, and E. P. Ippen, Measurement of the Raman gain spectrum of optical fibers, Opt. Lett. 20, 31 (1995).
[CrossRef] [PubMed]

A. Dogariu, T. Xia, D. J. Hagan, A. A. Said, E. W. Van Stryland and N. Bloembergen, Purely refractive transient energy transfer by stimulated Rayleigh-wing scattering, J. Opt. Soc. Am. B, 14, 796 (1997).
[CrossRef]

J. P. Gordon, Theory of the soliton self-frequency shift, Opt. Lett. 11, 662 (1986).
[CrossRef] [PubMed]

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, Raman response function of silica-core fibers, J. Opt. Soc. Am. B, 6, 1159 (1989).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Two-beam coupling data (circles) (a) in PbF2 and (b) in SiO2 with theoretical fits (solid lines) assuming a Raman gain linearly dependent on time-delay. The pulses are linearly chirped with C = 1.3. Here C is measured to be 1.3±0.1.

Fig. 2
Fig. 2

Low frequency Raman spectra for PbF2 (squares) and SiO2 (circles) obtained using the chirped-two-beam coupling method, along with linear fits.

Equations (6)

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E ( r , t ) = E 0 e i ( k r ω t ) e r 2 w 0 2 e ( 1 + iC ) t 2 τ p 2 ,
Ω = ω pump ω probe = C τ τ p 2 .
d I p dz = g I e I p .
( Δ T ( τ ) T ) p = 1 2 ( 1 + w 0 p 2 w 0 e 2 ) I 0 e L exp ( 1 2 ( τ τ p ) 2 ) g ( τ ) ,
g ( ν ) PbF 2 = ( 9.6 ± 1.9 ) 10 13 ν
g ( ν ) SiO 2 = ( 8.4 ± 1.7 ) 10 14 ν ,

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