Abstract

A holey fiber having a core with an elliptical-hole lattice structure, which is referred to as an elliptical-hole core circular-hole holey fiber (EC-CHF), can be easily designed as a single-polarization fiber by using the fundamental space-filling modes of the core and cladding lattices. However, because the guided mode in an EC-CHF has a polarization that arises from the large geometric anisotropy of the core lattice, the influence of the bending direction on the bending loss is a crucial issue for the practical implementation of EC-CHFs. Here, the bending losses of an EC-CHF bent in arbitrary angular orientations with respect to the core cross section are calculated numerically using the equivalent anisotropic step-index circular fiber model for a real EC-CHF, and the influence of the bending direction of the fiber on the bending loss is discussed.

© 2010 Optical Society of America

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2010 (1)

M. Eguchi and Y. Tsuji, “Bending loss evaluations of holey fibers having a core consisting of an elliptical-hole lattice by various approaches,” IEEE J. Quantum Electron. 46, 601–609 (2010).
[CrossRef]

2008 (2)

2007 (3)

2006 (1)

2005 (4)

2004 (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]

M. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, “Predicting macrobending loss for large-mode area photonic crystal fibers,” Opt. Express 12, 1775–1779 (2004).
[CrossRef] [PubMed]

2002 (1)

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

1997 (1)

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]

1989 (1)

K. Tajima, M. Ohashi, and Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503(1989).
[CrossRef]

1986 (1)

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 1071–1089 (1986).
[CrossRef]

1983 (4)

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, and R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. 1, 370–374 (1983).
[CrossRef]

A. W. Snyder and F. Rühl, “New single-mode single-polarisation fibre,” Electron. Lett. 19, 185–186 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, and E. J. Tarbox, “Single-polarisation operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

T. Okoshi, T. Aihara, and K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarisation fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

1982 (2)

D. N. Payne, A. J. Barlow, and J. J. R. Hansen, “Development of low- and high-birefringence optical fibers,” IEEE J. Quantum Electron. 18, 477–488 (1982).
[CrossRef]

D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21, 4208–4213 (1982).
[CrossRef] [PubMed]

1976 (1)

1975 (1)

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75–83 (1975).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems3rd ed. (Wiley-Interscience, 2002).
[CrossRef]

Aihara, T.

T. Okoshi, T. Aihara, and K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarisation fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

Albertsen, M.

Barlow, A. J.

D. N. Payne, A. J. Barlow, and J. J. R. Hansen, “Development of low- and high-birefringence optical fibers,” IEEE J. Quantum Electron. 18, 477–488 (1982).
[CrossRef]

Belardi, W.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[CrossRef]

Berghmans, F.

J. Olszewski, M. Szpulak, T. Martynkien, W. Urbańczyk, F. Berghmans, T. Nasiłowski, and H. Thienpont, “Analytical evaluation of bending loss oscillations in photonic crystal fibers,” Opt. Commun. 269, 261–270 (2007).
[CrossRef]

T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers,” Opt. Express 15, 13547–13556 (2007).
[CrossRef] [PubMed]

Birch, R. D.

M. P. Varnham, D. N. Payne, R. D. Birch, and E. J. Tarbox, “Single-polarisation operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Birks, T. A.

Bjarklev, A.

M. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, “Predicting macrobending loss for large-mode area photonic crystal fibers,” Opt. Express 12, 1775–1779 (2004).
[CrossRef] [PubMed]

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

Blondy, J.-M.

Bonacinni, D.

Bouwmans, G.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[CrossRef]

Broeng, J.

T. Schreiber, F. Röser, O. Schmidt, J. Limpert, R. Iliew, F. Lederer, A. Petersson, C. Jacobsen, K. P. Hansen, J. Broeng, and A. Tünnermann, “Stress-induced single-polarization single-transverse mode photonic crystal fiber with low nonlinearity,” Opt. Express 13, 7621–7630 (2005).
[CrossRef] [PubMed]

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

Bubnov, M. M.

Dianov, E. M.

Douay, M.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[CrossRef]

Eguchi, M.

Février, S.

Folkenberg, J. R.

Golojuch, G.

Guryanov, A. N.

Hansen, J. J. R.

D. N. Payne, A. J. Barlow, and J. J. R. Hansen, “Development of low- and high-birefringence optical fibers,” IEEE J. Quantum Electron. 18, 477–488 (1982).
[CrossRef]

Hansen, K. P.

Hansen, T. P.

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

Harris, J. H.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 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. 11, 75–83 (1975).
[CrossRef]

Howard, R. E.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, and R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. 1, 370–374 (1983).
[CrossRef]

Hwang, I.-K.

Iliew, R.

Jacobsen, C.

Jakobsen, C.

Jamier, R.

Jensen, J. R.

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

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]

Khopin, V. F.

Kikuchi, K.

T. Okoshi, T. Aihara, and K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarisation fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

Knight, J. C.

Knudsen, E.

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

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]

Lederer, F.

Lee, Y.-H.

Libori, S. E. B.

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

Likhachev, M. E.

Limpert, J.

MacChesney, J. B.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, and R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. 1, 370–374 (1983).
[CrossRef]

Marcuse, D.

Martynkien, T.

J. Olszewski, M. Szpulak, T. Martynkien, W. Urbańczyk, F. Berghmans, T. Nasiłowski, and H. Thienpont, “Analytical evaluation of bending loss oscillations in photonic crystal fibers,” Opt. Commun. 269, 261–270 (2007).
[CrossRef]

T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers,” Opt. Express 15, 13547–13556 (2007).
[CrossRef] [PubMed]

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]

Mortensen, N. A.

Nasilowski, T.

T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers,” Opt. Express 15, 13547–13556 (2007).
[CrossRef] [PubMed]

J. Olszewski, M. Szpulak, T. Martynkien, W. Urbańczyk, F. Berghmans, T. Nasiłowski, and H. Thienpont, “Analytical evaluation of bending loss oscillations in photonic crystal fibers,” Opt. Commun. 269, 261–270 (2007).
[CrossRef]

Nielsen, M.

Nielsen, M. D.

Noda, J.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 1071–1089 (1986).
[CrossRef]

Ohashi, M.

K. Tajima, M. Ohashi, and Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503(1989).
[CrossRef]

Okamoto, K.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 1071–1089 (1986).
[CrossRef]

Okoshi, T.

T. Okoshi, T. Aihara, and K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarisation fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

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]

Payne, D. N.

M. P. Varnham, D. N. Payne, R. D. Birch, and E. J. Tarbox, “Single-polarisation operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

D. N. Payne, A. J. Barlow, and J. J. R. Hansen, “Development of low- and high-birefringence optical fibers,” IEEE J. Quantum Electron. 18, 477–488 (1982).
[CrossRef]

Petersson, A.

Pleibel, W.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, and R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. 1, 370–374 (1983).
[CrossRef]

Provino, L.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron. 41, 1558–1564 (2005).
[CrossRef]

Röser, F.

Rühl, F.

A. W. Snyder and F. Rühl, “New single-mode single-polarisation fibre,” Electron. Lett. 19, 185–186 (1983).
[CrossRef]

Russell, P. St. J.

Salganskii, M. Y.

Sasaki, Y.

K. Tajima, M. Ohashi, and Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503(1989).
[CrossRef]

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4, 1071–1089 (1986).
[CrossRef]

Schmidt, O.

Schreiber, T.

Sears, F. M.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, and R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. 1, 370–374 (1983).
[CrossRef]

Semjonov, S. L.

Simonsen, H. R.

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

Simpson, J. R.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, and R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. 1, 370–374 (1983).
[CrossRef]

Snyder, A. W.

A. W. Snyder and F. Rühl, “New single-mode single-polarisation fibre,” Electron. Lett. 19, 185–186 (1983).
[CrossRef]

Sørensen, T.

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

Stolen, R. H.

J. R. Simpson, R. H. Stolen, F. M. Sears, W. Pleibel, J. B. MacChesney, and R. E. Howard, “A single-polarization fiber,” J. Lightwave Technol. 1, 370–374 (1983).
[CrossRef]

Szpulak, M.

Tajima, K.

K. Tajima, M. Ohashi, and Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503(1989).
[CrossRef]

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]

Tarbox, E. J.

M. P. Varnham, D. N. Payne, R. D. Birch, and E. J. Tarbox, “Single-polarisation operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Thienpont, H.

J. Olszewski, M. Szpulak, T. Martynkien, W. Urbańczyk, F. Berghmans, T. Nasiłowski, and H. Thienpont, “Analytical evaluation of bending loss oscillations in photonic crystal fibers,” Opt. Commun. 269, 261–270 (2007).
[CrossRef]

T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers,” Opt. Express 15, 13547–13556 (2007).
[CrossRef] [PubMed]

Tsuji, Y.

Tünnermann, A.

Urbanczyk, W.

Varnham, M. P.

M. P. Varnham, D. N. Payne, R. D. Birch, and E. J. Tarbox, “Single-polarisation operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

Vu, N. H.

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]

Appl. Opt. (1)

Electron. Lett. (3)

A. W. Snyder and F. Rühl, “New single-mode single-polarisation fibre,” Electron. Lett. 19, 185–186 (1983).
[CrossRef]

M. P. Varnham, D. N. Payne, R. D. Birch, and E. J. Tarbox, “Single-polarisation operation of highly birefringent bow-tie optical fibres,” Electron. Lett. 19, 246–247 (1983).
[CrossRef]

T. Okoshi, T. Aihara, and K. Kikuchi, “Prediction of the ultimate performance of side-tunnel single-polarisation fibre,” Electron. Lett. 19, 1080–1082 (1983).
[CrossRef]

IEE Proc. Optoelectron. (1)

T. Sørensen, J. Broeng, A. Bjarklev, T. P. Hansen, E. Knudsen, S. E. B. Libori, H. R. Simonsen, and J. R. Jensen, “Spectral macro-bending loss considerations for photonic crystal fibres,” IEE Proc. Optoelectron. 149, 206–210 (2002).
[CrossRef]

IEEE J. Quantum Electron. (4)

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of y EC - CHF , (b) two-ring y EC - CHF , (c) three-ring y EC - CHF , and (d) four-ring y EC - CHF .

Fig. 2
Fig. 2

Bending loss evaluations for a single-polarization three-ring y EC - CHF (open circles) bent in the orientation perpendicular to the polarization direction of the guided mode and two equivalent SI circular fibers (solid lines).

Fig. 3
Fig. 3

Bending of an equivalent anisotropic SI circular fiber in arbitrary bending directions.

Fig. 4
Fig. 4

Estimation of the bending losses for the directions along the major and minor axes of elliptical holes in the core.

Fig. 5
Fig. 5

Estimation of the bending loss ( R = 2.5 cm ) of an equivalent anisotropic SI circular fiber ( a = 2.5 Λ ) for a two-ring y EC - CHF in arbitrary bending directions.

Fig. 6
Fig. 6

Estimation of the bending loss ( R = 2.5 cm ) of an equivalent anisotropic SI circular fiber ( a = 3.5 Λ ) for a three-ring y EC - CHF in arbitrary bending directions.

Fig. 7
Fig. 7

Estimation of the bending loss ( R = 2.5 cm ) of an equivalent anisotropic SI circular fiber ( a = 4.5 Λ ) for a four-ring y EC - CHF in arbitrary bending directions.

Fig. 8
Fig. 8

(a) Mode field in an equivalent anisotropic SI circular fiber ( a = 3.5 Λ ) for a δ = 0 ° bent three-ring y EC - CHF with R = 1 cm . (b) Magnification around the core region.

Equations (5)

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ε r , 1 = [ ε X X , 1 0 0 0 ε Y Y , 1 0 0 0 ε Y Y , 1 ] ,
ε X X , 1 = ( n eff , E x ) 2 ,
ε Y Y , 1 = ( n eff , E y ) 2 ,
ε r , 2 = ( n eff , C ) 2 ,
α B ( δ = 90 ° ) α B ( δ = 0 ° ) α B ( δ = 0 ° ) × 100 .

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