Abstract

The aim of the present paper is to provide a comprehensive analysis of the coupling losses in multi-step index (MSI) fibres. Their light power acceptance properties are investigated to obtain the corresponding analytical expressions taking into account longitudinal, transverse, and angular misalignments. For this purpose, a uniform power distribution is assumed. In addition, we perform several experimental measurements and computer simulations in order to calculate the coupling losses for two different MSI polymer optical fibres (MSI-POFs). These results serve us to validate the theoretical expressions we have obtained.

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References

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  15. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  16. J. Arrue, J. Zubia, G. Durana, J. Mateo, and M. Lopez-Amo, �??Model for the propagation of pulses and mode scrambling in a real POF with structural imperfections,�?? in Proceedings of the Tenth International Conference on Plastic Optical Fibers and Applications�??POF�??01, pp. 301�??308 (Amsterdam (The Netherlands), 2001).
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  24. C. M. Miller and S. C. Mettler, �??A Loss Model for Parabolic�??Profile Fiber Splices,�?? Bell Syst. Tech. J. 57, 3167�??3180 (1978).
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  26. R. J. Pieper and A. Nassopoulos, �??The Eikonal Ray Equations in Optical Fibers,�?? IEEE Trans. Educ. 40, 139�??143 (1997).
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Appl. Opt.

Bell Syst. Tech. J.

C. M. Miller and S. C. Mettler, �??A Loss Model for Parabolic�??Profile Fiber Splices,�?? Bell Syst. Tech. J. 57, 3167�??3180 (1978).

S. C. Mettler, �??A General Characterization of Splice Loss for Multimode Optical Fibers,�?? Bell Syst. Tech. J. 58, 2163�??2182 (1979).

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

D. Gloge, �??Offset and Tilt Loss in Optical Fiber Splices,�?? Bell Syst. Tech. J. 55, 905�??916 (1976).

T. C. Chu and A. R. McCormick, �??Measurements of Loss Due to Offset, End Separation, and Angular Misalignment in Graded Index Fibers Excited by an Incoherent Source,�?? Bell Syst. Tech. J. 57, 595�??602 (1978).

Fiber and Integrated Optics

J. Zubia, G. Aldabaldetreku, G. Durana, J. Arrue, H. Poisel, and C. A. Bunge, �??Geometric Optics Analysis of Multi�??Step Index Optical Fibers,�?? Fiber and Integrated Optics 23, 121�??156 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

G. Jiang, R. F. Shi, and A. F. Garito, �??Mode Coupling and Equilibrium Mode Distribution Conditions in Plastic Optical Fibers,�?? IEEE Photon. Technol. Lett. 9, 1128�??1131 (1997).
[CrossRef]

IEEE Trans. Educ.

R. J. Pieper and A. Nassopoulos, �??The Eikonal Ray Equations in Optical Fibers,�?? IEEE Trans. Educ. 40, 139�??143 (1997).
[CrossRef]

J. Lightwave Technol.

Optical and Quantum Electronics

A. Ankiewicz and C. Pask, �??The effects of source configuration on bandwidth and loss measurements in optical fibres,�?? Optical and Quantum Electronics 15, 463�??470 (1983).
[CrossRef]

Plastic Optical Fibers and Applic. 2001

K. Irie, Y. Uozu, and T. Yoshimura, �??Structure design and analysis of broadband POF,�?? in Proceedings of the Tenth International Conference on Plastic Optical Fibers and Applications�??POF�??01, pp. 73�??79 (Amsterdam (The Netherlands), 2001).

Plastic Optical Fibers and Applicat 1999

V. Levin, T. Baskakova, Z. Lavrova, A. Zubkov, H. Poisel, and K. Klein, �??Production of multilayer polymer optical fibers,�?? in Proceedings of the Eighth International Conference on Plastic Optical Fibers and Applications�?? POF�??99, pp. 98�??101 (Chiba (Japan), 1999).

POF Conference 2001

J. Arrue, J. Zubia, G. Durana, J. Mateo, and M. Lopez-Amo, �??Model for the propagation of pulses and mode scrambling in a real POF with structural imperfections,�?? in Proceedings of the Tenth International Conference on Plastic Optical Fibers and Applications�??POF�??01, pp. 301�??308 (Amsterdam (The Netherlands), 2001).

POF Conference 2002

J. Zubia, H. Poisel, C.-A. Bunge, G. Aldabaldetreku, and J. Arrue, �??POF Modelling,�?? in 11th International POF Conference 2002: Proceedings, pp. 221�??224 (Tokyo (Japan), 2002).

B. Lohmüller, A. Bachmann, O. Ziemann, A. Sawaki, H. Shirai, and K. Suzuki, �??The Use of LEPAS System for POF Characterization,�?? in 11th International POF Conference 2002: Proceedings, pp. 263�??266 (Tokyo (Japan), 2002).

Tech. Rep. JIS C 6862

Japanese Standards Association, �??Test methods for structural parameters of all plastic multimode optical fibers,�?? Tech. Rep. JIS C 6862, JIS, Tokyo, Japan (1990).

Tech. Rep. JIS C 6863

Japanese Standards Association, �??Test methods for attenuation of all plastic multimode optical fibers,�?? Tech. Rep. JIS C 6863, JIS, Tokyo, Japan (1990).

Other

D. Marcuse, Principles of Optical Fiber Measurements, chap. 4 (Academic Press, Inc., London, 1981).

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

Mitsubishi Rayon Co., Ltd.: �??Eska�??Miu,�?? URL <a href="http://www.pofeska.com.">http://www.pofeska.com.</a>

D. Marcuse, D. Gloge, and E. A. J. Marcatili, �??Guiding Properties of Fibers,�?? in Optical Fiber Telecommunications, S. E. Miller and A. G. Chynoweth, eds., chap. 3 (Academic Press, Inc., San Diego, California, 1979).

G. Keiser, Optical Fiber Communications (McGraw�??Hill, Singapore, 1991).

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Figures (15)

Fig. 1.
Fig. 1.

Experimental set-up used to measure coupling losses of MSI-POFs.

Fig. 2.
Fig. 2.

Cross-section photographs of the MSI-POFs and their respective refractive-index profiles.

Fig. 3.
Fig. 3.

Eska-Miu fibre. Experimental near- and far-fields of the transmitting fibre for different source configurations used in the measurements.

Fig. 4.
Fig. 4.

TVER fibre. Experimental near- and far-fields of the transmitting fibre for different source configurations used in the measurements.

Fig. 5.
Fig. 5.

Experimental near- and far-fields of the transmitting fibre with an 8-shaped scrambler used in the measurements for the Eska-Miu and TVER fibres (NAinput =0.1).

Fig. 6.
Fig. 6.

Eska-Miu fibre. Near- and far-fields of the transmitting fibre for different source configurations used in the numerical computer simulations.

Fig. 7.
Fig. 7.

TVER fibre. Near- and far-fields of the transmitting fibre for different source configurations used in the numerical computer simulations.

Fig. 8.
Fig. 8.

Eska-Miu fibre. Coupling loss against normalized longitudinal separation s/Router for various transverse offsets and for different source configurations. Experimental and numerical results. The insets correspond to the results obtained when the source covers the whole input surface of the transmitting fibre. The analytical results denoted by ♦ are shown superimposed on the numerical results obtained with NAinput =0.65.

Fig. 9.
Fig. 9.

TVER fibre. Coupling loss against normalized longitudinal separation s/Router for various transverse offsets and for different source configurations. Experimental and numerical results. The insets correspond to the results obtained when the source covers the whole input surface of the transmitting fibre. The analytical results denoted by ♦ are shown superimposed on the numerical results obtained with NAinput =0.65.

Fig. 10.
Fig. 10.

Coupling loss against normalized longitudinal separation s/Router for various transverse offsets and using an 8-shaped scrambler in the transmitting fibre (NAinput =0.1). Experimental results obtained for the Eska-Miu and TVER fibres.

Fig. 11.
Fig. 11.

Eska-Miu fibre. Coupling loss against normalized transverse offset d/Router for various longitudinal separations and for different source configurations. Experimental and numerical results. The insets correspond to the results obtained when the source covers the whole input surface of the transmitting fibre. The analytical results denoted by ♦ are shown superimposed on the numerical results obtained with NAinput =0.65.

Fig. 12.
Fig. 12.

TVER fibre. Coupling loss against normalized transverse offset d/Router for various longitudinal separations and for different source configurations. Experimental and numerical results. The insets correspond to the results obtained when the source covers the whole input surface of the transmitting fibre. The analytical results denoted by ♦ are shown superimposed on the numerical results obtained with NAinput =0.65.

Fig. 13.
Fig. 13.

Coupling loss against normalized transverse offset d/Router for various longitudinal separations and using an 8-shaped scrambler in the transmitting fibre (NAinput =0.1). Experimental results obtained for the Eska-Miu and TVER fibres.

Fig. 14.
Fig. 14.

Coupling loss against angular misalignment α (in degrees) for various longitudinal separations for an input numerical aperture NAinput =0.65. Experimental and numerical results. The insets correspond to the results obtained when the source covers the whole input surface of the transmitting fibre. The analytical results denoted by ♦ are shown superimposed on the numerical results.

Fig. 15.
Fig. 15.

Coupling loss against angular misalignment α (in degrees) for various transverse offsets for an input numerical aperture NAinput =0.65. Experimental and numerical results. The insets correspond to the results obtained when the source covers the whole input surface of the transmitting fibre.

Tables (3)

Tables Icon

Table 1. Analytical expression of the coupling loss LLS for a longitudinal separation s for MSI fibres. (After Ref. [3].)

Tables Icon

Table 2. Analytical expression of the coupling loss LTO for a transverse offset d for MSI fibres. (After Ref. [3].)

Tables Icon

Table 3. Physical dimensions of the different layers (outer radii in mm).

Equations (9)

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n ( r ) = { n 1 ; r < ρ 1 , n 2 ; ρ 1 r < ρ 2 , n N ; ρ N 1 r < ρ N , n cl ; r ρ N .
P br = π 2 I 0 n 0 2 i = 1 N ( ρ i 2 ρ i 1 2 ) S i = i = 1 N P i ; S i = n i 2 n cl 2 ,
W i W 1 = P i A i P 1 A 1 = [ ( ρ i 2 ρ i 1 2 ) NA i 2 ] [ π ( ρ i 2 ρ i 1 2 ) ] [ ρ 1 2 NA 1 2 ] [ π ρ 1 2 ] = NA i 2 NA 1 2 .
L AM = 10 log 2 π i = 1 N ( ρ i 2 ρ i 1 2 ) NA i 2 { i = 2 j NA i 2 δ i + NA 1 2 ρ 1 2 [ arccos q 1 q 1 ( 1 q 1 2 ) 1 2 ] } ,
R 2 = r 2 + n 2 sin 2 θ z n 2 n cl 2
R 2 = ( 1 β 2 k 2 n 2 ) n 2 n 2 n cl 2
σ = n sin θ z ( n 2 n cl 2 ) 1 2 ,
R 2 = r 2 + σ 2 .
D 2 = d 2 + n 2 sin 2 α n 2 n cl 2 ,

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