Abstract

I present a new treatment of the theory of nonforward stimulated Raman scattering (SRS) in the field of a phase-modulated pump, where the pump phase modulation is an arbitrary function of time. The theory is accurate enough to determine the performance limitations on laser systems where SRS is a potentially controlling parasitic. Calculations are described for the Sr5(PO4)3F amplifier medium where the laser beam has a pure rf modulation typical of those attainable in the laboratory. The predictions of this theory are compared with the D’yakov approximation for SRS in the field of a laser beam whose phase is Gaussian noise.

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References

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  1. S. A. Akhmanov, Yu. E. D'yakov, and L. I. Pavlov, "Statistical phenomena in Raman scattering stimulated by a broad-band pump," Sov. Phys. JETP 39, 249-256 (1974) S. A. Akhmanov, Yu. E. D'yakov, and L. I. Pavlov, "Statistical phenomena in Raman scattering stimulated by a broad-band pump,"[Zh. Eksp. Teor. Fiz. 66, 520-536 (1974).]
  2. D. Eimerl, "Theory of temporal stochasticity in stimulated Raman scattering in dispersionless media," J. Math. Phys. 20, 1811-1819 (1979).
    [CrossRef]
  3. D. Eimerl, "Inhomogeneously pumped stimulated Raman scattering," in Proceedings of the International Conference on Lasers (STS, 1979), pp. 333-335.
  4. W. R. Truntna, Jr.,Y. K. Park, and R. L. Byer, "The dependence of Raman gain on pump laser bandwidth," IEEE J. Quantum Electron. QE-15, 648-655 (1979).
    [CrossRef]
  5. J. Eggleston and R. L. Byer, "Steady-state stimulated Raman scattering by a multimode laser," IEEE J. Quantum Electron. QE-16, 850-853 (1980).
    [CrossRef]
  6. G. C. Valley, "A review of stimulate Brillouin scattering excited with a broad-band laser," IEEE J. Quantum Electron. QE-22, 704-712 (1986).
    [CrossRef]
  7. J. F. Reintjes, "Stimulated Raman scattering," in CRC Handbook of Laser Science and Technology, Supplement 2: Optical Materials, M.J.Weber, ed., (CRC Press, 1995) Chap. 8.3.
  8. J. R. Murray, J. R. Smith, R. B. Ehrlich, D. T. Kyrakis, C. E. Thompson, T. L. Weiland, and R. B. Wilcox, "Experimental observation and supprression of transverse stimulated Brillouin scattering in large optical components," J. Opt. Soc. Am. B 6, 2402-2411 (1989).
    [CrossRef]
  9. A. J. Bayramian, C. Bibeau, R. J. Beach, C. D. Marshall, and S. A. Payne, "Consideration of stimulated Raman scattering in Yb:Sr5(PO4)3F laser amplifiers," Appl. Opt. 39, 3746-3753 (2000).
    [CrossRef]
  10. H. Haken, Laser Theory (Springer, 1984).
  11. H. Ritsch and M. A. M. Marte, "Quantum noise in Raman amplifiers: effect of pump bandwidth and super- and sub-Poisson pumping," Phys. Rev. A 47, 2354-2359 (1993).
    [CrossRef] [PubMed]

2000 (1)

1993 (1)

H. Ritsch and M. A. M. Marte, "Quantum noise in Raman amplifiers: effect of pump bandwidth and super- and sub-Poisson pumping," Phys. Rev. A 47, 2354-2359 (1993).
[CrossRef] [PubMed]

1989 (1)

1986 (1)

G. C. Valley, "A review of stimulate Brillouin scattering excited with a broad-band laser," IEEE J. Quantum Electron. QE-22, 704-712 (1986).
[CrossRef]

1980 (1)

J. Eggleston and R. L. Byer, "Steady-state stimulated Raman scattering by a multimode laser," IEEE J. Quantum Electron. QE-16, 850-853 (1980).
[CrossRef]

1979 (2)

D. Eimerl, "Theory of temporal stochasticity in stimulated Raman scattering in dispersionless media," J. Math. Phys. 20, 1811-1819 (1979).
[CrossRef]

W. R. Truntna, Jr.,Y. K. Park, and R. L. Byer, "The dependence of Raman gain on pump laser bandwidth," IEEE J. Quantum Electron. QE-15, 648-655 (1979).
[CrossRef]

1974 (1)

S. A. Akhmanov, Yu. E. D'yakov, and L. I. Pavlov, "Statistical phenomena in Raman scattering stimulated by a broad-band pump," Sov. Phys. JETP 39, 249-256 (1974) S. A. Akhmanov, Yu. E. D'yakov, and L. I. Pavlov, "Statistical phenomena in Raman scattering stimulated by a broad-band pump,"[Zh. Eksp. Teor. Fiz. 66, 520-536 (1974).]

Appl. Opt. (1)

IEEE J. Quantum Electron. (3)

W. R. Truntna, Jr.,Y. K. Park, and R. L. Byer, "The dependence of Raman gain on pump laser bandwidth," IEEE J. Quantum Electron. QE-15, 648-655 (1979).
[CrossRef]

J. Eggleston and R. L. Byer, "Steady-state stimulated Raman scattering by a multimode laser," IEEE J. Quantum Electron. QE-16, 850-853 (1980).
[CrossRef]

G. C. Valley, "A review of stimulate Brillouin scattering excited with a broad-band laser," IEEE J. Quantum Electron. QE-22, 704-712 (1986).
[CrossRef]

J. Math. Phys. (1)

D. Eimerl, "Theory of temporal stochasticity in stimulated Raman scattering in dispersionless media," J. Math. Phys. 20, 1811-1819 (1979).
[CrossRef]

J. Opt. Soc. Am. B (1)

Phys. Rev. A (1)

H. Ritsch and M. A. M. Marte, "Quantum noise in Raman amplifiers: effect of pump bandwidth and super- and sub-Poisson pumping," Phys. Rev. A 47, 2354-2359 (1993).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

S. A. Akhmanov, Yu. E. D'yakov, and L. I. Pavlov, "Statistical phenomena in Raman scattering stimulated by a broad-band pump," Sov. Phys. JETP 39, 249-256 (1974) S. A. Akhmanov, Yu. E. D'yakov, and L. I. Pavlov, "Statistical phenomena in Raman scattering stimulated by a broad-band pump,"[Zh. Eksp. Teor. Fiz. 66, 520-536 (1974).]

Other (3)

D. Eimerl, "Inhomogeneously pumped stimulated Raman scattering," in Proceedings of the International Conference on Lasers (STS, 1979), pp. 333-335.

J. F. Reintjes, "Stimulated Raman scattering," in CRC Handbook of Laser Science and Technology, Supplement 2: Optical Materials, M.J.Weber, ed., (CRC Press, 1995) Chap. 8.3.

H. Haken, Laser Theory (Springer, 1984).

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Figures (2)

Fig. 1
Fig. 1

SRS gain suppresion in S:FAP using rf pump bandwidth.

Fig. 2
Fig. 2

D’yakov approximation.

Equations (62)

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H int = α E 2 ,
α = α 0 + α Q .
E E ( z , t ) exp ( i ( ω s [ t n s z c ] ) ) .
E p = a A ( τ ) exp ( i ω p τ )
τ = t ( n p c ) ( z cos θ x sin θ ) .
Q Q ( z , t ) exp ( i ω p τ + i ω s [ t n s z c ] ) .
ω p = ω R + ω s .
( z + n s c t ) E s = 1 2 γ A Q * ,
( Γ + t ) Q = Γ A E s * .
T = t ( n p c ) z cos θ ,
Z = z .
( Z + n s n p cos θ c T ) E s = 1 2 γ A Q * ,
( Γ + T ) Q = Γ A E s * .
τ = T ( n p c ) x sin θ .
T = T ( n p c ) x sin θ ,
( Z + n s n p cos θ c T ) E s = 1 2 γ A ( T ) Q * ,
( Γ + T ) Q = Γ A ( T ) E s * .
( z + 1 V t ) E s = 1 2 γ A ( t ) Q * ,
( Γ + t ) Q = Γ A ( t ) E s * ,
1 V = n s c ( n p c ) cos θ .
A ( t ) = A 0 exp ( i φ ( t ) ) ,
( i k V + d d t ) e s = 1 2 γ V A 0 e i φ ( t ) q * ,
( Γ + d d t ) q = Γ A 0 e i φ ( t ) e s * ,
Z = q * e i φ e s A 0 .
i k V + d d t ln e s = 1 2 g 0 V Z ,
Γ + d d t ln q * = Γ ( 1 Z ) ,
Z = i k ( g 0 2 ) ,
1 Z = 1 .
ln e s ( k , t ) = ln e s ( k , ) + d t ( 1 2 g 0 V Z ( k , t ) i k V ) ,
E s ( z , t ) = d k 2 π e s ( k , t ) e i k z .
ln e s ( k , t ) = ln e s ( k , ) + ( 1 2 ) g 0 V t ( Z i k ( g 0 2 ) ) + 0 d t ( 1 2 g 0 V Z ( k , t ) i k V ) + ( 1 2 g 0 V ) 0 t d t δ Z ( k , t ) .
g g 0 = Re Z .
d Z d t = 1 2 g 0 V Z ( Z p ) + Γ ( 1 Z ) + i Z d φ d t .
1 2 g 0 V ( Z p ) = Γ ( 1 Z 1 ) ,
d X d t = 1 2 g 0 V ( ( X u ) X ( Y v ) Y ) + Γ ( 1 X ) Y d φ d t ,
d Y d t = 1 2 g 0 V ( ( X u ) Y + ( Y v ) X ) + Γ ( Y ) + X d φ d t .
d u d t = α ( X u ) ,
d v d t = α ( Y v ) ,
d u 3 d t = α ( X u ) ,
d v 3 d t = α ( Y v ) ,
d u d t = α ( X u 3 ) ,
d v d t = α ( Y v 3 ) .
φ ( t ) = β sin ( Ω t ) ,
( g g 0 ) 2 ( 1 2 π c ( Δ ν ¯ R + Δ ν ¯ p ) g 0 V ) ( g g 0 ) 2 π c Δ ν ¯ R g 0 V = 0 ,
Δ ω eff = ξ β Ω 2 ,
( i k V + d d t ) e s = 1 2 γ V A 0 e i φ ( t ) q * + s ( k , t ) ,
( Γ + d d t ) q = Γ A 0 e i φ ( t ) e s * .
Ω ( k , t 1 , t 2 ) = 1 2 g 0 V t 1 t 2 d t Z ( k , t ) ,
e s ( k , t ) = t d t e Ω ( k , t , t ) i k V ( t t ) s ( k , t ) ,
E ( z , t ) = t d t 0 z d z G ( z z , t , t ) S ( z , t ) ,
G ( z , t , t ) = d k 2 π e Ω ( k , t , t ) i k V ( t t z V ) ,
S ( z , t ) S * ( z , t ) = I N δ ( z z ) δ ( t t ) .
I ( z , t ) = I N t d t 0 z d z G ( z z , t , t ) 2 .
G ( z , t , t ) = d k 2 π K e i k z ,
I s = I N d k d t e p ,
p = g 0 V Re t t d t Z ( k , t ) i k V ( t t z V ) .
p = g 0 V ( t t ) Z R ( k ) i k V ( t t z V ) + fluctuations ,
p k = g 0 V ( t t ) d Z R ( k ) d k i V ( t t z V ) = 0 .
p p 1 = p ( k s ( t ) , t ) = g 0 V ( t t ) Z R ( k s ) i k s V ( t t z V ) .
p k s d k s d t + p t = 0 .
g 0 V Z R ( k s ) i k s V = 0 .
p = g 0 V ( t t ) Z R ( k s ) i k s V ( t t z V ) = i k s z = ( g 0 z ) Z R .

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