Abstract

We have manufactured and characterized a birefringent holey fiber of a new construction. The birefringence in this fiber is induced by the highly elliptical shape of the core, which consists of a triple defect in a hexagonal structure. Using a hybrid edge–nodal finite-element method, we calculated the spectral dependence of phase and group modal birefringence for spatial modes E11 and E21 in idealized and in real fiber, whose geometry we determined by using a scanning-electron microscope. Results of our calculations show that technological imperfections significantly affect the fiber's birefringence. Normalized cutoff wavelengths for higher-order modes relative to the filling factor were also determined for the idealized structure. We observed a significant disagreement between theoretical and experimental values of cutoff wavelengths, which was attributed to high confinement losses near the cutoff condition. We also measured the spectral dependence of the phase and the group modal birefringence for spatial modes E11 and E21. The measured parameters showed good agreement with the results of modeling.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2004 (2)

P. R. Chaudhuri, V. Paulose, C. Zhao, C. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photonics Technol. Lett. 16, 1307–1303 (2004).
[CrossRef]

N. A. Issa, M. A. van Eijkelenborg, G. Henry, M. Fellew, F. Cox, M. C. J. Large, “Fabrication and study of microstructured optical fibers with elliptical holes,” Opt. Lett. 29, 1336–1338 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (2)

2001 (6)

2000 (2)

1994 (1)

M. Koshiba, S. Maruyama, K. Hirayama, “A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

1989 (1)

R. Calvani, R. Caponi, F. Cisternino, “Polarization measurements of single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

1984 (1)

A. Kumar, R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: a perturbation approach,” Opt. Quantum Electron. 16, 349–354 (1984).
[CrossRef]

Andres, M. V.

Andres, P.

Arriaga, J.

Birks, T. A.

Bjarklev, A.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Bock, W. J.

Botten, L. C.

Broeng, J.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Calvani, R.

R. Calvani, R. Caponi, F. Cisternino, “Polarization measurements of single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

Caponi, R.

R. Calvani, R. Caponi, F. Cisternino, “Polarization measurements of single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

Chaudhuri, P. R.

P. R. Chaudhuri, V. Paulose, C. Zhao, C. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photonics Technol. Lett. 16, 1307–1303 (2004).
[CrossRef]

Cisternino, F.

R. Calvani, R. Caponi, F. Cisternino, “Polarization measurements of single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

Cox, F.

de Sterke, C. M.

Dyott, R. B.

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, Boston, Mass., 1995).

Fellew, M.

Ferrando, A.

Hansen, T. P.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Henry, G.

Hirayama, K.

M. Koshiba, S. Maruyama, K. Hirayama, “A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

Issa, N. A.

Jensen, J. R.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Kawanishi, S.

Knight, J. C.

Knudsen, E.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Koshiba, M.

M. Koshiba, K. Saitoh, “Finite-element analysis of birefringence and dispersion properties in actual and idealized holey-fiber structures,” Appl. Opt. 42, 6267–6275 (2003).
[CrossRef] [PubMed]

M. Koshiba, S. Maruyama, K. Hirayama, “A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

Kubota, H.

Kuhlmey, B. T.

Kumar, A.

A. Kumar, R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: a perturbation approach,” Opt. Quantum Electron. 16, 349–354 (1984).
[CrossRef]

Large, M. C. J.

Libori, S. E. B.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Lu, C.

P. R. Chaudhuri, V. Paulose, C. Zhao, C. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photonics Technol. Lett. 16, 1307–1303 (2004).
[CrossRef]

Mangan, B. J.

Martynkien, T.

Maruyama, S.

M. Koshiba, S. Maruyama, K. Hirayama, “A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

Maystre, D.

McPhedran, R. C.

Miret, J. J.

Ortigosa-Blanch, A.

Osgood, R. M.

M. J. Steel, R. M. Osgood, “Elliptical-hole photonic crystal fibers,” Opt. Lett. 26, 229–231 (2001).
[CrossRef]

M. J. Steel, R. M. Osgood, “Polarization and dispersive properties of elliptical-hole,” J. Lightwave Technol. 19, 1966–1979 (2001).
[CrossRef]

Paulose, V.

P. R. Chaudhuri, V. Paulose, C. Zhao, C. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photonics Technol. Lett. 16, 1307–1303 (2004).
[CrossRef]

Renversez, G.

Saitoh, K.

Silvestre, E.

Simonsen, H.

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

St. J. Russell, P.

Steel, M. J.

Suzuki, K.

Urbanczyk, W.

van Eijkelenborg, M. A.

Varshney, R. K.

A. Kumar, R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: a perturbation approach,” Opt. Quantum Electron. 16, 349–354 (1984).
[CrossRef]

Wadsworth, W. J.

White, T. P.

Zhao, C.

P. R. Chaudhuri, V. Paulose, C. Zhao, C. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photonics Technol. Lett. 16, 1307–1303 (2004).
[CrossRef]

Appl. Opt. (2)

IEEE Photonics Technol. Lett. (2)

T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, H. Simonsen, “Highly birefringent index guiding photonic crystal fibers,” IEEE Photonics Technol. Lett. 13, 588–590 (2001).
[CrossRef]

P. R. Chaudhuri, V. Paulose, C. Zhao, C. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photonics Technol. Lett. 16, 1307–1303 (2004).
[CrossRef]

J. Lightwave Technol. (3)

M. Koshiba, S. Maruyama, K. Hirayama, “A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems,” J. Lightwave Technol. 12, 495–502 (1994).
[CrossRef]

R. Calvani, R. Caponi, F. Cisternino, “Polarization measurements of single-mode fibers,” J. Lightwave Technol. 7, 1187–1196 (1989).
[CrossRef]

M. J. Steel, R. M. Osgood, “Polarization and dispersive properties of elliptical-hole,” J. Lightwave Technol. 19, 1966–1979 (2001).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

A. Kumar, R. K. Varshney, “Propagation characteristics of highly elliptical core optical waveguides: a perturbation approach,” Opt. Quantum Electron. 16, 349–354 (1984).
[CrossRef]

Other (1)

R. B. Dyott, Elliptical Fiber Waveguides (Artech House, Boston, Mass., 1995).

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Figures (7)

Fig. 1
Fig. 1

(a) Structure of the birefringent holey fiber with the core consisting of a triple defect, (b) photograph of the manufactured fiber obtained using a SEM, and (c) the same photograph after image processing, which shows a ring around every hole, caused the carbon layer filling the holes.

Fig. 2
Fig. 2

Geometry of (a) the real fiber reproduced from the SEM photograph and (b) the idealized fiber cross section with equal hole diameters.

Fig. 3
Fig. 3

(a) Phase modal birefringence and (b) group modal birefringence measured (dots) and calculated versus wavelength. The calculations were carried out for the real (solid curves) and for the idealized fiber geometries.

Fig. 4
Fig. 4

Normalized cut-off wavelength λc/Λ versus filling factor 2a/Λ for the spatial modes of the lowest order. For the investigated fiber with idealized geometry (Λ = 960 nm, 2a/Λ = 0.34) the cutoff wavelengths for the respective mode orders are λc21 = 1000 and λc31 = 500 nm.

Fig. 5
Fig. 5

Spectral dependence of the confinement losses for three spatial modes in the fiber with idealized geometry.

Fig. 6
Fig. 6

Schematic of the system for measurement of phase modal birefringence.

Fig. 7
Fig. 7

(a) Schematic of the system for measurement of the group modal birefringence by the scanning-wavelength method and (b) output spectrogram for a 0.751-m-long tested fiber.

Equations (10)

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B = λ 2 π ( β x β y ) ,
G = B λ d B d λ
τ = G / c ,
n i j x , y ( λ c ) = n cl ( λ c )
L B = Δ L / Δ M ,
B = λ 0 / L B ,
φ = 2 π λ B L ,
d φ d λ Δ λ = ± 2 π ,
± 2 π = 2 π L λ 2 ( B λ d B d λ ) Δ λ ,
| G | = λ 2 Δ λ L ,

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