Abstract

We present a closed-form expression for the evaluation of the transfer function of a multimode fiber (MMF) link based on the electric field propagation model. After validating the result we investigate the potential for broadband transmission in regions far from baseband. We find that MMFs offer the potential for broadband ROF transmission in the microwave and millimetre wave regions in short and middle reach distances.

© 2006 Optical Society of America

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References

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  1. G. P. Agrawal, Fiber-optic communication systems, (John Wiley, 3rd edition, 2002).
  2. A. M.J. Koonen, "Novel signal multiplexing methods for integration of services in in-building broadband multimode fibre networks," in Proceedings of ISSLS, (Edinburgh, Scotland, 2004).
  3. A. M.J. Koonen, A. Ng'Oma, H. P. A. van den Boom, I. Tafur Monroy, G. D. Khoe, "New techniques for extending the capabilities of multimode fibre networks," in Proceedings of NOC, (2003) pp. 204-211.
  4. A. M. J. Koonen, H. P. A. van den Boom, F. Willems, J. W. M. Bergmans, G. D. Khoe, "Broadband multi-service in-house networks using mode group diversity multiplexing," in Proceedings of POF conference, (2002) pp. 87-90.
  5. M. Boer, C. P. Tsekrekos, A. Martinez, H. Kurniawan, J. W. Bergmans, A. M. J. Koonen, H. P. A. van den Boom, F. M. J. Willems, "A First Demonstrator For A Mode Group Diversity Multiplexing Communication System," in Proceedings of IEEE seminar on Optical Fibre Communication. and Electrical. Signal Processing, (London, England, 2005) pp. 16/1-16/5.
  6. H. R. Stuart, "Dispersive multiplexing in multimode fiber," Science 289, 305-307, (2000).
    [CrossRef]
  7. L. Raddatz and I. H. White, "Overcoming the Modal Bandwidth Limitation of Multimode Fiber by Using Passband Modulation," IEEE Photon. Technol. Lett. 11, 266-268, (1999).
    [CrossRef]
  8. S. Kanprachar and I. Jacobs, "Diversity of coding for subcarrier multiplexing on multimode fibers," IEEE Trans. Commun. 51, 1546-1553 (2003).
    [CrossRef]
  9. 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]
  10. 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]
  11. P. Pepeljugosky, "Next generation High-Speed Multimode Fiber Links and their specifications," in Proceedings of OFC, (Anaheim, CA, USA, 2005), paper OWH1.
  12. R. Yuen, X. N. Fernando and S. Krishnan, "Radio Over Multimode Fiber for Wireless Access," in Proceedings of. Canadian Conference on Electrical and Computer Engineering, (Ontario, Canada, 2004), pp. 1715-1718.
  13. 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]
  14. D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1783 (1972).Q1
  15. D. Marcuse, Theory of Dielectric Optical Waveguide, (Academic Press, 2nd edition, 1991).
  16. R. Olshansky, "Mode coupling effects in graded-index core fibers," Appl. Opt. 14, 935-945 (1975).
    [PubMed]
  17. G. Yabre, "Comprehensive Theory of Dispersion in Graded-Index Optical Fibers," J. Lightwave Technol. 18, 166-177 (2000).
    [CrossRef]
  18. R. Steinberg, "Pulse propagation in Multimode Fibers with Frequency-Dependent Coupling," IEEE Trans. Microwave Theory Tech. 23, 121-122 (1975).
    [CrossRef]
  19. K. Tatekura, K. Itoh and T. Matsumoto, "Techniques and formulations for Mode Coupling of Multimode Optical Fibers," IEEE Trans. Microwave Theory Tech. 26, 487-493 (1978).
    [CrossRef]
  20. T. P. Tanaka and S. Yamada, "Numerical solution of power flow in multimode W-type optical fibers," Appl. Opt. 19, 1647-1652 (1985).
    [CrossRef]
  21. M. J. Yadlowsky and A. R. Mickelson, "Distributed loss and mode coupling and their effect on time-dependent propagation in multimode fibers," Appl. Opt. 32, 6664-6677 (1993).
    [CrossRef] [PubMed]
  22. A. Djordjevich and S. Savovic, "Investigation of Mode Coupling in Step Index Plastic Optical Fibers using the Power Flow Equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
    [CrossRef]
  23. D. Gloge, "Impulse response of Clad Optical Multimode Fibers," Bell Syst. Tech. J. 52, 801-815 (1973).Q2
  24. D. Yevick and B. Stoltz, "Effect of mode coupling on the total pulse response of perturbed optical fibers," Appl. Opt. 22, 1010-1015 (1983).
    [CrossRef] [PubMed]
  25. A. Djordjevich and S. Savovic, "Numerical solution of the power flow equation in step-index plastic optical fibers," J. Opt. Soc. Am. 21, 1437-1442 (2004).
    [CrossRef]
  26. G. Aldabaldetreku, G. Durana, J. Zubia and J. Arrue, "Analytical expression for measurement of Intrinsic Coupling Loss in Multistep Index Optical Fibers," J. Lightwave Technol. 24, 1364-1375 (2006).
    [CrossRef]
  27. M. A. Losada, I. Garces, J. Mateo, I. Salinas, J. Lou and J. Zubia, "Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers," J. Lightwave Technol. 20, 1160-1164 (2002).
    [CrossRef]
  28. J. Zubia, G. Durana, G. Aldabaldetreku, J. Arrue, M. A. Losada and M. Lopez-Higuera, "New method to calculate mode conversion coefficients in SI multimode optical fibers," J. Lightwave Technol. 21, 776-781 (2003).
    [CrossRef]
  29. B. E. A. Saleh and R. M. Abdula, "Optical Interference and Pulse Propagation in Multimode Fibers," Fiber Integr. Opt. 5, 161-201 (1985).Q3
    [CrossRef]
  30. B. E. A. Saleh and M. I. Irshid, "Coherence and intersymbol interference in Digital Fiber Optic Communication Systems," IEEE J. Quantum Electron. 18, 944-951 (1982).
    [CrossRef]
  31. G. Yabre, "Influence of Core Diameter on the 3-dB Bandwidth of Graded-Index Optical Fibers," J. Lightwave Technol. 18, 668-676 (2000).
    [CrossRef]
  32. J. Capmany, A. Martínez, B. Ortega and D. Pastor, "Transfer function of analog fiber optic systems driven by Fabry-Perot sources," J. Opt. Soc. Amer. B 22, 2099-2106 (2005).
    [CrossRef]
  33. J. Capmany, B. Ortega, D. Pastor and S. Sales, "Discrete-time optical processing of microwave signals," J. Lightwave Technol. 23, 702-723 (2005).
    [CrossRef]

2006

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]

G. Aldabaldetreku, G. Durana, J. Zubia and J. Arrue, "Analytical expression for measurement of Intrinsic Coupling Loss in Multistep Index Optical Fibers," J. Lightwave Technol. 24, 1364-1375 (2006).
[CrossRef]

2005

2004

A. Djordjevich and S. Savovic, "Numerical solution of the power flow equation in step-index plastic optical fibers," J. Opt. Soc. Am. 21, 1437-1442 (2004).
[CrossRef]

2003

2002

2000

G. Yabre, "Comprehensive Theory of Dispersion in Graded-Index Optical Fibers," J. Lightwave Technol. 18, 166-177 (2000).
[CrossRef]

G. Yabre, "Influence of Core Diameter on the 3-dB Bandwidth of Graded-Index Optical Fibers," J. Lightwave Technol. 18, 668-676 (2000).
[CrossRef]

H. R. Stuart, "Dispersive multiplexing in multimode fiber," Science 289, 305-307, (2000).
[CrossRef]

A. Djordjevich and S. Savovic, "Investigation of Mode Coupling in Step Index Plastic Optical Fibers using the Power Flow Equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[CrossRef]

1999

L. Raddatz and I. H. White, "Overcoming the Modal Bandwidth Limitation of Multimode Fiber by Using Passband Modulation," IEEE Photon. Technol. Lett. 11, 266-268, (1999).
[CrossRef]

1993

1985

T. P. Tanaka and S. Yamada, "Numerical solution of power flow in multimode W-type optical fibers," Appl. Opt. 19, 1647-1652 (1985).
[CrossRef]

B. E. A. Saleh and R. M. Abdula, "Optical Interference and Pulse Propagation in Multimode Fibers," Fiber Integr. Opt. 5, 161-201 (1985).Q3
[CrossRef]

1983

1982

B. E. A. Saleh and M. I. Irshid, "Coherence and intersymbol interference in Digital Fiber Optic Communication Systems," IEEE J. Quantum Electron. 18, 944-951 (1982).
[CrossRef]

1978

K. Tatekura, K. Itoh and T. Matsumoto, "Techniques and formulations for Mode Coupling of Multimode Optical Fibers," IEEE Trans. Microwave Theory Tech. 26, 487-493 (1978).
[CrossRef]

1975

R. Steinberg, "Pulse propagation in Multimode Fibers with Frequency-Dependent Coupling," IEEE Trans. Microwave Theory Tech. 23, 121-122 (1975).
[CrossRef]

R. Olshansky, "Mode coupling effects in graded-index core fibers," Appl. Opt. 14, 935-945 (1975).
[PubMed]

1973

D. Gloge, "Impulse response of Clad Optical Multimode Fibers," Bell Syst. Tech. J. 52, 801-815 (1973).Q2

1972

D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1783 (1972).Q1

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).Q3
[CrossRef]

Aldabaldetreku, G.

Arrue, J.

Capmany, J.

J. Capmany, A. Martínez, B. Ortega and D. Pastor, "Transfer function of analog fiber optic systems driven by Fabry-Perot sources," J. Opt. Soc. Amer. B 22, 2099-2106 (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]

Djordjevich, A.

A. Djordjevich and S. Savovic, "Numerical solution of the power flow equation in step-index plastic optical fibers," J. Opt. Soc. Am. 21, 1437-1442 (2004).
[CrossRef]

A. Djordjevich and S. Savovic, "Investigation of Mode Coupling in Step Index Plastic Optical Fibers using the Power Flow Equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[CrossRef]

Dudley, S. E. M.

Durana, G.

Garces, I.

Gloge, D.

D. Gloge, "Impulse response of Clad Optical Multimode Fibers," Bell Syst. Tech. J. 52, 801-815 (1973).Q2

D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1783 (1972).Q1

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.

Irshid, M. I.

B. E. A. Saleh and M. I. Irshid, "Coherence and intersymbol interference in Digital Fiber Optic Communication Systems," IEEE J. Quantum Electron. 18, 944-951 (1982).
[CrossRef]

Itoh, K.

K. Tatekura, K. Itoh and T. Matsumoto, "Techniques and formulations for Mode Coupling of Multimode Optical Fibers," IEEE Trans. Microwave Theory Tech. 26, 487-493 (1978).
[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]

Kourtessis, P.

Lopez-Higuera, M.

Losada, M. A.

Lou, J.

Martínez, A.

J. Capmany, A. Martínez, B. Ortega and D. Pastor, "Transfer function of analog fiber optic systems driven by Fabry-Perot sources," J. Opt. Soc. Amer. B 22, 2099-2106 (2005).
[CrossRef]

Mateo, J.

Matsumoto, T.

K. Tatekura, K. Itoh and T. Matsumoto, "Techniques and formulations for Mode Coupling of Multimode Optical Fibers," IEEE Trans. Microwave Theory Tech. 26, 487-493 (1978).
[CrossRef]

Mickelson, A. R.

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]

Olshansky, R.

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]

J. Capmany, A. Martínez, B. Ortega and D. Pastor, "Transfer function of analog fiber optic systems driven by Fabry-Perot sources," J. Opt. Soc. Amer. B 22, 2099-2106 (2005).
[CrossRef]

Pastor, D.

J. Capmany, A. Martínez, B. Ortega and D. Pastor, "Transfer function of analog fiber optic systems driven by Fabry-Perot sources," J. Opt. Soc. Amer. B 22, 2099-2106 (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]

Penty, R. V.

Quinlan, T.

Raddatz, L.

L. Raddatz and I. H. White, "Overcoming the Modal Bandwidth Limitation of Multimode Fiber by Using Passband Modulation," IEEE Photon. Technol. Lett. 11, 266-268, (1999).
[CrossRef]

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).Q3
[CrossRef]

B. E. A. Saleh and M. I. Irshid, "Coherence and intersymbol interference in Digital Fiber Optic Communication Systems," IEEE J. Quantum Electron. 18, 944-951 (1982).
[CrossRef]

Sales, S.

Salinas, I.

Savovic, S.

A. Djordjevich and S. Savovic, "Numerical solution of the power flow equation in step-index plastic optical fibers," J. Opt. Soc. Am. 21, 1437-1442 (2004).
[CrossRef]

A. Djordjevich and S. Savovic, "Investigation of Mode Coupling in Step Index Plastic Optical Fibers using the Power Flow Equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[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]

Steinberg, R.

R. Steinberg, "Pulse propagation in Multimode Fibers with Frequency-Dependent Coupling," IEEE Trans. Microwave Theory Tech. 23, 121-122 (1975).
[CrossRef]

Stoltz, B.

Stuart, H. R.

H. R. Stuart, "Dispersive multiplexing in multimode fiber," Science 289, 305-307, (2000).
[CrossRef]

Tanaka, T. P.

Tarighat, A.

Tatekura, K.

K. Tatekura, K. Itoh and T. Matsumoto, "Techniques and formulations for Mode Coupling of Multimode Optical Fibers," IEEE Trans. Microwave Theory Tech. 26, 487-493 (1978).
[CrossRef]

Tyler, E. J.

Walker, S. D.

Webster, M.

White, I. H.

Yabre, G.

Yadlowsky, M. J.

Yamada, S.

Yevick, D.

Zubia, J.

Appl. Opt.

Bell Syst. Tech. J.

D. Gloge, "Optical power flow in multimode fibers," Bell Syst. Tech. J. 51, 1767-1783 (1972).Q1

D. Gloge, "Impulse response of Clad Optical Multimode Fibers," Bell Syst. Tech. J. 52, 801-815 (1973).Q2

Fiber Integr. Opt.

B. E. A. Saleh and R. M. Abdula, "Optical Interference and Pulse Propagation in Multimode Fibers," Fiber Integr. Opt. 5, 161-201 (1985).Q3
[CrossRef]

IEEE J. Quantum Electron.

B. E. A. Saleh and M. I. Irshid, "Coherence and intersymbol interference in Digital Fiber Optic Communication Systems," IEEE J. Quantum Electron. 18, 944-951 (1982).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Djordjevich and S. Savovic, "Investigation of Mode Coupling in Step Index Plastic Optical Fibers using the Power Flow Equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[CrossRef]

L. Raddatz and I. H. White, "Overcoming the Modal Bandwidth Limitation of Multimode Fiber by Using Passband Modulation," IEEE Photon. Technol. Lett. 11, 266-268, (1999).
[CrossRef]

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.

S. Kanprachar and I. Jacobs, "Diversity of coding for subcarrier multiplexing on multimode fibers," IEEE Trans. Commun. 51, 1546-1553 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

R. Steinberg, "Pulse propagation in Multimode Fibers with Frequency-Dependent Coupling," IEEE Trans. Microwave Theory Tech. 23, 121-122 (1975).
[CrossRef]

K. Tatekura, K. Itoh and T. Matsumoto, "Techniques and formulations for Mode Coupling of Multimode Optical Fibers," IEEE Trans. Microwave Theory Tech. 26, 487-493 (1978).
[CrossRef]

J. Lightwave Technol.

G. Yabre, "Comprehensive Theory of Dispersion in Graded-Index Optical Fibers," J. Lightwave Technol. 18, 166-177 (2000).
[CrossRef]

G. Yabre, "Influence of Core Diameter on the 3-dB Bandwidth of Graded-Index Optical Fibers," J. Lightwave Technol. 18, 668-676 (2000).
[CrossRef]

M. A. Losada, I. Garces, J. Mateo, I. Salinas, J. Lou and J. Zubia, "Mode coupling contribution to radiation losses in curvatures for high and low numerical aperture plastic optical fibers," J. Lightwave Technol. 20, 1160-1164 (2002).
[CrossRef]

J. Zubia, G. Durana, G. Aldabaldetreku, J. Arrue, M. A. Losada and M. Lopez-Higuera, "New method to calculate mode conversion coefficients in SI multimode optical fibers," J. Lightwave Technol. 21, 776-781 (2003).
[CrossRef]

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]

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

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]

G. Aldabaldetreku, G. Durana, J. Zubia and J. Arrue, "Analytical expression for measurement of Intrinsic Coupling Loss in Multistep Index Optical Fibers," J. Lightwave Technol. 24, 1364-1375 (2006).
[CrossRef]

J. Opt. Soc. Am.

A. Djordjevich and S. Savovic, "Numerical solution of the power flow equation in step-index plastic optical fibers," J. Opt. Soc. Am. 21, 1437-1442 (2004).
[CrossRef]

J. Opt. Soc. Amer. B

J. Capmany, A. Martínez, B. Ortega and D. Pastor, "Transfer function of analog fiber optic systems driven by Fabry-Perot sources," J. Opt. Soc. Amer. B 22, 2099-2106 (2005).
[CrossRef]

Science

H. R. Stuart, "Dispersive multiplexing in multimode fiber," Science 289, 305-307, (2000).
[CrossRef]

Other

G. P. Agrawal, Fiber-optic communication systems, (John Wiley, 3rd edition, 2002).

A. M.J. Koonen, "Novel signal multiplexing methods for integration of services in in-building broadband multimode fibre networks," in Proceedings of ISSLS, (Edinburgh, Scotland, 2004).

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

A. M. J. Koonen, H. P. A. van den Boom, F. Willems, J. W. M. Bergmans, G. D. Khoe, "Broadband multi-service in-house networks using mode group diversity multiplexing," in Proceedings of POF conference, (2002) pp. 87-90.

M. Boer, C. P. Tsekrekos, A. Martinez, H. Kurniawan, J. W. Bergmans, A. M. J. Koonen, H. P. A. van den Boom, F. M. J. Willems, "A First Demonstrator For A Mode Group Diversity Multiplexing Communication System," in Proceedings of IEEE seminar on Optical Fibre Communication. and Electrical. Signal Processing, (London, England, 2005) pp. 16/1-16/5.

D. Marcuse, Theory of Dielectric Optical Waveguide, (Academic Press, 2nd edition, 1991).

P. Pepeljugosky, "Next generation High-Speed Multimode Fiber Links and their specifications," in Proceedings of OFC, (Anaheim, CA, USA, 2005), paper OWH1.

R. Yuen, X. N. Fernando and S. Krishnan, "Radio Over Multimode Fiber for Wireless Access," in Proceedings of. Canadian Conference on Electrical and Computer Engineering, (Ontario, Canada, 2004), pp. 1715-1718.

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Figures (9)

Fig. 1.
Fig. 1.

Layout of the Multimode Fiber link.

Fig. 2.
Fig. 2.

Frequency responses for an 80/125 µm POF showing the effect of the mode-coupling (M.C.) and the differential mode attenuation (DMA). L=2014 m and α=2.02.

Fig. 3.
Fig. 3.

Frequency responses for an 80/125 µm POF illustrating the influence of the graded index exponent in absence of mode-coupling and differential mode attenuation. L=2014 m.

Fig. 4.
Fig. 4.

Influence of the core radius on the frequency response for a fiber with fixed cladding radius b=62.5 µm. L=2014 m and α=2.02.

Fig. 5.
Fig. 5.

Influence of the temporal coherence of the source on the frequency response for a 62.5/125 µm silica fiber. L=2014 m.

Fig. 6.
Fig. 6.

Transfer functions and Carrier suppression effect for a 62.5/125 µm silica fiber for different values of the source chirp. L=5 Km.

Fig. 7.
Fig. 7.

Transfer functions and Carrier suppression effect for a 10 Km link of 62.5/125 µm silica fiber for different values of the graded index exponent and a chirp free source.

Fig. 8.
Fig. 8.

Transfer functions for a 62.5/125 µm MMF silica fiber for different link lengths: L=10, 20 and 50 Km and a chirp free source.

Fig. 9.
Fig. 9.

Influence of the correlation length, D, on the transfer function for a 62.5/125 µm MMF silica fiber link of 2014 m and an rms deviation σ=0.001 m.

Equations (80)

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

E ( t , r ̅ , z ) = ν = 1 N μ = 1 N [ h μ ν ( t ) * E ν ( z , 0 ) ] e ν ( r ̅ )
I ( t , r ̅ , z ) E ( t , r ̅ , z ) 2 =
= μ = 1 N ν = 1 N μ = 1 N ν = 1 N e ν * ( r ̅ ) e ν ( r ̅ ) . h ν μ * ( t t ) h ν μ ( t t ) E μ * ( t , 0 ) E μ ( t , 0 ) dt dt .
E * ( t , r ̅ 1 , 0 ) E ( t , r ̅ 2 , 0 ) = S * ( t 1 ) S ( t 2 ) R ( t , t ) R s ( r ̅ 1 , r ̅ 2 )
E ν * ( t ,0 ) E μ ( t ,0 ) = S * ( t ) S ( t ) R ( t , t ) C ν μ
C ν μ = A f A f R s ( r ̅ 1 , r ̅ 2 ) = Is ( r ̅ 1 ) Is ( r ̅ 2 ) .
R s ( r ̅ 1 , r ̅ 2 ) = Is ( r ̅ 1 ) Is ( r ̅ 2 ) δ ( r ̅ 1 r ̅ 2 )
C ν μ = C μ μ δ ν μ .
I ( t , r ̅ , z ) = S * ( t ) S ( t ) q ( t t , t t , r ̅ ) dt dt
q ( t , t , r ̅ ) = R ( t , t ) q o ( t , t , r ̅ )
q o ( t , t , r ̅ ) = μ = 1 N ν = 1 N μ = 1 N ν = 1 N e ν * ( r ̅ ) e ν ( r ̅ ) . C μμ h ν μ * ( t ) h ν μ ( t ) .
P ( t ) = A R I ( t , r ̅ , z ) d r ̅ .
P ( t ) = S * ( t ) S ( t ) Q ( t t , t t ) dt dt
Q ( t , t ) = R ( t , t ) Q o ( t , t )
Q o ( t , t ) = μ = 1 N ν = 1 N μ = 1 N ν = 1 N C μμ D νν h μ ν * ( t ) h μ ν ( t )
D νν = A R e ν * ( r ̅ ) e ν ( r ̅ ) d r ̅ .
h μ ν * ( t t ) h μ ν ( t t )
P ( t ) = S ( t ) Q ( t t , t t ) dt .
n ( r , λ ) = { n 1 ( λ ) . [ 1 2 Δ ( λ ) . ( r a ) α ] 1 2 , for 0 r a n 1 ( λ ) . [ 1 2 Δ ( λ ) ] 1 2 , for r a
d E ˜ μ ( w , z ) dz = Γ μ E ˜ μ ( w , z ) + ν = 1 ν μ N K ̂ μ ν f ( z ) E ˜ ν ( w , z )
E ˜ μ ( w , z ) = E μ ( t , z ) e jwt dt .
Γ μ ν ( w ) = α μ ( w ) + j β μ ( w ) .
ε ˜ ( w , z ) = [ ε 1 ( w , z ) , ε 2 ( w , z ) , ⋯⋯ , ε N ( w , z ) ]
d ε ˜ ( w , z ) dz = A ( w , z ) ε ˜ ( w , z )
A ij = { Γ i ( w ) i = j K ij f ( z ) i j .
ε ˜ ( w , z ) = H ˜ ( w ) ε ( w , 0 )
H ˜ ( w ) = exp [ 0 z A ( z ) dz ] = l = 0 [ 0 z A ( z ) dz ] l l ! .
H μμ ( w ) = exp Γ μ ( w ) z
H μν ( w ) = K ̂ μν [ 0 z f ( z ) dz ] Φ μν ( w ) , μ v
Φ μν ( w ) = H μμ ( w ) H νν ( w ) Γ μ ( w ) Γ ν ( w ) .
P U ( t ) = S * ( t ) S ( t ) R ( t , t ) Q o U ( t t , t t ) dt dt
Q o U ( t , t ) = v = 1 N v = 1 N C vv D vv h vv * ( t ) h v v ( t ) .
P C ( t ) = g 2 S * ( t ) S ( t ) R ( t , t ) Q o C ( t t , t t ) dt dt
Q o C ( t , t ) = μ = 1 N ν = 1 ν μ N μ = 1 N ν = 1 ν μ N C μμ D νν h μν * ( t ) h μ′ ν ( t ) = μ = 1 N ν = 1 ν μ N μ = 1 N ν = 1 ν μ N C μμ D νν K ̂ μν * K ̂ μ′ ν Φ μν * ( t ) Φ μ' ν ' ( t )
g 2 = 0 z 0 z f * ( z 1 ) f ( z 2 ) dz 1 dz 2 = 0 z 0 z R f ( z 1 z 2 ) dz 1 dz 2
α μ ( w ) α μ ( w o ) = α μ 0
β μ ( w ) β μ ( w o ) + d β μ ( w ) dw w = w o ( w w o ) + 1 2 d β μ 2 ( w ) d w 2 w = w o ( w w o ) 2 +
= β μ 0 + β μ 1 ( w w o ) + 1 2 β μ 2 ( w w o ) 2 + .
h μμ ( t ) = 1 2 π e Γ μ ( w ) z e jwt dw = e ( α μ 0 + j β μ 0 ) z 1 j 2 π β μ 2 z e ( ( t β μ 1 z ) 2 2 j β μ 2 z ) .
Φ μν ( t ) = 1 2 π Φ μν ( w ) e jwt dw = ξ μν ( t ) * [ h μμ ( t ) h νν ( t ) ]
ξ μ ( t ) = B μν [ e j a μν + t e j a μν t ] U ( t )
B μν = 1 2 ( β μ 2 β ν 2 ) z χ μν 2 2 λ μν ,
a μν ( ± ) = χ μν ± χ μν 2 2 λ μν ,
χ μν = τ μ τ ν z [ β μ 2 β ν 2 ]
λ μν = ( α μ 0 α ν 0 ) + j ( β μ 0 β ν 0 ) β μ 2 β ν 2
β μ ( w ) β ν ( w ) β μ 0 β ν 0
ϕ μν ( t ) = h μμ ( t ) h νν ( t ) z [ α ν 0 α μ 0 + j ( β ν 0 β μ 0 ) ] .
l = m , m 2 , . . . . . . . . . . . . . . , ( m 2 ) , m
m = 1 M 2 ( m + 1 ) M 2 = N .
β m = n 1 k [ 1 2 Δ ( m M ( α ) ) 2 α α + 2 ] 1 2
M ( α , λ ) = 2 π a n 1 ( λ ) λ [ α . Δ ( λ ) α + 2 ] 1 2 .
τ ( m , λ ) = N 1 ( λ ) c [ 1 Δ ( λ ) ( 4 + ε ( λ ) ) α + 2 ( m M ) 2 α α + 2 ] · [ 1 2 Δ ( λ ) ( m M ) 2 α α + 2 ] 1 2
ε ( λ ) = 2 n 1 ( λ ) N 1 ( λ ) λ d Δ ( λ ) d λ Δ ( λ )
N 1 ( λ ) = n 1 ( λ ) λ · d n 1 ( λ ) d λ .
α ( m , λ ) = α 0 ( λ ) + α 0 ( λ ) · I ρ [ η ( m 1 M ) 2 α α + 2 ]
d P μ ( z ) dz = 2 α μ P μ ( z ) + ν = 1 N d μν ( P ν ( z ) P μ ( z ) )
d μν = K ̂ μν 2 · F ( β μ β ν ) 2
F ( β μ β ν ) 2 = 1 L 0 L f ( z ) · e i ( β μ β ν ) z dz .
d ( α , m ) = 1 8 ( n 1 ka ) 2 · ( m M ( α ) ) 4 α + 2 · F ( β μ β ν ) 2 · ( β μ β ν ) 4 .
K ̂ m , m + 1 2 = 1 8 ( n 1 ka ) 2 · [ n M ( α ) ] 4 α + 2 · ( β m ( ω ) β m + 1 ( ω ) ) 4 .
R f ( z 1 z 2 ) = σ 2 δ ( z 1 z 2 )
R f ( z 1 z 2 ) = σ 2 e z 1 z 2 D
R f ( z 1 z 2 ) = σ 2 e ( z 1 z 2 D ) 2
P ( t ) = m = 1 M P m ( t ) = m = 1 M 2 m P ̅ m ( t )
S ( t ) = P { 1 + m 8 ( 1 + j α ) e j Ω t + m 8 ( 1 + j α ) e j Ω t }
R ( t t ) = e ( t t ) 2 2 σ c 2
P UL ( t ) = ν = 1 M 2 ν · C νν D νν { 1 + m 8 ( 1 j α ) e j Ω t + m 8 ( 1 j α ) e j Ω t } · { 1 + m 8 ( 1 j α ) e j Ωt + m 8 ( 1 j α ) e j Ω t }
· e 1 2 ( t t σ c ) 2 e 2 α ν z · 1 2 β ν 2 z e ( t t τ ν ) 2 2 j β ν 2 z e ( t t τ ν ) 2 2 j β ν 2 z dt dt .
P UL ( t ) = m 4 1 + α 2 [ ν = 1 M 2 ν · C νν D νν e 2 α ν z e 1 2 ( β ν 2 z Ω σ c ) 2 · cos ) β ν 2 z Ω 2 2 + arctan ( α ) [ e j Ω τ ν ] e j Ω t .
P CL ( t ) = m 4 1 + α 2 [ ν = 1 M 2 ν · G νν e 2 α ν z e 1 2 ( β ν 2 z Ω σ c ) 2 · cos ( β ν 2 z Ω 2 2 + arctan ( α ) ) e j Ω τ ν e j Ω t ]
G νν = g 2 μ = 1 M ν = 1 ν μ M [ ψ νν ( μ , ν ) ψ μ′ ν ( ν , ν ) ψ νν ' ( μ , ν ) + ψ μ′ ν ( ν , ν ) ]
ψ mn ( r , s ) = { C mn D rs K ̂ mr * K ̂ ns f mr * f ns m r & n s 0 otherwise
f mn = ( α m α n + j ( β m 0 β n 0 ) ) · z .
H ( Ω ) = 1 + α 2 ν = 1 M 2 ν · ( C νν + G νν ) e 2 α ν z e 1 2 ( β ν 2 z Ω σ c ) 2 · cos [ β ν 2 z Ω 2 2 + arctan ( α ) ] e j Ω τ ν .
β ν 2 β o 2 , ν
H ( 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 ) ) · ν = 1 M 2 ν · ( C νν + G νν ) · e 2 α ν z e j Ω τ ν .
D νν = δ νν
C νμ = C μμ δ νμ
G νν = g 2 ν = 1 ν ν M [ ψ νν ( ν , ν ) + ψ ν′ ν ( ν , ν ) ] .
G νν = g 2 · 2 · [ ψ νν ( ν + 1 , ν + 1 ) + ψ ν 1 ν 1 ( ν , ν ) ] .

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