Abstract

In this work we have analyzed theoretically and experimentally the critical angle for the emission generated in doped polymer optical fibers as a function of different launching conditions by using the side-illumination fluorescence technique. A theoretical model has been developed in order to explain the experimental measurements. It is shown that both the theoretical and experimental critical angles are appreciably higher than the meridional critical angle corresponding to the maximum acceptance angle for a single source placed at the fiber axis. This increase changes the value of several important parameters in the performance of active fibers. The analysis has been performed in polymer optical fibers doped with a conjugated polymer.

© 2012 OSA

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2011

C. Pulido and O. Esteban, “Multiple fluorescence sensing with side-pumped tapered polymer fiber,” Sens. Actuators B Chem. 157(2), 560–564 (2011).
[CrossRef]

I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A 208(8), 1845–1848 (2011).
[CrossRef]

J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011).
[CrossRef]

2010

H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

J. Clark and G. Lanzani, “Organic photonics for communications,” Nat. Photonics 4(7), 438–446 (2010).
[CrossRef]

C. Pulido and O. Esteban, “Improved fluorescence signal with tapered polymer optical fibers under side-illumination,” Sens. Actuators B Chem. 146(1), 190–194 (2010).
[CrossRef]

2009

G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009).
[CrossRef] [PubMed]

M. A. Illarramendi, J. Zubia, L. Bazzana, G. Durana, G. Aldabaldetreku, and J. R. Sarasua, “Spectroscopic characterization of plastic optical fibers doped with fluorene oligomers,” J. Lightwave Technol. 27(15), 3220–3226 (2009).
[CrossRef]

2008

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

2007

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

M. Sheeba, K. J. Thomas, M. Rajesh, V. P. N. Nampoori, C. P. G. Vallabhan, and P. Radhakrishnan, “Multimode laser emission from dye doped polymer optical fiber,” Appl. Opt. 46(33), 8089–8094 (2007).
[CrossRef] [PubMed]

2006

Y. Xu, A. Cotteden, and N. B. Jones, “A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors,” Opt. Lasers Eng. 44(2), 93–101 (2006).
[CrossRef]

M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006).
[CrossRef]

C.-A. Bunge, R. Kruglov, and H. Poisel, “Rayleigh and Mie scattering in polymer optical fibers,” J. Lightwave Technol. 24(8), 3137–3146 (2006).
[CrossRef]

2004

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

2003

C. P. Achenbach and J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimodal active fibres,” J. Opt. A, Pure Appl. Opt. 5(3), 239–249 (2003).
[CrossRef]

2001

J. Zubia and J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7(2), 101–140 (2001).
[CrossRef]

1999

1998

1997

1989

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989).
[CrossRef]

1961

Achenbach, C. P.

C. P. Achenbach and J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimodal active fibres,” J. Opt. A, Pure Appl. Opt. 5(3), 239–249 (2003).
[CrossRef]

Adawi, A. M.

G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009).
[CrossRef] [PubMed]

Aldabaldetreku, G.

Arrue, J.

I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A 208(8), 1845–1848 (2011).
[CrossRef]

J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011).
[CrossRef]

J. Zubia and J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7(2), 101–140 (2001).
[CrossRef]

Aslund, M.

M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006).
[CrossRef]

Ayesta, I.

I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A 208(8), 1845–1848 (2011).
[CrossRef]

J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011).
[CrossRef]

Barnes, W. L.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989).
[CrossRef]

Bazzana, L.

M. A. Illarramendi, J. Zubia, L. Bazzana, G. Durana, G. Aldabaldetreku, and J. R. Sarasua, “Spectroscopic characterization of plastic optical fibers doped with fluorene oligomers,” J. Lightwave Technol. 27(15), 3220–3226 (2009).
[CrossRef]

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Bradley, D.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Bunge, C.-A.

Canning, J.

M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006).
[CrossRef]

Chen, B.

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

Cheng, X.

H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

Clark, J.

J. Clark and G. Lanzani, “Organic photonics for communications,” Nat. Photonics 4(7), 438–446 (2010).
[CrossRef]

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Cobb, J. H.

C. P. Achenbach and J. H. Cobb, “Computational studies of light acceptance and propagation in straight and curved multimodal active fibres,” J. Opt. A, Pure Appl. Opt. 5(3), 239–249 (2003).
[CrossRef]

Cotteden, A.

Y. Xu, A. Cotteden, and N. B. Jones, “A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors,” Opt. Lasers Eng. 44(2), 93–101 (2006).
[CrossRef]

Dolotov, S. M.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Durana, G.

Esteban, O.

C. Pulido and O. Esteban, “Multiple fluorescence sensing with side-pumped tapered polymer fiber,” Sens. Actuators B Chem. 157(2), 560–564 (2011).
[CrossRef]

C. Pulido and O. Esteban, “Improved fluorescence signal with tapered polymer optical fibers under side-illumination,” Sens. Actuators B Chem. 146(1), 190–194 (2010).
[CrossRef]

Fleming, S.

Fox, A. M.

G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009).
[CrossRef] [PubMed]

Gonzalez, J.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Illarramendi, M. A.

I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A 208(8), 1845–1848 (2011).
[CrossRef]

J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011).
[CrossRef]

M. A. Illarramendi, J. Zubia, L. Bazzana, G. Durana, G. Aldabaldetreku, and J. R. Sarasua, “Spectroscopic characterization of plastic optical fibers doped with fluorene oligomers,” J. Lightwave Technol. 27(15), 3220–3226 (2009).
[CrossRef]

M. A. Illarramendi, “Side-illumination scattering theory in step-index polymer optical fibers,” J. Opt. Soc. Am. B (to be published).

Iraqi, A.

G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009).
[CrossRef] [PubMed]

Jackson, S. D.

M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006).
[CrossRef]

Jeff-Pun, C.-F.

H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

Jimenez, F.

J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011).
[CrossRef]

I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A 208(8), 1845–1848 (2011).
[CrossRef]

Jones, N. B.

Y. Xu, A. Cotteden, and N. B. Jones, “A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors,” Opt. Lasers Eng. 44(2), 93–101 (2006).
[CrossRef]

Khalil, G. E.

G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009).
[CrossRef] [PubMed]

Koike, Y.

Kopylova, T. N.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Kruglov, R.

Kruhlak, R. J.

Kuzyk, M. G.

Lanzani, G.

J. Clark and G. Lanzani, “Organic photonics for communications,” Nat. Photonics 4(7), 438–446 (2010).
[CrossRef]

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Li, Z.

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

Liang, H.

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

Lidzey, D.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Lidzey, D. G.

G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009).
[CrossRef] [PubMed]

Lyytikainen-Digweed, K.

M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006).
[CrossRef]

Maier, G. V.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Ming, H.

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

Monich, A. E.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Monich, E. A.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Morgado, J.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Nampoori, V. P. N.

Nihei, E.

Nocivelli, A.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

Payne, D. N.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989).
[CrossRef]

Podgaetskii, V. M.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Poisel, H.

Ponomareva, O. V.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Poole, S. B.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989).
[CrossRef]

Potter, R. J.

Pulido, C.

C. Pulido and O. Esteban, “Multiple fluorescence sensing with side-pumped tapered polymer fiber,” Sens. Actuators B Chem. 157(2), 560–564 (2011).
[CrossRef]

C. Pulido and O. Esteban, “Improved fluorescence signal with tapered polymer optical fibers under side-illumination,” Sens. Actuators B Chem. 146(1), 190–194 (2010).
[CrossRef]

Radhakrishnan, P.

Rajesh, M.

Reekie, L.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989).
[CrossRef]

Sarasua, J. R.

Sasaki, K.

Sheeba, M.

Svetlichnyi, V. A.

G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

Tagaya, A.

Tam, H. Y.

H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

Taylor, D. J.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989).
[CrossRef]

Teixeira, A.

M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006).
[CrossRef]

Teramoto, S.

Thomas, K. J.

Townsend, J. E.

W. L. Barnes, S. B. Poole, J. E. Townsend, L. Reekie, D. J. Taylor, and D. N. Payne, “Er3+ -Yb3+ and Er3+ doped fiber lasers,” J. Lightwave Technol. 7(10), 1461–1465 (1989).
[CrossRef]

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H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

Tsoi, W.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

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Virgili, T.

J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

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J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
[CrossRef]

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H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

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Y. Xu, A. Cotteden, and N. B. Jones, “A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors,” Opt. Lasers Eng. 44(2), 93–101 (2006).
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H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

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H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

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Zheng, Z.

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
[CrossRef]

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H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

Zubia, J.

J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011).
[CrossRef]

I. Ayesta, J. Arrue, F. Jimenez, M. A. Illarramendi, and J. Zubia, “Computational analysis of the amplification features of active plastic optical fibers,” Phys. Status Solidi A 208(8), 1845–1848 (2011).
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M. A. Illarramendi, J. Zubia, L. Bazzana, G. Durana, G. Aldabaldetreku, and J. R. Sarasua, “Spectroscopic characterization of plastic optical fibers doped with fluorene oligomers,” J. Lightwave Technol. 27(15), 3220–3226 (2009).
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Appl. Opt.

J. Appl. Polym. Sci.

H. Liang, Z. Zheng, Z. Li, J. Xu, B. Chen, H. Zhao, Q. Zhang, and H. Ming, “Fabrication and amplification of rhodamine B-doped step-index polymer optical fiber,” J. Appl. Polym. Sci. 93(2), 681–685 (2004).
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G. E. Khalil, A. M. Adawi, A. M. Fox, A. Iraqi, and D. G. Lidzey, “Single molecule spectroscopy of red- and green-emitting fluorene-based copolymers,” J. Chem. Phys. 130(4), 044903 (2009).
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J. Clark, L. Bazzana, D. Bradley, J. Gonzalez, G. Lanzani, D. Lidzey, J. Morgado, A. Nocivelli, W. Tsoi, T. Virgili, and R. Xia, “Blue polymer optical fiber amplifiers based on conjugated fluorine oligomers,” J. Nanophoton. 2(1), 023504 (2008).
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M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikainen-Digweed, “The influence of skew rays on angular losses in air-cladd fibres,” Opt. Commun. 262(1), 77–81 (2006).
[CrossRef]

Opt. Fiber Technol.

J. Zubia and J. Arrue, “Plastic optical fibers: an introduction to their technological processes and applications,” Opt. Fiber Technol. 7(2), 101–140 (2001).
[CrossRef]

H. Y. Tam, C.-F. Jeff-Pun, G. Zhou, X. Cheng, and M. L. V. Tse, “Special structured polymer fibers for sensing applications,” Opt. Fiber Technol. 16(6), 357–366 (2010).

Opt. Lasers Eng.

Y. Xu, A. Cotteden, and N. B. Jones, “A theoretical evaluation of fibre-optic evanescent wave absorption in spectroscopy and sensors,” Opt. Lasers Eng. 44(2), 93–101 (2006).
[CrossRef]

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Phys. Status Solidi A

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[CrossRef]

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J. Arrue, F. Jimenez, I. Ayesta, M. A. Illarramendi, and J. Zubia, “Polymer-optical-fiber lasers and amplifiers doped with organic dyes,” Polymers 3(3), 1162–1180 (2011).
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G. V. Maier, T. N. Kopylova, V. A. Svetlichnyi, V. M. Podgaetskii, S. M. Dolotov, O. V. Ponomareva, A. E. Monich, and E. A. Monich, “Active polymer fibers doped with organic dyes: generation and amplification of coherent radiation,” Quantum Electron. 37(1), 53–59 (2007).
[CrossRef]

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C. Pulido and O. Esteban, “Improved fluorescence signal with tapered polymer optical fibers under side-illumination,” Sens. Actuators B Chem. 146(1), 190–194 (2010).
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Figures (13)

Fig. 1
Fig. 1

Measurement of the angular distribution of the emission at the output of the fiber as a function of the launching conditions. (a) Angular scan: ai is the angle made by the incident beam with the normal to the fiber surface at yP = 0 μm. The incident beam always lies in the xz-plane. (b) Lateral scan: yP refers to the y-coordinate of the point of incidence relative to yP = 0 μm. The incident beam lies in the xy-plane.

Fig. 2
Fig. 2

Experimental set-up used to measure the angular distribution of the emission at the output end of doped POFs. Legend: L1 and L2: plane-concave and plane-convex lenses; BS: beam splitter; OBJ: 0.1-NA objective or cylindrical lens; xy POS: xy-micropositioner; RS: rotation stage; RPD: reference photodetector; RMM: reference multimeter; LEPAS-12: optical beam measurement system + integrated narrowband filter (emission wavelength: 535 nm). λexc: excitation wavelength.

Fig. 3
Fig. 3

Geometrical arrangement of the POF with respect to the incident beam. (a) angular scan: αi is the angle made by the incident beam with the normal to the fiber surface at yP = 0 μm. The incident beam i always lies in the xz-plane. e represents the emitted beam, while r is the refracted beam. (b) lateral scan: yP refers to the y-coordinate of the point of incidence relative to yP = 0 μm. The incident beam i lies in the xy-plane. e represents the emitted beam, while r is the refracted beam.

Fig. 4
Fig. 4

2D image of the sin(θz)c as a function of parameters xQ and ϕ x for angular incidence. Black painted areas indicate the forbidden regions for xQ and ϕ x giving no real sin(θz)c . White solid lines correspond to xQ = ± ρ core nratio(λemi). Calculations performed with NAmeridional = 0.5, ncore(λemi) = 1.495, and ρ core = 490 μm.

Fig. 5
Fig. 5

Average value of the sine of the critical angle as a function of the position of the emission point source in the fiber core, or <sin(θz)c>(xQ), calculated from Eq. (10) (solid line); meridional sin(θz)c = 0.335, from Eq. (3) (dotted line); <sin(θz)c> = 0.375 obtained from Eq. (8) (dash-dotted line); <sin(θz)c> = 0.381 obtained from Eq. (6) (dashed line). Calculations performed with NAmeridional = 0.5, ncore(λemi) = 1.495, and rcore = 490 μm.

Fig. 6
Fig. 6

Sine of the critical angle as a function of nratio(λemi). Meridional sin(θz)c obtained from Eq. (3) (dotted line); <sin(θz)c> from Eq. (8) (dotted line); <sin(θz)c> from Eq. (6) (dash-dotted line).

Fig. 7
Fig. 7

2D image of sin(θz)c as a function of parameters x'Q and ϕ x for lateral incidence. The lateral height yP has been fixed to yP = ρ core/2. Black areas indicate the forbidden regions for x'Q and ϕ x giving no real sin(θz)c. The white solid vertical lines correspond to x'Q(min) and x'Q(max). Calculations performed with NAmeridional = 0.5, ncore(λemi) = ncore(λexc) = 1.495, and ρ core = 490 μm.

Fig. 8
Fig. 8

Average of the sine of the critical angle as a function of yP, i.e. <sin(θz)c>(yP), calculated from Eq. (14) (solid line); meridional sin(θz)c = 0.335 from Eq. (3) (dotted line); <sin(θz)c> = 0.391 (for all values of yP) (dashed line). Calculations performed with NAmeridional = 0.5, ncore(λemi) = ncore(λexc) = 1.495, and rcore = 490 μm.

Fig. 9
Fig. 9

Normalized FFP of the emission (λemi = 535 nm) at the output of the fiber for different angles of incidence: αi = −45°, αi = 0°, and αi = +45°.

Fig. 10
Fig. 10

Evolution of NA at the output end of an F8BT-doped POF sample as a function of the angle of incidence: experimental values (■) and NA = 0.557 calculated from the fitting to Eq. (6) (solid line). NAmeridional = 0.489 calculated from Eq. (3) (dotted line).

Fig. 11
Fig. 11

Normalized FFP of the emission (λemi = 535 nm) at the output of the fiber for different positions of the lateral exciting beam: yP = −450 μm, yP = 0 μm, and yP = +450 μm.

Fig. 12
Fig. 12

Evolution of the NA at the output end of the F8BT-doped POF as a function of yP: Experimental values (■); fitting to NA = <sin(θz)c>(yP) ncore(λemi) (solid line); NAmeridional = 0.489 obtained from Eq. (3) (dotted line); theoretical average NA = <sin(θz)c> ncore(λemi) = 0.572 (dash-dotted line); measured NA exciting the fiber with a cylindrical lens NA = 0.575 (dashed line).

Fig. 13
Fig. 13

Evolution of the measured NA of the emission (λemi = 535 nm) for the F8BT-doped POF as a function of the propagation distance.

Equations (16)

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sin( ( θ z ) c )( x Q , ϕ x )= 1 n ratio 2 ( λ emi ) 1 ( x Q ρ core sin ϕ x ) 2 ,
sin( ( θ z ) c )= 1 ( n clad n core ) 2 = 1 n ratio 2 ( λ emi ) .
1> n ratio 2 ( λ emi ) ( x Q ρ core sin ϕ x ) 2 .
sin( ( θ z ) c ) = [ 0 arcsin( n ratio ) d ϕ x ρ core + ρ core sin ( θ z ) c ( x Q , ϕ x )d x Q + πarcsin( n ratio ) π d ϕ x ρ core + ρ core sin ( θ z ) c ( x Q , ϕ x )d x Q + + arcsin( n ratio ) πarcsin( n ratio ) d ϕ x 0 ρ core n ratio sin ϕ x sin ( θ z ) c ( x Q , ϕ x )d x Q ] / [ 0 arcsin( n ratio ) d ϕ x ρ core + ρ core d x Q + + πarcsin( n ratio ) π d ϕ x ρ core + ρ core d x Q + arcsin( n ratio ) πarcsin( n ratio ) d ϕ x 0 ρ core n ratio sin ϕ x d x Q ].
sin ( θ z ) c = = i 1 n ratio 2 ( λ emi ) 2( arcsin( n ratio ( λ emi ) )+ n ratio ( λ emi )log( cot( arcsin( n ratio ( λ emi ) ) 2 ) ) ) k=1 ( ( i n ratio ( λ emi ) 1 n ratio 2 ( λ emi ) ) k k 2 ( i n ratio ( λ emi ) 1 n ratio 2 ( λ emi ) ) k k 2 + ( i n ratio ( λ emi )+ 1 n ratio 2 ( λ emi ) ) k k 2 ( i n ratio ( λ emi )+ 1 n ratio 2 ( λ emi ) ) k k 2 ).
sin ( θ z ) c = n ρ core +n ρ core d x Q 0 2π sin ( θ z ) c ( x, ϕ x )d ϕ x n ρ core +n ρ core d x Q 0 2π d ϕ x .
sin ( θ z ) c = 1 n ratio 2 ( λ emi ) F 3 2 [{ 1 2 , 1 2 , 1 2 },{1, 3 2 }, n ratio 2 ( λ emi )],
sin ( θ z ) c ( x Q )= 0 2π sin ( θ z ) c ( x Q , ϕ x )d ϕ x 0 2π d ϕ x .
sin ( θ z ) c ( x Q )= 1 n ratio 2 ( λ emi ) π ( K ( x Q ρ core ) 2 + K( ( x Q / ρ core ) 2 ( x Q / ρ core ) 2 1 ) 1 ( x Q / ρ core ) 2 ),
sin ( θ z ) c 1 n ratio 2 ( λ emi ) = 4Catalan π ,
sin ( θ z ) c ( x Q ', ϕ x , y P )= 1 n ratio 2 ( λ emi ) sinΔ ,
sinΔ= [ 1 ( x ' Q ) 2 + ( y P n core ( λ ext ) ) 2 ρ core 2 sin 2 ( ϕ x +arctan( y P n core ( λ ext )x ' Q )+arctan( y P ρ core 2 y P 2 )arcsin( y P ρ core n core ( λ ext ) ) ) ] 1 2 .
1> n ratio 2 ( λ emi ) ( x ' Q ) 2 + ( y P n core ( λ ext ) ) 2 ρ core 2 sin 2 ( ϕ x +arctan( y P n core ( λ ext )x ' Q )+arctan( y P ρ core 2 y P 2 )arcsin( y P ρ core n core ( λ ext ) ) ).
sin ( θ z ) c ( y P )= R R sin ( θ z ) c ( x ' Q , ϕ x , y P )dx ' Q d ϕ x R R dx ' Q d ϕ x .
x Q (min)= ρ core n ratio 2 ( λ emi ) y P 2 n core 2 ( λ ext ) x Q (max)=+ ρ core n ratio 2 ( λ emi ) y P 2 n core 2 ( λ ext ) ,
sin ( θ z ) c ( y P )= x Q (min) x Q (max) d x Q 0 2π sin ( θ z ) c ( x Q , ϕ x , y P )d ϕ x x Q (min) x Q (max) d x Q 0 2π d ϕ x .

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