Abstract

Abstract

We study the effects of bending on single polarization fiber performance through the use of finite element method in conjunction with the perfectly matched layer (PML) in cylindrical geometry. The cylindrical PML used in this paper allows us to calculate the loss associated with each polarization mode at a given wavelength, specified bending diameter, and specific orientation. We identified a series of bending characteristics of the single polarization fiber by choosing different bending diameters and different orientations. We also conducted experiments to study some aspects of the bending. Good qualitative agreement between numerical and experimental results is found, which helps to understand fiber deployment conditions and can potentially facilitate new design efforts.

©2007 Optical Society of America

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References

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  1. M. J. Messerly, J. R. Onstott, and R. C. Mikkelson, “A broad-band single polarization optical fiber,” J. Lightwave Technol. 9, 817–820 (1991).
    [Crossref]
  2. H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
    [Crossref]
  3. J. R. Folkenberg, M. D. Nielsen, and C. Jakobsen, “Broadband single-polarization photonic crystal fiber,” Opt. Lett. 30, 1446–1448 (2005)
    [Crossref] [PubMed]
  4. T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)
  5. D. A. Nolan, G. E. Berkey, M.-J. Li, X. Chen, W. A. Wood, and L. A. Zenteno, “Single-polarization fiber with a high extinction ratio,” Opt. Lett. 29, 1855–1857 (2004)
    [Crossref] [PubMed]
  6. D. A. Nolan, M.-J. Li, X. Chen, and J. Koh, “Single polarization fibers and applications,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington DC, 2006) OWA1
  7. S. Li, X. Chen, D. V. Kuksenkov, J. Koh, M.-J. Li, L. A. Zenteno, and D. A. Nolan, “Wavelength tunable stretched-pulse mode-locked all-fiber erbium ring laser with single polarization fiber,” Opt. Express 14, 6098–6102 (2006)
    [Crossref] [PubMed]
  8. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers”, Appl. Opt. 21,4208–4213, (1982)
    [Crossref] [PubMed]
  9. K. Okamoto, “Single-polarization operation in highly birefringent optical fibers,” Appl. Opt. 23, 2638–2642 (1984)
    [Crossref] [PubMed]
  10. J. Olszewski, M. Szpulak, and W. Urbanczyk, “Effect of coupling between fundamental and cladding modes on bending losses in photonic crystal fibers,” Opt. Express 13, 6015–6022 (2005)
    [Crossref] [PubMed]
  11. Y. Tsuchida, K. Saitoh, and M. Koshiba, “Design and characterization of single-mode holey fibers with low bending losses,” Opt. Express 13, 4770–4779 (2005)
    [Crossref] [PubMed]
  12. M.J. Li, X. Chen, D.A. Nolan, G. E. Berkey, J. Wang, W. A. Wood, and L.A. Zenteno “High Bandwidth Single Polarization Fiber With Elliptical Central Air Hole”, J. Lightwave Technol. 23, 3454–3460 (2005)
    [Crossref]
  13. W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” IEEE Photon. Tech. Lett. 7, 599–604 (1994)
  14. Jianming Jin, “The Finite Element Method in Electromagnetics,” Second Edition, John Wiley & Sons, Inc, New York2002.
  15. P.L. Teixeira and W. C. Chew, “Systematic Derivation of Anisotropic PML Absorbing media in Cylindrical and Spherical Coordinates,” IEEE Microwave and Guid. Wave Lett. 7, 371–373 (1997)
    [Crossref]
  16. Electromagnetics Module User’s Guide, COMSOL 3.2, Chapter 2, COMSOL AB (2005)
  17. M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. QE- 11, 75–83 (1975)
    [Crossref]
  18. L. Faustini and G. Martini, “Bending Loss in Single-Mode Fibers,” J. Lightwave Technol.,  15, 671–679 (1997)
    [Crossref]

2006 (2)

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

S. Li, X. Chen, D. V. Kuksenkov, J. Koh, M.-J. Li, L. A. Zenteno, and D. A. Nolan, “Wavelength tunable stretched-pulse mode-locked all-fiber erbium ring laser with single polarization fiber,” Opt. Express 14, 6098–6102 (2006)
[Crossref] [PubMed]

2005 (4)

2004 (2)

D. A. Nolan, G. E. Berkey, M.-J. Li, X. Chen, W. A. Wood, and L. A. Zenteno, “Single-polarization fiber with a high extinction ratio,” Opt. Lett. 29, 1855–1857 (2004)
[Crossref] [PubMed]

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

1997 (2)

P.L. Teixeira and W. C. Chew, “Systematic Derivation of Anisotropic PML Absorbing media in Cylindrical and Spherical Coordinates,” IEEE Microwave and Guid. Wave Lett. 7, 371–373 (1997)
[Crossref]

L. Faustini and G. Martini, “Bending Loss in Single-Mode Fibers,” J. Lightwave Technol.,  15, 671–679 (1997)
[Crossref]

1994 (1)

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” IEEE Photon. Tech. Lett. 7, 599–604 (1994)

1991 (1)

M. J. Messerly, J. R. Onstott, and R. C. Mikkelson, “A broad-band single polarization optical fiber,” J. Lightwave Technol. 9, 817–820 (1991).
[Crossref]

1984 (1)

1982 (1)

1975 (1)

M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. QE- 11, 75–83 (1975)
[Crossref]

Berkey, G. E.

Broeng, J.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Chen, X.

Chew, W. C.

P.L. Teixeira and W. C. Chew, “Systematic Derivation of Anisotropic PML Absorbing media in Cylindrical and Spherical Coordinates,” IEEE Microwave and Guid. Wave Lett. 7, 371–373 (1997)
[Crossref]

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” IEEE Photon. Tech. Lett. 7, 599–604 (1994)

Faustini, L.

L. Faustini and G. Martini, “Bending Loss in Single-Mode Fibers,” J. Lightwave Technol.,  15, 671–679 (1997)
[Crossref]

Folkenberg, J. R.

Hansen, K. P.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Harris, J. H.

M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. QE- 11, 75–83 (1975)
[Crossref]

Heiblum, M.

M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. QE- 11, 75–83 (1975)
[Crossref]

Iliew, R.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Jacobsen, C.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Jakobsen, C.

Jin, Jianming

Jianming Jin, “The Finite Element Method in Electromagnetics,” Second Edition, John Wiley & Sons, Inc, New York2002.

Kawanishi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Koh, J.

S. Li, X. Chen, D. V. Kuksenkov, J. Koh, M.-J. Li, L. A. Zenteno, and D. A. Nolan, “Wavelength tunable stretched-pulse mode-locked all-fiber erbium ring laser with single polarization fiber,” Opt. Express 14, 6098–6102 (2006)
[Crossref] [PubMed]

D. A. Nolan, M.-J. Li, X. Chen, and J. Koh, “Single polarization fibers and applications,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington DC, 2006) OWA1

Koshiba, M.

Koyanagi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Kubota, H.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Kuksenkov, D. V.

Li, M.J.

Li, M.-J.

Li, S.

Limpert, J.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Marcuse, D.

Martini, G.

L. Faustini and G. Martini, “Bending Loss in Single-Mode Fibers,” J. Lightwave Technol.,  15, 671–679 (1997)
[Crossref]

Messerly, M. J.

M. J. Messerly, J. R. Onstott, and R. C. Mikkelson, “A broad-band single polarization optical fiber,” J. Lightwave Technol. 9, 817–820 (1991).
[Crossref]

Mikkelson, R. C.

M. J. Messerly, J. R. Onstott, and R. C. Mikkelson, “A broad-band single polarization optical fiber,” J. Lightwave Technol. 9, 817–820 (1991).
[Crossref]

Nielsen, M. D.

Nolan, D. A.

Nolan, D.A.

Okamoto, K.

Olszewski, J.

Onstott, J. R.

M. J. Messerly, J. R. Onstott, and R. C. Mikkelson, “A broad-band single polarization optical fiber,” J. Lightwave Technol. 9, 817–820 (1991).
[Crossref]

Petersson, A.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Röser, F.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Saitoh, K.

Schmidt, O.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Schreiber, T.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Schultz, H.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Szpulak, M.

Tanaka, M.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Teixeira, P.L.

P.L. Teixeira and W. C. Chew, “Systematic Derivation of Anisotropic PML Absorbing media in Cylindrical and Spherical Coordinates,” IEEE Microwave and Guid. Wave Lett. 7, 371–373 (1997)
[Crossref]

Tsuchida, Y.

Tünnermann, A.

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Urbanczyk, W.

Wang, J.

Weedon, W. H.

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” IEEE Photon. Tech. Lett. 7, 599–604 (1994)

Wood, W. A.

Yamaguchi, S.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

Zenteno, L. A.

Zenteno, L.A.

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

M. Heiblum and J. H. Harris, “Analysis of Curved Optical Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. QE- 11, 75–83 (1975)
[Crossref]

IEEE Microwave and Guid. Wave Lett. (1)

P.L. Teixeira and W. C. Chew, “Systematic Derivation of Anisotropic PML Absorbing media in Cylindrical and Spherical Coordinates,” IEEE Microwave and Guid. Wave Lett. 7, 371–373 (1997)
[Crossref]

IEEE Photon. Tech. Lett. (1)

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” IEEE Photon. Tech. Lett. 7, 599–604 (1994)

IEEE Photon. Technol. Lett. (1)

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004).
[Crossref]

J. Lightwave Technol. (3)

M. J. Messerly, J. R. Onstott, and R. C. Mikkelson, “A broad-band single polarization optical fiber,” J. Lightwave Technol. 9, 817–820 (1991).
[Crossref]

L. Faustini and G. Martini, “Bending Loss in Single-Mode Fibers,” J. Lightwave Technol.,  15, 671–679 (1997)
[Crossref]

M.J. Li, X. Chen, D.A. Nolan, G. E. Berkey, J. Wang, W. A. Wood, and L.A. Zenteno “High Bandwidth Single Polarization Fiber With Elliptical Central Air Hole”, J. Lightwave Technol. 23, 3454–3460 (2005)
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Proc. SPIE (1)

T. Schreiber, H. Schultz, F. Röser, O. Schmidt, J. Limpert, R. Iliew, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Design and high power operation of a stress-induced single-polarization single-transverse mode LMA Yb-doped photonic crystal fiber,” Proc. SPIE6102, 61020C-1–61020C-9 (2006)

Other (3)

D. A. Nolan, M.-J. Li, X. Chen, and J. Koh, “Single polarization fibers and applications,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference on CD-ROM (Optical Society of America, Washington DC, 2006) OWA1

Jianming Jin, “The Finite Element Method in Electromagnetics,” Second Edition, John Wiley & Sons, Inc, New York2002.

Electromagnetics Module User’s Guide, COMSOL 3.2, Chapter 2, COMSOL AB (2005)

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Figures (6)

Fig. 1.
Fig. 1. Cross section view of the fiber with PML.
Fig. 2.
Fig. 2. Calculated loss as a function of wavelength for two fundamental polarization modes in a straight fiber.
Fig. 3.
Fig. 3. Calculated loss as a function of wavelength for both polarization modes at several different bending diameters with 0 degree rotation.
Fig. 4.
Fig. 4. Calculated loss as a function of wavelength for both polarization modes at several orientations of 0, 45 and 90 degrees. Bending diameter is fixed at 20 cm.
Fig. 5.
Fig. 5. Measured fundamental mode cutoff wavelength shifts at different bending diameters for 1060 nm single polarization fiber
Fig. 6.
Fig. 6. Measured fundamental mode cutoff wavelength shifts at different bending diameters for 1550 nm single polarization fiber

Equations (11)

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

× ( μ 1 × E ( r ) k 0 2 ε E ( r ) = 0
E ( r ) = S 1 E ( r ̅ ) .
S = ( s x 1 0 0 0 s y 1 0 0 0 s z 1 )
r ̅ = [ x ˜ , y ˜ , z ˜ ] = [ 0 x S x ( x ) dx , 0 y S x ( y ) dy , 0 z S x ( z ) dz ]
μ = μ 0 μ r L
ε = ε 0 ε r L
L = ( S y S z S x 0 0 0 S z S x S y 0 0 0 S z S y S z ) .
L = ( S z ( S φ S ρ cos 2 φ + S ρ S φ sin 2 φ ) S z cos φ sin φ ( S φ S ρ S ρ S φ ) 0 S z cos φ sin φ ( S φ S ρ S ρ S φ ) S z ( S φ S ρ sin 2 φ + S ρ S φ cos 2 φ ) 0 0 0 S ρ S φ S z )
s ρ ( ρ ) = { 1 ρ ρ PML 1 i α ( ρ ρ PML d PML ) 2 ρ > ρ PML
n eq ( x , y ) = n ( x , y ) exp ( x R )
α B = 20 ln ( 10 ) Im ( β ) 8.686 Im ( β )

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