Abstract

We calculate the probability distribution P(W) for the energy W of pulses generated by transient stimulated Raman scattering and find that 100% macroscopic fluctuations are predicted. In the limit of large numbers of Stokes photons we find that P(W) is essentially exponential, implying that the most probable value for Stokes pulse energy is near zero. The macroscopic energy fluctuations, whose origin is quantum mechanical, may impose a fundamental limitation on the stability of the Raman generation process.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Q. H. F. Vrehen, in Laser Spectroscopy IV, H. Walther, K. Rothe, eds. (Springer-Verlag, Berlin, 1979), p. 471.
  2. F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
    [CrossRef]
  3. D. Polder, M. F. H. Schuurmans, Q. H. F. Vrehen, Phys. Rev. A 19, 1192 (1979).
    [CrossRef]
  4. J. Mostowski, M. G. Raymer, Opt. Commun. 36, 237 (1981).
    [CrossRef]
  5. M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
    [CrossRef]
  6. R. Glauber, F. Haake, Phys. Lett. 68A, 29 (1978); F. A. Hopf, Phys. Rev. A 20, 2064 (1979).
    [CrossRef]
  7. D. F. Walls, J. Phys. A 6, 496 (1973).
    [CrossRef]
  8. F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
    [CrossRef]
  9. For simplicity a detector with a quantum efficiency of unity has been assumed. For a review, see L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965); C. L. Mehta, in Progress in Optics VIII, E. Wolf, ed. (North-Holland, New York, 1970), p. 375.
    [CrossRef]

1981 (2)

J. Mostowski, M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

1980 (1)

F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
[CrossRef]

1979 (2)

F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
[CrossRef]

D. Polder, M. F. H. Schuurmans, Q. H. F. Vrehen, Phys. Rev. A 19, 1192 (1979).
[CrossRef]

1978 (1)

R. Glauber, F. Haake, Phys. Lett. 68A, 29 (1978); F. A. Hopf, Phys. Rev. A 20, 2064 (1979).
[CrossRef]

1973 (1)

D. F. Walls, J. Phys. A 6, 496 (1973).
[CrossRef]

1965 (1)

For simplicity a detector with a quantum efficiency of unity has been assumed. For a review, see L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965); C. L. Mehta, in Progress in Optics VIII, E. Wolf, ed. (North-Holland, New York, 1970), p. 375.
[CrossRef]

Glauber, R.

F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
[CrossRef]

F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
[CrossRef]

R. Glauber, F. Haake, Phys. Lett. 68A, 29 (1978); F. A. Hopf, Phys. Rev. A 20, 2064 (1979).
[CrossRef]

Haake, F.

F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
[CrossRef]

F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
[CrossRef]

R. Glauber, F. Haake, Phys. Lett. 68A, 29 (1978); F. A. Hopf, Phys. Rev. A 20, 2064 (1979).
[CrossRef]

Haus, J.

F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
[CrossRef]

F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
[CrossRef]

King, H.

F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
[CrossRef]

F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
[CrossRef]

Mandel, L.

For simplicity a detector with a quantum efficiency of unity has been assumed. For a review, see L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965); C. L. Mehta, in Progress in Optics VIII, E. Wolf, ed. (North-Holland, New York, 1970), p. 375.
[CrossRef]

Mostowski, J.

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

J. Mostowski, M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

Polder, D.

D. Polder, M. F. H. Schuurmans, Q. H. F. Vrehen, Phys. Rev. A 19, 1192 (1979).
[CrossRef]

Raymer, M. G.

J. Mostowski, M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

Schröder, G.

F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
[CrossRef]

F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
[CrossRef]

Schuurmans, M. F. H.

D. Polder, M. F. H. Schuurmans, Q. H. F. Vrehen, Phys. Rev. A 19, 1192 (1979).
[CrossRef]

Vrehen, Q. H. F.

D. Polder, M. F. H. Schuurmans, Q. H. F. Vrehen, Phys. Rev. A 19, 1192 (1979).
[CrossRef]

Q. H. F. Vrehen, in Laser Spectroscopy IV, H. Walther, K. Rothe, eds. (Springer-Verlag, Berlin, 1979), p. 471.

Walls, D. F.

D. F. Walls, J. Phys. A 6, 496 (1973).
[CrossRef]

Wolf, E.

For simplicity a detector with a quantum efficiency of unity has been assumed. For a review, see L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965); C. L. Mehta, in Progress in Optics VIII, E. Wolf, ed. (North-Holland, New York, 1970), p. 375.
[CrossRef]

J. Phys. A (1)

D. F. Walls, J. Phys. A 6, 496 (1973).
[CrossRef]

Opt. Commun. (1)

J. Mostowski, M. G. Raymer, Opt. Commun. 36, 237 (1981).
[CrossRef]

Phys. Lett. (1)

R. Glauber, F. Haake, Phys. Lett. 68A, 29 (1978); F. A. Hopf, Phys. Rev. A 20, 2064 (1979).
[CrossRef]

Phys. Rev. A (3)

M. G. Raymer, J. Mostowski, Phys. Rev. A 24, 1980 (1981).
[CrossRef]

F. Haake, H. King, G. Schröder, J. Haus, R. Glauber, Phys. Rev. A 20, 2047 (1979).
[CrossRef]

D. Polder, M. F. H. Schuurmans, Q. H. F. Vrehen, Phys. Rev. A 19, 1192 (1979).
[CrossRef]

Phys. Rev. Lett. (1)

F. Haake, J. Haus, H. King, G. Schröder, R. Glauber, Phys. Rev. Lett. 45, 558 (1980).
[CrossRef]

Rev. Mod. Phys. (1)

For simplicity a detector with a quantum efficiency of unity has been assumed. For a review, see L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965); C. L. Mehta, in Progress in Optics VIII, E. Wolf, ed. (North-Holland, New York, 1970), p. 375.
[CrossRef]

Other (1)

Q. H. F. Vrehen, in Laser Spectroscopy IV, H. Walther, K. Rothe, eds. (Springer-Verlag, Berlin, 1979), p. 471.

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 (1)

Fig. 1
Fig. 1

Ratio of second-largest to largest eigenvalues of the matrix Aij as a function of β = 4κ1κ2|EL|2zτL, which is a measure of the laser intensity and pulse duration. It is seen that λ2 is always much less than λ1, making the form of the probability distribution in Eq. (16) valid.

Equations (22)

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

L ( z , t ) = E L ( z , t ) exp [ i ( ω L t k L z ) ] + c . c .
( z + 1 c t ) E ^ S = i κ 2 Q ^ E L , t Q ^ = i κ 1 E L * E ^ S ( 1 ) ,
[ Q ^ ( z , 0 ) , Q ^ ( z , 0 ) ] = ( AN ) 1 δ ( z z ) .
E ^ S ( z , τ ) = i κ 2 E L ( τ ) × 0 z d z Q ^ ( z , 0 ) I 0 ( [ ατ ( z z ) ] 1 / 2 ) .
W ^ = A c 2 πћ ω S 0 τL d τ E ^ S ( z , τ ) E ^ S ( z , τ ) ,
W ^ = 0 z d z 0 z d z A ( z , z ) Q ^ ( z , 0 ) Q ^ ( z , 0 ) ,
A ( z , z ) = A c | κ 2 E L | 2 2 πℏ ω S × 0 τL d τ I 0 ( [ ατ ( z z ) ] 1 / 2 ) × I 0 ( [ ατ ( z z ) ] 1 / 2 ) .
P ( W ) = 1 2 π d ζ exp ( iζW ) C ( ζ ) ,
C ( ζ ) = : exp ( W ^ ) : ,
q ˆ i = ( AN Δ z ) 1 / 2 Q ˆ ( z i , 0 ) ,
[ q ˆ i , q ˆ j ] = δ ij .
W ˆ = i , j = 1 M A ij q ˆ i q ˆ j ,
A ij = β 2 M ( x i x j ) [ x i I 0 ( β x i ) I 1 ( β x j ) x j I 0 ( β x j ) I 1 ( β x i ) ] , A ii = β 4 M [ I 0 2 ( β x i ) I 1 2 ( β x i ) ] ,
q ˆ i 1 q ˆ i 2 q ˆ i n q ˆ j 1 q ˆ j 2 q ˆ j n = P q ˆ i 1 q ˆ j 1 q ˆ i 2 q ˆ j 2 q ˆ i n q ˆ j n ,
q ˆ i q ˆ j = δ ij .
C ( ζ ) = lim M d 2 q 1 d 2 q 2 d 2 q M 1 π M × exp ( | q 1 | 2 | q 2 | 2 | q M | 2 ) × exp ( i , j M A ij q i * q j ) ,
C ( ζ ) = lim M 1 ( 1 λ 1 ) ( 1 λ 2 ) ( 1 λ M ) .
P ( W ) = lim M i = 1 M λ i M 2 exp ( W / λ i ) ( λ i λ 1 ) ( λ i λ 2 ) ( λ i λ M ) ,
P ( W ) 1 W exp ( W / W ) ,
W = Tr ( A ij ) λ 1 .
p ( n ) = 0 1 n ! W n exp ( W ) P ( W ) d W ,
p ( n ) = lim M i = 1 M λ i M 1 ( λ i λ 1 ) ( λ i λ 2 ) ( λ i λ M ) × λ i ( 1 + λ i ) 1 + n ,

Metrics