Abstract

Abstract

Although a considerable number of multimode fiber (MMF) links operate in a wavelength region around 850 nm where chromatic dispersion of a given modal group µ is described adequately by the second derivative β2µ of the propagation constant βµ(ω), there is also an increasing interest in MMF links transmitting in the second spectral window (@1300nm) where this second derivative vanishes being thus necessary to consider the third derivative β3µ in the evaluation of the transfer function of the multimode fiber link. We present in this paper, for the first time to our knowledge, an analytical model for the transfer function of a multimode fiber (MMF) optic link taken into account the impact of third-order dispersion. The model extends the operation of a previously reported one for second-order dispersion. Our results show that the performance of broadband radio over fiber transmission through middle-reach distances can be improved by working at the minimum-dispersion wavelength as long as low-linewidth lasers are employed.

©2007 Optical Society of America

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References

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  1. I. Gasulla and J. Capmany, “Transfer function of multimode fiber links using an electric field propagation model: Application to Radio over Fibre Systems,” Opt. Express 14, 9051–9070 (2006).
    [Crossref] [PubMed]
  2. I. Gasulla and J. Capmany, “Analysis of the harmonic and intermodulation distortion in a multimode fiber optic link,” Opt. Express 15, 9366–9371 (2007).
    [Crossref] [PubMed]
  3. M. Miyagi and S. Nishida, “Pulse spreading in a single-mode fiber due to third-order dispersion,” Appl. Opt. 18, 678–682 (1979).
    [Crossref] [PubMed]
  4. M. Miyagi and S. Nishida, “Pulse spreading in a single-mode optical fiber due to third-order dispersion: effect of optical source bandwidth,” Appl. Opt. 18, 2237–2240 (1979).
    [Crossref] [PubMed]
  5. D. Marcuse, “Pulse Distortion in single-mode fibers,” Appl. Opt. 19, 1653–1660 (1980).
    [Crossref] [PubMed]
  6. L. G. Cohen, W. L. Mammel, and S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. 18, 49–53 (1982).
    [Crossref]
  7. E. Hellström, H. Sunnerud, M. Westlund, and M. Karlsson, “Third-Order Dispersion Compensation Using a Phase Modulator,” J. Lightwave Technol. 21, 1188–1197 (2003).
    [Crossref]
  8. S. Kumar, “Compensation of third-order dispersion using time reversal in optical transmission systems,” Opt. Lett. 32, 346–348 (2007).
    [Crossref] [PubMed]
  9. TIA/EIA-455-168, “Chromatic dispersion measurement of multimode graded-index and single-mode optical fibers by spectral group delay measurement in the time domain.”
  10. G. D. Brown, “Chromatic Dispersion Measurement in Graded-Index Multimode Optical Fibers,” J. Lightwave Technol. 12, 1907–1909 (1994).
    [Crossref]

2007 (2)

2006 (1)

2003 (1)

1994 (1)

G. D. Brown, “Chromatic Dispersion Measurement in Graded-Index Multimode Optical Fibers,” J. Lightwave Technol. 12, 1907–1909 (1994).
[Crossref]

1982 (1)

L. G. Cohen, W. L. Mammel, and S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. 18, 49–53 (1982).
[Crossref]

1980 (1)

1979 (2)

Brown, G. D.

G. D. Brown, “Chromatic Dispersion Measurement in Graded-Index Multimode Optical Fibers,” J. Lightwave Technol. 12, 1907–1909 (1994).
[Crossref]

Capmany, J.

Cohen, L. G.

L. G. Cohen, W. L. Mammel, and S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. 18, 49–53 (1982).
[Crossref]

Gasulla, I.

Hellström, E.

Karlsson, M.

Kumar, S.

Lumish, S.

L. G. Cohen, W. L. Mammel, and S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. 18, 49–53 (1982).
[Crossref]

Mammel, W. L.

L. G. Cohen, W. L. Mammel, and S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. 18, 49–53 (1982).
[Crossref]

Marcuse, D.

Miyagi, M.

Nishida, S.

Sunnerud, H.

Westlund, M.

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

L. G. Cohen, W. L. Mammel, and S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. 18, 49–53 (1982).
[Crossref]

J. Lightwave Technol. (2)

E. Hellström, H. Sunnerud, M. Westlund, and M. Karlsson, “Third-Order Dispersion Compensation Using a Phase Modulator,” J. Lightwave Technol. 21, 1188–1197 (2003).
[Crossref]

G. D. Brown, “Chromatic Dispersion Measurement in Graded-Index Multimode Optical Fibers,” J. Lightwave Technol. 12, 1907–1909 (1994).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Other (1)

TIA/EIA-455-168, “Chromatic dispersion measurement of multimode graded-index and single-mode optical fibers by spectral group delay measurement in the time domain.”

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Figures (3)

Fig. 1.
Fig. 1. Influence of the temporal coherence of the source on the frequency response of a 5 Km MMF link for second and third order dispersions.
Fig. 2.
Fig. 2. Evaluation of the transfer function for different link lengths for second and third order dispersions.
Fig. 3.
Fig. 3. Evaluation of the transfer function for different source chirps for second and third order dispersions.

Equations (14)

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β μ ( ω ) β μ ( ω o ) + d β μ ( ω ) d ω ω = ω o ( ω ω o ) + 1 2 ! d β μ 2 ( ω ) d ω 2 ω = ω o ( ω ω o ) 2 + 1 3 ! d β μ 3 ( ω ) d ω 3 ω = ω o ( ω ω o ) 3
= β μ 0 + β μ 1 ( ω ω o ) + 1 2 ! β μ 2 ( ω ω o ) + 1 3 ! β μ 3 ( ω ω o ) 3 .
H μ μ ( ω ) = e Γ μ ( ω ) z = e α μ 0 z · e j [ β μ 0 + β μ 1 ( ω ω o ) + β μ 3 6 ( ω ω o ) 3 ] z
H μ ν ( ω ) = K ̂ μ ν [ 0 z f ( z ) d z ] Φ μ ν ( ω ) , μ ν
Φ μ ν ( ω ) = e Γ μ ( ω ) z e Γ ν ( ω ) z [ Γ ν ( ω ) Γ μ ( ω ) ] · z e Γ μ ( ω ) z e Γ ν ( ω ) z [ α ν 0 α μ 0 + j ( β ν 0 β μ 0 ) ] · z
S 0 = ( 2 π c λ 0 2 ) 2 β 0 3 ,
h μ μ ( t ) = 1 2 π H μ μ ( ω ) · e j ω t d ω and Φ μ ν ( t ) = 1 2 π Φ μ ν ( ω ) · e j ω t d ω
P U ( t ) = ν = 1 N ν ' = 1 N C ν ν D ν ν S * ( t ) S ( t ) · R ( t , t ) · h ν ν * ( t t ) h ν ' ν ' ( t t ) · dt dt
S ( t ) = P { 1 + m o 4 ( 1 + j α ) cos ( Ω t ) }
P C ( t ) = g 2 S * ( t ) S ( t ) · R ( t , t ) .
· μ = 1 N ν = 1 ν μ N μ = 1 N ν = 1 ν μ N C μ μ D ν ν K ̂ μ ν * K ̂ μ ν * · Φ μ ν * ( t t ) Φ μ ν ( t t ) · dt dt
H 3 rd ( Ω ) = 1 + α 2 · [ 1 + ( Ω β o 2 z σ c 2 ) 2 ] 1 4 · e Ω 4 8 · σ c 2 Ω 2 + ( σ c 2 β o 3 z ) 2 · e j arctg ( Ω β o 3 z σ c 2 ) 2 · e j Ω 3 β o 3 z 24 · 1 + 4 ( σ c 2 Ω β o 3 z ) 2 1 + ( σ c 2 Ω β o 3 z ) 2 .
· m = 1 M 2 m · ( C mm + G mm ) · e 2 α m z · e j Ω τ m
H 2 nd ( Ω ) = 1 + α 2 · e 1 2 ( β o 2 z Ω σ c ) 2 · cos ( β o 2 z Ω 2 2 + arctan ( α ) ) · m = 1 M 2 m · ( C mm + G mm ) · e 2 α m z · e j Ω τ m

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