Abstract

We present an analytical evaluation of the harmonic and the intermodulation distortion effects produced in the transmission of an analog signal composed of various RF tones through a multimode fiber link. It is based on the electric field propagation model previously published by the authors. Results show the possibility of implementing subcarrier multiplexing techniques (SCM) with Composite Second Order (CSO) values below -50 dBc over short and middle reach multimode fiber links.

©2007 Optical Society of America

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References

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  1. A. M. J. Koonen, A. Ng’Oma, H. P. A. van den Boom, I. Tafur Monroy, and G. D. Khoe, “New techniques for extending the capabilities of multimode fibre networks,” in Proceedings of NOC, (2003), pp. 204–211.
  2. H. R. Stuart, “Dispersive multiplexing in multimode fiber,” Science 289, 305–307 (2000).
    [Crossref]
  3. S. Kanprachar and I. Jacobs, “Diversity of coding for subcarrier multiplexing on multimode fibers,” IEEE Trans. Commun. 51, 1546–1553 (2003).
    [Crossref]
  4. X. J. Gu, W. Mohammed, and P. W. Smith, “Demonstration of all-fiber WDM for multimode fiber local area networks,” IEEE Photon. Technol. Lett. 18, 244–246 (2006).
    [Crossref]
  5. E. J. Tyler, P. Kourtessis, M. Webster, E. Rochart, T. Quinlan, S. E. M. Dudley, S. D. Walker, R. V. Penty, and I. H. White, “Toward terabit-per-second capacities over multimode fiber links using SCM/WDM techniques,” J. Lightwave Technol. 21, 3237–3243 (2003).
    [Crossref]
  6. A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, and B. Jalali, “Coherent Optical MIMO (COMIMO),” J. Lightwave Technol. 23, 2410–2419 (2005).
    [Crossref]
  7. G. Yabre, “Comprehensive Theory of Dispersion in Graded-Index Optical Fibers,” J. Lightwave Technol. 18, 166–177 (2000).
    [Crossref]
  8. 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]
  9. B. E. A. Saleh and R. M. Abdula, “Optical Interference and Pulse Propagation in Multimode Fibers,” Fiber Integr. Opt. 5, 161–201 (1985).
    [Crossref]
  10. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J.Lightwave Technol. 23, 702–723 (2005).
    [Crossref]
  11. C. S. Ih and W. Gu, “Fiber Induced Distortions in a Subcarrier Multiplexed Lightwave System,” IEEE J. Sel. Areas Commun. 8, 1296–1303 (1990).
    [Crossref]

2006 (2)

X. J. Gu, W. Mohammed, and P. W. Smith, “Demonstration of all-fiber WDM for multimode fiber local area networks,” IEEE Photon. Technol. Lett. 18, 244–246 (2006).
[Crossref]

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]

2005 (2)

A. R. Shah, R. C. J. Hsu, A. Tarighat, A. H. Sayed, and B. Jalali, “Coherent Optical MIMO (COMIMO),” J. Lightwave Technol. 23, 2410–2419 (2005).
[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]

2003 (2)

2000 (2)

1990 (1)

C. S. Ih and W. Gu, “Fiber Induced Distortions in a Subcarrier Multiplexed Lightwave System,” IEEE J. Sel. Areas Commun. 8, 1296–1303 (1990).
[Crossref]

1985 (1)

B. E. A. Saleh and R. M. Abdula, “Optical Interference and Pulse Propagation in Multimode Fibers,” Fiber Integr. Opt. 5, 161–201 (1985).
[Crossref]

Abdula, R. M.

B. E. A. Saleh and R. M. Abdula, “Optical Interference and Pulse Propagation in Multimode Fibers,” Fiber Integr. Opt. 5, 161–201 (1985).
[Crossref]

Capmany, J.

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]

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

Dudley, S. E. M.

Gasulla, I.

Gu, W.

C. S. Ih and W. Gu, “Fiber Induced Distortions in a Subcarrier Multiplexed Lightwave System,” IEEE J. Sel. Areas Commun. 8, 1296–1303 (1990).
[Crossref]

Gu, X. J.

X. J. Gu, W. Mohammed, and P. W. Smith, “Demonstration of all-fiber WDM for multimode fiber local area networks,” IEEE Photon. Technol. Lett. 18, 244–246 (2006).
[Crossref]

Hsu, R. C. J.

Ih, C. S.

C. S. Ih and W. Gu, “Fiber Induced Distortions in a Subcarrier Multiplexed Lightwave System,” IEEE J. Sel. Areas Commun. 8, 1296–1303 (1990).
[Crossref]

Jacobs, I.

S. Kanprachar and I. Jacobs, “Diversity of coding for subcarrier multiplexing on multimode fibers,” IEEE Trans. Commun. 51, 1546–1553 (2003).
[Crossref]

Jalali, B.

Kanprachar, S.

S. Kanprachar and I. Jacobs, “Diversity of coding for subcarrier multiplexing on multimode fibers,” IEEE Trans. Commun. 51, 1546–1553 (2003).
[Crossref]

Khoe, G. D.

A. M. J. Koonen, A. Ng’Oma, H. P. A. van den Boom, I. Tafur Monroy, and G. D. Khoe, “New techniques for extending the capabilities of multimode fibre networks,” in Proceedings of NOC, (2003), pp. 204–211.

Koonen, A. M. J.

A. M. J. Koonen, A. Ng’Oma, H. P. A. van den Boom, I. Tafur Monroy, and G. D. Khoe, “New techniques for extending the capabilities of multimode fibre networks,” in Proceedings of NOC, (2003), pp. 204–211.

Kourtessis, P.

Mohammed, W.

X. J. Gu, W. Mohammed, and P. W. Smith, “Demonstration of all-fiber WDM for multimode fiber local area networks,” IEEE Photon. Technol. Lett. 18, 244–246 (2006).
[Crossref]

Ng’Oma, A.

A. M. J. Koonen, A. Ng’Oma, H. P. A. van den Boom, I. Tafur Monroy, and G. D. Khoe, “New techniques for extending the capabilities of multimode fibre networks,” in Proceedings of NOC, (2003), pp. 204–211.

Ortega, B.

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

Pastor, D.

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

Penty, R. V.

Quinlan, T.

Rochart, E.

Saleh, B. E. A.

B. E. A. Saleh and R. M. Abdula, “Optical Interference and Pulse Propagation in Multimode Fibers,” Fiber Integr. Opt. 5, 161–201 (1985).
[Crossref]

Sales, S.

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

Sayed, A. H.

Shah, A. R.

Smith, P. W.

X. J. Gu, W. Mohammed, and P. W. Smith, “Demonstration of all-fiber WDM for multimode fiber local area networks,” IEEE Photon. Technol. Lett. 18, 244–246 (2006).
[Crossref]

Stuart, H. R.

H. R. Stuart, “Dispersive multiplexing in multimode fiber,” Science 289, 305–307 (2000).
[Crossref]

Tafur Monroy, I.

A. M. J. Koonen, A. Ng’Oma, H. P. A. van den Boom, I. Tafur Monroy, and G. D. Khoe, “New techniques for extending the capabilities of multimode fibre networks,” in Proceedings of NOC, (2003), pp. 204–211.

Tarighat, A.

Tyler, E. J.

van den Boom, H. P. A.

A. M. J. Koonen, A. Ng’Oma, H. P. A. van den Boom, I. Tafur Monroy, and G. D. Khoe, “New techniques for extending the capabilities of multimode fibre networks,” in Proceedings of NOC, (2003), pp. 204–211.

Walker, S. D.

Webster, M.

White, I. H.

Yabre, G.

Fiber Integr. Opt. (1)

B. E. A. Saleh and R. M. Abdula, “Optical Interference and Pulse Propagation in Multimode Fibers,” Fiber Integr. Opt. 5, 161–201 (1985).
[Crossref]

IEEE J. Sel. Areas Commun. (1)

C. S. Ih and W. Gu, “Fiber Induced Distortions in a Subcarrier Multiplexed Lightwave System,” IEEE J. Sel. Areas Commun. 8, 1296–1303 (1990).
[Crossref]

IEEE Photon. Technol. Lett. (1)

X. J. Gu, W. Mohammed, and P. W. Smith, “Demonstration of all-fiber WDM for multimode fiber local area networks,” IEEE Photon. Technol. Lett. 18, 244–246 (2006).
[Crossref]

IEEE Trans. Commun. (1)

S. Kanprachar and I. Jacobs, “Diversity of coding for subcarrier multiplexing on multimode fibers,” IEEE Trans. Commun. 51, 1546–1553 (2003).
[Crossref]

J. Lightwave Technol. (3)

J.Lightwave Technol. (1)

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

Opt. Express (1)

Science (1)

H. R. Stuart, “Dispersive multiplexing in multimode fiber,” Science 289, 305–307 (2000).
[Crossref]

Other (1)

A. M. J. Koonen, A. Ng’Oma, H. P. A. van den Boom, I. Tafur Monroy, and G. D. Khoe, “New techniques for extending the capabilities of multimode fibre networks,” in Proceedings of NOC, (2003), pp. 204–211.

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Figures (3)

Fig. 1.
Fig. 1. Layout of the Multimode Fiber link.

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Fig. 2.
Fig. 2. Power received for the fundamental tones, harmonic and intermodulation distortions for a multimode fiber link of 5 Km and a modulating index mo =0.01.

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Fig. 3.
Fig. 3. CSO relative to the harmonic and intermodulation distortions for a link of 5 Km.

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Equations (12)

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S ( t ) = P · [ 1 + m o 4 ( 1 + j α ) cos ⁡ ( Ω t ) ]
S ( t ) = P { 1 + m o 4 ( 1 + j α ) · [ cos ⁡ ( Ω 1 t ) + cos ⁡ ( Ω 2 t ) ] } .
P ( Ω ) = ∑ m = 1 M 2 m ∑ n = 1 M [ U mn · A mn ( Ω 1 , Ω 2 ) ]
U mn = ( C mn + G mn ) · e − ( α m + α n ) z · e − j ( β n 0 − β m 0 ) z · e − ( τ n − τ m ) 2 2 σ c 2
A mn ( Ω 1 , Ω 2 ) = A mn 1 ( Ω 1 ) + A mn 1 ( Ω 2 ) + A mn 2 ( 2 Ω 1 ) + A mn 2 ( 2 Ω 2 ) + A mn 3 ( Ω 2 − Ω 1 ) + A mn 3 ( Ω 2 + Ω 1 ) ,
A mn 1 ( Ω ′ ) = m o π 4 1 + α 2 e − ( Ω ′ β o 2 z ) 2 2 σ c 2 · e Ω ′ β o 2 z ( τ m − τ n ) σ c 2 · { e j [ arctan ⁡ ( α ) Ω ′ 2 β o 2 z 2 ] e − j Ω ′ τ n +
+ e − j [ arctan ⁡ ( α ) − Ω ′ 2 β o 2 z 2 ] e − j Ω ′ τ m } · δ ( Ω − Ω ′ ) ,
A mn 2 ( 2 Ω ′ ) = m o 2 π 32 ( 1 + α 2 ) · e − ( 2 Ω ′ β o 2 z ) 2 2 σ c 2 · e 2 Ω ′ β o 2 z ( τ m − τ n ) σ c 2 · e − j Ω ′ ( τ m + τ n ) · δ ( Ω − 2 Ω ′ ) ,
A mn 3 ( Ω 2 ∓ Ω 1 ) = m o 2 π 32 ( 1 + α 2 ) · e − ( ( Ω 2 ∓ Ω 1 ) β o 2 z ) 2 2 σ c 2 · e ( Ω 2 ∓ Ω 1 ) β o 2 z ( τ m − τ n ) σ c 2 · e ( Ω 2 2 − Ω 1 2 ) j β o 2 z 2 ·
· e − j Ω 2 τ n · e ± j Ω 1 τ m · δ [ Ω − ( Ω 2 ∓ Ω 1 ) ]
CSO HD ( Ω ) = [ P 2 ( 2 Ω 2 or 1 ) ] 2 [ P 1 ( Ω 1 ) ] 2 = { ∑ m = 1 M 2 m ∑ n = 1 M [ U mn · A mn 2 ( 2 Ω 2 or 1 ) ] } 2 { ∑ m = 1 M 2 m ∑ n = 1 M [ U mn · A mn 1 ( Ω 1 ) ] } 2
CSO HD ( Ω ) = [ P 2 ( Ω 2 ∓ Ω 1 ) ] 2 [ P 1 ( Ω 1 ) ] 2 = { ∑ m = 1 M 2 m ∑ n = 1 M [ U mn · A mn 2 ( Ω 2 ∓ Ω 1 ) ] } 2 { ∑ m = 1 M 2 m ∑ n = 1 M [ U mn · A mn 1 ( Ω 1 ) ] } 2

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