Abstract

Here, we propose a method to estimate misalignment losses that is based on the calculation of the radiated angular power distribution as light propagates through space using the fiber far field pattern (FFP) and simplifying and speeding calculations with the Hankel transform. This method gives good estimates for combined transversal and longitudinal losses at short, intermediate and long offset distances. In addition, the same methodology can be adapted to describe not only scalar loss but also its angular dependence caused by misalignments. We show that this approach can be applied to upgrade a connector matrix included in a propagation model that is integrated into simulation software. This way, we assess the effects of misalignments at different points in the link and are able to predict the performance of different layouts at system level.

© 2015 Optical Society of America

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References

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  1. N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).
  2. A. Esteban, M. A. Losada, J. Mateo, N. Antoniades, and A. López, “Effects of connectors in SI-POFs transmission properties studied in a matrix propagation framework,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 341–346 (2011).
  3. M. A. Losada, F. A. Domínguez-Chapman, J. Mateo, A. López, and J. Zubia, “Influence of termination on connector loss for plastic optical fibres,” in Proceedings of 16th Intl. Conf. on Transparent Optical Networks, paper Mo.C7.4 (2014).
    [Crossref]
  4. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
    [Crossref]
  5. S. Nemoto and T. Makimoto, “Analysis of splice loss in single-mode fibres using a Gaussian field approximation,” Opt. Quantum Electron. 11(5), 447–457 (1979).
    [Crossref]
  6. D. Gloge, “Offset and tilt loss in optical fiber splices,” Opt. Quantum Electron. 55(7), 905–916 (1976).
  7. W. van Etten, W. Lambo, and P. Simons, “Loss in multimode fiber connections with a gap,” Appl. Opt. 24(7), 970–976 (1985).
    [Crossref] [PubMed]
  8. C. Gao and G. Farrell, “Power coupling between two step-index multimode fibers of different numerical apertures with an angular misalignment,” Microw. Opt. Technol. Lett. 43(3), 231–234 (2004).
    [Crossref]
  9. J. Mateo, M. A. Losada, N. Antoniades, D. Richards, A. López, and J. Zubia, “Connector misalignment matrix model,” in Proceedings of 21st Intl. Conf. on Plastic Optical Fibres and Applications, pp. 90–95 (2012).
  10. S. Werzinger, C. A. Bunge, S. Loquai, and O. Ziemann, “An analytic connector loss model for step-index polymer optical fiber links,” J. Lightwave Technol. 31(16), 2769–2776 (2013).
    [Crossref]
  11. J. Mateo, M. A. Losada, I. Garcés, and J. Zubia, “Global characterization of optical power propagation in step-index plastic optical fibers,” Opt. Express 14(20), 9028–9035 (2006).
    [Crossref] [PubMed]
  12. D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
    [Crossref]
  13. E. Grivas, D. Syvridis, and G. Friedrich, “Influence of connectors on the performance of a VCSEL-based standard step-index POF link,” IEEE Photon. Technol. Lett. 21(24), 1888–1890 (2009).
    [Crossref]
  14. J. Mateo, M. A. Losada, and J. Zubia, “Frequency response in step index plastic optical fibers obtained from the generalized power flow equation,” Opt. Express 17(4), 2850–2860 (2009).
    [Crossref] [PubMed]
  15. J. Xu, M. Bloos, and H. Poisel, “Improved modelling of connector losses for SI-POF based on exact values for the radiance at fiber end faces,” in Proceedings of 16th Intl. Conf. on Transparent Optical Networks, paper Mo.C7.4 (2014).
  16. N. Baddour, “Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates,” J. Opt. Soc. Am. A 26(8), 1767–1777 (2009).
    [Crossref] [PubMed]
  17. O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF handbook, 2nd ed. (Springer, 2008).
  18. M. A. Losada, J. Mateo, and A. López, “Matrix model of optical power propagation in plastic optical fibres,” in Proceedings of 12th Intl. Conf. on Transparent Optical Networks, paper We.C3.3 (2010).
    [Crossref]

2013 (2)

2009 (3)

2006 (1)

2004 (1)

C. Gao and G. Farrell, “Power coupling between two step-index multimode fibers of different numerical apertures with an angular misalignment,” Microw. Opt. Technol. Lett. 43(3), 231–234 (2004).
[Crossref]

1985 (1)

1979 (1)

S. Nemoto and T. Makimoto, “Analysis of splice loss in single-mode fibres using a Gaussian field approximation,” Opt. Quantum Electron. 11(5), 447–457 (1979).
[Crossref]

1977 (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
[Crossref]

1976 (1)

D. Gloge, “Offset and tilt loss in optical fiber splices,” Opt. Quantum Electron. 55(7), 905–916 (1976).

Antoniades, N.

D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
[Crossref]

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

A. Esteban, M. A. Losada, J. Mateo, N. Antoniades, and A. López, “Effects of connectors in SI-POFs transmission properties studied in a matrix propagation framework,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 341–346 (2011).

J. Mateo, M. A. Losada, N. Antoniades, D. Richards, A. López, and J. Zubia, “Connector misalignment matrix model,” in Proceedings of 21st Intl. Conf. on Plastic Optical Fibres and Applications, pp. 90–95 (2012).

Baddour, N.

Bunge, C. A.

Esteban, A.

A. Esteban, M. A. Losada, J. Mateo, N. Antoniades, and A. López, “Effects of connectors in SI-POFs transmission properties studied in a matrix propagation framework,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 341–346 (2011).

Farrell, G.

C. Gao and G. Farrell, “Power coupling between two step-index multimode fibers of different numerical apertures with an angular misalignment,” Microw. Opt. Technol. Lett. 43(3), 231–234 (2004).
[Crossref]

Friedrich, G.

E. Grivas, D. Syvridis, and G. Friedrich, “Influence of connectors on the performance of a VCSEL-based standard step-index POF link,” IEEE Photon. Technol. Lett. 21(24), 1888–1890 (2009).
[Crossref]

Gao, C.

C. Gao and G. Farrell, “Power coupling between two step-index multimode fibers of different numerical apertures with an angular misalignment,” Microw. Opt. Technol. Lett. 43(3), 231–234 (2004).
[Crossref]

Garcés, I.

Gloge, D.

D. Gloge, “Offset and tilt loss in optical fiber splices,” Opt. Quantum Electron. 55(7), 905–916 (1976).

Grivas, E.

E. Grivas, D. Syvridis, and G. Friedrich, “Influence of connectors on the performance of a VCSEL-based standard step-index POF link,” IEEE Photon. Technol. Lett. 21(24), 1888–1890 (2009).
[Crossref]

Jiang, X.

D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
[Crossref]

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

Lambo, W.

López, A.

D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
[Crossref]

J. Mateo, M. A. Losada, N. Antoniades, D. Richards, A. López, and J. Zubia, “Connector misalignment matrix model,” in Proceedings of 21st Intl. Conf. on Plastic Optical Fibres and Applications, pp. 90–95 (2012).

A. Esteban, M. A. Losada, J. Mateo, N. Antoniades, and A. López, “Effects of connectors in SI-POFs transmission properties studied in a matrix propagation framework,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 341–346 (2011).

Loquai, S.

Losada, M. A.

D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
[Crossref]

J. Mateo, M. A. Losada, and J. Zubia, “Frequency response in step index plastic optical fibers obtained from the generalized power flow equation,” Opt. Express 17(4), 2850–2860 (2009).
[Crossref] [PubMed]

J. Mateo, M. A. Losada, I. Garcés, and J. Zubia, “Global characterization of optical power propagation in step-index plastic optical fibers,” Opt. Express 14(20), 9028–9035 (2006).
[Crossref] [PubMed]

J. Mateo, M. A. Losada, N. Antoniades, D. Richards, A. López, and J. Zubia, “Connector misalignment matrix model,” in Proceedings of 21st Intl. Conf. on Plastic Optical Fibres and Applications, pp. 90–95 (2012).

A. Esteban, M. A. Losada, J. Mateo, N. Antoniades, and A. López, “Effects of connectors in SI-POFs transmission properties studied in a matrix propagation framework,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 341–346 (2011).

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

Madamopoulos, N.

D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
[Crossref]

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

Makimoto, T.

S. Nemoto and T. Makimoto, “Analysis of splice loss in single-mode fibres using a Gaussian field approximation,” Opt. Quantum Electron. 11(5), 447–457 (1979).
[Crossref]

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
[Crossref]

Mateo, J.

D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
[Crossref]

J. Mateo, M. A. Losada, and J. Zubia, “Frequency response in step index plastic optical fibers obtained from the generalized power flow equation,” Opt. Express 17(4), 2850–2860 (2009).
[Crossref] [PubMed]

J. Mateo, M. A. Losada, I. Garcés, and J. Zubia, “Global characterization of optical power propagation in step-index plastic optical fibers,” Opt. Express 14(20), 9028–9035 (2006).
[Crossref] [PubMed]

J. Mateo, M. A. Losada, N. Antoniades, D. Richards, A. López, and J. Zubia, “Connector misalignment matrix model,” in Proceedings of 21st Intl. Conf. on Plastic Optical Fibres and Applications, pp. 90–95 (2012).

A. Esteban, M. A. Losada, J. Mateo, N. Antoniades, and A. López, “Effects of connectors in SI-POFs transmission properties studied in a matrix propagation framework,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 341–346 (2011).

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

Nemoto, S.

S. Nemoto and T. Makimoto, “Analysis of splice loss in single-mode fibres using a Gaussian field approximation,” Opt. Quantum Electron. 11(5), 447–457 (1979).
[Crossref]

Richards, D.

D. Richards, M. A. Losada, N. Antoniades, A. López, J. Mateo, X. Jiang, and N. Madamopoulos, “Modeling methodology for engineering SI-POF and connectors in an avionics system,” J. Lightwave Technol. 31(3), 468–475 (2013).
[Crossref]

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

J. Mateo, M. A. Losada, N. Antoniades, D. Richards, A. López, and J. Zubia, “Connector misalignment matrix model,” in Proceedings of 21st Intl. Conf. on Plastic Optical Fibres and Applications, pp. 90–95 (2012).

Simons, P.

Syvridis, D.

E. Grivas, D. Syvridis, and G. Friedrich, “Influence of connectors on the performance of a VCSEL-based standard step-index POF link,” IEEE Photon. Technol. Lett. 21(24), 1888–1890 (2009).
[Crossref]

Truong, T. K.

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

van Etten, W.

Werzinger, S.

Ziemann, O.

Zubia, J.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
[Crossref]

IEEE Photon. Technol. Lett. (1)

E. Grivas, D. Syvridis, and G. Friedrich, “Influence of connectors on the performance of a VCSEL-based standard step-index POF link,” IEEE Photon. Technol. Lett. 21(24), 1888–1890 (2009).
[Crossref]

J. Lightwave Technol. (2)

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

Microw. Opt. Technol. Lett. (1)

C. Gao and G. Farrell, “Power coupling between two step-index multimode fibers of different numerical apertures with an angular misalignment,” Microw. Opt. Technol. Lett. 43(3), 231–234 (2004).
[Crossref]

Opt. Express (2)

Opt. Quantum Electron. (2)

S. Nemoto and T. Makimoto, “Analysis of splice loss in single-mode fibres using a Gaussian field approximation,” Opt. Quantum Electron. 11(5), 447–457 (1979).
[Crossref]

D. Gloge, “Offset and tilt loss in optical fiber splices,” Opt. Quantum Electron. 55(7), 905–916 (1976).

Other (7)

N. Antoniades, M. A. Losada, J. Mateo, D. Richards, T. K. Truong, X. Jiang, and N. Madamopoulos, “Modeling and characterization of SI-POF and connectors for use in an avionics system,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 105–110 (2011).

A. Esteban, M. A. Losada, J. Mateo, N. Antoniades, and A. López, “Effects of connectors in SI-POFs transmission properties studied in a matrix propagation framework,” in Proceedings of 20th Intl. Conf. on Plastic Optical Fibres and Applications, pp. 341–346 (2011).

M. A. Losada, F. A. Domínguez-Chapman, J. Mateo, A. López, and J. Zubia, “Influence of termination on connector loss for plastic optical fibres,” in Proceedings of 16th Intl. Conf. on Transparent Optical Networks, paper Mo.C7.4 (2014).
[Crossref]

J. Mateo, M. A. Losada, N. Antoniades, D. Richards, A. López, and J. Zubia, “Connector misalignment matrix model,” in Proceedings of 21st Intl. Conf. on Plastic Optical Fibres and Applications, pp. 90–95 (2012).

J. Xu, M. Bloos, and H. Poisel, “Improved modelling of connector losses for SI-POF based on exact values for the radiance at fiber end faces,” in Proceedings of 16th Intl. Conf. on Transparent Optical Networks, paper Mo.C7.4 (2014).

O. Ziemann, J. Krauser, P. E. Zamzow, and W. Daum, POF handbook, 2nd ed. (Springer, 2008).

M. A. Losada, J. Mateo, and A. López, “Matrix model of optical power propagation in plastic optical fibres,” in Proceedings of 12th Intl. Conf. on Transparent Optical Networks, paper We.C3.3 (2010).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic of the geometry of power radiation from the fiber end surface. The power radiated from A that reaches B is given by g (θ), where θ is the angle defined by A, A’ and B.
Fig. 2
Fig. 2 The radiated power from all points at the radiating fiber end surface is superposed to obtain the total power at plane z = z0, where the receiving fiber is placed.
Fig. 3
Fig. 3 Schematic that shows the fiber radiating light only at a specific direction given by angle θr and the projection of the radiation pattern onto the plane of the second fiber.
Fig. 4
Fig. 4 The surface plot on the upper side represents the model prediction of the power transferred between two fibers with longitudinal and transversal offsets. Superimposed black dots are experimental measurements obtained shifting two fibers along the longitudinal and transversal axis. On the lower side, the predictions of our model (red lines) for transversal (left) and longitudinal (right) offsets are compared to predictions of the traditional model (blue circles) and experimental measurements (black circles).
Fig. 5
Fig. 5 Angle-dependent transferred power for three longitudinal z0 and four transversal misalignments, r0.
Fig. 6
Fig. 6 Matrices for a polished ST connector. From left to right: basic matrix; 0.5 mm longitudinal offset; 0.5 mm axial offset and combined axial and longitudinal 0.5 mm offsets.
Fig. 7
Fig. 7 Five-meter POF link with a) a connector at 0.5 m from the emitter; (b) without connectors and (c) with a connector at 4.5 m from the emitter. The connector is misaligned (r0=0.5 mm, z0=0.5 mm).
Fig. 8
Fig. 8 Absolute value of the normalized transfer function measured at the detector for a LED (FWHM of 30°) on the left and a VCSEL (10°) on the right.

Equations (11)

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

C( r 1 , φ 1 )C( r 1 )={ 1, r 1 a 0, r 1 >a
R( r,z )= 0 2π 0 C( r 1 , φ 1 ) g( θ( r 1 , φ 1 ,r,φ,z ) ) r 1 d r 1 d φ 1 .
θ= tan 1 ( r 1 2 + r 2 2 r 1 rcos( φ 1 φ ) z ).
R( r,z )= 0 2π 0 a g( tan 1 ( r 1 2 + r 2 2 r 1 rcos( φ 1 φ ) z ) ) r 1 d r 1 d φ 1 .
R( r,z )=C( r )g( r )=C( r )g( r z )= z 2 Η 1 { a J 1 ( 2πaρ )G( zρ ) ρ },
P( r 0 , z 0 )= C' R( r, z 0 )rdrdφ ,
P( r 0 , z 0 )={ 2 r 0 a r 0 +a cos 1 ( r 0 2 + r 2 a 2 2r r 0 )R( r, z 0 )rdr 2π 0 R( r, z 0 )rdr , if r 0 a 2π 0 a r 0 R( r, z 0 )rdr +2 a r 0 a+ r 0 cos 1 ( r 0 2 + r 2 a 2 2r r 0 )R( r, z 0 )rdr 2π 0 R( r, z 0 )rdr , if r 0 <a
R( θ r ,r,z )=2πztan( θ r ) a 2 Η 1 { J 1 ( 2πaρ ) aρ J 0 ( 2πztan( θ r )ρ ) },
P( r 0 , z 0 )= 0 π 2 g( θ )P( θ, r 0 , z 0 )sin( θ )dθ .
C( r 0 , z 0 )=P( r 0 , z 0 )C,
a) p D = M 0.5m C( 0.5,0.5 ) M 4.5m p E b) p D = M 0.5m M 4.5m p E , c) p D = M 4.5m C( 0.5,0.5 ) M 0.5m p E

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