Abstract

Equations describing stimulated Brillouin backscattering including absorption in the media are solved by the method of integration along the characteristic equations of the fields. More complete analytical expressions for pump and Stokes wave intensities and for the width of the backscattered pulse are obtained. A comparison between theoretical and experimental data is made to explain the pulse compression.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi, ed. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.
  2. N. M. Kroll, “Excitation of the hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–44 (1965).
    [CrossRef]
  3. D. T. Hon, “Pulse compression by stimulated Brillouin scattering,” Opt. Lett. 5, 516–518 (1980).
    [CrossRef] [PubMed]
  4. M. J. Damzen and M. H. R. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–15 (1983).
    [CrossRef]
  5. A. A. Filippo and M. R. Perrone, “Shortening of free-running Xe-Cl laser pulse by stimulated Brillouin scattering,” J. Mod. Opt. 39, 1829–1836 (1992).
    [CrossRef]
  6. V. Nassisi and A. Pecoraro, “Stimulated Brillouin and Raman scattering for the generation of short excimer laser pulses,” IEEE J. Quantum Electron. 29, 2547–2552 (1993).
    [CrossRef]
  7. B. Dane, W. A. Neuman, and L. A. Hackel, “High-energy SBS pulse compression,” IEEE J. Quantum Electron. 30, 1907–1915 (1994).
    [CrossRef]
  8. B. L. Rojdestvensky and N. N. Ivanenko, Quasilinear Systems of Equations (Science, Moscow, 1978), pp. 16–133 (in Russian).
  9. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1941 (1962).
    [CrossRef]
  10. M. Maier, “Quasisteady state in the stimulated Brillouin scattering of liquids,” Phys. Rev. 166, 113–120 (1968).
    [CrossRef]
  11. D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonons lifetimes,” Phys. Rev. B 1, 31–44 (1970).
    [CrossRef]
  12. N. M. Kroll and P. L. Kelley, “Temporal and spatial gain in stimulated light scattering,” Phys. Rev. A 4, 763–776 (1971).
    [CrossRef]
  13. R. V. Johnson and J. H. Marburger, “Relaxations oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4, 1175–1182 (1971).
    [CrossRef]
  14. N. M. Nguyen-Vo and S. J. Pfeifer, “A model of spontaneous Brillouin scattering as the noise source for stimulated scattering,” 29, 508–514 (1993).
  15. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 387–394.
  16. D. T. Hon, “Applications of wavefront reversal by stimulated Brillouin scattering,” Opt. Eng. 21, 252–256 (1982).
    [CrossRef]
  17. V. I. Kliatkin, Statistical Linear Problems–Deterministic Nonlinear Problems (Institute of Applied Physics of The USSR Academy, Moscow, 1981) (in Russian).
  18. V. I. Kliatkin, Averaging Problems and the Scattering Theory of Waves (Science, Moscow, 1986) (in Russian).

1994

B. Dane, W. A. Neuman, and L. A. Hackel, “High-energy SBS pulse compression,” IEEE J. Quantum Electron. 30, 1907–1915 (1994).
[CrossRef]

1993

V. Nassisi and A. Pecoraro, “Stimulated Brillouin and Raman scattering for the generation of short excimer laser pulses,” IEEE J. Quantum Electron. 29, 2547–2552 (1993).
[CrossRef]

1992

A. A. Filippo and M. R. Perrone, “Shortening of free-running Xe-Cl laser pulse by stimulated Brillouin scattering,” J. Mod. Opt. 39, 1829–1836 (1992).
[CrossRef]

1983

M. J. Damzen and M. H. R. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–15 (1983).
[CrossRef]

1982

D. T. Hon, “Applications of wavefront reversal by stimulated Brillouin scattering,” Opt. Eng. 21, 252–256 (1982).
[CrossRef]

1980

1971

N. M. Kroll and P. L. Kelley, “Temporal and spatial gain in stimulated light scattering,” Phys. Rev. A 4, 763–776 (1971).
[CrossRef]

R. V. Johnson and J. H. Marburger, “Relaxations oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4, 1175–1182 (1971).
[CrossRef]

1970

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonons lifetimes,” Phys. Rev. B 1, 31–44 (1970).
[CrossRef]

1968

M. Maier, “Quasisteady state in the stimulated Brillouin scattering of liquids,” Phys. Rev. 166, 113–120 (1968).
[CrossRef]

1965

N. M. Kroll, “Excitation of the hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–44 (1965).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1941 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1941 (1962).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1941 (1962).
[CrossRef]

Damzen, M. J.

M. J. Damzen and M. H. R. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–15 (1983).
[CrossRef]

Dane, B.

B. Dane, W. A. Neuman, and L. A. Hackel, “High-energy SBS pulse compression,” IEEE J. Quantum Electron. 30, 1907–1915 (1994).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1941 (1962).
[CrossRef]

Filippo, A. A.

A. A. Filippo and M. R. Perrone, “Shortening of free-running Xe-Cl laser pulse by stimulated Brillouin scattering,” J. Mod. Opt. 39, 1829–1836 (1992).
[CrossRef]

Hackel, L. A.

B. Dane, W. A. Neuman, and L. A. Hackel, “High-energy SBS pulse compression,” IEEE J. Quantum Electron. 30, 1907–1915 (1994).
[CrossRef]

Hon, D. T.

D. T. Hon, “Applications of wavefront reversal by stimulated Brillouin scattering,” Opt. Eng. 21, 252–256 (1982).
[CrossRef]

D. T. Hon, “Pulse compression by stimulated Brillouin scattering,” Opt. Lett. 5, 516–518 (1980).
[CrossRef] [PubMed]

Hutchinson, M. H. R.

M. J. Damzen and M. H. R. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–15 (1983).
[CrossRef]

Johnson, R. V.

R. V. Johnson and J. H. Marburger, “Relaxations oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4, 1175–1182 (1971).
[CrossRef]

Kaiser, W.

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonons lifetimes,” Phys. Rev. B 1, 31–44 (1970).
[CrossRef]

Kelley, P. L.

N. M. Kroll and P. L. Kelley, “Temporal and spatial gain in stimulated light scattering,” Phys. Rev. A 4, 763–776 (1971).
[CrossRef]

Kroll, N. M.

N. M. Kroll and P. L. Kelley, “Temporal and spatial gain in stimulated light scattering,” Phys. Rev. A 4, 763–776 (1971).
[CrossRef]

N. M. Kroll, “Excitation of the hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–44 (1965).
[CrossRef]

Maier, M.

M. Maier, “Quasisteady state in the stimulated Brillouin scattering of liquids,” Phys. Rev. 166, 113–120 (1968).
[CrossRef]

Marburger, J. H.

R. V. Johnson and J. H. Marburger, “Relaxations oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4, 1175–1182 (1971).
[CrossRef]

Nassisi, V.

V. Nassisi and A. Pecoraro, “Stimulated Brillouin and Raman scattering for the generation of short excimer laser pulses,” IEEE J. Quantum Electron. 29, 2547–2552 (1993).
[CrossRef]

Neuman, W. A.

B. Dane, W. A. Neuman, and L. A. Hackel, “High-energy SBS pulse compression,” IEEE J. Quantum Electron. 30, 1907–1915 (1994).
[CrossRef]

Pecoraro, A.

V. Nassisi and A. Pecoraro, “Stimulated Brillouin and Raman scattering for the generation of short excimer laser pulses,” IEEE J. Quantum Electron. 29, 2547–2552 (1993).
[CrossRef]

Perrone, M. R.

A. A. Filippo and M. R. Perrone, “Shortening of free-running Xe-Cl laser pulse by stimulated Brillouin scattering,” J. Mod. Opt. 39, 1829–1836 (1992).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1941 (1962).
[CrossRef]

Pohl, D.

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonons lifetimes,” Phys. Rev. B 1, 31–44 (1970).
[CrossRef]

IEEE J. Quantum Electron.

M. J. Damzen and M. H. R. Hutchinson, “Laser pulse compression by stimulated Brillouin scattering in tapered waveguides,” IEEE J. Quantum Electron. QE-19, 7–15 (1983).
[CrossRef]

V. Nassisi and A. Pecoraro, “Stimulated Brillouin and Raman scattering for the generation of short excimer laser pulses,” IEEE J. Quantum Electron. 29, 2547–2552 (1993).
[CrossRef]

B. Dane, W. A. Neuman, and L. A. Hackel, “High-energy SBS pulse compression,” IEEE J. Quantum Electron. 30, 1907–1915 (1994).
[CrossRef]

J. Appl. Phys.

N. M. Kroll, “Excitation of the hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves,” J. Appl. Phys. 36, 34–44 (1965).
[CrossRef]

J. Mod. Opt.

A. A. Filippo and M. R. Perrone, “Shortening of free-running Xe-Cl laser pulse by stimulated Brillouin scattering,” J. Mod. Opt. 39, 1829–1836 (1992).
[CrossRef]

Opt. Eng.

D. T. Hon, “Applications of wavefront reversal by stimulated Brillouin scattering,” Opt. Eng. 21, 252–256 (1982).
[CrossRef]

Opt. Lett.

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1941 (1962).
[CrossRef]

M. Maier, “Quasisteady state in the stimulated Brillouin scattering of liquids,” Phys. Rev. 166, 113–120 (1968).
[CrossRef]

Phys. Rev. A

N. M. Kroll and P. L. Kelley, “Temporal and spatial gain in stimulated light scattering,” Phys. Rev. A 4, 763–776 (1971).
[CrossRef]

R. V. Johnson and J. H. Marburger, “Relaxations oscillations in stimulated Raman and Brillouin scattering,” Phys. Rev. A 4, 1175–1182 (1971).
[CrossRef]

Phys. Rev. B

D. Pohl and W. Kaiser, “Time-resolved investigations of stimulated Brillouin scattering in transparent and absorbing media: determination of phonons lifetimes,” Phys. Rev. B 1, 31–44 (1970).
[CrossRef]

Other

B. L. Rojdestvensky and N. N. Ivanenko, Quasilinear Systems of Equations (Science, Moscow, 1978), pp. 16–133 (in Russian).

N. M. Nguyen-Vo and S. J. Pfeifer, “A model of spontaneous Brillouin scattering as the noise source for stimulated scattering,” 29, 508–514 (1993).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975), pp. 387–394.

V. I. Kliatkin, Statistical Linear Problems–Deterministic Nonlinear Problems (Institute of Applied Physics of The USSR Academy, Moscow, 1981) (in Russian).

V. I. Kliatkin, Averaging Problems and the Scattering Theory of Waves (Science, Moscow, 1986) (in Russian).

W. Kaiser and M. Maier, “Stimulated Rayleigh, Brillouin and Raman spectroscopy,” in Laser Handbook, F. T. Arecchi, ed. (North-Holland, Amsterdam, 1972), Vol. 2, pp. 1077–1150.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Characteristics lines Γ1 and Γ2 associated with equation system (3); zc and tL are defined by Eq. (6); Q is the intersection of the Stokes wave front with the time axis at z=0; L is the intersection of the pump wave front with the time axis at z=0; P is the intersection of the Stokes and pump wave fronts. (b) The dashed volume represents the intersection region between the optical and the acoustical fields. IL0 is the intensity of the pump pulse defined at z=0; ILc is the intensity of the pump pulse defined at the exit of the interaction region, z=zc; IS is the intensity of the Stokes field. (c) The surface (QP2L2) is the domain of interaction when tL<τ and zc=ctL/n; Γ1 and Γ2 are the light wave fronts; Γ3 is the acoustical wave front; P3L3 is the pump wave front at z=cτ/n. (d) The surface of triangle (QP1L1) represents the domain of interaction when tL>τ and zc=cτ/n.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Dependence of the energy-conversion efficiency (ES/EL) on the pump energy, for tL equal to 40, 20, and 8 ns. The theoretical curves were derived from Eq. (5), and the experimental points are represented by circles.

Fig. 4
Fig. 4

Dependence of the compression ratio (tL/tS) on optical pump energy. The theoretical curves were derived from Eq. (25), and the experimental points are represented by circles.

Fig. 5
Fig. 5

Dependence of the compression ratio (tL/tS) on optical pump intensity available experimentally, for different values of dispersion σ. The theoretical curves were derived from Eq. (42), and the experimental points are represented by circles.

Fig. 6
Fig. 6

Dependence of the compression ratio (tL/tS) on optical pump intensity, for different values of dispersion σ.

Equations (75)

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

(Δρ)v2γe2cn(ILcIs)1/2,
=φL-φS-φf=0,
ncILct+ILcz=-αILc-gBeILcIS,
ncISt-ISz=-αIS+gBeILcIS,
ξL=cnt+z,
ξS=cnt+zc-z.
ILc(z, t)|z=0=IL0(t),
IS(z, t)|z=zc=IS0(t),
zc=ctLn,tL<τcτn,tL>τ,
ξL=12nct+z,
ξS=12nct-z.
ξS=12nct+(zC-z).
-ξL=ξS=ddη,
dILcdη=-αILc-gBeILcIS,
dISdη=-αIS+gBeILcIS.
ILccnt+z=ILc(t)[IL0(t)+IS0]exp(-αz)IL0(t)+IS0(exp{gBe[IL0(t)+IS0]l(z)}),
IScnt+zc-z=IS0[IL0(t)+IS0]exp{-α(zc-z)+gBe[IL0(t)+IS0]l(zc-z)}IL0(t)+IS0(exp{gBe[IL0(t)+IS0]l(zc-z)}),
ILc(t)=ILCcnt+zz=zc,
IS(t)=IScnt+zC-zz=0.
IS(t)=IL0(t)exp[-αzC+gBeIL0(t)l(zc)-G]1+exp[gBeIL0(t)l(zc)-G],
ILc(t)=IL0(t)exp[-αzC-gBeIL0(t)l(zc)+G].
IL0(t)=I0f(t),
0<f(t)1ift[0, tL]
f(t)=0elsewhere.
IL0=I022ttL-2ttL2.
ts=tL[gBeI0l(zc)]1/2forzc=ctLn.
tLtStL<τ=[gBeI0l(zc)]1/2forgBeIL0l(zc)-G<01forgBeIL0·l(zc)-G>0.
IS(t)IL0(t)tL<τ=exp[-αze+gBeIL0(t)l(zc)-G]gBeIL0(t)l(zc)-G<0exp(-αze)gBeIL0(t)l(zc)-G>0.
IS(t)=IL0(t)exp(-αzc)(tL<τ).
IS(t)=IL0(t)exp-αcτn+gBeIL0(t)lcτn-G1+expgBeIL0(t)lcτn-G,
ts=tLgBeI0lcτn1/2.
tLtStL>τ=gBeI0lcτn1/2gBeIL0lcτn-G<01gBeIL0lcτn-G>0.
GgBeI0cτn.
GgBeI0ctLn.
ncILct+ILcz=-αILc-(1-)gBeILcIS,
ncISt-ISz=-αIS+(1-)gBeILcIS,
(η)=0,
(η)(η)=2σ2gBeI0δ(η-η),
=φL-φS-φd,
ncILct+ILcz
=-αILc-gBeILcIS-σ2(gBe)2(ILcIS2-ILc2IS),
ncISt-ISz
=-αIS+gBeILcIS-σ2(gBe)2(ILc2IS-ILcIs2).
ILcη=-αILc-gBeILcIS-σ2(gBe)2(ILcIS2-ILc2IS),
ISη=-αIS+gBeILcIS-σ2(gBe)2(ILc2IS-ILcIs2).
η(ILc+LS)=-α(ILc+LS)
η(ILc+LS)=-α(ILc+LS).
c1=IL0(t)+IS0IL0(t).
I02ILcη=ILc3-Q2ILc2+Q1ILc,
I02ISη=Is3-h2Is2+h1IS,
η=-2η(σgBeIL0)2,
Q1=12IL0IL0 exp(-αη)+1σ2gBeexp(-αη),
Q2=32IL0 exp(-αη)+13σ2gBe,
h1=12IL0IL0 exp(-αη)-1σ2gBeexp(-αη),
h2=32IL0 exp(-αη)-13σ2gBe.
dηdη=12(σgBeIL0)2ctLn.
α<2(σgBeIL0)2.
ILcILc-12IL0+1σ2gBe2σ2gBeIL0/1-σ2gBeIL0
=c2|ILc-IL0|1+σ2gBeIL0/1-σ2gBeIL0×exp[-(σ2gBe2IL02+gBeIL0)η],
IS=c3|IS-IL0|1-σ2gBeIL0/1+σ2gBeIL0×IS-12IL0-1σ2gBe2σ2gBeIL0/1+σ2gBeIL0×exp[-(σ2gBe2IL02-gBeIL0)η],
IS(t)=IL0(t)exp(gBeIL0-α-σ2gBe2IL02)cτn-G1+exp(gBeIL0-σ2gBe2IL02)cτn-G,ILc(t)=IL0(t)1+exp(gBeIL0-σ2gBe2IL02)cτn-G.
tLts=gBeI0lcτn1/212(1-2σ2gBeIL0)2+4σ2ncτ1/2+1-2σ2gBeI01/2.
limtLtSσ20tL>τ=tLtStL>τ.
limσ21/gBeIL0limtLtLtStL>τ
=1σ2<1gBeIL0; σ2>12gBeIL0,
limIL0tLtStL>τ=1σ2=1gBeIL0.
EL0=AL0tLIL0(t)dt,
ES=AS0ISIS(t)dt.
R=ESEL=0ISIS(t)dt0tLIL0(t)dt.
IS(t)=IS[IL0(t)].
R=lL0(0)IL0(tS)IS(IL0)dIL0dt-1dIL00tLIL0(t)dt.
ESEL=3 exp(-αzC-G)4tLtS2π2tLtS2-12×erftLtS-erftLtS-2exptLtS2+12tLtS-12tLtS-2exp4tLtS-1,
tLtSG exp(-αzC),gBeIL0l(zC)-G>0,
tLtS=[gBeI0l(zC)]1/2.
limtL/tSGESEL03π8tStLerftLtS-erftLtS-2×exp(-αzC).

Metrics