Abstract

We calculated the sensitivity of phase (dB/dp) and group (dG/dp) modal birefringence to hydrostatic pressure versus wavelength in two birefringent holey fibers of different construction, where B is the phase modal birefringence, G is the group modal birefringence, and p is the pressure applied to the fiber. The contributions of the geometrical effects that were related only to deformation of the holey structure and the stress-related contribution to the overall pressure sensitivities were analyzed separately. Our results show that these two factors decrease the phase modal birefringence in both structures, which results in negative signs of dB/dp and dG/dp. Furthermore, we demonstrate that the geometrical effects are much weaker than the stress-related effects and contribute only a few percent to the overall pressure sensitivity.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2003

2002

2001

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

W. Urbanczyk, T. Martynkien, W. J. Bock, “Dispersion effects in elliptical core highly birefringent fibers,” Appl. Opt. 40, 1911–1920 (2001).
[CrossRef]

W. Urbańczyk, M. Nawrocka, W. J. Bock, “Digital demodulation system for low-coherence interferometric sensors based on highly birefringent fibers,” Appl. Opt. 40, 6618–6625 (2001).
[CrossRef]

W. J. Bock, M. S. Nawrocka, W. Urbańczyk, “Highly sensitive fiber-optic sensor for dynamic pressure measurements,” IEEE Trans. Instrum. Meas. Technol. 50, 1085–1088 (2001).
[CrossRef]

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

M. Koshiba, K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
[CrossRef]

A. Ferrando, J. J. Miret, “Single-polarization single-mode intraband guidance in supersquare photonic crystal fibers,” Appl. Phys. Lett. 78, 3184–3186 (2001).
[CrossRef]

2000

T. Martynkien, W. Urbańczyk, W. J. Bock, “Spectral dependence of sensitivity of highly birefringent fibers to temperature elongation and hydrostatic pressure,” Optik 111, 97–102 (2000).

A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325–1327 (2000).
[CrossRef]

1997

1994

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]

1986

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

H. M. Xie, Ph. Dabkiewicz, R. Ulrich, K. Okamoto, “Side-hole fiber for fiber-optic pressure sensing,” Opt. Lett. 11, 333–335 (1986).
[CrossRef] [PubMed]

Antkowiak, M.

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 5th International Conference on Transparent Optical Networks and 2nd European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 340–343.

Arriaga, J.

Baggett, J. C.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Belardi, W.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Berghmans, F.

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 5th International Conference on Transparent Optical Networks and 2nd European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 340–343.

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Bock, W. J.

W. Urbańczyk, M. Nawrocka, W. J. Bock, “Digital demodulation system for low-coherence interferometric sensors based on highly birefringent fibers,” Appl. Opt. 40, 6618–6625 (2001).
[CrossRef]

W. Urbanczyk, T. Martynkien, W. J. Bock, “Dispersion effects in elliptical core highly birefringent fibers,” Appl. Opt. 40, 1911–1920 (2001).
[CrossRef]

W. J. Bock, M. S. Nawrocka, W. Urbańczyk, “Highly sensitive fiber-optic sensor for dynamic pressure measurements,” IEEE Trans. Instrum. Meas. Technol. 50, 1085–1088 (2001).
[CrossRef]

T. Martynkien, W. Urbańczyk, W. J. Bock, “Spectral dependence of sensitivity of highly birefringent fibers to temperature elongation and hydrostatic pressure,” Optik 111, 97–102 (2000).

M. Szpulak, W. Urbańczyk, T. Martynkien, J. Wójcik, W. J. Bock, “Temperature sensitivity of the photonic crystal holey fibers,” in XIth Conference on Optical Fibers and Their Applications VIII, J. Dorosz, R. S. Romaniuk, eds., Proc. SPIE5028, 108–114 (2003).

M. Szpulak, T. Martynkien, W. Urbańczyk, J. Wójcik, W. J. Bock, “Influence of temperature on birefringence and polarization mode dispersion in photonic crystal holey fibers,” in Proceedings of the 4th International Conference on Transparent Optical Networks and European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), pp. 89–92.

Broderick, N. G. R.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Brown, T. G.

Cucinotta, A.

Dabkiewicz, Ph.

Dyott, R. B.

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

Ferrando, A.

A. Ferrando, J. J. Miret, “Single-polarization single-mode intraband guidance in supersquare photonic crystal fibers,” Appl. Phys. Lett. 78, 3184–3186 (2001).
[CrossRef]

Fuochi, M.

Furusawa, K.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

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]

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Koshiba, M.

K. Saitoh, M. Koshiba, “Single-polarization single-mode photonic crystal fibers,” Technol. Lett. 15, 1384–1386 (2003).
[CrossRef]

M. Koshiba, K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
[CrossRef]

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]

Kotynski, R.

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 5th International Conference on Transparent Optical Networks and 2nd European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 340–343.

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

Mangan, B. J.

Martin Man, T. P.

Martynkien, T.

W. Urbanczyk, T. Martynkien, W. J. Bock, “Dispersion effects in elliptical core highly birefringent fibers,” Appl. Opt. 40, 1911–1920 (2001).
[CrossRef]

T. Martynkien, W. Urbańczyk, W. J. Bock, “Spectral dependence of sensitivity of highly birefringent fibers to temperature elongation and hydrostatic pressure,” Optik 111, 97–102 (2000).

M. Szpulak, W. Urbańczyk, T. Martynkien, J. Wójcik, W. J. Bock, “Temperature sensitivity of the photonic crystal holey fibers,” in XIth Conference on Optical Fibers and Their Applications VIII, J. Dorosz, R. S. Romaniuk, eds., Proc. SPIE5028, 108–114 (2003).

M. Szpulak, T. Martynkien, W. Urbańczyk, J. Wójcik, W. J. Bock, “Influence of temperature on birefringence and polarization mode dispersion in photonic crystal holey fibers,” in Proceedings of the 4th International Conference on Transparent Optical Networks and European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), pp. 89–92.

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]

Miret, J. J.

A. Ferrando, J. J. Miret, “Single-polarization single-mode intraband guidance in supersquare photonic crystal fibers,” Appl. Phys. Lett. 78, 3184–3186 (2001).
[CrossRef]

Monro, T. M.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Nasilowski, T.

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 5th International Conference on Transparent Optical Networks and 2nd European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 340–343.

Nawrocka, M.

Nawrocka, M. S.

W. J. Bock, M. S. Nawrocka, W. Urbańczyk, “Highly sensitive fiber-optic sensor for dynamic pressure measurements,” IEEE Trans. Instrum. Meas. Technol. 50, 1085–1088 (2001).
[CrossRef]

Noda, J.

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

Okamoto, K.

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

H. M. Xie, Ph. Dabkiewicz, R. Ulrich, K. Okamoto, “Side-hole fiber for fiber-optic pressure sensing,” Opt. Lett. 11, 333–335 (1986).
[CrossRef] [PubMed]

Ortigosa-Blanch, A.

Osgood, R. M.

Poli, F.

Richardson, D. J.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Saitoh, K.

K. Saitoh, M. Koshiba, “Single-polarization single-mode photonic crystal fibers,” Technol. Lett. 15, 1384–1386 (2003).
[CrossRef]

M. Koshiba, K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
[CrossRef]

Sasaki, Y.

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

Selleri, S.

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

St. J. Russell, P.

Steel, M. J.

Szpulak, M.

M. Szpulak, T. Martynkien, W. Urbańczyk, J. Wójcik, W. J. Bock, “Influence of temperature on birefringence and polarization mode dispersion in photonic crystal holey fibers,” in Proceedings of the 4th International Conference on Transparent Optical Networks and European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), pp. 89–92.

M. Szpulak, W. Urbańczyk, T. Martynkien, J. Wójcik, W. J. Bock, “Temperature sensitivity of the photonic crystal holey fibers,” in XIth Conference on Optical Fibers and Their Applications VIII, J. Dorosz, R. S. Romaniuk, eds., Proc. SPIE5028, 108–114 (2003).

Thienpont, H.

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 5th International Conference on Transparent Optical Networks and 2nd European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 340–343.

Ulrich, R.

Urbanczyk, W.

W. Urbańczyk, M. Nawrocka, W. J. Bock, “Digital demodulation system for low-coherence interferometric sensors based on highly birefringent fibers,” Appl. Opt. 40, 6618–6625 (2001).
[CrossRef]

W. J. Bock, M. S. Nawrocka, W. Urbańczyk, “Highly sensitive fiber-optic sensor for dynamic pressure measurements,” IEEE Trans. Instrum. Meas. Technol. 50, 1085–1088 (2001).
[CrossRef]

W. Urbanczyk, T. Martynkien, W. J. Bock, “Dispersion effects in elliptical core highly birefringent fibers,” Appl. Opt. 40, 1911–1920 (2001).
[CrossRef]

T. Martynkien, W. Urbańczyk, W. J. Bock, “Spectral dependence of sensitivity of highly birefringent fibers to temperature elongation and hydrostatic pressure,” Optik 111, 97–102 (2000).

M. Szpulak, W. Urbańczyk, T. Martynkien, J. Wójcik, W. J. Bock, “Temperature sensitivity of the photonic crystal holey fibers,” in XIth Conference on Optical Fibers and Their Applications VIII, J. Dorosz, R. S. Romaniuk, eds., Proc. SPIE5028, 108–114 (2003).

M. Szpulak, T. Martynkien, W. Urbańczyk, J. Wójcik, W. J. Bock, “Influence of temperature on birefringence and polarization mode dispersion in photonic crystal holey fibers,” in Proceedings of the 4th International Conference on Transparent Optical Networks and European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), pp. 89–92.

Vincentia, L.

Wadsworth, W. J.

Wójcik, J.

M. Szpulak, T. Martynkien, W. Urbańczyk, J. Wójcik, W. J. Bock, “Influence of temperature on birefringence and polarization mode dispersion in photonic crystal holey fibers,” in Proceedings of the 4th International Conference on Transparent Optical Networks and European Symposium on Photonic Crystals (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), pp. 89–92.

M. Szpulak, W. Urbańczyk, T. Martynkien, J. Wójcik, W. J. Bock, “Temperature sensitivity of the photonic crystal holey fibers,” in XIth Conference on Optical Fibers and Their Applications VIII, J. Dorosz, R. S. Romaniuk, eds., Proc. SPIE5028, 108–114 (2003).

Xie, H. M.

Zhu, Z.

Appl. Opt.

Appl. Phys. Lett.

A. Ferrando, J. J. Miret, “Single-polarization single-mode intraband guidance in supersquare photonic crystal fibers,” Appl. Phys. Lett. 78, 3184–3186 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

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 Photon. Technol. Lett. 13, 588–590 (2001).
[CrossRef]

M. Koshiba, K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
[CrossRef]

IEEE Trans. Instrum. Meas. Technol.

W. J. Bock, M. S. Nawrocka, W. Urbańczyk, “Highly sensitive fiber-optic sensor for dynamic pressure measurements,” IEEE Trans. Instrum. Meas. Technol. 50, 1085–1088 (2001).
[CrossRef]

J. Lightwave Technol.

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

J. Lightwave. Technol.

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]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Meas. Sci. Technol.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, D. J. Richardson, “Sensing with microstructured optical fibers,” Meas. Sci. Technol. 12, 854–858 (2001).
[CrossRef]

Opt. Lett.

Optik

T. Martynkien, W. Urbańczyk, W. J. Bock, “Spectral dependence of sensitivity of highly birefringent fibers to temperature elongation and hydrostatic pressure,” Optik 111, 97–102 (2000).

Technol. Lett.

K. Saitoh, M. Koshiba, “Single-polarization single-mode photonic crystal fibers,” Technol. Lett. 15, 1384–1386 (2003).
[CrossRef]

Other

T. Yamamoto, H. Kubota, S. Kawanishi, M. Tanaka, S. Yamaguchi, “Supercontinuum generation at 1.55 m in a dispersion-flattened polarization-maintaining photonic crystal fiber,” Opt. Express11, 1537–1540 (2003), http://www.opticsexpress.org .
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Cross sections of the birefringent holey fibers analyzed in this paper. Structure B is produced by Blaze Photonics, Inc. Each fiber contains five circles of air holes. The following geometrical parameters were assumed in the calculations. Structure A: pith length, Λ = 1.95 μm; diameters of the greater and the smaller holes, 2a cl = 1.1 and 2a s = 0.4 μm, respectively. Structure B: Λ = 4.4 μm; diameters of the greater and the smaller holes, 2a h = 4.5 and 2a cl = 2.2 μm, respectively.

Fig. 2
Fig. 2

Spectral dependence of the phase and the group modal birefringence in structures A and B.

Fig. 3
Fig. 3

Distribution of material birefringence Δn x - Δn y induced by pressure p = 1 GPa along x and y symmetry axes in structures A and B.

Fig. 4
Fig. 4

Pressure-induced deformation in the core region for one quarter of structures A and B calculated for applied pressure p = 10 GPa. The positions and shapes of the holes before and after deformation are indicated by filled and open circles, respectively.

Fig. 5
Fig. 5

(a), (c) Pressure sensitivity of phase modal birefringence dB/dp and (b), (d) group modal birefringence dG/dp versus wavelength for structures A and B. Dashed curves represent stress contributions dB S /dp and G S /dp to the overall pressure sensitivities.

Equations (11)

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B=λ2πβx-βy,
G=B-λ dBdλ.
τ=G/c,
n1=n+C1σ1+C2σ2+σ3,n2=n+C1σ2+C2σ1+σ3,n3=n+C1σ3+C2σ1+σ2,
nix, y=nx, y+Δnix, y, i=x, y
Δnxx, y=C1σ1x, y+C2σ2x, y,Δnyx, y=C1σ2x, y+C2σ1x, y.
σ1,2=σx+σy±σx-σy2+4τxy21/22.
dBdp=Bp=1 GPa-Bp=0p.
dBSdp=dBdp-dBGdp.
dGdp=dBdp-λ d2Bdλdp.
KP=2πλdBdp,

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