Abstract

A novel analysis is given on the statistics of modal noise for a graded-index multimode fiber (MMF) link excited by an analog intensity modulated laser diode. We present the speckle contrast as a function of the power spectrum of the modulated source and the transfer function of the MMF which behaves as an imperfect transversal microwave photonic filter. The theoretical results confirm that the modal noise is directly connected with the coherence properties of the optical source and show that the performance of high-frequency Radio Over Fiber (ROF) transmission through MMF links for short and middle reach distances is not substantially degraded by modal noise.

©2008 Optical Society of America

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References

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  1. R. E. Epworth, “The phenomenon of modal noise in analog and digital optical fiber systems,” in Proceedings of Fourth European Conference and Exhibition on Optical Communication (1978), pp. 492–501.
  2. B. Daino, G. de Marchis, and S. Piazzolla, “Analysis and measurement of modal noise in an optical fibre,” Electron. Lett. 15, 755–756 (1979).
    [Crossref]
  3. E.G. Rawson, J.W. Goodman, and R.E. Norton, “Analysis and measurement of the modal-noise probability distribution for a step-index optical fiber,” Opt. Lett. 5, 357–358 (1980).
    [Crossref] [PubMed]
  4. E.G. Rawson, J.W. Goodman, and R.E. Norton, “Frequency dependence of modal noise in multimode fiber,” J. Opt. Soc. Am. 70, 968–976 (1980).
    [Crossref]
  5. B. Moslehi, J. W. Goodman, and E. G. Rawson, “Bandwidth estimation for multimode optical fibers using the frequency correlation function of speckle patterns,” Appl. Opt. 22, 995–999 (1983).
    [Crossref] [PubMed]
  6. T. Kanada and K. Aoyama, “Modal-noise evaluation in multimode-fiber transmission,” Opt. Lett. 8, 339–341 (1983).
    [Crossref] [PubMed]
  7. B. Crosignani and A. Yariv, “Statistical properties of modal noise in fiber-laser systems,” J. Opt. Soc. Am. 73, 1022–1027 (1983).
    [Crossref]
  8. J. Weierholt, E. G. Rawson, and J. W. Goodman, “Frequency-correlation properties of optical waveguide intensity patterns,” J. Opt. Soc. Am. A 1, 201–205 (1984).
    [Crossref]
  9. T. Kanada, “Evaluation of Modal Noise in Multimode Fiber-optic Systems,” J. Lightwave Technol. 5, 11–18 (1984).
    [Crossref]
  10. R. Dandliker, A. Bertholds, and F. Maystre, “How Modal Noise in Multimode Fibers Depends on Source Spectrum and Fiber Dispersion,” J. Lightwave Technol. 3, 7–12 (1985).
    [Crossref]
  11. M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link Due to Modal Noise,” J. Sel. Areas Commun. 4, 1515–1521 (1986).
    [Crossref]
  12. J. Ohtsubo and M. Kourogi, “Frequency Correlation Function of Modal Noise in Multimode Optical Fibers,” J. Lightwave Technol. 7, 1300–1307 (1989).
    [Crossref]
  13. P. Pepeljugoski, D. Kutchta, and A. Risteski, “Modal Noise BER Calculations in 10-Gb/s in Multimode Fiber LAN Links,” IEEE Photon. Technol. Lett. 17, 2586–2588 (2005).
    [Crossref]
  14. 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]
  15. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23, 702–723 (2005).
    [Crossref]
  16. D. Wake, S. Dupont, J. P. Vilcot, and A. J. Seeds, “32-QAM Radio transmission over multimode fibre beyond the fibre bandwidth,” in Proceedings of Microwave Photonics 2001, (California, USA, 2001), 4 pp.
  17. P. Hartmann, Xin Qian, A. Wonfor, R. V. Penty, and I. H White, “1–20 GHz Directly Modulated Radio over MMF Link,” in Proceedings of Microwave Photonics 2005, (Seoul, South Korea, 2005), pp. 95–98.
  18. I. Gasulla and J. Capmany, “High-frequency Radio over fibre QPSK transmission through a 5 Km Multimode Fibre link,” in Proceedings of 33rd European Conference and Exhibition on Optical Communication, (Berlin, Germany, 2007), pp. .

2006 (1)

2005 (2)

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23, 702–723 (2005).
[Crossref]

P. Pepeljugoski, D. Kutchta, and A. Risteski, “Modal Noise BER Calculations in 10-Gb/s in Multimode Fiber LAN Links,” IEEE Photon. Technol. Lett. 17, 2586–2588 (2005).
[Crossref]

1989 (1)

J. Ohtsubo and M. Kourogi, “Frequency Correlation Function of Modal Noise in Multimode Optical Fibers,” J. Lightwave Technol. 7, 1300–1307 (1989).
[Crossref]

1986 (1)

M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link Due to Modal Noise,” J. Sel. Areas Commun. 4, 1515–1521 (1986).
[Crossref]

1985 (1)

R. Dandliker, A. Bertholds, and F. Maystre, “How Modal Noise in Multimode Fibers Depends on Source Spectrum and Fiber Dispersion,” J. Lightwave Technol. 3, 7–12 (1985).
[Crossref]

1984 (2)

1983 (3)

1980 (2)

1979 (1)

B. Daino, G. de Marchis, and S. Piazzolla, “Analysis and measurement of modal noise in an optical fibre,” Electron. Lett. 15, 755–756 (1979).
[Crossref]

Aoyama, K.

Bertholds, A.

R. Dandliker, A. Bertholds, and F. Maystre, “How Modal Noise in Multimode Fibers Depends on Source Spectrum and Fiber Dispersion,” J. Lightwave Technol. 3, 7–12 (1985).
[Crossref]

Capmany, J.

Crosignani, B.

Daino, B.

B. Daino, G. de Marchis, and S. Piazzolla, “Analysis and measurement of modal noise in an optical fibre,” Electron. Lett. 15, 755–756 (1979).
[Crossref]

Dandliker, R.

R. Dandliker, A. Bertholds, and F. Maystre, “How Modal Noise in Multimode Fibers Depends on Source Spectrum and Fiber Dispersion,” J. Lightwave Technol. 3, 7–12 (1985).
[Crossref]

de Marchis, G.

B. Daino, G. de Marchis, and S. Piazzolla, “Analysis and measurement of modal noise in an optical fibre,” Electron. Lett. 15, 755–756 (1979).
[Crossref]

Dupont, S.

D. Wake, S. Dupont, J. P. Vilcot, and A. J. Seeds, “32-QAM Radio transmission over multimode fibre beyond the fibre bandwidth,” in Proceedings of Microwave Photonics 2001, (California, USA, 2001), 4 pp.

Epworth, R. E.

R. E. Epworth, “The phenomenon of modal noise in analog and digital optical fiber systems,” in Proceedings of Fourth European Conference and Exhibition on Optical Communication (1978), pp. 492–501.

Gasulla, I.

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]

I. Gasulla and J. Capmany, “High-frequency Radio over fibre QPSK transmission through a 5 Km Multimode Fibre link,” in Proceedings of 33rd European Conference and Exhibition on Optical Communication, (Berlin, Germany, 2007), pp. .

Goodman, J. W.

Goodman, J.W.

Hartmann, P.

P. Hartmann, Xin Qian, A. Wonfor, R. V. Penty, and I. H White, “1–20 GHz Directly Modulated Radio over MMF Link,” in Proceedings of Microwave Photonics 2005, (Seoul, South Korea, 2005), pp. 95–98.

Kanada, T.

T. Kanada, “Evaluation of Modal Noise in Multimode Fiber-optic Systems,” J. Lightwave Technol. 5, 11–18 (1984).
[Crossref]

T. Kanada and K. Aoyama, “Modal-noise evaluation in multimode-fiber transmission,” Opt. Lett. 8, 339–341 (1983).
[Crossref] [PubMed]

Koonen, M. J.

M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link Due to Modal Noise,” J. Sel. Areas Commun. 4, 1515–1521 (1986).
[Crossref]

Kourogi, M.

J. Ohtsubo and M. Kourogi, “Frequency Correlation Function of Modal Noise in Multimode Optical Fibers,” J. Lightwave Technol. 7, 1300–1307 (1989).
[Crossref]

Kutchta, D.

P. Pepeljugoski, D. Kutchta, and A. Risteski, “Modal Noise BER Calculations in 10-Gb/s in Multimode Fiber LAN Links,” IEEE Photon. Technol. Lett. 17, 2586–2588 (2005).
[Crossref]

Maystre, F.

R. Dandliker, A. Bertholds, and F. Maystre, “How Modal Noise in Multimode Fibers Depends on Source Spectrum and Fiber Dispersion,” J. Lightwave Technol. 3, 7–12 (1985).
[Crossref]

Moslehi, B.

Norton, R.E.

Ohtsubo, J.

J. Ohtsubo and M. Kourogi, “Frequency Correlation Function of Modal Noise in Multimode Optical Fibers,” J. Lightwave Technol. 7, 1300–1307 (1989).
[Crossref]

Ortega, B.

Pastor, D.

Penty, R. V.

P. Hartmann, Xin Qian, A. Wonfor, R. V. Penty, and I. H White, “1–20 GHz Directly Modulated Radio over MMF Link,” in Proceedings of Microwave Photonics 2005, (Seoul, South Korea, 2005), pp. 95–98.

Pepeljugoski, P.

P. Pepeljugoski, D. Kutchta, and A. Risteski, “Modal Noise BER Calculations in 10-Gb/s in Multimode Fiber LAN Links,” IEEE Photon. Technol. Lett. 17, 2586–2588 (2005).
[Crossref]

Piazzolla, S.

B. Daino, G. de Marchis, and S. Piazzolla, “Analysis and measurement of modal noise in an optical fibre,” Electron. Lett. 15, 755–756 (1979).
[Crossref]

Qian, Xin

P. Hartmann, Xin Qian, A. Wonfor, R. V. Penty, and I. H White, “1–20 GHz Directly Modulated Radio over MMF Link,” in Proceedings of Microwave Photonics 2005, (Seoul, South Korea, 2005), pp. 95–98.

Rawson, E. G.

Rawson, E.G.

Risteski, A.

P. Pepeljugoski, D. Kutchta, and A. Risteski, “Modal Noise BER Calculations in 10-Gb/s in Multimode Fiber LAN Links,” IEEE Photon. Technol. Lett. 17, 2586–2588 (2005).
[Crossref]

Sales, S.

Seeds, A. J.

D. Wake, S. Dupont, J. P. Vilcot, and A. J. Seeds, “32-QAM Radio transmission over multimode fibre beyond the fibre bandwidth,” in Proceedings of Microwave Photonics 2001, (California, USA, 2001), 4 pp.

Vilcot, J. P.

D. Wake, S. Dupont, J. P. Vilcot, and A. J. Seeds, “32-QAM Radio transmission over multimode fibre beyond the fibre bandwidth,” in Proceedings of Microwave Photonics 2001, (California, USA, 2001), 4 pp.

Wake, D.

D. Wake, S. Dupont, J. P. Vilcot, and A. J. Seeds, “32-QAM Radio transmission over multimode fibre beyond the fibre bandwidth,” in Proceedings of Microwave Photonics 2001, (California, USA, 2001), 4 pp.

Weierholt, J.

White, I. H

P. Hartmann, Xin Qian, A. Wonfor, R. V. Penty, and I. H White, “1–20 GHz Directly Modulated Radio over MMF Link,” in Proceedings of Microwave Photonics 2005, (Seoul, South Korea, 2005), pp. 95–98.

Wonfor, A.

P. Hartmann, Xin Qian, A. Wonfor, R. V. Penty, and I. H White, “1–20 GHz Directly Modulated Radio over MMF Link,” in Proceedings of Microwave Photonics 2005, (Seoul, South Korea, 2005), pp. 95–98.

Yariv, A.

Appl. Opt. (1)

Electron. Lett. (1)

B. Daino, G. de Marchis, and S. Piazzolla, “Analysis and measurement of modal noise in an optical fibre,” Electron. Lett. 15, 755–756 (1979).
[Crossref]

IEEE Photon. Technol. Lett. (1)

P. Pepeljugoski, D. Kutchta, and A. Risteski, “Modal Noise BER Calculations in 10-Gb/s in Multimode Fiber LAN Links,” IEEE Photon. Technol. Lett. 17, 2586–2588 (2005).
[Crossref]

J. Lightwave Technol. (4)

T. Kanada, “Evaluation of Modal Noise in Multimode Fiber-optic Systems,” J. Lightwave Technol. 5, 11–18 (1984).
[Crossref]

R. Dandliker, A. Bertholds, and F. Maystre, “How Modal Noise in Multimode Fibers Depends on Source Spectrum and Fiber Dispersion,” J. Lightwave Technol. 3, 7–12 (1985).
[Crossref]

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23, 702–723 (2005).
[Crossref]

J. Ohtsubo and M. Kourogi, “Frequency Correlation Function of Modal Noise in Multimode Optical Fibers,” J. Lightwave Technol. 7, 1300–1307 (1989).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Sel. Areas Commun. (1)

M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link Due to Modal Noise,” J. Sel. Areas Commun. 4, 1515–1521 (1986).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Other (4)

R. E. Epworth, “The phenomenon of modal noise in analog and digital optical fiber systems,” in Proceedings of Fourth European Conference and Exhibition on Optical Communication (1978), pp. 492–501.

D. Wake, S. Dupont, J. P. Vilcot, and A. J. Seeds, “32-QAM Radio transmission over multimode fibre beyond the fibre bandwidth,” in Proceedings of Microwave Photonics 2001, (California, USA, 2001), 4 pp.

P. Hartmann, Xin Qian, A. Wonfor, R. V. Penty, and I. H White, “1–20 GHz Directly Modulated Radio over MMF Link,” in Proceedings of Microwave Photonics 2005, (Seoul, South Korea, 2005), pp. 95–98.

I. Gasulla and J. Capmany, “High-frequency Radio over fibre QPSK transmission through a 5 Km Multimode Fibre link,” in Proceedings of 33rd European Conference and Exhibition on Optical Communication, (Berlin, Germany, 2007), pp. .

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Figures (4)

Fig. 1.
Fig. 1. Layout of the multimode fiber optic link.
Fig. 2.
Fig. 2. Influence of the modulation index on the speckle contrast for different link lengths.
Fig. 3.
Fig. 3. Influence of the source linewidth on the speckle contrast for a MMF link up to 5 Km.
Fig. 4.
Fig. 4. Simulated speckle contrast for a 5 Km link and different launch conditions.

Equations (11)

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

γ 2 = σ 2 I D 2 = I D 2 I D 2 I D 2
γ 2 = C p ( ν ) H f ( ν ) 2 dv
C P ( ν ) = 1 I D 2 P ( ν ) P ( ν ν ) dv ,
H f ( ν ) = μ = 1 N C μ μ e 2 α μ z e j 2 π τ μ ν , for μ = 1 to N modes
s ( t ) = A [ 1 + m o 4 ( 1 + j α c ) cos ( Ω t ) ] ,
P ( ω , 0 ) = E ˜ ( ω , 0 ) 2 = A { P s ( ω ) + m o 2 64 ( 1 + α c 2 ) [ P s ( ω Ω ) + P s ( ω + Ω ) ] } ,
P s ( ω ) = P π W e ω 2 ( 2 W ) 2
C P ( ω ) = ( P · A ) 2 π 2 · W I D 2 { ( 1 + 2 B 2 ) e ω 2 8 W 2 + 2 B [ e ( ω Ω ) 2 8 W 2 + e ( ω + Ω ) 2 8 W 2 ] + B 2 [ e ( ω 2 Ω ) 8 W 2 2 + e ( ω + 2 Ω ) 8 W 2 2 ] }
B = m o 2 64 ( 1 + α c 2 ) .
γ 2 = 1 ( 1 + 2 B ) 2 m = 1 M n = 1 M 4 m n C mm C nn m = 1 M n = 1 M 4 m n C mm C nn e 2 ( α m + α n ) z e 2 ( τ m τ n ) 2 W 2 · · { 1 + 2 B 2 + 4 B cos [ ( τ m τ n ) Ω ] + 2 B 2 cos [ ( τ m τ n ) 2 Ω ] } , m n
SNR = I D σ = 1 γ

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