Abstract

An exact result for the spectral density of intensity variations that occur after propagation of ergodic light in a medium having lowest-order-only group-velocity dispersion is obtained and applied to the problem of semiconductor laser phase noise to intensity noise conversion in a single-mode optical fiber. It is shown that the intensity spectrum after propagation formally approaches, for a large laser linewidth or a long (or high-dispersion) fiber, the intensity spectrum of a thermal source having the same line shape as the laser.

© 2000 Optical Society of America

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References

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  1. A. Chraplyvy, R. Tkach, L. Buhl, and R. Alferness, Electron. Lett. 22, 409 (1986).
    [CrossRef]
  2. S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
    [CrossRef]
  3. J. Wang and K. Petermann, J. Lightwave Technol. 10, 96 (1992).
    [CrossRef]
  4. K. Petermann, Electron. Lett. 26, 2097 (1990).
    [CrossRef]
  5. W. K. Marshall and A. Yariv, “Spectrum of the intensity of modulated noisy light after propagation in dispersive fiber,” IEEE Photon. Technol. Lett. (to be published).
  6. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  7. It is useful to note that β0″zΩΔω≪1 implies that either β0″zΩ2≪1 or Δω/Ω≪1.

1992

J. Wang and K. Petermann, J. Lightwave Technol. 10, 96 (1992).
[CrossRef]

1990

K. Petermann, Electron. Lett. 26, 2097 (1990).
[CrossRef]

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
[CrossRef]

1986

A. Chraplyvy, R. Tkach, L. Buhl, and R. Alferness, Electron. Lett. 22, 409 (1986).
[CrossRef]

Alferness, R.

A. Chraplyvy, R. Tkach, L. Buhl, and R. Alferness, Electron. Lett. 22, 409 (1986).
[CrossRef]

Buhl, L.

A. Chraplyvy, R. Tkach, L. Buhl, and R. Alferness, Electron. Lett. 22, 409 (1986).
[CrossRef]

Chraplyvy, A.

A. Chraplyvy, R. Tkach, L. Buhl, and R. Alferness, Electron. Lett. 22, 409 (1986).
[CrossRef]

Edagawa, N.

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Marshall, W. K.

W. K. Marshall and A. Yariv, “Spectrum of the intensity of modulated noisy light after propagation in dispersive fiber,” IEEE Photon. Technol. Lett. (to be published).

Petermann, K.

J. Wang and K. Petermann, J. Lightwave Technol. 10, 96 (1992).
[CrossRef]

K. Petermann, Electron. Lett. 26, 2097 (1990).
[CrossRef]

Taga, H.

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
[CrossRef]

Tkach, R.

A. Chraplyvy, R. Tkach, L. Buhl, and R. Alferness, Electron. Lett. 22, 409 (1986).
[CrossRef]

Wakabayashi, H.

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
[CrossRef]

Wang, J.

J. Wang and K. Petermann, J. Lightwave Technol. 10, 96 (1992).
[CrossRef]

Yamamoto, S.

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
[CrossRef]

Yariv, A.

W. K. Marshall and A. Yariv, “Spectrum of the intensity of modulated noisy light after propagation in dispersive fiber,” IEEE Photon. Technol. Lett. (to be published).

Yoshida, Y.

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
[CrossRef]

Electron. Lett.

K. Petermann, Electron. Lett. 26, 2097 (1990).
[CrossRef]

A. Chraplyvy, R. Tkach, L. Buhl, and R. Alferness, Electron. Lett. 22, 409 (1986).
[CrossRef]

J. Lightwave Technol.

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, J. Lightwave Technol. 8, 1716 (1990).
[CrossRef]

J. Wang and K. Petermann, J. Lightwave Technol. 10, 96 (1992).
[CrossRef]

Other

W. K. Marshall and A. Yariv, “Spectrum of the intensity of modulated noisy light after propagation in dispersive fiber,” IEEE Photon. Technol. Lett. (to be published).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

It is useful to note that β0″zΩΔω≪1 implies that either β0″zΩ2≪1 or Δω/Ω≪1.

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Figures (2)

Fig. 1
Fig. 1

RIN from Eq. (13) plotted versus frequency, f=Ω/2π, for linewidths Δω/2π=1 GHz, 100 MHz, 10 MHz, 1 MHz and β0z=1000 ps2 (equivalent to 50 km of standard single-mode fiber at 1550 nm).

Fig. 2
Fig. 2

RIN from Eq. (13) plotted versus frequency, f=Ω/2π, for β0z=60000, 6000, 600 ps2 and linewidth Δω/2π=30 MHz. The equivalent distances in standard single-mode fiber would be z30, 300, 3000 km.

Equations (16)

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RINΩ,z=4SΔΔΩcos2 θ-Re SΔϕΩsin 2θ+SϕϕΩsin2 θ,
Ez+β0Et-i2β02Et2=0,
Et,z=i2πβ0z1/2-E0t+sexpis22β0zds,
SIIΩ,z=2-I0,zIτ,zexp-iΩτdτ,
I0,zIτ,z=14π2β02z2×E0*s1E0s2E0*τ+s3E0τ+s4×expi-s12+s22-s32+s422β0zds1ds2ds3ds4,
SIIΩ,z=2-E0*0E0β0zΩE0*β0zΩ+uE0u×exp-iΩudu.
E0*t1E0t2E0*t3E0t4=E0*t1E0t2×E0*t3E0t4+E0*t1E0t4E0*t3E0t2.
SIIΩ,z=2-E0*0E0β0zΩ2+E0*0E0u2exp-iΩudu=4πE0*t22δΩ+14π-SE0*E0ωSE0*E0ω-Ωdω,
E0*t1E0t2=I0expiψt1,t22=I0 exp-ψt1,t22/2.
ψt1,t2+ψt3,t42=p=13q=p3-1p+qψtp,tq+12
E0*t1E0t2E0*t3E0t4=I02p=13q=p3×exp-1p+q+12ψtp,tq+12.
RINΩ,z=2 exp-ψ0,β0zΩ2-exp-iΩu×expψ0,u-β0zΩ22+ψ0,u+β0zΩ22-ψ0,u2-1du,
RINΩ,z=4ΔωΔω2+Ω21-exp-Δωβ0zΩ×cosΩβ0zΩ+ΔωΩsinΩβ0zΩ.
RINΩ,z8ΔωΩ2sin212β0zΩ2,
RINΩ,z4ΔωΔω2+Ω2,
SIIΩ,z=2-exp-iΩuE0*0E0u-E0*0E0uE0*β0zΩ+u×E0β0zΩ-E0*uE00du+2-E0*0E0u2 exp-iΩudu.

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