Abstract

The photon statistics of amplified spontaneous emission in the few-modes regime and in single mode, conditions that are typical of dense wavelength-division multiplexing transmission, have been experimentally proved by direct detection. The dependence of the degeneracy factor for the Bose–Einstein distribution on the degree of second-order coherence of light is stated. The theoretical dependence of the number of amplified spontaneous emission modes on the ratio between the optical channel and the detector bandwidths has also been confirmed by experiments, thus quantifying the loss of validity of asymptotic approximations when they are extended to the few-modes regime.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer-Verlag, Berlin, 2000), pp. 324–330.
  2. W. S. Wong, H. Haus, L. A. Jiang, P. B. Hansen, and M. Margalit, Opt. Lett. 23, 1832 (1998).
    [Crossref]
  3. W. S. Wong, J. D. Moores, J. Korn, and H. Haus, in Optical Fiber Communication, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 265.
  4. R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Oxford, 1983), pp. 219–221 and 261–263.
  5. K. Shimoda, G. Takahashi, and C. H. Townes, Phys. Soc. Jpn. 12, 686 (1957).
    [Crossref]
  6. L. Mandel, Proc. Phys. Soc. London 74, 233 (1959).
    [Crossref]
  7. H. A. Haus and J. A. Mullen, Phys. Rev. A 128, 2407 (1962).
    [Crossref]
  8. B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), p. 178, Eq. (5.4).
  9. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 475–479.
  10. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994), pp. 39–42 and Eq. (3.69).
  11. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 242, Eq. (6.1-20).
  12. P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, in IEEE LEOS 1999 Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2 p. 736.
    [Crossref]
  13. P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
    [Crossref]

2000 (1)

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
[Crossref]

1998 (1)

1962 (1)

H. A. Haus and J. A. Mullen, Phys. Rev. A 128, 2407 (1962).
[Crossref]

1959 (1)

L. Mandel, Proc. Phys. Soc. London 74, 233 (1959).
[Crossref]

1957 (1)

K. Shimoda, G. Takahashi, and C. H. Townes, Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 475–479.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 242, Eq. (6.1-20).

Hansen, P. B.

Haus, H.

W. S. Wong, H. Haus, L. A. Jiang, P. B. Hansen, and M. Margalit, Opt. Lett. 23, 1832 (1998).
[Crossref]

W. S. Wong, J. D. Moores, J. Korn, and H. Haus, in Optical Fiber Communication, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 265.

Haus, H. A.

H. A. Haus and J. A. Mullen, Phys. Rev. A 128, 2407 (1962).
[Crossref]

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer-Verlag, Berlin, 2000), pp. 324–330.

Jiang, L. A.

Korn, J.

W. S. Wong, J. D. Moores, J. Korn, and H. Haus, in Optical Fiber Communication, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 265.

Kumar, P.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
[Crossref]

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, in IEEE LEOS 1999 Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2 p. 736.
[Crossref]

Levandovsky, D.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
[Crossref]

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, in IEEE LEOS 1999 Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2 p. 736.
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Oxford, 1983), pp. 219–221 and 261–263.

Mandel, L.

L. Mandel, Proc. Phys. Soc. London 74, 233 (1959).
[Crossref]

Margalit, M.

Milburn, G. J.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994), pp. 39–42 and Eq. (3.69).

Moores, J. D.

W. S. Wong, J. D. Moores, J. Korn, and H. Haus, in Optical Fiber Communication, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 265.

Mullen, J. A.

H. A. Haus and J. A. Mullen, Phys. Rev. A 128, 2407 (1962).
[Crossref]

Noh, T. G.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
[Crossref]

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, in IEEE LEOS 1999 Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2 p. 736.
[Crossref]

Saleh, B. E. A.

B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), p. 178, Eq. (5.4).

Shimoda, K.

K. Shimoda, G. Takahashi, and C. H. Townes, Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Takahashi, G.

K. Shimoda, G. Takahashi, and C. H. Townes, Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Townes, C. H.

K. Shimoda, G. Takahashi, and C. H. Townes, Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Vasilyev, M.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
[Crossref]

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, in IEEE LEOS 1999 Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2 p. 736.
[Crossref]

Voss, P.

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
[Crossref]

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, in IEEE LEOS 1999 Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2 p. 736.
[Crossref]

Walls, D. F.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994), pp. 39–42 and Eq. (3.69).

Wong, W. S.

W. S. Wong, H. Haus, L. A. Jiang, P. B. Hansen, and M. Margalit, Opt. Lett. 23, 1832 (1998).
[Crossref]

W. S. Wong, J. D. Moores, J. Korn, and H. Haus, in Optical Fiber Communication, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 265.

IEEE Photon. Technol. Lett. (1)

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, IEEE Photon. Technol. Lett. 12, 1340 (2000).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

H. A. Haus and J. A. Mullen, Phys. Rev. A 128, 2407 (1962).
[Crossref]

Phys. Soc. Jpn. (1)

K. Shimoda, G. Takahashi, and C. H. Townes, Phys. Soc. Jpn. 12, 686 (1957).
[Crossref]

Proc. Phys. Soc. London (1)

L. Mandel, Proc. Phys. Soc. London 74, 233 (1959).
[Crossref]

Other (8)

W. S. Wong, J. D. Moores, J. Korn, and H. Haus, in Optical Fiber Communication, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 265.

R. Loudon, The Quantum Theory of Light, 2nd ed. (Oxford U. Press, Oxford, 1983), pp. 219–221 and 261–263.

B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), p. 178, Eq. (5.4).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 475–479.

D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994), pp. 39–42 and Eq. (3.69).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 242, Eq. (6.1-20).

P. Voss, M. Vasilyev, D. Levandovsky, T. G. Noh, and P. Kumar, in IEEE LEOS 1999 Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 1999), Vol. 2 p. 736.
[Crossref]

H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer-Verlag, Berlin, 2000), pp. 324–330.

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 (3)

Fig. 1
Fig. 1

Directly detected photon-count probability distribution for single-mode ASE on a logarithmic scale compared with the nondegenerate Bose–Einstein distribution. The experimental setup, optimized for measurement in single-mode condition, is shown schematically in the inset; two fiber-optic filters are used to select a single resonance peak of the FP transfer function. PD, photodiode; OAs, optical amplifiers.

Fig. 2
Fig. 2

Number of ASE modes M as functions of the ratio between optical and electrical bandwidths for both polarized and unpolarized ASE. The experimental data are compared with the theoretical predictions. In particular, for detection of polarized ASE with Bopt=18 GHz and Bel=11 GHz the measured number of modes is 2.03, equal to the value obtained by Eq. (8) and greater than the ratio Bopt/Bel=1.64.

Fig. 3
Fig. 3

Parameter gT20 as a function of the ratio between optical and electrical bandwidths for both polarized and unpolarized ASE. The experimental data are compared with the theoretical predictions.

Equations (8)

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

Pn;n¯,M= Γn+MΓn+1ΓM×1+Mn¯-n1+n¯M-M,
Δn2=n¯+n¯2/M.
gT20=1T2-T+TT-τg2τdτ,
gT20=1+Δn2-n¯n¯2.
M=1/gT20-1.
τc=-+g1τ2dτ
g2τpol=1+g1τ2.
Mpol=πBopt/Bel2exp-πBopt/Bel2-1+πBopt/Bel erfπBopt/Bel,

Metrics