Abstract

The aim of this paper is to present a new ray-tracing model which describes the propagation of light in multi-core polymer optical fibers (MCPOFs), taking into account the crosstalk among their cores. The new model overcomes many of the limitations of previous approaches allowing us to simulate MCPOFs of arbitrary designs. Additionally, it provides us with the output ray distribution at the end of the fiber, making it possible to calculate useful parameters related to the fiber performance such as the Near-Field Pattern, the Far-Field Pattern or the bandwidth. We also present experimental measurements in order to validate the computational model and we analyze the importance of crosstalk in different MCPOF configurations.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Poisel, and O. Ziemann, “Trends in Polymer Optical Fibers,” in Proceedings of Third GR-I International Conference on New Laser Technologies and Applications. Proceedings of the SPIE (2003), Carabelas, Alexis; Baldacchini, Giuseppe; Di Lazzaro, Paolo; Zevgolis, Dimitrios, eds. Vol. 5131, pp. 213–219.
  2. “Asahi Kasei Co.” Available: http://www.asahi-kasei.co.jp/pof/en/products/multicore.html .
  3. “Asahi Glass Co.” Available: http://www.agc.co.jp .
  4. Y. Koike, “Status of High Speed Plastic Optical Fiber Towards Giga House Town,” in 18th International POF Conference. Proceedings (2009).
  5. D. Kalymnios, “Using Plastic Optical Fibre (POF) Cables in Multimedia Applications and Meeting Relevant Recent Standards,” in 17th International POF Conference Proceedings (Santa Clara, Calif., 2008).
  6. K. Shimada, H. Sasaki, and Y. Noguchi, “The home networking system based on IEEE1394 and Ethernet Technologies,” in Proceedings of ICCE: International Conference on Consumer Electronics, (2001). pp. 234–235.
  7. N. Ortega-Quijano, F. Fanjul-Vélez, and J. L. Arce-Diego, “Optical crosstalk influence in fiber imaging endoscopes design,” Opt. Commun. 283(4), 633–638 (2010).
    [CrossRef]
  8. G. Durana, G. Aldabaldetreku, J. Zubia, J. Arrue, and C. Tanaka, “Coupling losses in perfluorinated multi-core polymer optical fibers,” Opt. Express 16(11), 7929–7942 (2008).
    [CrossRef] [PubMed]
  9. A. W. Snyder, “Coupled-Mode Theory for Optical Fibers,” J. Opt. Soc. Am. 62(11), 1267–1277 (1972).
    [CrossRef]
  10. A. W. Snyder and P. McIntyre, “Crosstalk between light pipes,” J. Opt. Soc. Am. 66(9), 877–882 (1976).
    [CrossRef]
  11. A. W. Snyder, and J. D. Love, Optical waveguide theory, Chapman and Hall, ed. (London, 1983).
  12. J.-M. Liu, Photonic Devices, Cambridge University Press, ed. (Cambridge, 2005).
  13. K. L. Reichenbach and C. Xu, “Numerical analysis of light propagation in image fibers or coherent fiber bundles,” Opt. Express 15(5), 2151–2165 (2007).
    [CrossRef] [PubMed]
  14. G. Aldabaldetreku, J. Zubia, G. Durana, and J. Arrue, “Numerical implementation of the ray-tracing method in the propagation of light through multimode optical fibres,” in POF Modelling: Theory, Measurement and Application, C.-A. Bunge and H. Poisel, eds. (Books on Demand GmbH, Norderstedt, Germany, 2007), pp. 25–48.
  15. N. S. Kapany, Fiber Optics: Principles and Applications, Academic Press, ed. (London, 1968).
  16. A. H. Cherin and E. J. Murphy, “Quasi-Ray Analysis of Crosstalk between Multimode Optical Fibers,” Bell Syst. Tech. J. 54(1), 17–45 (1975).
  17. M. G. Kuzyk, Polymer Fiber Optics: Materials, Physics and Applications, Taylor & Francis, ed. (London, 2007).
  18. D. Gloge and E. A. J. Marcatili, “Multimode Theory of Graded-Core Fibers,” J. Bell Syst. Tech. 52, 1563–1578 (1973).
  19. “Hamamatsu Photonics,” Available: http://sales.hamamatsu.com/en/products.php .
  20. S. Sasho, “A Comprehensive Bending Loss Study of Multi-core POF,” in Proceedings of 17th International POF Conference Proceedings (Santa Clara, Calif., 2008).
  21. J. Arrue, J. Zubia, G. Durana, and J. Mateo, “Parameters Affecting Bending Losses in Graded-Index Polymer Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 7(5), 836–844 (2001).
    [CrossRef]
  22. D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt. 11(11), 2506–2513 (1972).
    [CrossRef] [PubMed]

2010 (1)

N. Ortega-Quijano, F. Fanjul-Vélez, and J. L. Arce-Diego, “Optical crosstalk influence in fiber imaging endoscopes design,” Opt. Commun. 283(4), 633–638 (2010).
[CrossRef]

2008 (1)

2007 (1)

2001 (1)

J. Arrue, J. Zubia, G. Durana, and J. Mateo, “Parameters Affecting Bending Losses in Graded-Index Polymer Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 7(5), 836–844 (2001).
[CrossRef]

1976 (1)

1975 (1)

A. H. Cherin and E. J. Murphy, “Quasi-Ray Analysis of Crosstalk between Multimode Optical Fibers,” Bell Syst. Tech. J. 54(1), 17–45 (1975).

1973 (1)

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

1972 (2)

Aldabaldetreku, G.

Arce-Diego, J. L.

N. Ortega-Quijano, F. Fanjul-Vélez, and J. L. Arce-Diego, “Optical crosstalk influence in fiber imaging endoscopes design,” Opt. Commun. 283(4), 633–638 (2010).
[CrossRef]

Arrue, J.

G. Durana, G. Aldabaldetreku, J. Zubia, J. Arrue, and C. Tanaka, “Coupling losses in perfluorinated multi-core polymer optical fibers,” Opt. Express 16(11), 7929–7942 (2008).
[CrossRef] [PubMed]

J. Arrue, J. Zubia, G. Durana, and J. Mateo, “Parameters Affecting Bending Losses in Graded-Index Polymer Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 7(5), 836–844 (2001).
[CrossRef]

Cherin, A. H.

A. H. Cherin and E. J. Murphy, “Quasi-Ray Analysis of Crosstalk between Multimode Optical Fibers,” Bell Syst. Tech. J. 54(1), 17–45 (1975).

Durana, G.

G. Durana, G. Aldabaldetreku, J. Zubia, J. Arrue, and C. Tanaka, “Coupling losses in perfluorinated multi-core polymer optical fibers,” Opt. Express 16(11), 7929–7942 (2008).
[CrossRef] [PubMed]

J. Arrue, J. Zubia, G. Durana, and J. Mateo, “Parameters Affecting Bending Losses in Graded-Index Polymer Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 7(5), 836–844 (2001).
[CrossRef]

Fanjul-Vélez, F.

N. Ortega-Quijano, F. Fanjul-Vélez, and J. L. Arce-Diego, “Optical crosstalk influence in fiber imaging endoscopes design,” Opt. Commun. 283(4), 633–638 (2010).
[CrossRef]

Gloge, D.

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

D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt. 11(11), 2506–2513 (1972).
[CrossRef] [PubMed]

Marcatili, E. A. J.

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

Mateo, J.

J. Arrue, J. Zubia, G. Durana, and J. Mateo, “Parameters Affecting Bending Losses in Graded-Index Polymer Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 7(5), 836–844 (2001).
[CrossRef]

McIntyre, P.

Murphy, E. J.

A. H. Cherin and E. J. Murphy, “Quasi-Ray Analysis of Crosstalk between Multimode Optical Fibers,” Bell Syst. Tech. J. 54(1), 17–45 (1975).

Ortega-Quijano, N.

N. Ortega-Quijano, F. Fanjul-Vélez, and J. L. Arce-Diego, “Optical crosstalk influence in fiber imaging endoscopes design,” Opt. Commun. 283(4), 633–638 (2010).
[CrossRef]

Reichenbach, K. L.

Snyder, A. W.

Tanaka, C.

Xu, C.

Zubia, J.

G. Durana, G. Aldabaldetreku, J. Zubia, J. Arrue, and C. Tanaka, “Coupling losses in perfluorinated multi-core polymer optical fibers,” Opt. Express 16(11), 7929–7942 (2008).
[CrossRef] [PubMed]

J. Arrue, J. Zubia, G. Durana, and J. Mateo, “Parameters Affecting Bending Losses in Graded-Index Polymer Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 7(5), 836–844 (2001).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

A. H. Cherin and E. J. Murphy, “Quasi-Ray Analysis of Crosstalk between Multimode Optical Fibers,” Bell Syst. Tech. J. 54(1), 17–45 (1975).

IEEE J. Sel. Top. Quantum Electron. (1)

J. Arrue, J. Zubia, G. Durana, and J. Mateo, “Parameters Affecting Bending Losses in Graded-Index Polymer Optical Fibers,” IEEE J. Sel. Top. Quantum Electron. 7(5), 836–844 (2001).
[CrossRef]

J. Bell Syst. Tech. (1)

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

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

N. Ortega-Quijano, F. Fanjul-Vélez, and J. L. Arce-Diego, “Optical crosstalk influence in fiber imaging endoscopes design,” Opt. Commun. 283(4), 633–638 (2010).
[CrossRef]

Opt. Express (2)

Other (13)

G. Aldabaldetreku, J. Zubia, G. Durana, and J. Arrue, “Numerical implementation of the ray-tracing method in the propagation of light through multimode optical fibres,” in POF Modelling: Theory, Measurement and Application, C.-A. Bunge and H. Poisel, eds. (Books on Demand GmbH, Norderstedt, Germany, 2007), pp. 25–48.

N. S. Kapany, Fiber Optics: Principles and Applications, Academic Press, ed. (London, 1968).

“Hamamatsu Photonics,” Available: http://sales.hamamatsu.com/en/products.php .

S. Sasho, “A Comprehensive Bending Loss Study of Multi-core POF,” in Proceedings of 17th International POF Conference Proceedings (Santa Clara, Calif., 2008).

M. G. Kuzyk, Polymer Fiber Optics: Materials, Physics and Applications, Taylor & Francis, ed. (London, 2007).

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

J.-M. Liu, Photonic Devices, Cambridge University Press, ed. (Cambridge, 2005).

H. Poisel, and O. Ziemann, “Trends in Polymer Optical Fibers,” in Proceedings of Third GR-I International Conference on New Laser Technologies and Applications. Proceedings of the SPIE (2003), Carabelas, Alexis; Baldacchini, Giuseppe; Di Lazzaro, Paolo; Zevgolis, Dimitrios, eds. Vol. 5131, pp. 213–219.

“Asahi Kasei Co.” Available: http://www.asahi-kasei.co.jp/pof/en/products/multicore.html .

“Asahi Glass Co.” Available: http://www.agc.co.jp .

Y. Koike, “Status of High Speed Plastic Optical Fiber Towards Giga House Town,” in 18th International POF Conference. Proceedings (2009).

D. Kalymnios, “Using Plastic Optical Fibre (POF) Cables in Multimedia Applications and Meeting Relevant Recent Standards,” in 17th International POF Conference Proceedings (Santa Clara, Calif., 2008).

K. Shimada, H. Sasaki, and Y. Noguchi, “The home networking system based on IEEE1394 and Ethernet Technologies,” in Proceedings of ICCE: International Conference on Consumer Electronics, (2001). pp. 234–235.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

(a) A radiating ray travelling along the lower fiber (solid lines) gives rise to coupled rays (dashed lines) in the upper fiber. (b) Parameters of the rays projected on the cross section of a fiber bundle. n co is the refractive index of the cores, n cl is the refractive index of the cladding, θ is the axial angle of the ray, θ 1 is the complementary angle of the axial one, ρ is the core radius, s C is the separation between the centers of the cores, A is the exit point of the radiating ray, B is the coupling point, s is the separation between points A and B, and ϕ is the angle between the line that joins the core centers and the line from the center of the radiating core to the point A.

Fig. 2
Fig. 2

(a) A skew ray (solid line) travelling in the central core gives rise to coupled rays (dashed lines) in the surrounding cores. (b) A meridional ray (solid line) travelling in the central core generates coupled rays (dashed lines) in the surrounding cores.

Fig. 3
Fig. 3

Cross section of an MCPOF composed by a hexagonal array of cores, that is, a ring of six cores, around a central one.

Fig. 4
Fig. 4

Comparison of the FEXT values obtained using the ray-tracing model with those calculated evaluating the analytical expressions of the quasi-ray tracing model. The measurements have been carried out as a function of 2ρ/s C, being ρ the core radius and s C the separation distance between the centers of the radiating core and of the neighboring core. The parameters used in these simulations are: 2ρ = 25.4 µm, NA = 0.1, fiber length = 1000 m and the input power distribution is F(θ) = exp(-θ/0.5θC )2, being θC the critical angle, which is the maximum value of the axial angle θ in order the ray to be confined in the core.

Fig. 5
Fig. 5

Cross section of an MCPOF composed of three concentric rings of cores around a central one. The nomenclature followed to name each core is ij , being i the index of the core and j the index of the ring. The red dashed lines mark the symmetry planes of the fiber. Hence, the core 12 has six neighboring cores marked with sloping lines.

Fig. 6
Fig. 6

Parameters for calculating the separation distance sC between core centers (a) when crosstalk takes place to one of the two neighboring cores in the same jth ring as the radiating core, and (b) when crosstalk takes place to one of the neighboring cores of the outer kth ring (i.e. k = j + 1).

Fig. 7
Fig. 7

Cross section of the investigated SI-MCPOF.

Fig. 8
Fig. 8

Cross section of the investigated GI-MCPOF.

Fig. 9
Fig. 9

Experimental set-up employed to measure the NFP and the FFP of the analyzed MCPOFs. Legend: LENS 1: symmetric-concave lens (f´ = −20 mm); LENS 2: symmetric-convex lens (f´ = + 150 mm); LENS 3: plano-convex lens (f´ = + 100 mm); LENS 4: plano-convex lens (f´ = + 50 mm); OBJECT LENS: 0.65-NA object lens.

Fig. 10
Fig. 10

Normalized NFP and FFP obtained at the end of a 1 m SI-MCPOF when only the core 00 is excited.

Fig. 11
Fig. 11

Normalized NFP and FFP obtained at the end of a 1 m SI-MCPOF when only the core 72 is excited.

Fig. 12
Fig. 12

Normalized NFP and FFP obtained at the output of a 1 m GI-MCPOF when only the core 00 is excited.

Fig. 13
Fig. 13

Normalized NFP and FFP obtained at the output of a 1 m GI-MCPOF when only the core 224 is excited.

Tables (2)

Tables Icon

Table 1 Characteristics of the investigated SI-MCPOF

Tables Icon

Table 2 Characteristics of the investigated GI-MCPOF

Equations (14)

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

T ( θ , s ) = 1 2 [ 1 cosh 2 β + [ ( n cl 2 γ 2 n co 2 cos 2 θ 1 ) / ( 2 n co n cl γ cos θ 1 ) ] 2 sinh 2 β ]                                   + 1 2 [ 1 cosh 2 β + [ ( n cl 2 cos 2 θ 1 γ 2 n co 2 ) / ( 2 n co n cl γ cos θ 1 ) ] 2 sinh 2 β ]
γ = [ ( n co n cl ) 2 sin 2 θ 1 1 ] 1 / 2
β = 2 π λ n cl s γ
s = s C cos ϕ ρ ρ 2 s C 2 sin 2 ϕ
P xt | ray = P in [ 1 ( 1 T 1 ) ( 1 T 2 ) ... ( 1 T N ) ]
P out | ray = P in ( 1 T 1 ) ( 1 T 2 ) ... ( 1 T N ) .
F E X T = 10 log 10 ( P out P xt )
s C = d
d = a ρ N rings
s C = j d 2 [ 1 cos ( Δ φ j ) ]
s C = d 2 j k [ 1 cos ( Δ φ ) ] + 1
V = 2 π ρ λ N A
M V 2 2
M V 2 4

Metrics