Abstract

The behavior of tapered graded-index polymer optical fibers is analyzed computationally for different refractive indices of the surrounding medium. This serves to clarify the main parameters affecting their possible performance as refractive-index sensors and extends an existing study of similar structures in glass fibers. The ray-tracing method is employed, its specific implementation is explained, and its results are compared with experimental ones, both from our laboratory and from the literature. The results show that the current commercial graded-index polymer optical fibers can be used to measure a large range of refractive indices with several advantages over glass fibers.

© 2008 Optical Society of America

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References

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  1. J.  Villatoro, D.  Monzón-Hernández, and D.  Luna-Moreno, "In-line optical fiber sensors based on cladded multimode tapered fibers," Appl. Opt. 43, 5933-5938 (2004).
    [CrossRef] [PubMed]
  2. G.  Shangping and S.  Albin, "Transmission property and evanescent wave absorption of cladded multimode fiber tapers," Opt. Express 11, 215-223 (2003).
    [CrossRef]
  3. S.  Xue, M. A.  van Eijkelenborg, G.W.  Barton, and P.  Hambley, "Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering," J. Lightwave Technol. 25, 1169-1176 (2007).
    [CrossRef]
  4. O.  Ziemann, H.  Poisel, A.  Bachmann, and J.  Vinogradov, "Special problems measuring POF," in POF Modelling: Theory, Measurement and Application, C.-A. Bunge and H. Poisel, eds., (Books on Demand GmbH, Norderstedt, Germany, 2008).
  5. J.  Zubia and J.  Arrue, "Plastic Optical Fibers: An Introduction to Their Technological Processes and Applications," Opt. Fiber Technol.  7, 101-140 (2001).
    [CrossRef]
  6. J.  Munisami and D.  Kalymnios, "High NA POF performance versus the requirements of the recent standard ISO/IEC JTC 1 FDIS 24702," in Proceedings of 15th International Conference on Plastic Optical Fibers and Applications POF�??2006, (Korea, 2006), pp. 102-109.
  7. M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
    [CrossRef]
  8. J.  Arrue, G.  Aldabaldetreku, G.  Durana, J.  Zubia, and F.  Jiménez, "Computational research on the behaviour of bent plastic optical fibres in communications links and sensing applications," in Recent Research Developments in Optics, S. G. Pandalai, ed., (Research Signpost, Kerala, India, 2005), Chap. 5.
  9. A. W.  Snyder and J. D.  Love, Optical waveguide theory (Chapman & Hall, New York, 1983).
  10. Chromis FiberOptics Co., "Chromis Fiberoptics," (Head office in 6 Powder Horn Dr., Warren, NJ 07059, USA). http://www.chromisfiber.com.
  11. FiberFin Inc., "FiberFin," (Head office in 201 Beaver Street, Yorkville, Illinois, USA.).http://www.fiberfin.com.
  12. Asahi Glass Co. Ltd., "Asahi Glass," (Lucina Division; Head office in 1-12-1, Yurakucho, Chiyoda-ku, Tokyo 100-8405, Japan). http://www.lucina.jp/eg_lucina/productsengf2.htm.
  13. A.  Sharma, D.  Vizia, and A. K.  Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt.  21, 984-987 (1982).
    [CrossRef] [PubMed]
  14. F.  Jiménez, J.  Arrue, G.  Aldabaldetreku, and J.  Zubia, "Numerical Simulation of Light Propagation in Plastic Optical Fibres of Arbitrary 3D Geometry," WSEAS Trans. Math.  3, 824-829 (2004).
  15. T. A.  Birks and Y. W.  Li, "The shape of fiber tapers," J. Lightwave Technol. 10, 432-438 (1992).
    [CrossRef]
  16. J.  Arrue, F.  Jimémez, M.  Lomer, G.  Aldabaldetreku, G.  Durana, and J.  Zubia "Characterization of tapered, polished or uncladded SI and GI POF geometries for use in tapers and multipoint sensors," in Proceedings of 15th International Conference on Plastic Optical Fibers and Applications POF�??2006, (Korea, 2006), pp. 187-192.
  17. C.  McAtamney, A.  Cronin, R.  Sherlock, G. M.  O�??Connor, and T. J.  Glynn, "Reproducible method for fabricating fused biconical tapered couplers using a CO2 laser based process," in Proceedings of 3rd International WLT Conference on Lasers in Manufacturing, (Munich, 2005), pp. 673-678.
  18. J.  Zubia, J.  Arrue, G.  Fuster, and D.  Kalymnios, "Light power behavior when bending plastic optical fibers," IEE Proc.Optoelectron. 145, 313-318 (1998).
    [CrossRef]
  19. J.  Mateo, I.  Garces, and A.  Losada, "A novel technique to fabricate low loss POF tapers," in Proceedings of 9th International Conference on Plastic Optical Fibers and Applications POF�??2000, (Boston, 2000), pp. 72-76.
  20. M.  Kezmah and D.  Donlagic, "Multimode all-fiber quasi-distributed refractometer sensor array and cross-talk mitigation," Appl. Opt. 46, 4081-4091 (2007).
    [CrossRef] [PubMed]

2007

S.  Xue, M. A.  van Eijkelenborg, G.W.  Barton, and P.  Hambley, "Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering," J. Lightwave Technol. 25, 1169-1176 (2007).
[CrossRef]

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

M.  Kezmah and D.  Donlagic, "Multimode all-fiber quasi-distributed refractometer sensor array and cross-talk mitigation," Appl. Opt. 46, 4081-4091 (2007).
[CrossRef] [PubMed]

2004

J.  Villatoro, D.  Monzón-Hernández, and D.  Luna-Moreno, "In-line optical fiber sensors based on cladded multimode tapered fibers," Appl. Opt. 43, 5933-5938 (2004).
[CrossRef] [PubMed]

F.  Jiménez, J.  Arrue, G.  Aldabaldetreku, and J.  Zubia, "Numerical Simulation of Light Propagation in Plastic Optical Fibres of Arbitrary 3D Geometry," WSEAS Trans. Math.  3, 824-829 (2004).

2003

2001

J.  Zubia and J.  Arrue, "Plastic Optical Fibers: An Introduction to Their Technological Processes and Applications," Opt. Fiber Technol.  7, 101-140 (2001).
[CrossRef]

1998

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

1992

T. A.  Birks and Y. W.  Li, "The shape of fiber tapers," J. Lightwave Technol. 10, 432-438 (1992).
[CrossRef]

1982

A.  Sharma, D.  Vizia, and A. K.  Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt.  21, 984-987 (1982).
[CrossRef] [PubMed]

Aiestaran, P.

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

Albin, S.

Aldabaldetreku, G.

F.  Jiménez, J.  Arrue, G.  Aldabaldetreku, and J.  Zubia, "Numerical Simulation of Light Propagation in Plastic Optical Fibres of Arbitrary 3D Geometry," WSEAS Trans. Math.  3, 824-829 (2004).

Arrue, J.

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

F.  Jiménez, J.  Arrue, G.  Aldabaldetreku, and J.  Zubia, "Numerical Simulation of Light Propagation in Plastic Optical Fibres of Arbitrary 3D Geometry," WSEAS Trans. Math.  3, 824-829 (2004).

J.  Zubia and J.  Arrue, "Plastic Optical Fibers: An Introduction to Their Technological Processes and Applications," Opt. Fiber Technol.  7, 101-140 (2001).
[CrossRef]

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

Barton, G.W.

S.  Xue, M. A.  van Eijkelenborg, G.W.  Barton, and P.  Hambley, "Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering," J. Lightwave Technol. 25, 1169-1176 (2007).
[CrossRef]

Birks, T. A.

T. A.  Birks and Y. W.  Li, "The shape of fiber tapers," J. Lightwave Technol. 10, 432-438 (1992).
[CrossRef]

Donlagic, D.

Fuster, G.

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

Ghatak, A. K.

A.  Sharma, D.  Vizia, and A. K.  Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt.  21, 984-987 (1982).
[CrossRef] [PubMed]

Hambley, P.

S.  Xue, M. A.  van Eijkelenborg, G.W.  Barton, and P.  Hambley, "Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering," J. Lightwave Technol. 25, 1169-1176 (2007).
[CrossRef]

Jáuregui, C.

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

Jiménez, F.

F.  Jiménez, J.  Arrue, G.  Aldabaldetreku, and J.  Zubia, "Numerical Simulation of Light Propagation in Plastic Optical Fibres of Arbitrary 3D Geometry," WSEAS Trans. Math.  3, 824-829 (2004).

Kalymnios, D.

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

Kezmah, M.

Li, Y. W.

T. A.  Birks and Y. W.  Li, "The shape of fiber tapers," J. Lightwave Technol. 10, 432-438 (1992).
[CrossRef]

Lomer, M.

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

López Higuera, J. M.

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

Luna-Moreno, D.

Monzón-Hernández, D.

Shangping, G.

Sharma, A.

A.  Sharma, D.  Vizia, and A. K.  Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt.  21, 984-987 (1982).
[CrossRef] [PubMed]

van Eijkelenborg, M. A.

S.  Xue, M. A.  van Eijkelenborg, G.W.  Barton, and P.  Hambley, "Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering," J. Lightwave Technol. 25, 1169-1176 (2007).
[CrossRef]

Villatoro, J.

Vizia, D.

A.  Sharma, D.  Vizia, and A. K.  Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt.  21, 984-987 (1982).
[CrossRef] [PubMed]

Xue, S.

S.  Xue, M. A.  van Eijkelenborg, G.W.  Barton, and P.  Hambley, "Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering," J. Lightwave Technol. 25, 1169-1176 (2007).
[CrossRef]

Zubia, J.

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

F.  Jiménez, J.  Arrue, G.  Aldabaldetreku, and J.  Zubia, "Numerical Simulation of Light Propagation in Plastic Optical Fibres of Arbitrary 3D Geometry," WSEAS Trans. Math.  3, 824-829 (2004).

J.  Zubia and J.  Arrue, "Plastic Optical Fibers: An Introduction to Their Technological Processes and Applications," Opt. Fiber Technol.  7, 101-140 (2001).
[CrossRef]

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

Appl. Opt.

Appl. Opt.

A.  Sharma, D.  Vizia, and A. K.  Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt.  21, 984-987 (1982).
[CrossRef] [PubMed]

IEE Proc.Optoelectron.

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

J. Lightwave Technol.

T. A.  Birks and Y. W.  Li, "The shape of fiber tapers," J. Lightwave Technol. 10, 432-438 (1992).
[CrossRef]

S.  Xue, M. A.  van Eijkelenborg, G.W.  Barton, and P.  Hambley, "Theoretical, Numerical, and Experimental Analysis of Optical Fiber Tapering," J. Lightwave Technol. 25, 1169-1176 (2007).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

J.  Zubia and J.  Arrue, "Plastic Optical Fibers: An Introduction to Their Technological Processes and Applications," Opt. Fiber Technol.  7, 101-140 (2001).
[CrossRef]

Sens. Actuators, A

M.  Lomer, J.  Arrue, C.  Jáuregui, P.  Aiestaran, J.  Zubia, and J.M.  López Higuera, "Lateral polishing of bends in plastic optical fibres applied to a multipoint liquid-level measurement sensor," Sens. Actuators, A 137, 68-73 (2007).
[CrossRef]

WSEAS Trans. Math.

F.  Jiménez, J.  Arrue, G.  Aldabaldetreku, and J.  Zubia, "Numerical Simulation of Light Propagation in Plastic Optical Fibres of Arbitrary 3D Geometry," WSEAS Trans. Math.  3, 824-829 (2004).

Other

J.  Arrue, F.  Jimémez, M.  Lomer, G.  Aldabaldetreku, G.  Durana, and J.  Zubia "Characterization of tapered, polished or uncladded SI and GI POF geometries for use in tapers and multipoint sensors," in Proceedings of 15th International Conference on Plastic Optical Fibers and Applications POF�??2006, (Korea, 2006), pp. 187-192.

C.  McAtamney, A.  Cronin, R.  Sherlock, G. M.  O�??Connor, and T. J.  Glynn, "Reproducible method for fabricating fused biconical tapered couplers using a CO2 laser based process," in Proceedings of 3rd International WLT Conference on Lasers in Manufacturing, (Munich, 2005), pp. 673-678.

J.  Mateo, I.  Garces, and A.  Losada, "A novel technique to fabricate low loss POF tapers," in Proceedings of 9th International Conference on Plastic Optical Fibers and Applications POF�??2000, (Boston, 2000), pp. 72-76.

J.  Arrue, G.  Aldabaldetreku, G.  Durana, J.  Zubia, and F.  Jiménez, "Computational research on the behaviour of bent plastic optical fibres in communications links and sensing applications," in Recent Research Developments in Optics, S. G. Pandalai, ed., (Research Signpost, Kerala, India, 2005), Chap. 5.

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

Chromis FiberOptics Co., "Chromis Fiberoptics," (Head office in 6 Powder Horn Dr., Warren, NJ 07059, USA). http://www.chromisfiber.com.

FiberFin Inc., "FiberFin," (Head office in 201 Beaver Street, Yorkville, Illinois, USA.).http://www.fiberfin.com.

Asahi Glass Co. Ltd., "Asahi Glass," (Lucina Division; Head office in 1-12-1, Yurakucho, Chiyoda-ku, Tokyo 100-8405, Japan). http://www.lucina.jp/eg_lucina/productsengf2.htm.

J.  Munisami and D.  Kalymnios, "High NA POF performance versus the requirements of the recent standard ISO/IEC JTC 1 FDIS 24702," in Proceedings of 15th International Conference on Plastic Optical Fibers and Applications POF�??2006, (Korea, 2006), pp. 102-109.

O.  Ziemann, H.  Poisel, A.  Bachmann, and J.  Vinogradov, "Special problems measuring POF," in POF Modelling: Theory, Measurement and Application, C.-A. Bunge and H. Poisel, eds., (Books on Demand GmbH, Norderstedt, Germany, 2008).

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Figures (12)

Fig. 1.
Fig. 1.

Variables in the eikonal equation of the ray path.

Fig. 2.
Fig. 2.

Cross section of the sensing probe. The surfaces of constant refractive index are represented by dotted lines. The undeformed core radius is ρ0 .

Fig. 3.
Fig. 3.

Rays follow curved paths in the core and straight ones in the cladding. Calculating the normal n at interfaces is needed in all three sections of the taper.

Fig. 4.
Fig. 4.

Core of a taper with a sinusoidal shape.

Fig. 5.
Fig. 5.

Tapers manufactured by the authors. Proportions have been altered slightly, specially on the right (with 0.6-mm taper at the top, 0.4-mm one at the bottom) to increase cross-dimensions over axial ones, so that the taper shape can be appreciated better.

Fig. 6.
Fig. 6.

Comparison between our computational results (labeled Comp) and the experimental ones reported in [1] (labeled [1](exper)) for NR=0.64. The results calculated in [1] (labeled [1](calc)) for a graded-index glass taper with narrowing ratios NR=0.7 and NR=0.6 (the closest ones to 0.64) are also shown (dashed lines).

Fig. 7.
Fig. 7.

Ray paths inside a taper, with some angles of incidence on the external surface. Angles appear distorted because of the different scales employed in the horizontal and vertical axes for a better visualization. The internal(external) exponential curves represent the contour of the core(cladding) in the meridional plane. The oscillating curve illustrates the trajectory of a meridional ray for the same launching conditions in two cases: (a) Length L=2 mm; (b) L=5 mm.

Fig. 8.
Fig. 8.

Example to illustrate that, for certain values of the taper length L, power loss can increase as L increases for a given narrowing ratio. The fiber is a Lucina one with ρ0 =60 µm. The rays entering the taper and the narrowing ratio (NR=0.3) are identical in (a) and (b), but in (a), with L=2 mm, 5 rays escape, while in (b), with L=10 mm, 7 rays escape.

Fig. 9.
Fig. 9.

Fraction of power transmitted with the GigaPOF/OM-Giga fibers, as a function of the narrowing ratio and the critical angle (or outer refractive index).

Fig. 10.
Fig. 10.

Influence of NR on the sensitivity (slope) of the sensor and on the range of measurable refractive indices (critical angles), for the OM-Giga/POF and the Lucina fibers.

Fig. 11.
Fig. 11.

Trajectory of a light ray from the core-cladding interface (P 1) to the outer surface of a thin cladding (P 2) and a thick one (P 3), with the corresponding angles of incidence α2 and α3 .

Fig. 12.
Fig. 12.

Manufacturing of a taper in a plastic optical fiber by heating and pulling.

Tables (2)

Tables Icon

Table 1. Different possible fiber candidates for a refractive index sensor.

Tables Icon

Table 2. Comparison between author’s experimental and computational results.

Equations (12)

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

d d s ( n ( r ) · d r d s ) = n ( r ) ,
t = d s n d t = d s n d 2 r d t 2 = n ( r ) n ( r ) = n ( r ) ( n ( r ) x n ( r ) y n ( r ) z ) T = D ( r ) .
d 2 r d t 2 = D ( r ) { d r d t = t d t d t = D ( r ) .
{ r n + 1 = r n + ( t n + k 1 + 2 k 2 6 ) h t n + 1 = t n + k 1 + 4 k 2 + k 3 6 where { k 1 = D ( r n ) h k 2 = D ( r n + h 2 t n + h 8 k 1 ) h k 3 = D ( r n + h t n + h 2 k 2 ) h .
ρ ( z ) = ρ 0 ( ρ 0 ρ min ) z L ,
d ρ ( z ) = r ρ 0 n ( r ) = n ( ρ 0 d ρ ( z ) ) = n ( ρ 0 d ρ 0 ( ρ 0 ρ min ) z L ) = n ( ( ρ 0 ρ min ) z L d ) = n ( d , z ) .
n ( r ) = n 1 1 2 Δ ( r ρ 0 ) g with Δ = n 1 2 n 1 2 2 n 1 2 ,
n ( z , d ) = n 1 1 2 Δ ρ 0 g d g ( ρ min ρ 0 ) z g L .
grad n = ( n x , n y , n z ) T = ( x x 2 + y 2 n d , y x 2 + y 2 n d , n z ) T ,
n 2 D = ( n 2 D , z n 2 D , ρ ) T = ( d ρ ( z ) d z 1 ) T ( d ρ ( z ) d z ) 2 + 1 2 ,
n = ( x x 2 + y 2 n 2 D , ρ y x 2 + y 2 n 2 D , ρ n 2 D , z ) T .
M 1 2 ( 2 π ρ 0 λ n 1 2 n 2 2 ) 2 g g + 2

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