Abstract

When a Raman active material is placed inside the optical Fabry-Perot cavity resonator of a giant pulse (“Q-switched”) laser, the high-power laser light pulse induces gain in the Raman material at frequencies shifted from the giant pulse frequency by well-known Raman frequencies. If this gain is large enough to overcome cavity losses, a strong buildup of coherent light at the shifted frequency(s) may ensue; the process is analogous to stimulated fluorescence and is an example of stimulated Raman scattering. We calculate here the Raman output power as a function of time and its spectral content when the Raman material is in the laser cavity. From the resulting expressions (which contain no undetermined parameters) we calculate the properties of the light generated by nitrobenzene inside a giant pulse ruby laser and find that the results agree with (as yet incomplete) observations that have been made on that system.

© 1963 Optical Society of America

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References

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  1. G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
    [Crossref]
  2. R. W. Hellwarth, in Advances in Quantum Electronics (Columbia University Press, New York, 1961), p. 334.
  3. F. J. McClung, R. W. Hellwarth, Proc. IEEE 51, 46 (1963).
    [Crossref]
  4. R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
    [Crossref]
  5. G. Herzberg, Infrared and Raman Spectra (Van Nostrand, Princeton, N.J., 1959).
  6. F. J. McClung, D. Weiner (private communication).
  7. T. P. Hughes, K. M. Young, “Mode Sequences in Ruby Laser Emission” (to be published).

1963 (2)

F. J. McClung, R. W. Hellwarth, Proc. IEEE 51, 46 (1963).
[Crossref]

R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
[Crossref]

1962 (1)

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Eckhardt, G.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Hellwarth, R. W.

F. J. McClung, R. W. Hellwarth, Proc. IEEE 51, 46 (1963).
[Crossref]

R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
[Crossref]

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

R. W. Hellwarth, in Advances in Quantum Electronics (Columbia University Press, New York, 1961), p. 334.

Herzberg, G.

G. Herzberg, Infrared and Raman Spectra (Van Nostrand, Princeton, N.J., 1959).

Hughes, T. P.

T. P. Hughes, K. M. Young, “Mode Sequences in Ruby Laser Emission” (to be published).

McClung, F. J.

F. J. McClung, R. W. Hellwarth, Proc. IEEE 51, 46 (1963).
[Crossref]

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

F. J. McClung, D. Weiner (private communication).

Schwarz, S. E.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Weiner, D.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

F. J. McClung, D. Weiner (private communication).

Woodbury, E. J.

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Young, K. M.

T. P. Hughes, K. M. Young, “Mode Sequences in Ruby Laser Emission” (to be published).

Phys. Rev. (1)

R. W. Hellwarth, Phys. Rev. 130, 1850 (1963).
[Crossref]

Phys. Rev. Letters (1)

G. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Proc. IEEE (1)

F. J. McClung, R. W. Hellwarth, Proc. IEEE 51, 46 (1963).
[Crossref]

Other (4)

R. W. Hellwarth, in Advances in Quantum Electronics (Columbia University Press, New York, 1961), p. 334.

G. Herzberg, Infrared and Raman Spectra (Van Nostrand, Princeton, N.J., 1959).

F. J. McClung, D. Weiner (private communication).

T. P. Hughes, K. M. Young, “Mode Sequences in Ruby Laser Emission” (to be published).

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Figures (4)

Fig. 1
Fig. 1

A plot of Eq. (10) for the scattered power ϕ (normalized by factors defined in the text), as a function of time t (times w the natural decay rate of the incident light modes) minus ln r (where r is the ratio of the peak initial Raman gain x0Γ to incident mode losses w) and valid for weak scattering. The curves (a), (b), and (c) are for W/w = ½, 1, and 2, where W is the natural decay rate of the scattered modes.

Fig. 2
Fig. 2

A plot of Eq. (17) for the total fraction ξ of photons, available initially from the giant pulse, which are scattered as a function of the giant plus intensity x0 photons (expressed in the dimensionless ratio r of the peak initial gain x0Γ in the scattered modes to the incident mode loss rate w) and valid for weak scattering. The curves (a), (b), and (c) are for W/w = ½, 1, and 2 where W is the loss rate of the scattered modes.

Fig. 3
Fig. 3

Curve (a), using right side ordinate, gives a plot of Eq. (21) for the number of photons y in the scattered modes (in units of the number of photons x0 produced by the giant pulse) as a function of time t (times the cavity loss rate w) for the parameter values indicated by the circle in Fig. 4. Curve (b), using the left-side ordinate, gives the number of photons x (in units of x0) in the incident cavity modes as a function of wt during the output pulse of curve (a). Curve (c) gives x as it would evolve with time wt without stimulated Raman scattering.

Fig. 4
Fig. 4

A plot of Eq. (23) for the total fraction ξ of giant pulse photons scattered to output cavity modes as function of giant pulse intensity x0 (expressed in dimensionless units r = x0Γ/w) and valid for strong scattering. Curves (a)–(e) correspond to d(= x0/y0) = 109, 1011, 1013, 1015, and 1017, respectively, where y0 is the number of (thermal plus zero point) photons present initially in those modes in which most of the scattered output is concentrated.

Equations (26)

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g β l > γ β .
g β = Σ α I α σ α β λ β 4 [ 1 - exp ( - Δ α β / k T ) ] / c β cm - 1 .
d n β / d t = n β ( g β l - γ β ) / τ .
g β = Σ α σ α β n α λ β 4 ( 1 - exp - Δ α β / k T ) / ( c β τ a )
d n β / d t = n β ( Σ α n α Γ α β - w β ) ,
Γ α β = σ α β λ β 4 ( 1 - exp - Δ α β / k T ) l / ( c β τ 2 a ) ,
d n α / d t = - n α ( Σ β n β Γ α β + w α ) .
n β = η exp [ Γ β x 0 ( 1 - e - w t ) / w - w β t ] .
r β = Γ β x 0 / w w β / w ,
ϕ ( t ) W ρ η π 1 / 2 [ r ( 1 - e - w t ) ] - 1 / 2 exp [ r ( 1 - e - w t ) - W t ] ,
w t m = ln ( r w / W ) ,
ϕ m W ρ η ( W / w r ) W / w e r - W / w ( π / r ) 1 / 2 .
ξ β = Γ β 0 d s n β ( s ) x ( s ) / x 0 ,
ξ β = η r β - W / w ( exp r β ) 0 r d v e - v v W / w / x 0 .
ξ β r β - W / w x 0 - 1 Γ ( 1 + W / w ) exp - r β .
f 1 / 2 [ ( ln 2 ) / r ] 1 / 2 .
ξ ρ η r - 1 / 2 - W / w Γ ( 1 + W / w ) π 1 / 2 e r / x 0 .
d y / d t = y ( x Γ - W )
d x / d t = - x ( y Γ + w ) ,
( x - x 0 + y - y 0 ) Γ ω / W = ln ( x y 0 / y x 0 ) .
x + y = ( x 0 + y 0 ) e - w t ,
y = b e - w t { 1 + d exp [ Γ b ( e - w t - 1 ) / w ] } - 1 ,
y 0 ρ η [ ( ln 2 ) / r ] 1 / 2 ,
ξ = r - 1 ln [ ( d + e r ( 1 + 1 / d ) ) / ( d + 1 ) ] ,
Γ 1.15 × 10 - 8 sec - 1 .
x 0 3.3 × 10 17 photons ,

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