Abstract

We investigate the bend loss of highly multimode air-clad microstructured polymer optical fibre which displays low bend loss for small bend radii. After repeated bending the loss approached a plateau, decreasing significantly after a characteristic length. The loss at a particular point depended on the configuration of the fibre preceding that point. A simple analytical model based on a transfer-matrix method is derived to explain this behaviour in terms of the power distribution amongst different mode groups. This model allows the effect of a particular fibre configuration to be predicted.

© 2008 Optical Society of America

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References

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  1. M. Jouguet, "Effects of curvature on the propagation of electromagnetic waves in guides of circular cross section," Cables Transm. 1, 133-135 (1947).
  2. D. Marcuse, "Radiation loss of helically deformed optical fibre," J. Opt. Soc. Am. 66, 1025-1031 (1976).
    [CrossRef]
  3. C. Winkler, J. D. Love and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
    [CrossRef]
  4. O. Ziemann, J. Krauser, P. E. Zamzow and W. DaumPOF Handbook (Berlin, Springer, 2008).
  5. J. Arrue and J. Zubia, "Analysis of the decrease in attenuation achieved by properly bending plastic optical fibres," IEE Proc. Optoelectron. 143, 135-138 (1996).
    [CrossRef]
  6. J. Arrue, J. Zubia, G. Fuster and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
    [CrossRef]
  7. 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]
  8. A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, London, 1983).
  9. R. T. Schermer and J. H. Cole, "Improved bend loss formula verified for optical fiber by simulation and experiment," IEEE J. Quantum Electon. 43, 899-909 (2007).
    [CrossRef]
  10. D. Gloge, "Optical power flow in multimode fibres," Bell Syst. Tech. J. 51, 1767-1783 (1972).
  11. A. Djordjevic and S. Savovic, "Investigation of mode coupling in step index plastic optical fibres using the power flow equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
    [CrossRef]
  12. M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
    [CrossRef]
  13. M. C. J. Large, L. Poladian, G. W. Barton, and M. A. van Eijkelenborg, Microstructured polymer optical fibres (Springer, Berlin, 2007).
  14. J. Poulin, A. Argyros, R. Kashyap, and M. Large, "Fabrication and Characterisation of a Large-core Bridged Air-clad High Numerical Aperture Microstructured Polymer Optical Fibre," 16th international conference on plastic optical fibers, Turin, Italy, 10-12 September (2007), p.131-134.
  15. N. A. Issa, "High numerical aperture in multimode microstructured optical fibers," Appl. Opt. 43, 6191-6197 (2004).
    [CrossRef] [PubMed]
  16. http://www.pofeska.com/pofeskae/pofe/supere/supere.htm.
  17. http://www.optimedia.co.kr/eng_optimedia_main_b_01.htm.
  18. Deviations from this assumption were attempted but consistently produced worse fits to the experimental data. A differential mode attenuation measurement would determine the ? parameters.
  19. J. M. Fini and S. Ramachandran, " Natural bend-distortion immunity of higher-order-mode large-mode-area fibers," Opt. Lett. 32, 748-750 (2007).
    [CrossRef] [PubMed]
  20. J. M. Fini, "Intuitive modeling of bend distortion in large-mode-area fibers," Opt. Lett. 32, 1632-1634 (2007).
    [CrossRef] [PubMed]

2007 (3)

2006 (1)

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

2004 (1)

2000 (2)

A. Djordjevic and S. Savovic, "Investigation of mode coupling in step index plastic optical fibres using the power flow equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[CrossRef]

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]

1998 (1)

J. Arrue, J. Zubia, G. Fuster and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

1996 (1)

J. Arrue and J. Zubia, "Analysis of the decrease in attenuation achieved by properly bending plastic optical fibres," IEE Proc. Optoelectron. 143, 135-138 (1996).
[CrossRef]

1979 (1)

C. Winkler, J. D. Love and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
[CrossRef]

1976 (1)

1972 (1)

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

1947 (1)

M. Jouguet, "Effects of curvature on the propagation of electromagnetic waves in guides of circular cross section," Cables Transm. 1, 133-135 (1947).

Argyros, A.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Arrue, J.

J. Arrue, J. Zubia, G. Fuster and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

J. Arrue and J. Zubia, "Analysis of the decrease in attenuation achieved by properly bending plastic optical fibres," IEE Proc. Optoelectron. 143, 135-138 (1996).
[CrossRef]

Asawa, C. K.

Barton, G. W.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Bassett, I. M.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Cole, J. H.

R. T. Schermer and J. H. Cole, "Improved bend loss formula verified for optical fiber by simulation and experiment," IEEE J. Quantum Electon. 43, 899-909 (2007).
[CrossRef]

Cox, F.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Djordjevic, A.

A. Djordjevic and S. Savovic, "Investigation of mode coupling in step index plastic optical fibres using the power flow equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[CrossRef]

Fini, J. M.

Fuster, G.

J. Arrue, J. Zubia, G. Fuster and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

Ghatak, A. K.

C. Winkler, J. D. Love and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
[CrossRef]

Gloge, D.

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

Issa, N. A.

Jouguet, M.

M. Jouguet, "Effects of curvature on the propagation of electromagnetic waves in guides of circular cross section," Cables Transm. 1, 133-135 (1947).

Kalymnios, D.

J. Arrue, J. Zubia, G. Fuster and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

Large, M. C. J.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Love, J. D.

C. Winkler, J. D. Love and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
[CrossRef]

Lwin, R.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Marcuse, D.

Ponrathnam, S.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Pujari, N. S.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Ramachandran, S.

Savovic, S.

A. Djordjevic and S. Savovic, "Investigation of mode coupling in step index plastic optical fibres using the power flow equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[CrossRef]

Schermer, R. T.

R. T. Schermer and J. H. Cole, "Improved bend loss formula verified for optical fiber by simulation and experiment," IEEE J. Quantum Electon. 43, 899-909 (2007).
[CrossRef]

Taylor, H. F.

van Eijkelenborg, M. A.

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Winkler, C.

C. Winkler, J. D. Love and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
[CrossRef]

Zubia, J.

J. Arrue, J. Zubia, G. Fuster and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

J. Arrue and J. Zubia, "Analysis of the decrease in attenuation achieved by properly bending plastic optical fibres," IEE Proc. Optoelectron. 143, 135-138 (1996).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

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

Cables Transm. (1)

M. Jouguet, "Effects of curvature on the propagation of electromagnetic waves in guides of circular cross section," Cables Transm. 1, 133-135 (1947).

IEE Proc. Optoelectron. (2)

J. Arrue and J. Zubia, "Analysis of the decrease in attenuation achieved by properly bending plastic optical fibres," IEE Proc. Optoelectron. 143, 135-138 (1996).
[CrossRef]

J. Arrue, J. Zubia, G. Fuster and D. Kalymnios, "Light power behaviour when bending plastic optical fibres," IEE Proc. Optoelectron. 145, 313-318 (1998).
[CrossRef]

IEEE J. Quantum Electon. (1)

R. T. Schermer and J. H. Cole, "Improved bend loss formula verified for optical fiber by simulation and experiment," IEEE J. Quantum Electon. 43, 899-909 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Djordjevic and S. Savovic, "Investigation of mode coupling in step index plastic optical fibres using the power flow equation," IEEE Photon. Technol. Lett. 12, 1489-1491 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Mol. Cryst. Liq. Cryst. (1)

M. C. J. Large, S. Ponrathnam, A. Argyros, I. M. Bassett, N. S. Pujari, F. Cox, R. Lwin, G. W. Barton, and M. A. van Eijkelenborg, "Microstructured polymer optical fibres: New opportunities and challenges," Mol. Cryst. Liq. Cryst. 446, 219-232 (2006).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

C. Winkler, J. D. Love and A. K. Ghatak, "Loss calculations in bent multimode optical waveguides," Opt. Quantum Electron. 11, 173-183 (1979).
[CrossRef]

Other (7)

O. Ziemann, J. Krauser, P. E. Zamzow and W. DaumPOF Handbook (Berlin, Springer, 2008).

A. W. Snyder and J. D. Love, Optical waveguide theory (Chapman and Hall, London, 1983).

M. C. J. Large, L. Poladian, G. W. Barton, and M. A. van Eijkelenborg, Microstructured polymer optical fibres (Springer, Berlin, 2007).

J. Poulin, A. Argyros, R. Kashyap, and M. Large, "Fabrication and Characterisation of a Large-core Bridged Air-clad High Numerical Aperture Microstructured Polymer Optical Fibre," 16th international conference on plastic optical fibers, Turin, Italy, 10-12 September (2007), p.131-134.

http://www.pofeska.com/pofeskae/pofe/supere/supere.htm.

http://www.optimedia.co.kr/eng_optimedia_main_b_01.htm.

Deviations from this assumption were attempted but consistently produced worse fits to the experimental data. A differential mode attenuation measurement would determine the ? parameters.

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Figures (6)

Fig. 1.
Fig. 1.

(a). Photograph of stacked preform used to make the microstructured sleeve. Scanning electron microscope images of the endface of fibres drawn with (b) no pressure and (c) 10 mBars of pressure applied to the cladding holes. Inset to (c) shows the struts in the cladding. Defects in (c) are due to cleaving and are only present on the fibre endface.

Fig. 2.
Fig. 2.

(a). Schematic of the measurement setup; the variable (the bend radius) is indicated in red. (b). The average bend loss as a function of bend radius for the four fibres tested.

Fig. 3.
Fig. 3.

(a). Schematic of the measurement setup. (b). Bend loss as a function of bent fibre length for three bend radii. Each data point represents the loss after an additional five full turns. The black curve is the calculated loss using Eq. (13) as described in Section 4.

Fig. 4.
Fig. 4.

(a). Schematic of the measurement setup. (b). The average bend loss for the subsequent bends as a function of the straight length between them and the initial bends (indicated by the data points). The average loss of the initial bends is indicated by the solid red line for comparison. (c). The bend loss as a function of distance from first bend, each data point representing the effect of five full turns. The calculated results using Eq. (13), as described in Section 4, are shown by the dotted black lines in (b) and the black curves in (c).

Fig. 5.
Fig. 5.

Schematic of how the model parameters may be measured from extensive bending experiments such as those in Section 3.2.

Fig. 6.
Fig. 6.

Photograph of telephone-cord style mPOF patch cord made by keeping the fibre wound around the mandrel and annealing. The resulting cord has a minimum length of 2 cm, a maximum length of 30 cm and contains 31 windings with a 3 mm bend radius. The estimated total bend loss for the cord is 1.5 dB.

Tables (1)

Tables Icon

Table 1. Model parameters

Equations (16)

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d P l dz = ( α l + c ) P l + c P h ,
d P h dz = ( α h + c + β ) P h + c P l ,
P ( z ) = L β ( z ) . P ( 0 ) ,
P ( z ) = [ P l ( z ) P h ( z ) ] ,
L β ( z ) = exp ( C z ) 2 B [ B A + ( B + A ) exp ( B z ) 2 c [ exp ( Bz ) 1 ] 2 c [ exp ( B z ) 1 ] ( B A ) exp ( Bz ) + B + A ] .
A = α h α l + β ,
B = ( 4 c 2 + A 2 ) 1 2 ,
C = 1 2 ( 2 c + B + α l + α h + β ) .
P ( z 3 ) = L β ( z 3 z 2 ) . L 0 ( z 2 z 1 ) . L β ( z 1 0 ) . P ( 0 ) .
d dz ( P h P l ) = c A P l P h P l 2 P h 2 > 0 net coupling from l to h
< 0 net coupling from h to l .
P l P h P l 2 P h 2 = c A ,
1 P h 1 P l = A c
10 log 10 P b ( z 1 ) P s ( z 1 ) = 10 log 10 L 0 ( z 1 z ) . L β ( z ) . P ( 0 ) L 0 ( z 1 ) . P ( 0 ) .
Bend loss ( dB / m ) = β P h ( 0 ) P ( 0 ) at start of bend
= B C after plateau is reached .

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