Abstract

Selective excitation of graded-index multimode fibers (GI-MMFs) with a single-mode fiber (SMF) has gained increased interest for telecommunication applications. It has been proposed as a way to enhance the transmission bandwidth of GI-MMF links and/or create parallel communication channels over the same GI-MMF. Although the effect of SMF excitation on the transmission bandwidth has been investigated, its impact on the near-field intensity pattern at the output face of the GI-MMF has not been systematically addressed. We have carried out an analysis of the near-field intensity pattern at the output face of silica-based GI-MMFs excited by a radially offset SMF. Simulation results exhibit all of the features displayed by experimental ones. It turns out that differential mode attenuation and delay, full intra-group mode mixing, and small deviations in the refractive index profile of the GI-MMF do not affect the overall shape of the near-field intensity, which is determined by the radial offset of the input SMF. This can be exploited in mode group diversity multiplexing links. The effect of defects in the refractive index profile, such as a central dip or peak, is also examined.

© 2007 Optical Society of America

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References

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  1. Z. Haas and M. A. Santoro, “A Mode-filtering scheme for improvement of the bandwidth-distance product in Multimode Fiber Systems,” J. Lightwave Technol. 11,1125–1131 (1993).
    [CrossRef]
  2. M. Düser and P. Bayvel, “2.5 Gbit/s transmission over 4.5 km of 62.5 μm multimode fibre using centre launch technique,” Electron. Lett. 36,57–58 (2000).
    [CrossRef]
  3. S. S.-H. Yam and F. Achten, “Single wavelength 40 Gbit/s transmission over 3.4 km broad wavelength window multimode fibre,” Electron. Lett. 42,592–593 (2006).
    [CrossRef]
  4. L. Raddatz, I. H. White, D. G. Cunningham, and M. C. Nowell, “An Experimental and theoretical study of the offset launch technique for the enhancement of the bandwidth of multimode fiber links,” J. Lightwave Technol. 16,324–331 (1998).
    [CrossRef]
  5. L. Raddatz and I. H. White, “Overcoming the Modal Bandwidth Limitation of Multimode Fiber by using Pass-band Modulation,” IEEE Photon. Technol. Lett. 11,266–268 (1999).
    [CrossRef]
  6. K. M. Patel, A. Polley, K. Balemarthy, and S. E. Ralph, “Spatially resolved detection and equalization of modal dispersion limited multimode fiber links,” J. Lightwave Technol. 24,2629–2636 (2006).
    [CrossRef]
  7. H. R. Stuart, “Dispersive Multiplexing in Multimode Optical Fiber,” Science 289,281–283 (2000).
    [CrossRef] [PubMed]
  8. T. Koonen, H. van den Boom, I. Tafur Monroy, and G.-D. Khoe, ”High capacity multi-service in-house networks using mode group diversity multiplexing,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FG4.
  9. 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]
  10. P. L. Neo and T. D. Wilkinson, “Holographic Implementation of Optical Multiple-Inputs, Multiple-Outputs (MIMO) on a Multimode Fiber,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CMNN2.
  11. C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett. 18,2359–2361 (2006).
    [CrossRef]
  12. M. Wegmuller, S. Golowich, G. Giaretta, and M. Nuss, “Evolution of the beam diameter in a multimode fiber link through offset connectors,” IEEE Photon. Technol. Lett. 13,574–576 (2001).
    [CrossRef]
  13. C. K. Asawa and H. F. Taylor, “Propagation of light trapped within a set of lowest-order modes of graded-index multimode fiber undergoing bending,” Appl. Opt. 39,2029–2037 (2000).
    [CrossRef]
  14. S. Schöllmann and W. Rosenkranz, “Experimental investigations of mode coupling as limiting effect using mode group diversity multiplexing on GI-MMF,” in Proceedings of European Conference on Optical Communications, Sep. 2006, paper We3.P.87.
  15. A. M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link due to Modal Noise,” IEEE J. Sel. Areas Commun. SAC- 4,1515–1522 (1986).
    [CrossRef]
  16. D. Gloge and E. A. J. Marcatili, “Multimode Theory of Graded-Core Fibers,” Bell Syst. Tech. J. 52,1563–1578 (1973).
  17. A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, 1983).
  18. A. H. Cherin, An Introduction to Optical Fibers, (McGraw-Hill, 1983).
  19. S. Kawakami and H. Tanji, “Evolution of Power Distribution in Graded-Index Fibres,” Electron. Lett. 19,100–102 (1983).
    [CrossRef]
  20. G. Yabre, “Comprehensive Theory of Dispersion in Graded-Index Optical Fibers,” J. Lightwave Technol. 18,166–177 (2000).
    [CrossRef]
  21. M. Bingle and B. P. de Hon, “Differential Mode Delay Full-wave modeling and various levels of approximations,” in Proceedings of the General XXVIIth Assembly of the International Union of Radio Science, Aug. 2002, paper2060.
  22. J. G. Dil and H. Blok, “Propagation of Electromagnetic Surface Waves in a Radially Inhomogeneous Optical Waveguide,” Opto-electronics 5,415–428 (1973).
    [CrossRef]
  23. Y. Daido, E. Miyauchi, T. Iwama, and T. Otsuka, “Determination of modal power distribution in graded-index optical waveguides from near-field patterns and its application to differential mode attenuation measurement,” Appl. Opt. 18,2207–2213 (1979).
    [CrossRef] [PubMed]
  24. O. G. Leminger and G. K. Grau, “Near-Field Intensity and Modal Power Distribution in Multimode Graded-index Fibers,” Electron. Lett. 16,678–679 (1980).
    [CrossRef]
  25. M. Rousseau and L. Jeunhomme, “Optimum index profile in multimode optical fiber with respect to mode coupling,” Opt. Commun. 23,275–278 (1977).
    [CrossRef]
  26. M. Webster, L. Raddatz, I. H. White, and D. G. Cunningham, “A Statistical analysis of conditioned launch for gigabit ethernet links using multimode fiber,” J. Lightwave Technol. 17,1532–1541 (1999).
    [CrossRef]
  27. http://www.ieee802.org/3/aq/public/tools/
  28. http://www.ieee802.org/3/aq/public/tools/108fiberModel/CamMMF1p2/CamMMF1p2%20Supplement.pdf

2006 (4)

S. S.-H. Yam and F. Achten, “Single wavelength 40 Gbit/s transmission over 3.4 km broad wavelength window multimode fibre,” Electron. Lett. 42,592–593 (2006).
[CrossRef]

S. Schöllmann and W. Rosenkranz, “Experimental investigations of mode coupling as limiting effect using mode group diversity multiplexing on GI-MMF,” in Proceedings of European Conference on Optical Communications, Sep. 2006, paper We3.P.87.

C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett. 18,2359–2361 (2006).
[CrossRef]

K. M. Patel, A. Polley, K. Balemarthy, and S. E. Ralph, “Spatially resolved detection and equalization of modal dispersion limited multimode fiber links,” J. Lightwave Technol. 24,2629–2636 (2006).
[CrossRef]

2005 (1)

2001 (1)

M. Wegmuller, S. Golowich, G. Giaretta, and M. Nuss, “Evolution of the beam diameter in a multimode fiber link through offset connectors,” IEEE Photon. Technol. Lett. 13,574–576 (2001).
[CrossRef]

2000 (4)

C. K. Asawa and H. F. Taylor, “Propagation of light trapped within a set of lowest-order modes of graded-index multimode fiber undergoing bending,” Appl. Opt. 39,2029–2037 (2000).
[CrossRef]

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

H. R. Stuart, “Dispersive Multiplexing in Multimode Optical Fiber,” Science 289,281–283 (2000).
[CrossRef] [PubMed]

M. Düser and P. Bayvel, “2.5 Gbit/s transmission over 4.5 km of 62.5 μm multimode fibre using centre launch technique,” Electron. Lett. 36,57–58 (2000).
[CrossRef]

1999 (2)

L. Raddatz and I. H. White, “Overcoming the Modal Bandwidth Limitation of Multimode Fiber by using Pass-band Modulation,” IEEE Photon. Technol. Lett. 11,266–268 (1999).
[CrossRef]

M. Webster, L. Raddatz, I. H. White, and D. G. Cunningham, “A Statistical analysis of conditioned launch for gigabit ethernet links using multimode fiber,” J. Lightwave Technol. 17,1532–1541 (1999).
[CrossRef]

1998 (1)

1993 (1)

Z. Haas and M. A. Santoro, “A Mode-filtering scheme for improvement of the bandwidth-distance product in Multimode Fiber Systems,” J. Lightwave Technol. 11,1125–1131 (1993).
[CrossRef]

1986 (1)

A. M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link due to Modal Noise,” IEEE J. Sel. Areas Commun. SAC- 4,1515–1522 (1986).
[CrossRef]

1983 (1)

S. Kawakami and H. Tanji, “Evolution of Power Distribution in Graded-Index Fibres,” Electron. Lett. 19,100–102 (1983).
[CrossRef]

1980 (1)

O. G. Leminger and G. K. Grau, “Near-Field Intensity and Modal Power Distribution in Multimode Graded-index Fibers,” Electron. Lett. 16,678–679 (1980).
[CrossRef]

1979 (1)

1977 (1)

M. Rousseau and L. Jeunhomme, “Optimum index profile in multimode optical fiber with respect to mode coupling,” Opt. Commun. 23,275–278 (1977).
[CrossRef]

1973 (2)

J. G. Dil and H. Blok, “Propagation of Electromagnetic Surface Waves in a Radially Inhomogeneous Optical Waveguide,” Opto-electronics 5,415–428 (1973).
[CrossRef]

D. Gloge and E. A. J. Marcatili, “Multimode Theory of Graded-Core Fibers,” Bell Syst. Tech. J. 52,1563–1578 (1973).

Achten, F.

S. S.-H. Yam and F. Achten, “Single wavelength 40 Gbit/s transmission over 3.4 km broad wavelength window multimode fibre,” Electron. Lett. 42,592–593 (2006).
[CrossRef]

Asawa, C. K.

Balemarthy, K.

Bayvel, P.

M. Düser and P. Bayvel, “2.5 Gbit/s transmission over 4.5 km of 62.5 μm multimode fibre using centre launch technique,” Electron. Lett. 36,57–58 (2000).
[CrossRef]

Bingle, M.

M. Bingle and B. P. de Hon, “Differential Mode Delay Full-wave modeling and various levels of approximations,” in Proceedings of the General XXVIIth Assembly of the International Union of Radio Science, Aug. 2002, paper2060.

Blok, H.

J. G. Dil and H. Blok, “Propagation of Electromagnetic Surface Waves in a Radially Inhomogeneous Optical Waveguide,” Opto-electronics 5,415–428 (1973).
[CrossRef]

Boom, H. van den

T. Koonen, H. van den Boom, I. Tafur Monroy, and G.-D. Khoe, ”High capacity multi-service in-house networks using mode group diversity multiplexing,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FG4.

Cherin, A. H.

A. H. Cherin, An Introduction to Optical Fibers, (McGraw-Hill, 1983).

Cunningham, D. G.

Daido, Y.

Dil, J. G.

J. G. Dil and H. Blok, “Propagation of Electromagnetic Surface Waves in a Radially Inhomogeneous Optical Waveguide,” Opto-electronics 5,415–428 (1973).
[CrossRef]

Düser, M.

M. Düser and P. Bayvel, “2.5 Gbit/s transmission over 4.5 km of 62.5 μm multimode fibre using centre launch technique,” Electron. Lett. 36,57–58 (2000).
[CrossRef]

Giaretta, G.

M. Wegmuller, S. Golowich, G. Giaretta, and M. Nuss, “Evolution of the beam diameter in a multimode fiber link through offset connectors,” IEEE Photon. Technol. Lett. 13,574–576 (2001).
[CrossRef]

Gloge, D.

D. Gloge and E. A. J. Marcatili, “Multimode Theory of Graded-Core Fibers,” Bell Syst. Tech. J. 52,1563–1578 (1973).

Golowich, S.

M. Wegmuller, S. Golowich, G. Giaretta, and M. Nuss, “Evolution of the beam diameter in a multimode fiber link through offset connectors,” IEEE Photon. Technol. Lett. 13,574–576 (2001).
[CrossRef]

Grau, G. K.

O. G. Leminger and G. K. Grau, “Near-Field Intensity and Modal Power Distribution in Multimode Graded-index Fibers,” Electron. Lett. 16,678–679 (1980).
[CrossRef]

Haas, Z.

Z. Haas and M. A. Santoro, “A Mode-filtering scheme for improvement of the bandwidth-distance product in Multimode Fiber Systems,” J. Lightwave Technol. 11,1125–1131 (1993).
[CrossRef]

Hon, B. P. de

M. Bingle and B. P. de Hon, “Differential Mode Delay Full-wave modeling and various levels of approximations,” in Proceedings of the General XXVIIth Assembly of the International Union of Radio Science, Aug. 2002, paper2060.

Hsu, R. C. J.

Huijskens, F. M.

C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett. 18,2359–2361 (2006).
[CrossRef]

Iwama, T.

Jalali, B.

Jeunhomme, L.

M. Rousseau and L. Jeunhomme, “Optimum index profile in multimode optical fiber with respect to mode coupling,” Opt. Commun. 23,275–278 (1977).
[CrossRef]

Kawakami, S.

S. Kawakami and H. Tanji, “Evolution of Power Distribution in Graded-Index Fibres,” Electron. Lett. 19,100–102 (1983).
[CrossRef]

Khoe, G.-D.

T. Koonen, H. van den Boom, I. Tafur Monroy, and G.-D. Khoe, ”High capacity multi-service in-house networks using mode group diversity multiplexing,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FG4.

Koonen, A. M. J.

C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett. 18,2359–2361 (2006).
[CrossRef]

A. M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link due to Modal Noise,” IEEE J. Sel. Areas Commun. SAC- 4,1515–1522 (1986).
[CrossRef]

Koonen, T.

T. Koonen, H. van den Boom, I. Tafur Monroy, and G.-D. Khoe, ”High capacity multi-service in-house networks using mode group diversity multiplexing,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FG4.

Leminger, O. G.

O. G. Leminger and G. K. Grau, “Near-Field Intensity and Modal Power Distribution in Multimode Graded-index Fibers,” Electron. Lett. 16,678–679 (1980).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, 1983).

Marcatili, E. A. J.

D. Gloge and E. A. J. Marcatili, “Multimode Theory of Graded-Core Fibers,” Bell Syst. Tech. J. 52,1563–1578 (1973).

Martinez, A.

C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett. 18,2359–2361 (2006).
[CrossRef]

Miyauchi, E.

Monroy, I. Tafur

T. Koonen, H. van den Boom, I. Tafur Monroy, and G.-D. Khoe, ”High capacity multi-service in-house networks using mode group diversity multiplexing,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FG4.

Neo, P. L.

P. L. Neo and T. D. Wilkinson, “Holographic Implementation of Optical Multiple-Inputs, Multiple-Outputs (MIMO) on a Multimode Fiber,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CMNN2.

Nowell, M. C.

Nuss, M.

M. Wegmuller, S. Golowich, G. Giaretta, and M. Nuss, “Evolution of the beam diameter in a multimode fiber link through offset connectors,” IEEE Photon. Technol. Lett. 13,574–576 (2001).
[CrossRef]

Otsuka, T.

Patel, K. M.

Polley, A.

Raddatz, L.

Ralph, S. E.

Rosenkranz, W.

S. Schöllmann and W. Rosenkranz, “Experimental investigations of mode coupling as limiting effect using mode group diversity multiplexing on GI-MMF,” in Proceedings of European Conference on Optical Communications, Sep. 2006, paper We3.P.87.

Rousseau, M.

M. Rousseau and L. Jeunhomme, “Optimum index profile in multimode optical fiber with respect to mode coupling,” Opt. Commun. 23,275–278 (1977).
[CrossRef]

Santoro, M. A.

Z. Haas and M. A. Santoro, “A Mode-filtering scheme for improvement of the bandwidth-distance product in Multimode Fiber Systems,” J. Lightwave Technol. 11,1125–1131 (1993).
[CrossRef]

Sayed, A. H.

Schöllmann, S.

S. Schöllmann and W. Rosenkranz, “Experimental investigations of mode coupling as limiting effect using mode group diversity multiplexing on GI-MMF,” in Proceedings of European Conference on Optical Communications, Sep. 2006, paper We3.P.87.

Shah, A. R.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, 1983).

Stuart, H. R.

H. R. Stuart, “Dispersive Multiplexing in Multimode Optical Fiber,” Science 289,281–283 (2000).
[CrossRef] [PubMed]

Tanji, H.

S. Kawakami and H. Tanji, “Evolution of Power Distribution in Graded-Index Fibres,” Electron. Lett. 19,100–102 (1983).
[CrossRef]

Tarighat, A.

Taylor, H. F.

Tsekrekos, C. P.

C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett. 18,2359–2361 (2006).
[CrossRef]

Webster, M.

Wegmuller, M.

M. Wegmuller, S. Golowich, G. Giaretta, and M. Nuss, “Evolution of the beam diameter in a multimode fiber link through offset connectors,” IEEE Photon. Technol. Lett. 13,574–576 (2001).
[CrossRef]

White, I. H.

Wilkinson, T. D.

P. L. Neo and T. D. Wilkinson, “Holographic Implementation of Optical Multiple-Inputs, Multiple-Outputs (MIMO) on a Multimode Fiber,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CMNN2.

Yabre, G.

Yam, S. S.-H.

S. S.-H. Yam and F. Achten, “Single wavelength 40 Gbit/s transmission over 3.4 km broad wavelength window multimode fibre,” Electron. Lett. 42,592–593 (2006).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

D. Gloge and E. A. J. Marcatili, “Multimode Theory of Graded-Core Fibers,” Bell Syst. Tech. J. 52,1563–1578 (1973).

Electron. Lett. (4)

S. Kawakami and H. Tanji, “Evolution of Power Distribution in Graded-Index Fibres,” Electron. Lett. 19,100–102 (1983).
[CrossRef]

O. G. Leminger and G. K. Grau, “Near-Field Intensity and Modal Power Distribution in Multimode Graded-index Fibers,” Electron. Lett. 16,678–679 (1980).
[CrossRef]

M. Düser and P. Bayvel, “2.5 Gbit/s transmission over 4.5 km of 62.5 μm multimode fibre using centre launch technique,” Electron. Lett. 36,57–58 (2000).
[CrossRef]

S. S.-H. Yam and F. Achten, “Single wavelength 40 Gbit/s transmission over 3.4 km broad wavelength window multimode fibre,” Electron. Lett. 42,592–593 (2006).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

A. M. J. Koonen, “Bit-Error-Rate Degradation in a Multimode Fiber Optic Transmission Link due to Modal Noise,” IEEE J. Sel. Areas Commun. SAC- 4,1515–1522 (1986).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, “Design considerations for a transparent mode group diversity multiplexing link,” IEEE Photon. Technol. Lett. 18,2359–2361 (2006).
[CrossRef]

M. Wegmuller, S. Golowich, G. Giaretta, and M. Nuss, “Evolution of the beam diameter in a multimode fiber link through offset connectors,” IEEE Photon. Technol. Lett. 13,574–576 (2001).
[CrossRef]

L. Raddatz and I. H. White, “Overcoming the Modal Bandwidth Limitation of Multimode Fiber by using Pass-band Modulation,” IEEE Photon. Technol. Lett. 11,266–268 (1999).
[CrossRef]

J. Lightwave Technol. (6)

Opt. Commun. (1)

M. Rousseau and L. Jeunhomme, “Optimum index profile in multimode optical fiber with respect to mode coupling,” Opt. Commun. 23,275–278 (1977).
[CrossRef]

Opto-electronics (1)

J. G. Dil and H. Blok, “Propagation of Electromagnetic Surface Waves in a Radially Inhomogeneous Optical Waveguide,” Opto-electronics 5,415–428 (1973).
[CrossRef]

Science (1)

H. R. Stuart, “Dispersive Multiplexing in Multimode Optical Fiber,” Science 289,281–283 (2000).
[CrossRef] [PubMed]

Other (8)

T. Koonen, H. van den Boom, I. Tafur Monroy, and G.-D. Khoe, ”High capacity multi-service in-house networks using mode group diversity multiplexing,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper FG4.

P. L. Neo and T. D. Wilkinson, “Holographic Implementation of Optical Multiple-Inputs, Multiple-Outputs (MIMO) on a Multimode Fiber,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper CMNN2.

S. Schöllmann and W. Rosenkranz, “Experimental investigations of mode coupling as limiting effect using mode group diversity multiplexing on GI-MMF,” in Proceedings of European Conference on Optical Communications, Sep. 2006, paper We3.P.87.

http://www.ieee802.org/3/aq/public/tools/

http://www.ieee802.org/3/aq/public/tools/108fiberModel/CamMMF1p2/CamMMF1p2%20Supplement.pdf

M. Bingle and B. P. de Hon, “Differential Mode Delay Full-wave modeling and various levels of approximations,” in Proceedings of the General XXVIIth Assembly of the International Union of Radio Science, Aug. 2002, paper2060.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, (Chapman and Hall, 1983).

A. H. Cherin, An Introduction to Optical Fibers, (McGraw-Hill, 1983).

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup for the observation of the NFP at the output of a GI-MMF under selective excitation with a radially offset SMF.

Fig. 2.
Fig. 2.

Experimental NFP at the output of a 1-m, 75-m and 1-km long 62.5/125 μm silica-based GI-MMF, under selective excitation with a radially offset SMF. The radial offset was 0, 13 and 26 μm.

Fig. 3.
Fig. 3.

Simulated NFP at the output of a 62.5/125 μm silica-based GI-MMF with refractive index parameter (a) α = 1.97, (b) α = 2 and (c) α = 2.06. Each row corresponds to a different GI-MMF length (L) and each column to a different radial offset of the input SMF. Mode mixing is not taken into account.

Fig. 4.
Fig. 4.

Simulated NFP at the output of a (a) 75-m (b) 1-km long 62.5/125 μm silica-based GI-MMF, assuming full intra-group mode mixing. Each row corresponds to a different refractive index parameter (α) and each column to a different radial offset of the input SMF.

Fig. 5.
Fig. 5.

Simulated NFP at the output of a 62.5/125 μm silica-based GI-MMF using (a) fiber 26 and (c) fiber 78 from the 108-fiber model. Each row corresponds to a different GI-MMF length (L) and each column to a different radial offset of the input SMF. Mode mixing is not taken into account.

Fig. 6.
Fig. 6.

Simulated NFP at the output of a (a) 75-m (b) 1-km long 62.5/125 μm silica-based GI-MMF, assuming full intra-group mode mixing. Each row corresponds to a different refractive index profile and each column to a different radial offset of the input SMF.

Equations (7)

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

[ E r ϕ z t H r ϕ z t ] = v , μ c v , μ ( z ) [ e v , μ ( r , ϕ ) h v , μ ( r , ϕ ) ] exp ( j ωt ) .
I r ϕ L = 1 2 Re [ v , μ e v , μ r ϕ L × h v , μ * r ϕ L u ̂ z + v μ μ´ e v , μ r ϕ L × h , μ´ * r ϕ L u ̂ z ] .
c v , μ ( z ) = c v , μ ( 0 ) exp v , μ z exp ( γ v , μ z ) ,
c v , μ ( 0 ) = 0 2 π 0 e in ( r , ϕ ) × h v , μ * ( r , ϕ ) u ̂ z r d r d ϕ
c v , μ m ( L ) = v , μ c v , μ m ( 0 ) 2 N m ,
n ( r ) = { n 0 1 2 Δ ( r a ) α , r < a , n 0 1 2 Δ , r a ,
γ m ( λ ) = γ 0 ( λ ) + γ 0 ( λ ) I 9 [ 7.35 ( m 1 M 0 ) 2 α ( α + 2 ) ] ,

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