Abstract

The reflection and transmission characteristics of a high-birefringence fiber loop mirror (HiBi-FLM), which is composed of a standard fiber coupler and one-section or multisection high-birefringence fibers (HBFs), are analyzed and discussed in detail. Theoretical reflectivity and transmissivity expressions for HiBi-FLMs with one-, two-, and three-section HBFs were obtained. The procedure for calculating reflectivity and transmissivity for HiBi-FLMs with n-section HBFs is given. Experimental results have verified the theoretical model. The basic characteristics of the one-section HiBi-FLM when strain and high temperature are applied to HBFs were analyzed and investigated theoretically and experimentally. The experimental results are in good agreement with the theoretical analysis. Furthermore, a strain– temperature sensor that makes use of those characteristics, which is new for applications of HiBi-FLMs, has been proposed and demonstrated.

© 2005 Optical Society of America

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References

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  1. G. A. Pavlath, H. J. Shaw, “Birefringence and polarization effects in fiber gyroscopes,” Appl. Opt. 21, 1752–1757 (1982).
    [CrossRef] [PubMed]
  2. W. K. Burns, A. D. Kersey, “Fiber-optic gyroscopes with depolarized light,” J. Lightwave Technol. 10, 992–999 (1992).
    [CrossRef]
  3. B. Szafraniec, J. Blake, “Polarization modulation errors in all-fiber depolarized gyroscopes,” J. Lightwave Technol. 12, 1679–1684 (1994).
    [CrossRef]
  4. M. Campbell, G. Zheng, A. S. Holmes-Smith, P. A. Wallace, “A frequency-modulated continuous wave birefringent fibre-optic strain sensor based on a Sagnac ring configuration,” Meas. Sci. Technol. 10, 218–224 (1999).
    [CrossRef]
  5. E. De La Rosa, L. A. Zenteno, A. N. Starodumov, D. Monzon, “All-fiber absolute temperature sensor using an unbalanced high-birefringence Sagnac loop,” Opt. Lett. 22, 481–483 (1997).
    [CrossRef] [PubMed]
  6. A. N. Starodumov, L. A. Zenteno, D. Monzon, E. De La Rosa, “Fiber Sagnac interferometer temperature sensor,” Appl. Phys. Lett. 70, 19–21 (1997).
    [CrossRef]
  7. S. Li, K. S. Chiang, W. A. Gambling, “Gain flattening of an erbium-doped fiber amplifier using a high-birefringence fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 942–944 (2001).
    [CrossRef]
  8. S. Chung, J. Kim, B. A. Yu, B. Lee, “A fiber Bragg grating sensor demodulation technique using a polarization maintaining fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 1343–1345 (2001).
    [CrossRef]
  9. X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
    [CrossRef]
  10. S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
    [CrossRef]
  11. S. Chung, B. A. Yu, B. Lee, “Phase response design of a polarization-maintaining fiber loop mirror for dispersion compensation,” IEEE Photon. Technol. Lett. 15, 715–717 (2003).
    [CrossRef]
  12. X. Fang, R. O. Claus, “Polarization-independent all-fiber wavelength division multiplexer based on a Sagnac interferometer,” Opt. Lett. 20, 2146–2148 (1995).
    [CrossRef] [PubMed]
  13. X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
    [CrossRef]
  14. W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
    [CrossRef]

2003 (1)

S. Chung, B. A. Yu, B. Lee, “Phase response design of a polarization-maintaining fiber loop mirror for dispersion compensation,” IEEE Photon. Technol. Lett. 15, 715–717 (2003).
[CrossRef]

2002 (1)

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

2001 (2)

S. Li, K. S. Chiang, W. A. Gambling, “Gain flattening of an erbium-doped fiber amplifier using a high-birefringence fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 942–944 (2001).
[CrossRef]

S. Chung, J. Kim, B. A. Yu, B. Lee, “A fiber Bragg grating sensor demodulation technique using a polarization maintaining fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 1343–1345 (2001).
[CrossRef]

2000 (1)

X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
[CrossRef]

1999 (1)

M. Campbell, G. Zheng, A. S. Holmes-Smith, P. A. Wallace, “A frequency-modulated continuous wave birefringent fibre-optic strain sensor based on a Sagnac ring configuration,” Meas. Sci. Technol. 10, 218–224 (1999).
[CrossRef]

1997 (3)

A. N. Starodumov, L. A. Zenteno, D. Monzon, E. De La Rosa, “Fiber Sagnac interferometer temperature sensor,” Appl. Phys. Lett. 70, 19–21 (1997).
[CrossRef]

X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
[CrossRef]

E. De La Rosa, L. A. Zenteno, A. N. Starodumov, D. Monzon, “All-fiber absolute temperature sensor using an unbalanced high-birefringence Sagnac loop,” Opt. Lett. 22, 481–483 (1997).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

B. Szafraniec, J. Blake, “Polarization modulation errors in all-fiber depolarized gyroscopes,” J. Lightwave Technol. 12, 1679–1684 (1994).
[CrossRef]

1992 (1)

W. K. Burns, A. D. Kersey, “Fiber-optic gyroscopes with depolarized light,” J. Lightwave Technol. 10, 992–999 (1992).
[CrossRef]

1982 (1)

Aleen, C. T.

X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
[CrossRef]

Blake, J.

B. Szafraniec, J. Blake, “Polarization modulation errors in all-fiber depolarized gyroscopes,” J. Lightwave Technol. 12, 1679–1684 (1994).
[CrossRef]

Burns, W. K.

W. K. Burns, A. D. Kersey, “Fiber-optic gyroscopes with depolarized light,” J. Lightwave Technol. 10, 992–999 (1992).
[CrossRef]

Campbell, M.

M. Campbell, G. Zheng, A. S. Holmes-Smith, P. A. Wallace, “A frequency-modulated continuous wave birefringent fibre-optic strain sensor based on a Sagnac ring configuration,” Meas. Sci. Technol. 10, 218–224 (1999).
[CrossRef]

Chiang, K. S.

S. Li, K. S. Chiang, W. A. Gambling, “Gain flattening of an erbium-doped fiber amplifier using a high-birefringence fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 942–944 (2001).
[CrossRef]

X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
[CrossRef]

Chu, B. C. B.

X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
[CrossRef]

Chung, S.

S. Chung, B. A. Yu, B. Lee, “Phase response design of a polarization-maintaining fiber loop mirror for dispersion compensation,” IEEE Photon. Technol. Lett. 15, 715–717 (2003).
[CrossRef]

S. Chung, J. Kim, B. A. Yu, B. Lee, “A fiber Bragg grating sensor demodulation technique using a polarization maintaining fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 1343–1345 (2001).
[CrossRef]

Claus, R. O.

De La Rosa, E.

E. De La Rosa, L. A. Zenteno, A. N. Starodumov, D. Monzon, “All-fiber absolute temperature sensor using an unbalanced high-birefringence Sagnac loop,” Opt. Lett. 22, 481–483 (1997).
[CrossRef] [PubMed]

A. N. Starodumov, L. A. Zenteno, D. Monzon, E. De La Rosa, “Fiber Sagnac interferometer temperature sensor,” Appl. Phys. Lett. 70, 19–21 (1997).
[CrossRef]

Demarest, K.

X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
[CrossRef]

Dong, X.

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

Dong, X. P.

X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
[CrossRef]

Fang, X.

X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
[CrossRef]

X. Fang, R. O. Claus, “Polarization-independent all-fiber wavelength division multiplexer based on a Sagnac interferometer,” Opt. Lett. 20, 2146–2148 (1995).
[CrossRef] [PubMed]

Gambling, W. A.

S. Li, K. S. Chiang, W. A. Gambling, “Gain flattening of an erbium-doped fiber amplifier using a high-birefringence fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 942–944 (2001).
[CrossRef]

Holmes-Smith, A. S.

M. Campbell, G. Zheng, A. S. Holmes-Smith, P. A. Wallace, “A frequency-modulated continuous wave birefringent fibre-optic strain sensor based on a Sagnac ring configuration,” Meas. Sci. Technol. 10, 218–224 (1999).
[CrossRef]

Ji, H.

X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
[CrossRef]

Kai, G.

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

Kersey, A. D.

W. K. Burns, A. D. Kersey, “Fiber-optic gyroscopes with depolarized light,” J. Lightwave Technol. 10, 992–999 (1992).
[CrossRef]

Kim, J.

S. Chung, J. Kim, B. A. Yu, B. Lee, “A fiber Bragg grating sensor demodulation technique using a polarization maintaining fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 1343–1345 (2001).
[CrossRef]

Lee, B.

S. Chung, B. A. Yu, B. Lee, “Phase response design of a polarization-maintaining fiber loop mirror for dispersion compensation,” IEEE Photon. Technol. Lett. 15, 715–717 (2003).
[CrossRef]

S. Chung, J. Kim, B. A. Yu, B. Lee, “A fiber Bragg grating sensor demodulation technique using a polarization maintaining fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 1343–1345 (2001).
[CrossRef]

Li, S.

S. Li, K. S. Chiang, W. A. Gambling, “Gain flattening of an erbium-doped fiber amplifier using a high-birefringence fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 942–944 (2001).
[CrossRef]

Li, S. P.

X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
[CrossRef]

Li, Z.

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

Liang, L.

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

Liu, Z.

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

Monzon, D.

A. N. Starodumov, L. A. Zenteno, D. Monzon, E. De La Rosa, “Fiber Sagnac interferometer temperature sensor,” Appl. Phys. Lett. 70, 19–21 (1997).
[CrossRef]

E. De La Rosa, L. A. Zenteno, A. N. Starodumov, D. Monzon, “All-fiber absolute temperature sensor using an unbalanced high-birefringence Sagnac loop,” Opt. Lett. 22, 481–483 (1997).
[CrossRef] [PubMed]

Ng, M. N.

X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
[CrossRef]

Pavlath, G. A.

Pelz, L.

X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
[CrossRef]

Shaw, H. J.

Starodumov, A. N.

A. N. Starodumov, L. A. Zenteno, D. Monzon, E. De La Rosa, “Fiber Sagnac interferometer temperature sensor,” Appl. Phys. Lett. 70, 19–21 (1997).
[CrossRef]

E. De La Rosa, L. A. Zenteno, A. N. Starodumov, D. Monzon, “All-fiber absolute temperature sensor using an unbalanced high-birefringence Sagnac loop,” Opt. Lett. 22, 481–483 (1997).
[CrossRef] [PubMed]

Szafraniec, B.

B. Szafraniec, J. Blake, “Polarization modulation errors in all-fiber depolarized gyroscopes,” J. Lightwave Technol. 12, 1679–1684 (1994).
[CrossRef]

Wallace, P. A.

M. Campbell, G. Zheng, A. S. Holmes-Smith, P. A. Wallace, “A frequency-modulated continuous wave birefringent fibre-optic strain sensor based on a Sagnac ring configuration,” Meas. Sci. Technol. 10, 218–224 (1999).
[CrossRef]

Wu, Z.

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

Yang, S.

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

Yu, B. A.

S. Chung, B. A. Yu, B. Lee, “Phase response design of a polarization-maintaining fiber loop mirror for dispersion compensation,” IEEE Photon. Technol. Lett. 15, 715–717 (2003).
[CrossRef]

S. Chung, J. Kim, B. A. Yu, B. Lee, “A fiber Bragg grating sensor demodulation technique using a polarization maintaining fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 1343–1345 (2001).
[CrossRef]

Yuan, S.

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

Zenteno, L. A.

A. N. Starodumov, L. A. Zenteno, D. Monzon, E. De La Rosa, “Fiber Sagnac interferometer temperature sensor,” Appl. Phys. Lett. 70, 19–21 (1997).
[CrossRef]

E. De La Rosa, L. A. Zenteno, A. N. Starodumov, D. Monzon, “All-fiber absolute temperature sensor using an unbalanced high-birefringence Sagnac loop,” Opt. Lett. 22, 481–483 (1997).
[CrossRef] [PubMed]

Zhang, W.

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

Zhao, Q.

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

Zheng, G.

M. Campbell, G. Zheng, A. S. Holmes-Smith, P. A. Wallace, “A frequency-modulated continuous wave birefringent fibre-optic strain sensor based on a Sagnac ring configuration,” Meas. Sci. Technol. 10, 218–224 (1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. N. Starodumov, L. A. Zenteno, D. Monzon, E. De La Rosa, “Fiber Sagnac interferometer temperature sensor,” Appl. Phys. Lett. 70, 19–21 (1997).
[CrossRef]

Electron. Lett. (1)

X. P. Dong, S. P. Li, K. S. Chiang, M. N. Ng, B. C. B. Chu, “Multiwavelength erbium-doped fibre laser based on a high-birefringence fibre loop mirror,” Electron. Lett. 36, 1609–1610 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

S. Yang, Z. Li, X. Dong, S. Yuan, G. Kai, Q. Zhao, “Generation of wavelength-switched optical pulse from a fiber ring laser with an F-P semiconductor modulator and a HiBi fiber loop mirror,” IEEE Photon. Technol. Lett. 14, 774–776 (2002).
[CrossRef]

S. Chung, B. A. Yu, B. Lee, “Phase response design of a polarization-maintaining fiber loop mirror for dispersion compensation,” IEEE Photon. Technol. Lett. 15, 715–717 (2003).
[CrossRef]

X. Fang, H. Ji, C. T. Aleen, K. Demarest, L. Pelz, “A compound high-order polarization-independent birefringence filter using Sagnac interferometers,” IEEE Photon. Technol. Lett. 9, 458–460 (1997).
[CrossRef]

S. Li, K. S. Chiang, W. A. Gambling, “Gain flattening of an erbium-doped fiber amplifier using a high-birefringence fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 942–944 (2001).
[CrossRef]

S. Chung, J. Kim, B. A. Yu, B. Lee, “A fiber Bragg grating sensor demodulation technique using a polarization maintaining fiber loop mirror,” IEEE Photon. Technol. Lett. 13, 1343–1345 (2001).
[CrossRef]

J. Lightwave Technol. (2)

W. K. Burns, A. D. Kersey, “Fiber-optic gyroscopes with depolarized light,” J. Lightwave Technol. 10, 992–999 (1992).
[CrossRef]

B. Szafraniec, J. Blake, “Polarization modulation errors in all-fiber depolarized gyroscopes,” J. Lightwave Technol. 12, 1679–1684 (1994).
[CrossRef]

Meas. Sci. Technol. (1)

M. Campbell, G. Zheng, A. S. Holmes-Smith, P. A. Wallace, “A frequency-modulated continuous wave birefringent fibre-optic strain sensor based on a Sagnac ring configuration,” Meas. Sci. Technol. 10, 218–224 (1999).
[CrossRef]

Opt. Lett. (2)

Other (1)

W. Zhang, Z. Wu, L. Liang, Q. Zhao, G. Kai, Z. Liu, X. Dong, “Analyses and measurement of strain and deflection of standard beam based on fiber grating,” in Optical Fiber and Planar Waveguide Technology, S. Jian, Y. Liu, eds., Proc. SPIE4579, 269–273 (2001).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic illustration of an n-section HiBi-FLM.

Fig. 2
Fig. 2

Schematic illustration of the connection between SMFs and HBFs.

Fig. 3
Fig. 3

Comparison of the transmitted spectrum in our theoretical calculation (left) and the experimental measurement (right) for a typical two-section HiBi-FLM with equal HBF lengths and a 3-dB coupler when θ2 = 45° and (A) θ1 + θ3 = 0°, (B) θ1 + θ3 = 45°, (C) θ1 + θ3 = 40°, (D) θ1 + θ3 = 50°.

Fig. 4
Fig. 4

Experimental setup adding strain to the HBF via an equal-intensity beam. PC, polarization controller.

Fig. 5
Fig. 5

Experimental curve of the shift in peak wavelength versus displacement at the end of the beam.

Fig. 6
Fig. 6

Experimental curve of the shift in peak wavelength versus temperature of the HBF.

Fig. 7
Fig. 7

Experimental setup with a HBF used as the sensing head in a HiBi-FLM: PC, polarization controller; PDs, photodetectors.

Fig. 8
Fig. 8

Transmission spectra of a HiBi-FLM at two temperatures.

Fig. 9
Fig. 9

Curve of the transmission light power versus temperature.

Equations (37)

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

E in = [ E x in E y in ] ,
E 3 = k E in , E 4 = 1 k H E in ,
H = [ exp [ i ( π / 2 ) ] 0 0 exp [ i ( π / 2 ) ] ]
M c = R n + 1 T n R n R 3 T 2 R 2 T 1 R 1 , M a = R 1 1 T 1 R 2 1 T 2 R 3 1 R n 1 T n R n + 1 1 ,
T i = exp ( i 2 π n e l i λ ) [ 1 0 0 exp ( i ) 2 π l i ( n o n e ) λ ] i = 1 , 2 , n , ,
R i = [ cos θ i sin θ i sin θ i cos θ i ] , i = 1 , 2 , n ,
R n + 1 = [ cos θ n + 1 sin θ n + 1 sin θ n + 1 cos θ n + 1 ]
P 1 out = 1 k H M c E 3 + K M a E 4 = [ k ( 1 k ) ] 1 / 2 H R n + 1 T n R n R 3 T 2 R 2 T 1 R 1 E in + [ k ( 1 k ) ] 1 / 2 R 1 1 T 1 R 2 1 T 2 R 3 1 R n 1 T n R n + 1 1 H E in = K r E in ,
K r = i [ k ( 1 k ) ] 1 / 2 [ R n + 1 i = n 1 T i R i + ( i = 1 n R i 1 T i ) R n + 1 1 ]
P 2 out = k M c E 3 + 1 k H M a E 4 = k R n + 1 T n R n R 3 T 2 R 2 T 1 R 1 E in + H R 1 1 T 1 R 2 1 T 2 R 3 1 R n 1 T n R n + 1 1 H E in = K t E in ,
K t = k R n + 1 i = n 1 T i R i ( 1 k ) ( i = 1 n R i 1 T i ) R n + 1 1
I 1 out = ( P 1 out * ) T P 1 out = ( K r * E in * ) T K r E in ,
I 2 out = ( P 2 out * ) T P 2 out = ( K t * E in * ) T K t E in ,
R = I 1 out I in = ( K r * E in * ) T K r E in E in * E in , T = I 2 out I in = ( K t * E in * ) T K t E in E in * E in ,
R = 4 k ( 1 k ) { 1 sin 2 ( θ ) cos 2 ( β / 2 ) } , T = ( 1 2 k ) 2 + 4 k ( 1 k ) sin 2 ( θ ) cos 2 ( β / 2 ) ,
R = 1 [ sin ( θ ) cos ( β / 2 ) ] 2 , T = [ sin ( θ ) cos ( β / 2 ) ] 2 .
R = 4 k ( 1 k ) ( 1 A 2 ) , T = ( 1 2 k ) 2 + 4 k ( 1 k ) A 2 ,
A = cos ( β 1 + β 2 2 ) sin ( θ 1 + θ 3 ) cos θ 2 + cos ( β 1 β 2 2 ) cos ( θ 1 + θ 3 ) sin θ 2 , β i = 2 π l i ( n o n e ) λ , i = 1 , 2 .
R = 1 [ cos ( β 1 + β 2 2 ) sin ( θ 1 + θ 3 ) cos θ 2 + cos ( β 1 β 2 2 ) cos ( θ 1 + θ 3 ) sin θ 2 ] 2 ,
T = [ cos ( β 1 + β 2 2 ) sin ( θ 1 + θ 3 ) cos θ 2 + cos ( β 1 β 2 2 ) cos ( θ 1 + θ 3 ) sin θ 2 ] 2 .
R = 4 k ( 1 k ) [ 1 ( A 1 + A 2 + A 3 + A 4 ) 2 ] , T = ( 1 2 k ) 2 + 4 k ( 1 k ) ( A 1 + A 2 + A 3 + A 4 ) 2 .
R = 1 ( A 1 + A 2 + A 3 + A 4 ) 2 , T = ( A 1 + A 2 + A 3 + A 4 ) 2 ,
A 1 = cos ( β 1 + β 2 + β 3 2 ) sin ( θ 1 + θ 4 ) cos θ 2 cos θ 3 , A 2 = cos ( β 1 + β 2 + β 3 2 ) cos ( θ 1 + θ 4 ) sin θ 2 cos θ 3 , A 3 = cos ( β 1 + β 2 β 3 2 ) cos ( θ 1 + θ 4 ) cos θ 2 sin θ 3 , A 4 = cos ( β 1 β 2 β 3 2 ) sin ( θ 1 + θ 4 ) sin θ 2 cos θ 3 , β i = 2 π l i ( n o n e ) λ , i = 1 , 2 , 3 .
β 1 = β 2 = β = 2 π l ( n o n e ) λ = 2 π l λ 0 L B λ ,
T = [ cos β sin ( θ 1 + θ 3 ) cos θ 2 + cos ( θ 1 + θ 3 ) sin θ 2 ] 2 .
T ( λ ) = { sin ( θ ) cos [ π l ( n e n o ) λ ] } 2 .
T λ = λ 2 l ( n e n o ) + λ = L B λ 2 l λ 0 + L B λ ,
l ( n e n o ) = k p λ p ,
( l + Δ l ) [ ( n e n o ) + Δ ( n e n o ) ] = k p ( λ p + Δ λ ) .
Δ λ = ( 1 / k p ) [ l Δ ( n e n o ) + ( n e n o ) Δ l + Δ l Δ ( n e n o ) ] .
ɛ = ( h / L 2 ) x .
Δ l = l 1 ɛ = ( l 1 h / L 2 ) x = C s 1 l 1 x ,
Δ B [ ɛ ( x ) ] = Δ ( n e n o ) = C s 2 x ,
Δ λ = ( 1 / k p ) [ l C s 2 x + ( n e n o ) C s 1 l 1 x + l 1 C s 1 C s 2 x 2 ] .
Δ λ = ( 1 / k p ) [ l C s 2 + ( n e n o ) C s 1 l 1 ] x .
Δ λ = ( 1 / k p ) [ l C T 2 Δ T + ( n e n o ) C T 1 Δ T + C T 1 C T 2 ( Δ T ) 2 ] .
Δ λ = ( 1 / k p ) [ l C T 2 + ( n e n o ) C T 1 ] Δ T .

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