Abstract

Bend loss from optical fibers can have positive applications, which need to be characterized and related to fiber curvature in a systematic approach to be useful. One potential application for optical fibers is a shape sensor for tracking flexible bodies in remote access environments, such as in endoscopy or boroscopy. We conducted a review of bend-loss characterization and evaluated several methods for characterizing bend loss in multimode optical fibers for an endoscopic shape-tracking application. Specifically, closed-form equation-based methods and numerical simulations were examined. Beam propagation method (BPM) simulations were determined to be the most applicable characterization tool. Results from simulations using BPM software were compared to experimentally obtained data. BPM simulation was sufficiently accurate for modeling 50μm fibers but impractical for larger, multimode fibers.

© 2010 Optical Society of America

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2008 (2)

C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
[CrossRef]

J. Van Erps, C. Debaes, T. Nasilowski, J. Watté, J. Wojcik, and H. Thienpont, “Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology,” Opt. Express 16, 5061-5074 (2008).
[CrossRef] [PubMed]

2007 (5)

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

R. W. Smink, B. P. de Hon, and A. G. Tijhuis, “Bending loss in optical fibers--a full-wave approach,” J. Opt. Soc. Am. B 24, 2610-2618 (2007).
[CrossRef]

C.-Y. Huang, W.-C. Wang, W.-J. Wu, and W. R. Ledoux, “Composite optical bend loss sensor for pressure and shear measurement,” IEEE Sens. J. 7, 1554-1565 (2007).
[CrossRef]

Y. Chen, “Power losses in bent and elongated polymer optical fibers,” Appl. Opt. 46, 4570-4578 (2007).
[CrossRef] [PubMed]

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

2006 (3)

2005 (2)

I. Kiyat, A. Aydinli, and N. Dagli, “High-Q silicon-on-insulator optical rib waveguide racetrack resonators,” Opt. Express 13, 1900-1905 (2005).
[CrossRef] [PubMed]

A. T. Augousti, F. X. Maletras, and J. Mason, “The use of a figure-of-eight coil for fibre optic respiratory plethysmography: geometrical analysis and experimental characterisation,” Opt. Fiber Technol. 11, 346-360 (2005).
[CrossRef]

2003 (2)

G. Durana, J. Zubia, J. Arrue, G. Aldabaldetreku, and J. Mateo, “Dependence of bending losses on cladding thickness in plastic optical fibers,” Appl. Opt. 42, 997-1002 (2003).
[CrossRef] [PubMed]

E. Papagiakoumou, D. N. Papadopoulos, N. Anastasopoulou, and A. A. Serafetinides, “Comparative evaluation of HP oxide glass fibers for Q-switched and free-running Er:YAG laser beam propagation,” Opt. Commun. 220, 151-160 (2003).
[CrossRef]

2000 (2)

N. Anastasopoulou, C. Ziolek, A. A. Serafetinides, and H. Lubatschowski, “Q-switched Er:YAG radiation transmission through fluoride glass fibers and dielectric-coated metallic hollow waveguides,” Opt. Commun. 186, 167-171 (2000).
[CrossRef]

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-162(2000).
[CrossRef]

1997 (2)

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

1992 (1)

H. Renner, “Bending losses of coated single-mode fibers: a simple approach,” J. Lightwave Technol. 10, 544-551 (1992).
[CrossRef]

1991 (2)

1990 (1)

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

1986 (1)

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol. 4, 34-40 (1986).
[CrossRef]

1985 (1)

C. Vassallo, “Scalar-field theory and 2-D ray theory for bent single-mode weakly guiding optical fibers,” J. Lightwave Technol. 3, 416-423 (1985).
[CrossRef]

1984 (1)

1977 (1)

M. Miyagi and G. L. Yip, “Mode conversion and radiation losses in a step-index optical fibre due to bending,” Opt. Quantum Electron. 9, 51-60 (1977).
[CrossRef]

1976 (1)

1972 (1)

Aldabaldetreku, G.

Anastasopoulou, N.

E. Papagiakoumou, D. N. Papadopoulos, N. Anastasopoulou, and A. A. Serafetinides, “Comparative evaluation of HP oxide glass fibers for Q-switched and free-running Er:YAG laser beam propagation,” Opt. Commun. 220, 151-160 (2003).
[CrossRef]

N. Anastasopoulou, C. Ziolek, A. A. Serafetinides, and H. Lubatschowski, “Q-switched Er:YAG radiation transmission through fluoride glass fibers and dielectric-coated metallic hollow waveguides,” Opt. Commun. 186, 167-171 (2000).
[CrossRef]

Arrue, J.

Augousti, A. T.

A. T. Augousti, F. X. Maletras, and J. Mason, “The use of a figure-of-eight coil for fibre optic respiratory plethysmography: geometrical analysis and experimental characterisation,” Opt. Fiber Technol. 11, 346-360 (2005).
[CrossRef]

Aydinli, A.

Banerjee, A.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Biswas, S.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Boechat, A. A. P.

Boyd, J. T.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

Cao, C. G. L.

C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
[CrossRef]

Castle, P.

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol. 4, 34-40 (1986).
[CrossRef]

Chakroborty, M.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Chen, Y.

Chung, Y.

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

Cole, J. H.

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

Dagli, N.

I. Kiyat, A. Aydinli, and N. Dagli, “High-Q silicon-on-insulator optical rib waveguide racetrack resonators,” Opt. Express 13, 1900-1905 (2005).
[CrossRef] [PubMed]

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

Das, R.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

De Brabander, G. N.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

de Hon, B. P.

Debaes, C.

Durana, G.

Faustini, L.

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Gavalis, R. M.

C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
[CrossRef]

Ghosh, A. K.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Gloge, D.

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-162(2000).
[CrossRef]

Gupta-Bhaya, P.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Hall, D. R.

Hallen, R. M.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Harris, A.

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol. 4, 34-40 (1986).
[CrossRef]

Hecht, J.

J. Hecht, Understanding Fiber Optics (Pearson Education, 2006).

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-162(2000).
[CrossRef]

Huang, C.-Y.

C.-Y. Huang, W.-C. Wang, W.-J. Wu, and W. R. Ledoux, “Composite optical bend loss sensor for pressure and shear measurement,” IEEE Sens. J. 7, 1554-1565 (2007).
[CrossRef]

Jana, B.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

John, J.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Jones, J. D. C.

Jones-Bey, H. A.

H. A. Jones-Bey, “Choosing software: different design paths lead to different solutions, part II,” http://www.optoiq.com/index/display/article-display/245100/articles/laser-focus-world/volume-42/issue-1/columns/software-computing/choosing-softwaredifferent-design-paths-lead-to-different-solutions-part-ii.html.

Khan, T. K.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Kiyat, I.

Kovacevic, M. S.

Kumar, S.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Ledoux, W. R.

C.-Y. Huang, W.-C. Wang, W.-J. Wu, and W. R. Ledoux, “Composite optical bend loss sensor for pressure and shear measurement,” IEEE Sens. J. 7, 1554-1565 (2007).
[CrossRef]

Lilge, L.

C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
[CrossRef]

Lu, Y. Y.

Y. Y. Lu, “Some techniques for computing wave propagation in optical waveguides,” Commun. Comput. Phys 1, 1056-1075(2006).

Lubatschowski, H.

N. Anastasopoulou, C. Ziolek, A. A. Serafetinides, and H. Lubatschowski, “Q-switched Er:YAG radiation transmission through fluoride glass fibers and dielectric-coated metallic hollow waveguides,” Opt. Commun. 186, 167-171 (2000).
[CrossRef]

Maletras, F. X.

A. T. Augousti, F. X. Maletras, and J. Mason, “The use of a figure-of-eight coil for fibre optic respiratory plethysmography: geometrical analysis and experimental characterisation,” Opt. Fiber Technol. 11, 346-360 (2005).
[CrossRef]

Marcuse, D.

Martini, G.

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Mason, J.

A. T. Augousti, F. X. Maletras, and J. Mason, “The use of a figure-of-eight coil for fibre optic respiratory plethysmography: geometrical analysis and experimental characterisation,” Opt. Fiber Technol. 11, 346-360 (2005).
[CrossRef]

Mateo, J.

Miyagi, M.

M. Miyagi and G. L. Yip, “Mode conversion and radiation losses in a step-index optical fibre due to bending,” Opt. Quantum Electron. 9, 51-60 (1977).
[CrossRef]

Mukherjee, S.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Naghski, D. H.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

Nasilowski, T.

Nikezic, D.

Okamoto, K.

Osgood, R. M.

Papadopoulos, D. N.

E. Papagiakoumou, D. N. Papadopoulos, N. Anastasopoulou, and A. A. Serafetinides, “Comparative evaluation of HP oxide glass fibers for Q-switched and free-running Er:YAG laser beam propagation,” Opt. Commun. 220, 151-160 (2003).
[CrossRef]

Papagiakoumou, E.

E. Papagiakoumou, D. N. Papadopoulos, N. Anastasopoulou, and A. A. Serafetinides, “Comparative evaluation of HP oxide glass fibers for Q-switched and free-running Er:YAG laser beam propagation,” Opt. Commun. 220, 151-160 (2003).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-162(2000).
[CrossRef]

Rajput, R. S.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Renner, H.

H. Renner, “Bending losses of coated single-mode fibers: a simple approach,” J. Lightwave Technol. 10, 544-551 (1992).
[CrossRef]

Saxena, A.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Saxena, V.

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-162(2000).
[CrossRef]

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[CrossRef]

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R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

Serafetinides, A. A.

E. Papagiakoumou, D. N. Papadopoulos, N. Anastasopoulou, and A. A. Serafetinides, “Comparative evaluation of HP oxide glass fibers for Q-switched and free-running Er:YAG laser beam propagation,” Opt. Commun. 220, 151-160 (2003).
[CrossRef]

N. Anastasopoulou, C. Ziolek, A. A. Serafetinides, and H. Lubatschowski, “Q-switched Er:YAG radiation transmission through fluoride glass fibers and dielectric-coated metallic hollow waveguides,” Opt. Commun. 186, 167-171 (2000).
[CrossRef]

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A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

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V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

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A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
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A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

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C.-Y. Huang, W.-C. Wang, W.-J. Wu, and W. R. Ledoux, “Composite optical bend loss sensor for pressure and shear measurement,” IEEE Sens. J. 7, 1554-1565 (2007).
[CrossRef]

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C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
[CrossRef]

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C.-Y. Huang, W.-C. Wang, W.-J. Wu, and W. R. Ledoux, “Composite optical bend loss sensor for pressure and shear measurement,” IEEE Sens. J. 7, 1554-1565 (2007).
[CrossRef]

Xing, H.

C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
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C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
[CrossRef]

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N. Anastasopoulou, C. Ziolek, A. A. Serafetinides, and H. Lubatschowski, “Q-switched Er:YAG radiation transmission through fluoride glass fibers and dielectric-coated metallic hollow waveguides,” Opt. Commun. 186, 167-171 (2000).
[CrossRef]

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Appl. Opt. (6)

Commun. Comput. Phys (1)

Y. Y. Lu, “Some techniques for computing wave propagation in optical waveguides,” Commun. Comput. Phys 1, 1056-1075(2006).

IEEE J. Quantum Electron. (2)

Y. Chung and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

R. T. Schermer and J. H. Cole, “Improved bend loss formula verified for optical fiber by simulation and experiment,” IEEE J. Quantum Electron. 43, 899-909 (2007).
[CrossRef]

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

R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150-162(2000).
[CrossRef]

IEEE Sens. J. (1)

C.-Y. Huang, W.-C. Wang, W.-J. Wu, and W. R. Ledoux, “Composite optical bend loss sensor for pressure and shear measurement,” IEEE Sens. J. 7, 1554-1565 (2007).
[CrossRef]

J. Lightwave Technol. (5)

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15, 990-997 (1997).
[CrossRef]

A. Harris and P. Castle, “Bend loss measurements on high numerical aperture single-mode fibers as a function of wavelength and bend radius,” J. Lightwave Technol. 4, 34-40 (1986).
[CrossRef]

C. Vassallo, “Scalar-field theory and 2-D ray theory for bent single-mode weakly guiding optical fibers,” J. Lightwave Technol. 3, 416-423 (1985).
[CrossRef]

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[CrossRef]

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[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Opt. Commun. (2)

E. Papagiakoumou, D. N. Papadopoulos, N. Anastasopoulou, and A. A. Serafetinides, “Comparative evaluation of HP oxide glass fibers for Q-switched and free-running Er:YAG laser beam propagation,” Opt. Commun. 220, 151-160 (2003).
[CrossRef]

N. Anastasopoulou, C. Ziolek, A. A. Serafetinides, and H. Lubatschowski, “Q-switched Er:YAG radiation transmission through fluoride glass fibers and dielectric-coated metallic hollow waveguides,” Opt. Commun. 186, 167-171 (2000).
[CrossRef]

Opt. Express (3)

Opt. Fiber Technol. (1)

A. T. Augousti, F. X. Maletras, and J. Mason, “The use of a figure-of-eight coil for fibre optic respiratory plethysmography: geometrical analysis and experimental characterisation,” Opt. Fiber Technol. 11, 346-360 (2005).
[CrossRef]

Opt. Quantum Electron. (1)

M. Miyagi and G. L. Yip, “Mode conversion and radiation losses in a step-index optical fibre due to bending,” Opt. Quantum Electron. 9, 51-60 (1977).
[CrossRef]

Proc. SPIE (1)

C. G. L. Cao, P. Y. Wong, L. Lilge, R. M. Gavalis, H. Xing, and N. Zamarripa, “Advanced shape tracking to improve flexible endoscopic diagnostics,” Proc. SPIE 6935, 693522 (2008).
[CrossRef]

Sens. Actuators B (1)

A. Banerjee, S. Mukherjee, R. K. Verma, B. Jana, T. K. Khan, M. Chakroborty, R. Das, S. Biswas, A. Saxena, V. Singh, R. M. Hallen, R. S. Rajput, P. Tewari, S. Kumar, V. Saxena, A. K. Ghosh, J. John, and P. Gupta-Bhaya, “Fiber optic sensing of liquid refractive index,” Sens. Actuators B 123, 594-605(2007).
[CrossRef]

Other (5)

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Lumerical Solutions, “MODE Solutions,” http://www.lumerical.com/mode.php.

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Figures (6)

Fig. 1
Fig. 1

BPM simulation and experimental results for a 200 μm core fiber showing the ratio of bent to straight fiber output power over a range of bend radii.

Fig. 2
Fig. 2

(a) Longitudinal cross section and (b) transverse cross section of fiber simulated using the BPM software.

Fig. 3
Fig. 3

Power monitors for the core region, core–cladding region, and core–cladding-buffer region for the fiber simulated using BPM software. Z represents the longitudinal direction of the fiber. Power was normalized against input power.

Fig. 4
Fig. 4

Cross section of fiber geometry modeled in the BPM simulation software. Tapered rectangles were used to approximate an arced region in the cladding.

Fig. 5
Fig. 5

Cross section of fiber modeled in the BPM simulation software. Tapered rectangles approximate the cladding region.

Fig. 6
Fig. 6

Power monitors for the core region, core–cladding region, core–cladding-buffer region, and “ core + rectangles ” region simulated using BPM software. The “ core + rectangles ” monitor sums the power in the tapered rectangles and the core region.

Tables (2)

Tables Icon

Table 1 Comparison of Different Bend-Loss Modeling Techniques

Tables Icon

Table 2 50 μm Core Fiber Results by Experiment and by BPM Simulation for Two Different Bend Radii a

Equations (37)

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

α f = 2 n k ( θ c 2 θ 2 ) exp { ( 2 / 3 ) n k R [ θ c 2 θ 2 ( 2 a / R ) ] 3 / 2 } ,
θ c = [ 1 ( n c / n ) 2 ] 1 / 2 ,
k = 2 π / λ ,
P r = [ 0 θ c P 0 ( θ ) d θ 0 θ f P 0 ( θ ) exp ( α f l ) d θ ] / 0 θ c P 0 ( θ ) d θ ,
θ f = θ c [ 1 ( 2 a / R θ c 2 ) ] 1 / 2 ,
2 α = { π 1 / 2 κ 2 exp [ ( 2 / 3 ) ( γ 3 / β 0 2 ) R ] } / [ e v γ 3 / 2 V 2 R 1 / 2 K v 1 ( γ a ) K v + 1 ( γ a ) ] ,
2 α = Δ P / P ,
V 2 = k 2 a 2 ( n 1 2 n 2 2 ) ,
κ = ( n 1 2 k 2 β 0 2 ) 1 / 2 ,
e v = { 2 , v = 0 1 , v 0 ,
γ = ( β 0 2 n 2 2 k 2 ) 1 / 2 ,
K v l ( 1 / 2 ) ( a γ ) = ( π / 2 a γ ) 1 / 2 e a γ μ = 0 v l 1 ( v l + μ 1 ) ! μ ! ( v l μ 1 ) ! ( a γ ) μ ,
μ = β 0 R ,
ψ ( x , y ) = [ ( π 1 / 2 a ) / ( 2 v ) ] ( x / x c 1 ) 1 / 4 W ( x ) 1 exp { i Θ y 2 / [ 4 W ( x ) 2 ] } ,
W ( x ) 2 = ( v / a x ) [ 1 + i ( x / x c 1 ) 1 / 2 ] ,
2 α B = ( 1 / 2 ) [ π / ( γ 3 R ) ] 1 / 2 { κ 2 / [ V 2 K 1 2 ( γ a ) ] } exp [ ( 2 γ 3 R ) / ( 3 β 0 2 ) ] ,
2 α = ( 2 κ 2 ) / [ β V 2 K 1 2 ( a γ ) ] 0 { exp [ a ( γ 2 + ζ 2 ) 1 / 2 ] / ( γ 2 + ζ 2 ) 1 / 2 } · { A i [ X 2 ( 0 , ζ ) ] / B i [ X 2 ( a , ζ ) ] } { ( x 2 1 / 2 x 3 1 / 2 ) / [ x 2 cos 2 θ ( ζ ) + x 3 sin 2 θ ( ζ ) ] } d ζ ,
T r = [ 4 sin θ i ( sin 2 θ i sin 2 θ c c ) 1 / 2 ] / [ sin θ i + ( sin 2 θ i sin 2 θ c c ) 1 / 2 ] 2 ,
T t = ( 4 sin θ i / sin θ c c ) [ 1 ( sin 2 θ i / sin 2 θ c c ) ] 1 / 2 × exp [ ( 2 / 3 ) n 1 k ( R + ρ ) ( θ c c 2 θ i 2 ) 3 / 2 ] ,
P ( θ , z ) z = V P ( θ , z ) θ + D 2 P ( θ , z ) θ 2 ,
D = Δ θ 2 d ( θ ) ,
Δ θ = λ / 4 a n 1 ,
V = D / θ ,
P R = ( δ P 1 δ P ) / δ P 1 ,
δ P 1 = P S / P 0 ,
δ P 2 = P B / P 0 ,
P 0 ( z ) = 2 π 0 θ C θ P 0 ( θ , z ) d θ ,
P i ( z ) = 2 π 0 θ C θ P i ( θ , z ) d θ ,
2 φ x 2 + 2 φ y 2 + 2 φ z 2 + k 0 n ( x , y , z ) 2 φ = 0 ,
L bend = ( 4.34 ) α bend θ R ,
α bend = { α y 2 k y 2 / [ k 0 3 n e ( 1 + α y w / 2 ) ( n e 2 2 n e 1 2 ) ] } exp ( α y w ) × exp ( 2 α y 3 R / 3 n e 2 k 0 2 ) ,
α y = k 0 ( n e 2 n e 1 2 ) 1 / 2 ,
k 0 = 2 π / λ 0 ,
k y = k o ( n e 2 2 n e 2 ) 1 / 2 ,
E ( y ) = E 0 ( y ) [ 1 + ( 1 / R ) ( k 0 n e 2 ω 0 ) 2 y ] ,
E 0 ( y ) = A exp [ ( 1 / 2 ) ( y / ω 0 ) 2 ] ,
2 E + k 0 2 ε r E = 0 ,

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