Multiwave stimulated Raman scattering with quasiphase matching

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Multiwave stimulated Raman scattering with
quasi-phase matching
Victor G. Bespalov Russian Research Center "S. I.
Vavilov State Optical Institute"
Nikolai S. Makarov Saint-Petersburg State
Institute of Fine Mechanics and Optics (Technical
University)
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Outline

• Principle of quasi-phase matching
• System of multiwave SRS equations
• Multiwave SRS with/without Raman gain dispersion
• QPM Multiwave SRS
• Conclusions
• References

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Principle of quasi-phase matching
Nonlinearity ?(2)
Nonlinearity ?(3)
Raman active medium
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Principle of quasi-phase matching at SRS
- Generalized phase ?2?p-?a-?s-(kaks-2kp)r, wher
e ki is the wave vector of interacting wave,
that describes the direction of energy conversion
pump Stokes anti-Stokes, on active layers
input (?1, ?3) do not practically change, that in
a final result provides a realization of
quasi-phase matching conditions.
?1
?3
?2
?0
?(3)?0
?(3)0
4
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System of steady-state multiwave SRS equations
?j wave mismatching, g steady-state Raman
gain coefficient, ?j frequencies of interacting
waves, Ej complex wave amplitudes.
In this system the wave mismatching and Raman
gain are the functions of coordinate for
nonlinear (?(3)?0) and linear (?(3)0) layers.
Raman gain dispersion
Ba(NO3)2
H2
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Multiwave SRS in hydrogen and barium nitrate
Hydrogen
Barium nitrate
Without dispersion of g P pump, S1 first
Stokes, S2 second Stokes, S3 third Stokes
With dispersion of g P pump, S1 first
Stokes, S2 second Stokes, S3 third Stokes.
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Multiwave QPM SRS in hydrogen and barium nitrate
Hydrogen
Barium nitrate
1 pump, 2 first Stokes, 3 first
Anti-Stokes, 4 second Stokes.
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Influence of high SRS components on calculations
precision

• For best calculation accuracy it is necessary to
  take into account at least the generation of 4
  Stokes and 4 anti-Stokes SRS components.

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Multiwave QPM SRSperiodical structure
Hydrogen
Barium nitrate
1 pump, 2 first Stokes, 3 first
Anti-Stokes, 4 second Stokes, 5 second
Anti-Stokes, 6 third Stokes, 7 third
Anti-Stokes.
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Layers length errorsfor periodical QPM structure
Maximum allowed error is 15
Maximum allowed error is 0.2

• For periodical QPM structure it is necessary to
  choose the passive layers length with high
  accuracy, because even the small error in layer
  length causes the essential decreasing of
  anti-Stokes SRS generation efficiency, whereas
  for aperiodical QPM structure the error may
  reached more than 5 of layer length.

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• Conclusion

• Our numerical calculations have shown that for
  best accuracy of QPM SRS simulations it is
  necessary to take into account the dispersion of
  Raman gain coefficient and for studying of
  multiwave SRS influence on QPM structure
  realization it is necessary to take into account
  the generation at least of 4 Stokes and 4
  anti-Stokes SRS components.
• We received the model of periodical QPM Raman
  media in which the efficiency of multiwave
  anti-Stokes generation reached 40.
• We determined that high precision of passive
  layers length of periodical QPM structure in
  hydrogen is required due to strongly influence of
  layers length error on anti-Stokes SRS generation
  efficiency.
• In barium nitrate it is possible to realize
  periodical structure for efficient generation of
  3 Stokes and 3 Anti-Stokes SRS components.

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Acknowledgments

• I would like to thank the organizing committee of
  Conference for partial supporting of my
  participation.
• This work was partly supported by Grant RP1-2249
  of U.S. Civilian Research and Development
  Foundation and Program of Ministry of Education
  Femtosecond optics and technologies.

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• References

• V. G. Bespalov, N. S. Makarov, Quasi-phase
  matching anti-Stokes SRS generation, Proc. SPIE,
  vol. 4268, 2001, pp. 109-116.
• V. G. Bespalov, and N. S. Makarov, Quasi-phase
  matching generation of blue coherent radiation at
  stimulated Raman scattering, Optics Comm., 203
  (3-6) (2002) pp. 413-420.
• V. G. Bespalov, N. S. Makarov, SRS generation of
  anti-Stokes radiation under phase quasi-matching
  conditions, Opt. Spectr., vol. 90, No. 6,
  2001, pp. 938-941.
• V. G. Bespalov, N. S. Makarov, Transient
  quasi-phase matching SRS generation, Proc. SPIE,
  (ICONO-2001), 2001 (accepted for publication).
• N. S. Makarov, Analytical solution of
  quasi-phase matching anti-Stokes SRS
  amplification in silica fiber, in book Modern
  technologies, pp. 166-175, SPb, 2001.
• V. G. Bespalov, N. S. Makarov, Simultaneously
  Stokes and anti-Stokes Raman amplification in
  silica fiber, Proc. SPIE, vol. 4638, 2002
  (accepted for publication).
• Bischel W. K., Dyer M. J. Wavelength dependence
  of the absolute Raman gain coefficient for the
  Q(1) transmission in H2, J. Opt. Soc. Am. B,
  vol. 3, 1985, pp. 677-682.

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