Abstract

The fluctuations and correlations of the light intensities associated with the two counterrotating modes of a ring laser have been investigated by measurement of the photoelectric counting statistics. With the laser tuned to line center, it is found that the weaker mode intensity does not grow with increasing pump parameter above threshold and that its relative intensity fluctuations do not die out, as in a conventional laser, but become thermal instead. The cross-correlation coefficient tends toward a constant negative value. The results are all in substantial quantitative agreement with the theory.

© 1977 Optical Society of America

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References

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  1. H. Haken, “Laser Theory,” in Handbuch der Physik, S. Flügge, ed. (Springer, Heidelberg and New York, 1970);V. S. Smirnov, B. L. Zhelnov, Zh. Eksp. Teor. Fiz. 57, 2043 (1969),translated in JETP 30, 1108 (1970);see also M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974);M. M-Tehrani, L. Mandel, Opt. Commun. 16, 16 (1976).
    [CrossRef]
  2. See Ref. 4 for a list of references.
  3. H. Haken, Z. Phys. 219, 246 (1969);S. Grossmann, P. H. Richter, Z. Phys 249, 43 (1971);P. H. Richter, S. Grossmann, Z. Phys 255, 59 (1972);S. Grossmann, H. Kümmel, P. H. Richter, Appl. Phys. 1, 257 (1973);R. Graham, W. A. Smith, Opt. Commun. 7, 289 (1973);F. T. Arecchi, A. M. Ricca, Phys. Rev. A 15, 308 (1977).
    [CrossRef]
  4. M. M-Tehrani, L. Mandel, Phys. Rev. A (to be published, 1977).
  5. H. Risken, Z. Phys. 191, 186 (1965);H. Risken, H. D. Vollmer, Z. Phys., 201, 323 (1967);R. D. Hempstead, M. Lax, Phys. Rev. 161, 350 (1967).
    [CrossRef]
  6. L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958) andProc. Phys. Soc. (London) 74, 233 (1959);Progress in Optics, W. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. 2, p. 181;see also L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
    [CrossRef]
  7. R. F. Chang, V. Korenman, C. O. Alley, R. W. Deten-beck, Phys. Rev. 178, 612 (1969).
    [CrossRef]
  8. D. Meltzer, L. Mandel, Phys. Rev. A 3, 1763 (1971);D. Meltzer, Photoelectric Investigations of Laser Light (Ph.D. Thesis, University of Rochester, 1970).
    [CrossRef]

1971 (1)

D. Meltzer, L. Mandel, Phys. Rev. A 3, 1763 (1971);D. Meltzer, Photoelectric Investigations of Laser Light (Ph.D. Thesis, University of Rochester, 1970).
[CrossRef]

1969 (2)

R. F. Chang, V. Korenman, C. O. Alley, R. W. Deten-beck, Phys. Rev. 178, 612 (1969).
[CrossRef]

H. Haken, Z. Phys. 219, 246 (1969);S. Grossmann, P. H. Richter, Z. Phys 249, 43 (1971);P. H. Richter, S. Grossmann, Z. Phys 255, 59 (1972);S. Grossmann, H. Kümmel, P. H. Richter, Appl. Phys. 1, 257 (1973);R. Graham, W. A. Smith, Opt. Commun. 7, 289 (1973);F. T. Arecchi, A. M. Ricca, Phys. Rev. A 15, 308 (1977).
[CrossRef]

1965 (1)

H. Risken, Z. Phys. 191, 186 (1965);H. Risken, H. D. Vollmer, Z. Phys., 201, 323 (1967);R. D. Hempstead, M. Lax, Phys. Rev. 161, 350 (1967).
[CrossRef]

1958 (1)

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958) andProc. Phys. Soc. (London) 74, 233 (1959);Progress in Optics, W. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. 2, p. 181;see also L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Alley, C. O.

R. F. Chang, V. Korenman, C. O. Alley, R. W. Deten-beck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Chang, R. F.

R. F. Chang, V. Korenman, C. O. Alley, R. W. Deten-beck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Deten-beck, R. W.

R. F. Chang, V. Korenman, C. O. Alley, R. W. Deten-beck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Haken, H.

H. Haken, Z. Phys. 219, 246 (1969);S. Grossmann, P. H. Richter, Z. Phys 249, 43 (1971);P. H. Richter, S. Grossmann, Z. Phys 255, 59 (1972);S. Grossmann, H. Kümmel, P. H. Richter, Appl. Phys. 1, 257 (1973);R. Graham, W. A. Smith, Opt. Commun. 7, 289 (1973);F. T. Arecchi, A. M. Ricca, Phys. Rev. A 15, 308 (1977).
[CrossRef]

H. Haken, “Laser Theory,” in Handbuch der Physik, S. Flügge, ed. (Springer, Heidelberg and New York, 1970);V. S. Smirnov, B. L. Zhelnov, Zh. Eksp. Teor. Fiz. 57, 2043 (1969),translated in JETP 30, 1108 (1970);see also M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974);M. M-Tehrani, L. Mandel, Opt. Commun. 16, 16 (1976).
[CrossRef]

Korenman, V.

R. F. Chang, V. Korenman, C. O. Alley, R. W. Deten-beck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Mandel, L.

D. Meltzer, L. Mandel, Phys. Rev. A 3, 1763 (1971);D. Meltzer, Photoelectric Investigations of Laser Light (Ph.D. Thesis, University of Rochester, 1970).
[CrossRef]

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958) andProc. Phys. Soc. (London) 74, 233 (1959);Progress in Optics, W. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. 2, p. 181;see also L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

M. M-Tehrani, L. Mandel, Phys. Rev. A (to be published, 1977).

Meltzer, D.

D. Meltzer, L. Mandel, Phys. Rev. A 3, 1763 (1971);D. Meltzer, Photoelectric Investigations of Laser Light (Ph.D. Thesis, University of Rochester, 1970).
[CrossRef]

M-Tehrani, M.

M. M-Tehrani, L. Mandel, Phys. Rev. A (to be published, 1977).

Risken, H.

H. Risken, Z. Phys. 191, 186 (1965);H. Risken, H. D. Vollmer, Z. Phys., 201, 323 (1967);R. D. Hempstead, M. Lax, Phys. Rev. 161, 350 (1967).
[CrossRef]

Phys. Rev. (1)

R. F. Chang, V. Korenman, C. O. Alley, R. W. Deten-beck, Phys. Rev. 178, 612 (1969).
[CrossRef]

Phys. Rev. A (1)

D. Meltzer, L. Mandel, Phys. Rev. A 3, 1763 (1971);D. Meltzer, Photoelectric Investigations of Laser Light (Ph.D. Thesis, University of Rochester, 1970).
[CrossRef]

Proc. Phys. Soc. (London) (1)

L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958) andProc. Phys. Soc. (London) 74, 233 (1959);Progress in Optics, W. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. 2, p. 181;see also L. Mandel, E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

Z. Phys. (2)

H. Risken, Z. Phys. 191, 186 (1965);H. Risken, H. D. Vollmer, Z. Phys., 201, 323 (1967);R. D. Hempstead, M. Lax, Phys. Rev. 161, 350 (1967).
[CrossRef]

H. Haken, Z. Phys. 219, 246 (1969);S. Grossmann, P. H. Richter, Z. Phys 249, 43 (1971);P. H. Richter, S. Grossmann, Z. Phys 255, 59 (1972);S. Grossmann, H. Kümmel, P. H. Richter, Appl. Phys. 1, 257 (1973);R. Graham, W. A. Smith, Opt. Commun. 7, 289 (1973);F. T. Arecchi, A. M. Ricca, Phys. Rev. A 15, 308 (1977).
[CrossRef]

Other (3)

M. M-Tehrani, L. Mandel, Phys. Rev. A (to be published, 1977).

H. Haken, “Laser Theory,” in Handbuch der Physik, S. Flügge, ed. (Springer, Heidelberg and New York, 1970);V. S. Smirnov, B. L. Zhelnov, Zh. Eksp. Teor. Fiz. 57, 2043 (1969),translated in JETP 30, 1108 (1970);see also M. Sargent, M. O. Scully, W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974);M. M-Tehrani, L. Mandel, Opt. Commun. 16, 16 (1976).
[CrossRef]

See Ref. 4 for a list of references.

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Figures (3)

Fig. 1
Fig. 1

Outline of the apparatus. The pulses in both counting channels go to similar counting systems, but only one is shown.

Fig. 2
Fig. 2

The measured values of the light intensities of the two laser modes for various displacements of the knife-edge, which are proportional to the pump parameter a1. The full curves are derived from Eqs. (4) and (5) with Δa = 0.8.

Fig. 3
Fig. 3

The measured values of the relative intensity fluctuations of the two laser modes and the normalized correlation for various displacements of the knife-edge, which are proportional to the pump parameter a1. The full curves are derived from Eqs. (6)(8), with Δa = 0.8.

Equations (8)

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ξ = [ 1 + ( Δ ω T 1 ) 2 ] 1 ,
n i ( n i 1 ) . ( n i r + 1 ) = α i r < T i r > T r , r = 1 , 2 , .
m = α 1 α 2 I 1 I 2 T T R ( 1 + Δ I 1 Δ I 2 / I 1 I 2 ) ,
I 1 = 2 a 2 a 1 + a 1 e ( 1 / 4 ) a 1 2 ( 1 + erf 1 2 a 1 ) + 2 / π e ( 1 / 4 ) a 1 2 ( 1 + erf 1 2 a 1 ) e ( 1 / 4 ) a 2 2 ( 1 + erf 1 2 a 2 ) ,
I 2 = 2 a 1 a 2 + a 2 e ( 1 / 4 ) a 2 2 ( 1 + erf 1 2 a 2 ) + 2 / π e ( 1 / 4 ) a 2 2 ( 1 + erf 1 2 a 2 ) e ( 1 / 4 ) a 1 2 ( 1 + erf 1 2 a 1 ) ,
( Δ I 1 ) 2 = 4 ( a 1 a 2 ) 2 ( I 1 + 2 a 1 a 2 ) 2 + e ( 1 / 4 ) a 1 2 ( 2 + a 1 2 ) ( 1 + erf 1 2 a 1 ) + 2 a 1 / π e ( 1 / 4 ) a 1 2 ( 1 + erf 1 2 a 1 ) e ( 1 / 4 ) a 2 2 ( 1 + erf 1 2 a 2 ) ,
( Δ I 2 ) 2 = 4 ( a 2 a 1 ) 2 ( I 2 + 2 a 2 a 1 ) 2 + e ( 1 / 4 ) a 2 2 ( 2 + a 2 2 ) ( 1 + erf 1 2 a 2 ) + 2 a 2 / π e ( 1 / 4 ) a 2 2 ( 1 + erf 1 2 a 2 ) e ( 1 / 4 ) a 1 2 ( 1 + erf 1 2 a 1 ) ,
Δ I 1 Δ I 2 = 2 ( I 1 I 2 ) a 1 a 2 I 1 I 2 .

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