Abstract

We analyzed theoretically the spectral dependence of polarimetric sensitivity to temperature (KT) and the susceptibility of phase modal birefringence to temperature (dB/dT) in several birefringent photonic crystal holey fibers of different construction. Contributions to dB/dT related to thermal expansion of the fiber dimensions and that related to temperature-induced changes in glass and air refractive indices were calculated separately. Our results showed that dB/dT depends strongly on the material used for manufacturing the fiber and on the fiber’s geometry. We demonstrate that, by properly designing the birefringent holey fiber, it is possible to reduce its temperature sensitivity significantly and even to ensure a null response to temperature at a specific wavelength. Furthermore, we show that the temperature sensitivity in a fiber with arbitrary geometry can be significantly reduced by proper choice of the glass used in the fiber’s manufacture. We also measured the polarimetric sensitivity to temperature and identified its sign in two silica–air fibers. The experimental values are in good agreement with the results of modeling.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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  20. W. Urbanczyk, W. J. Bock, “Analysis of dispersion effects for white-light interferometric fiber-optic sensors,” Appl. Opt. 33, 124–129 (1994).
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  21. W. Urbanczyk, T. Martynkien, W. J. Bock, “Dispersion effects in elliptical core highly birefringent fibers,” Appl. Opt. 40, 1911–1920 (2001).
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  22. G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, 1997).
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    [CrossRef]

2005

2004

Y. Park, U. Paek, S. Han, B. Kim, Ch. Kim, D. Y. Kim, “Inelastic frozen-in stress in optical fibers” Opt. Commun. 242, 431–436 (2004).
[CrossRef]

A. D. Yablon, “Optical and mechanical effects of frozen-in stresses and strains in optical fibers,” J. Sel. Top. Quantum Electron 10, 300–311 (2004).
[CrossRef]

D. Kim, J. U. Kang, “Sagnac loop interferometer based on polarization maintaining photonic crystal fiber with reduced temperature sensitivity,” Opt. Express 12, 4490–4495 (2004).
[CrossRef] [PubMed]

Ch.-L. Zhao, X. Yang, Ch. Lu, W. Jin, M. S. Demokan, “Temperature-Insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror,” IEEE Photon. Technol. Lett. 16, 2535–2537 (2004).
[CrossRef]

A. Michie, J. Canning, K. Lyytikäinen, M. Åslund, J. Digweed, “Temperature independent highly birefringent photonic crystal fibre,” Opt. Express 12, 5160–5165 (2004).
[CrossRef] [PubMed]

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. R. Folkenberg, M. D. Nielsen, “Experimental study of polarization properties of highly birefringent photonic crystal fibers,” Opt. Express 12, 5931–5939 (2004).
[CrossRef] [PubMed]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Temperature independence of birefringence and group velocity dispersion in photonic crystal fibers,” Electron. Lett. 40, 1327–1328 (2004).
[CrossRef]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Ultrahigh birefringent nonlinear microstructured fiber,” IEEE Photon. Technol. Lett. 16, 1667–1669 (2004).
[CrossRef]

P. R. Chaudhuri, V. Paulose, Ch. Zhao, Ch. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photon. Technol. Lett. 16, 1301–1303 (2004).
[CrossRef]

2003

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847–851 (2003).
[CrossRef] [PubMed]

T. Ritari, T. Niemi, H. Ludvigsen, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Petterson, “Polarization mode dispersion of large mode-area photonic crystal fibers,” Opt. Commun. 226, 233–239 (2003).
[CrossRef]

2001

2000

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]

W. Urbanczyk, W. J. Bock, “Analysis of dispersion effects for white-light interferometric fiber-optic sensors,” Appl. Opt. 33, 124–129 (1994).
[CrossRef] [PubMed]

1986

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

Andrés, M. V.

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Ultrahigh birefringent nonlinear microstructured fiber,” IEEE Photon. Technol. Lett. 16, 1667–1669 (2004).
[CrossRef]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Temperature independence of birefringence and group velocity dispersion in photonic crystal fibers,” Electron. Lett. 40, 1327–1328 (2004).
[CrossRef]

Antkowiak, M.

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 2003 5th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, 2003), pp. 340–343.
[CrossRef]

Arriaga, J.

Åslund, M.

Berghmans, F.

M. Szpulak, G. Statkiewicz, J. Olszewski, T. Martynkien, W. Urbanczyk, J. Wojcik, M. Makara, J. Klimek, T. Nasilowski, F. Berghmans, H. Thienpont, “Experimental and theoretical investigations of birefringent holey fiber with triple defect,” Appl. Opt. 44, 2652–2658 (2005).
[CrossRef] [PubMed]

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 2003 5th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, 2003), pp. 340–343.
[CrossRef]

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

W. Urbanczyk, W. J. Bock, “Analysis of dispersion effects for white-light interferometric fiber-optic sensors,” Appl. Opt. 33, 124–129 (1994).
[CrossRef] [PubMed]

M. Szpulak, T. Martynkien, W. Urbanczyk, J. Wojcik, W. J. Bock, “Influence of temperature on birefringence and polarization mode dispersion in photonic crystal holey fibers,” in Proceedings of 2002 4th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, 2002), pp. 89–92.
[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]

Canning, J.

Chaudhuri, P. R.

P. R. Chaudhuri, V. Paulose, Ch. Zhao, Ch. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photon. Technol. Lett. 16, 1301–1303 (2004).
[CrossRef]

Cruz, J. L.

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Temperature independence of birefringence and group velocity dispersion in photonic crystal fibers,” Electron. Lett. 40, 1327–1328 (2004).
[CrossRef]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Ultrahigh birefringent nonlinear microstructured fiber,” IEEE Photon. Technol. Lett. 16, 1667–1669 (2004).
[CrossRef]

Delgado-Pinar, M.

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Ultrahigh birefringent nonlinear microstructured fiber,” IEEE Photon. Technol. Lett. 16, 1667–1669 (2004).
[CrossRef]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Temperature independence of birefringence and group velocity dispersion in photonic crystal fibers,” Electron. Lett. 40, 1327–1328 (2004).
[CrossRef]

Demokan, M. S.

Ch.-L. Zhao, X. Yang, Ch. Lu, W. Jin, M. S. Demokan, “Temperature-Insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror,” IEEE Photon. Technol. Lett. 16, 2535–2537 (2004).
[CrossRef]

Diez, A.

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Ultrahigh birefringent nonlinear microstructured fiber,” IEEE Photon. Technol. Lett. 16, 1667–1669 (2004).
[CrossRef]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Temperature independence of birefringence and group velocity dispersion in photonic crystal fibers,” Electron. Lett. 40, 1327–1328 (2004).
[CrossRef]

Digweed, J.

Dyott, R. B.

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

Folkenberg, J. R.

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. R. Folkenberg, M. D. Nielsen, “Experimental study of polarization properties of highly birefringent photonic crystal fibers,” Opt. Express 12, 5931–5939 (2004).
[CrossRef] [PubMed]

T. Ritari, T. Niemi, H. Ludvigsen, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Petterson, “Polarization mode dispersion of large mode-area photonic crystal fibers,” Opt. Commun. 226, 233–239 (2003).
[CrossRef]

Fujita, M.

Ghosh, G.

G. Ghosh, Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic, 1997).

Gisin, N.

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. R. Folkenberg, M. D. Nielsen, “Experimental study of polarization properties of highly birefringent photonic crystal fibers,” Opt. Express 12, 5931–5939 (2004).
[CrossRef] [PubMed]

T. Ritari, T. Niemi, H. Ludvigsen, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Petterson, “Polarization mode dispersion of large mode-area photonic crystal fibers,” Opt. Commun. 226, 233–239 (2003).
[CrossRef]

Han, S.

Y. Park, U. Paek, S. Han, B. Kim, Ch. Kim, D. Y. Kim, “Inelastic frozen-in stress in optical fibers” Opt. Commun. 242, 431–436 (2004).
[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]

Jin, W.

Ch.-L. Zhao, X. Yang, Ch. Lu, W. Jin, M. S. Demokan, “Temperature-Insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror,” IEEE Photon. Technol. Lett. 16, 2535–2537 (2004).
[CrossRef]

Kang, J. U.

Kawanishi, S.

Kim, B.

Y. Park, U. Paek, S. Han, B. Kim, Ch. Kim, D. Y. Kim, “Inelastic frozen-in stress in optical fibers” Opt. Commun. 242, 431–436 (2004).
[CrossRef]

Kim, Ch.

Y. Park, U. Paek, S. Han, B. Kim, Ch. Kim, D. Y. Kim, “Inelastic frozen-in stress in optical fibers” Opt. Commun. 242, 431–436 (2004).
[CrossRef]

Kim, D.

Kim, D. Y.

Y. Park, U. Paek, S. Han, B. Kim, Ch. Kim, D. Y. Kim, “Inelastic frozen-in stress in optical fibers” Opt. Commun. 242, 431–436 (2004).
[CrossRef]

Klimek, J.

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.

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 2003 5th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, 2003), pp. 340–343.
[CrossRef]

Kubota, H.

Legré, M.

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]

Lu, Ch.

Ch.-L. Zhao, X. Yang, Ch. Lu, W. Jin, M. S. Demokan, “Temperature-Insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror,” IEEE Photon. Technol. Lett. 16, 2535–2537 (2004).
[CrossRef]

P. R. Chaudhuri, V. Paulose, Ch. Zhao, Ch. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photon. Technol. Lett. 16, 1301–1303 (2004).
[CrossRef]

Ludvigsen, H.

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. R. Folkenberg, M. D. Nielsen, “Experimental study of polarization properties of highly birefringent photonic crystal fibers,” Opt. Express 12, 5931–5939 (2004).
[CrossRef] [PubMed]

T. Ritari, T. Niemi, H. Ludvigsen, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Petterson, “Polarization mode dispersion of large mode-area photonic crystal fibers,” Opt. Commun. 226, 233–239 (2003).
[CrossRef]

Lyytikäinen, K.

Makara, M.

Mangan, B. J.

Martynkien, T.

M. Szpulak, G. Statkiewicz, J. Olszewski, T. Martynkien, W. Urbanczyk, J. Wojcik, M. Makara, J. Klimek, T. Nasilowski, F. Berghmans, H. Thienpont, “Experimental and theoretical investigations of birefringent holey fiber with triple defect,” Appl. Opt. 44, 2652–2658 (2005).
[CrossRef] [PubMed]

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

M. Szpulak, T. Martynkien, W. Urbanczyk, J. Wojcik, W. J. Bock, “Influence of temperature on birefringence and polarization mode dispersion in photonic crystal holey fibers,” in Proceedings of 2002 4th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, 2002), pp. 89–92.
[CrossRef]

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]

Michie, A.

Nasilowski, T.

M. Szpulak, G. Statkiewicz, J. Olszewski, T. Martynkien, W. Urbanczyk, J. Wojcik, M. Makara, J. Klimek, T. Nasilowski, F. Berghmans, H. Thienpont, “Experimental and theoretical investigations of birefringent holey fiber with triple defect,” Appl. Opt. 44, 2652–2658 (2005).
[CrossRef] [PubMed]

R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, H. Thienpont, “Sensitivity of holey fiber based sensors,” in Proceedings of 2003 5th International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, 2003), pp. 340–343.
[CrossRef]

Nielsen, M. D.

Niemi, T.

T. Ritari, T. Niemi, H. Ludvigsen, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Petterson, “Polarization mode dispersion of large mode-area photonic crystal fibers,” Opt. Commun. 226, 233–239 (2003).
[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]

Olszewski, J.

Ortigosa-Blanch, A.

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Temperature independence of birefringence and group velocity dispersion in photonic crystal fibers,” Electron. Lett. 40, 1327–1328 (2004).
[CrossRef]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz, M. V. Andrés, “Ultrahigh birefringent nonlinear microstructured fiber,” IEEE Photon. Technol. Lett. 16, 1667–1669 (2004).
[CrossRef]

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]

Osgood, R. M.

Paek, U.

Y. Park, U. Paek, S. Han, B. Kim, Ch. Kim, D. Y. Kim, “Inelastic frozen-in stress in optical fibers” Opt. Commun. 242, 431–436 (2004).
[CrossRef]

Park, Y.

Y. Park, U. Paek, S. Han, B. Kim, Ch. Kim, D. Y. Kim, “Inelastic frozen-in stress in optical fibers” Opt. Commun. 242, 431–436 (2004).
[CrossRef]

Paulose, V.

P. R. Chaudhuri, V. Paulose, Ch. Zhao, Ch. Lu, “Near-elliptic core polarization-maintaining photonic crystal fiber: modeling birefringence characteristics and realization,” IEEE Photon. Technol. Lett. 16, 1301–1303 (2004).
[CrossRef]

Petterson, A.

T. Ritari, T. Niemi, H. Ludvigsen, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Petterson, “Polarization mode dispersion of large mode-area photonic crystal fibers,” Opt. Commun. 226, 233–239 (2003).
[CrossRef]

Ritari, T.

T. Ritari, H. Ludvigsen, M. Wegmuller, M. Legré, N. Gisin, J. R. Folkenberg, M. D. Nielsen, “Experimental study of polarization properties of highly birefringent photonic crystal fibers,” Opt. Express 12, 5931–5939 (2004).
[CrossRef] [PubMed]

T. Ritari, T. Niemi, H. Ludvigsen, M. Wegmuller, N. Gisin, J. R. Folkenberg, A. Petterson, “Polarization mode dispersion of large mode-area photonic crystal fibers,” Opt. Commun. 226, 233–239 (2003).
[CrossRef]

Russell, J.

Sasaki, Y.

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

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, P.

Statkiewicz, G.

Steel, M. J.

Suzuki, K.

Szpulak, M.

M. Szpulak, G. Statkiewicz, J. Olszewski, T. Martynkien, W. Urbanczyk, J. Wojcik, M. Makara, J. Klimek, T. Nasilowski, F. Berghmans, H. Thienpont, “Experimental and theoretical investigations of birefringent holey fiber with triple defect,” Appl. Opt. 44, 2652–2658 (2005).
[CrossRef] [PubMed]

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[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Cross sections of the birefringent holey fibers.

Fig. 2
Fig. 2

(a), (c), (e) Dependence of modal birefringence B on the refractive index of glass (nglass) and on normalized wavelength (λ/Λ) calculated for nhole = nair. (b), (d), (f) Dependence of B on nhole and λ/Λ calculated for nglass = nSiO2 in structures A, B, C, respectively. Values of B(nSiO2, nair, λ/Λ) are shown by solid curves. Dashed curves show locations of the maximum values of birefringence B(nglassmax, nair, λ/Λ).

Fig. 3
Fig. 3

Spectral dependence of the overall susceptibility of modal birefringence on temperature dB/dT in all structures analyzed, and contributions to dB/dT related to thermal expansion, dB/dTgeom = ΛαSiO2 dB/dΛ, and to temperature-induced changes in the refractive index of air, dB/dTair = yair dB/dnair.

Fig. 4
Fig. 4

Spectral dependence of the polarimetric sensitivity in silica–air fibers calculated according to Eq. (2) (KT) and disregarding the term αSiO2B representing the effect of temperature-induced fiber elongation (KT). The experimental values and measurement errors are indicated by filled circles and bars, respectively.

Fig. 5
Fig. 5

Spectral dependence of polarimetric sensitivity KT in structure B desensitized to temperature at λ = 0.95 µm by use of an appropriate glass for its manufacture, glass type BK7; γglass = 2.3 × 10−6 1/K and αglass = 7.2 × 10−6 1/K.

Fig. 6
Fig. 6

Setup for measurement of temperature-induced phase shifts between polarization modes.

Fig. 7
Fig. 7

Variation of the phase shift between polarization modes measured for increasing temperature in birefringent holey fibers of types A and B. Length L of the tested fiber exposed to temperature changes is indicated in each figure.

Tables (1)

Tables Icon

Table 1 Geometrical Parameters of the Analyzed Birefringent Holey Fibers

Equations (12)

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K T = d Δ φ d T L ,
K T = 2 π λ ( d B d T + B α ) ,
B = λ 2 π ( β x β y ) ,
d B ( λ ) d T = d B d n glass d n glass d B + d B d n hole d n hole d T + d B d Λ / Λ d Λ / Λ d T ,
d B ( λ ) d T = d B d n glass γ glass + d B d n hole γ hole + d B d Λ / Λ α glass ,
K T ( λ ) = 2 π λ [ d B ( λ ) d n glass γ glass + d B ( λ ) d n hole γ hole + d B ( λ ) d Λ / Λ α glass + B ( λ ) α glass ] .
γ glass α glass = [ d B ( λ ) / ( d Λ / Λ ) ] + B ( λ ) d B ( λ ) / d n glass .
d B ( λ ) d n glass = 0 .
d B d Λ / Λ = λ Λ d B d ( Λ / Λ ) .
Δ φ = 2 π L d d λ [ B ( λ ) λ ] Δ λ ,
Δ φ = 2 π L λ 2 G Δ λ ,
G = B λ d B d λ .

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