Abstract

A theoretical model is developed to address the fringe visibility and additional phase in the interference spectra of low-finesse extrinsic optical fiber excited Fabry-Pérot interferometers. The model described in the paper applies to both single-mode and multimode fiber excitations; according to the theory, the fringe visibility and additional phase term are primarily determined by the working wavelength and angular power density distribution outputting from the excitation fiber, rather than based on spatial and temporal degree of coherence. Under certain approximations, the output interference intensity and the spatial power density distribution projected onto the fiber axis form a Fourier-transform pair, which potentially provides a tool for spatial density distribution analysis of fiber output. With excellent agreement with experiments, the theory presented in this paper leads to design guidelines for Fabry-Pérot interferometric sensors and insightful physical understanding of such devices.

© 2011 OSA

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References

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  1. C. E. Lee and H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” Lightwave Technology Journalism 9, 129–134 (1991).
  2. Y. Zhu, Z. Huang, F. Shen, and A. Wang, “Sapphire-fiber-based white-light interferometric sensor for high-temperature measurements,” Opt. Lett. 30(7), 711–713 (2005).
    [CrossRef] [PubMed]
  3. C. Belleville and G. Duplain, “White-light interferometric multimode fiber-optic strain sensor,” Opt. Lett. 18(1), 78–80 (1993).
    [CrossRef] [PubMed]
  4. A. Wang, H. Xiao, J. Wang, Z. Wang, W. Zhao, and R. G. May, “Self-Calibrated Interferometric-Intensity-Based Optical Fiber Sensors,” J. Lightwave Technol. 19(10), 1495–1501 (2001).
    [CrossRef]
  5. Y. Kim and D. P. Neikirk, “Micromachined Fabry-Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7(12), 1471–1473 (1995).
    [CrossRef]
  6. N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
    [CrossRef]
  7. B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
    [CrossRef]
  8. M. Han, Y. Zhang, F. Shen, G. R. Pickrell, and A. Wang, “Signal-processing algorithm for white-light optical fiber extrinsic Fabry-Perot interferometric sensors,” Opt. Lett. 29(15), 1736–1738 (2004).
    [CrossRef] [PubMed]
  9. F. Shen and A. Wang, “Frequency-estimation-based signal-processing algorithm for white-light optical fiber Fabry-Perot interferometers,” Appl. Opt. 44(25), 5206–5214 (2005).
    [CrossRef] [PubMed]
  10. S. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression (Corresp.),” IEEE Trans. Info. Theory 31(6), 832–835 (1985).
    [CrossRef]
  11. C. Ma and A. Wang, “Multimode excitation-induced phase shifts in intrinsic Fabry-Perot interferometric fiber sensor spectra,” Appl. Opt. 49(25), 4836–4845 (2010).
    [CrossRef] [PubMed]
  12. C. Ma, E. Lally, and A. Wang, “Toward Eliminating Signal Demodulation Jumps in Optical Fiber Intrinsic Fabry-Perot Interferometric Sensors,” to be published in J. Lightwave Technol. (2011).
  13. V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
    [CrossRef]
  14. F. Pérennès, P. C. Beard, and T. N. Mills, “Analysis of a low-finesse Fabry-Perot sensing interferometer illuminated by a multimode optical fiber,” Appl. Opt. 38(34), 7026–7034 (1999).
    [CrossRef] [PubMed]
  15. M. Han and A. Wang, “Exact analysis of low-finesse multimode fiber extrinsic Fabry-Perot interferometers,” Appl. Opt. 43(24), 4659–4666 (2004).
    [CrossRef] [PubMed]
  16. M. Han and A. Wang, “Mode power distribution effect in white-light multimode fiber extrinsic Fabry-Perot interferometric sensor systems,” Opt. Lett. 31(9), 1202–1204 (2006).
    [CrossRef] [PubMed]
  17. M. Born and E. Wolf, Principles of optics: electromagnetic theory of proagation, interference and diffraction of light, 7 ed. (Cambrige University Press, 2003).
  18. A. Yariv, Optical electronics in modern communications, 5th ed. (Oxford University Press, Inc., 1997).
  19. E. D. Becker and T. C. Farrar, “Fourier Transform Spectroscopy: New methods dramatically improve the sensitivity of infrared and nuclear magnetic resonance spectroscopy,” Science 178(4059), 361–368 (1972).
    [CrossRef] [PubMed]
  20. M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).
  21. Y. Kokubun and K. Iga, “Mode analysis of graded-index optical fibers using a scalar wave equation including gradient-index terms and direct numerical integration,” J. Opt. Soc. Am. 70(4), 388–394 (1980).
    [CrossRef]
  22. G. Keiser, Optical Fiber Communications (McGraw-Hill, Boston,Mass., 2000).

2011 (1)

C. Ma, E. Lally, and A. Wang, “Toward Eliminating Signal Demodulation Jumps in Optical Fiber Intrinsic Fabry-Perot Interferometric Sensors,” to be published in J. Lightwave Technol. (2011).

2010 (1)

2006 (1)

2005 (2)

2004 (2)

2003 (1)

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

2001 (1)

1999 (1)

1997 (1)

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
[CrossRef]

1995 (2)

Y. Kim and D. P. Neikirk, “Micromachined Fabry-Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7(12), 1471–1473 (1995).
[CrossRef]

V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
[CrossRef]

1993 (1)

1991 (1)

C. E. Lee and H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” Lightwave Technology Journalism 9, 129–134 (1991).

1989 (1)

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).

1985 (1)

S. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression (Corresp.),” IEEE Trans. Info. Theory 31(6), 832–835 (1985).
[CrossRef]

1980 (1)

1972 (1)

E. D. Becker and T. C. Farrar, “Fourier Transform Spectroscopy: New methods dramatically improve the sensitivity of infrared and nuclear magnetic resonance spectroscopy,” Science 178(4059), 361–368 (1972).
[CrossRef] [PubMed]

Artiglia, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).

Arya, V.

V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
[CrossRef]

Beard, P. C.

Becker, E. D.

E. D. Becker and T. C. Farrar, “Fourier Transform Spectroscopy: New methods dramatically improve the sensitivity of infrared and nuclear magnetic resonance spectroscopy,” Science 178(4059), 361–368 (1972).
[CrossRef] [PubMed]

Belleville, C.

Claus, R. O.

V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
[CrossRef]

Coppa, G.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).

de Vries, M.

V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
[CrossRef]

Di Vita, P.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).

Duan, Y.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Duplain, G.

Farrar, T. C.

E. D. Becker and T. C. Farrar, “Fourier Transform Spectroscopy: New methods dramatically improve the sensitivity of infrared and nuclear magnetic resonance spectroscopy,” Science 178(4059), 361–368 (1972).
[CrossRef] [PubMed]

Fürstenau, N.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
[CrossRef]

Goetze, W.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
[CrossRef]

Han, M.

Horack, H.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
[CrossRef]

Huang, Z.

Y. Zhu, Z. Huang, F. Shen, and A. Wang, “Sapphire-fiber-based white-light interferometric sensor for high-temperature measurements,” Opt. Lett. 30(7), 711–713 (2005).
[CrossRef] [PubMed]

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Huo, W.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Iga, K.

Kim, Y.

Y. Kim and D. P. Neikirk, “Micromachined Fabry-Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7(12), 1471–1473 (1995).
[CrossRef]

Kokubun, Y.

Lally, E.

C. Ma, E. Lally, and A. Wang, “Toward Eliminating Signal Demodulation Jumps in Optical Fiber Intrinsic Fabry-Perot Interferometric Sensors,” to be published in J. Lightwave Technol. (2011).

Lee, C. E.

C. E. Lee and H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” Lightwave Technology Journalism 9, 129–134 (1991).

Ma, C.

C. Ma, E. Lally, and A. Wang, “Toward Eliminating Signal Demodulation Jumps in Optical Fiber Intrinsic Fabry-Perot Interferometric Sensors,” to be published in J. Lightwave Technol. (2011).

C. Ma and A. Wang, “Multimode excitation-induced phase shifts in intrinsic Fabry-Perot interferometric fiber sensor spectra,” Appl. Opt. 49(25), 4836–4845 (2010).
[CrossRef] [PubMed]

May, R. G.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

A. Wang, H. Xiao, J. Wang, Z. Wang, W. Zhao, and R. G. May, “Self-Calibrated Interferometric-Intensity-Based Optical Fiber Sensors,” J. Lightwave Technol. 19(10), 1495–1501 (2001).
[CrossRef]

Mills, T. N.

Murphy, K. A.

V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
[CrossRef]

Neikirk, D. P.

Y. Kim and D. P. Neikirk, “Micromachined Fabry-Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7(12), 1471–1473 (1995).
[CrossRef]

Peng, W.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Pérennès, F.

Pickrell, G. R.

M. Han, Y. Zhang, F. Shen, G. R. Pickrell, and A. Wang, “Signal-processing algorithm for white-light optical fiber extrinsic Fabry-Perot interferometric sensors,” Opt. Lett. 29(15), 1736–1738 (2004).
[CrossRef] [PubMed]

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Potenza, M.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).

Qi, B.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Schmidt, M.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
[CrossRef]

Schmidt, W.

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
[CrossRef]

Sharma, A.

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).

Shen, F.

Taylor, H. F.

C. E. Lee and H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” Lightwave Technology Journalism 9, 129–134 (1991).

Tretter, S.

S. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression (Corresp.),” IEEE Trans. Info. Theory 31(6), 832–835 (1985).
[CrossRef]

Wang, A.

C. Ma, E. Lally, and A. Wang, “Toward Eliminating Signal Demodulation Jumps in Optical Fiber Intrinsic Fabry-Perot Interferometric Sensors,” to be published in J. Lightwave Technol. (2011).

C. Ma and A. Wang, “Multimode excitation-induced phase shifts in intrinsic Fabry-Perot interferometric fiber sensor spectra,” Appl. Opt. 49(25), 4836–4845 (2010).
[CrossRef] [PubMed]

M. Han and A. Wang, “Mode power distribution effect in white-light multimode fiber extrinsic Fabry-Perot interferometric sensor systems,” Opt. Lett. 31(9), 1202–1204 (2006).
[CrossRef] [PubMed]

F. Shen and A. Wang, “Frequency-estimation-based signal-processing algorithm for white-light optical fiber Fabry-Perot interferometers,” Appl. Opt. 44(25), 5206–5214 (2005).
[CrossRef] [PubMed]

Y. Zhu, Z. Huang, F. Shen, and A. Wang, “Sapphire-fiber-based white-light interferometric sensor for high-temperature measurements,” Opt. Lett. 30(7), 711–713 (2005).
[CrossRef] [PubMed]

M. Han, Y. Zhang, F. Shen, G. R. Pickrell, and A. Wang, “Signal-processing algorithm for white-light optical fiber extrinsic Fabry-Perot interferometric sensors,” Opt. Lett. 29(15), 1736–1738 (2004).
[CrossRef] [PubMed]

M. Han and A. Wang, “Exact analysis of low-finesse multimode fiber extrinsic Fabry-Perot interferometers,” Appl. Opt. 43(24), 4659–4666 (2004).
[CrossRef] [PubMed]

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

A. Wang, H. Xiao, J. Wang, Z. Wang, W. Zhao, and R. G. May, “Self-Calibrated Interferometric-Intensity-Based Optical Fiber Sensors,” J. Lightwave Technol. 19(10), 1495–1501 (2001).
[CrossRef]

V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
[CrossRef]

Wang, J.

Wang, Z.

Xiao, H.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

A. Wang, H. Xiao, J. Wang, Z. Wang, W. Zhao, and R. G. May, “Self-Calibrated Interferometric-Intensity-Based Optical Fiber Sensors,” J. Lightwave Technol. 19(10), 1495–1501 (2001).
[CrossRef]

Xu, J.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Zhang, P.

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Zhang, Y.

Zhao, W.

Zhu, Y.

Appl. Opt. (4)

IEEE Photon. Technol. Lett. (1)

Y. Kim and D. P. Neikirk, “Micromachined Fabry-Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7(12), 1471–1473 (1995).
[CrossRef]

IEEE Proc. Optoelectron. (1)

N. Fürstenau, M. Schmidt, H. Horack, W. Goetze, and W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEEE Proc. Optoelectron. 144(3), 134–144 (1997).
[CrossRef]

IEEE Trans. Info. Theory (1)

S. Tretter, “Estimating the frequency of a noisy sinusoid by linear regression (Corresp.),” IEEE Trans. Info. Theory 31(6), 832–835 (1985).
[CrossRef]

J. Lightwave Technol. (2)

A. Wang, H. Xiao, J. Wang, Z. Wang, W. Zhao, and R. G. May, “Self-Calibrated Interferometric-Intensity-Based Optical Fiber Sensors,” J. Lightwave Technol. 19(10), 1495–1501 (2001).
[CrossRef]

C. Ma, E. Lally, and A. Wang, “Toward Eliminating Signal Demodulation Jumps in Optical Fiber Intrinsic Fabry-Perot Interferometric Sensors,” to be published in J. Lightwave Technol. (2011).

J. Opt. Soc. Am. (1)

Lightwave Technology Journalism (2)

C. E. Lee and H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” Lightwave Technology Journalism 9, 129–134 (1991).

M. Artiglia, G. Coppa, P. Di Vita, M. Potenza, and A. Sharma, “Mode field diameter measurements in single-mode optical fibers,” Lightwave Technology Journalism 7, 1139–1152 (1989).

Opt. Eng. (1)

B. Qi, G. R. Pickrell, J. Xu, P. Zhang, Y. Duan, W. Peng, Z. Huang, W. Huo, H. Xiao, R. G. May, and A. Wang, “Novel data processing techniques for dispersive white light interferometer,” Opt. Eng. 42(11), 3165–3171 (2003).
[CrossRef]

Opt. Fiber Technol. (1)

V. Arya, M. de Vries, K. A. Murphy, A. Wang, and R. O. Claus, “Exact Analysis of the Extrinsic Fabry-Perot Interferometric Optical Fiber Sensor Using Kirchhoff's Diffraction Formalism,” Opt. Fiber Technol. 1(4), 380–384 (1995).
[CrossRef]

Opt. Lett. (4)

Science (1)

E. D. Becker and T. C. Farrar, “Fourier Transform Spectroscopy: New methods dramatically improve the sensitivity of infrared and nuclear magnetic resonance spectroscopy,” Science 178(4059), 361–368 (1972).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of optics: electromagnetic theory of proagation, interference and diffraction of light, 7 ed. (Cambrige University Press, 2003).

A. Yariv, Optical electronics in modern communications, 5th ed. (Oxford University Press, Inc., 1997).

G. Keiser, Optical Fiber Communications (McGraw-Hill, Boston,Mass., 2000).

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Figures (10)

Fig. 1
Fig. 1

EFPI sensor schematics and spectrum. (a) EFPI sensor with air-gap cavity. (b) EFPI sensor with wafer cavity. (c) a typical sensor spectrum.

Fig. 2
Fig. 2

Schematic of the optical fiber low-finesse EFPI

Fig. 3
Fig. 3

Conversion schematic from angular power density distribution to the kz density distribution. The total power distributed from kz to kz + dkz is equal to the power flux in the ring area (in green color) defined by divergence angle from θ to θ + dθ

Fig. 4
Fig. 4

Experimental setup for measurement of the fringe visibility curve. Parallelism of the two reflection surfaces are guaranteed by tuning the two rotation stages, and the cavity length can be finely tuned by a 1-D translation stage.

Fig. 5
Fig. 5

Fringe visibility plotted as a function of FP cavity length. Solid and dashed curves represent simulation results, circles and dots are experimental data. The calculated mode field radii of the fibers are labeled and compared with the values in their specifications.

Fig. 6
Fig. 6

Conceptual illustration of the relationship between output divergence angle and the visibility curve. (a) I(kz) distribution of a beam with less divergence angle. (b) Visibility curve corresponding to the distribution in (a). (c) I(kz) distribution of a beam with larger divergence angle. (d) Visibility curve corresponding to the distribution in (c). The figures show qualitatively that the visibility curve gets broader as I(kz) becomes sharper.

Fig. 7
Fig. 7

Theoretical and experimental data showing the extra phase delay of an EFPI with SMF-28 as the lead-in fiber

Fig. 8
Fig. 8

Fringe visibility versus FP cavity length for fiber 1,2 and 3, all modes are equally excited. Simulation is based on Eq. (32) and the fiber mode analysis method in [15].

Fig. 9
Fig. 9

Theoretical and experimental results of the fringe visibilities and additional phases versus OPD for MMF-EFPI. MMF has core diameter 105μm and NA=0.22. (a) Measured angular distribution. (b) Calculated I(kz) distribution based on (a). (c) Fringe visibility versus OPD curve for 800nm, 1200nm and 1550nm light, theoretical and experimental. (d) Additional phase θ versus OPD for 800nm, 1200nm and 1550nm light, theoretical.

Fig. 10
Fig. 10

Comparing the fringe visibility curves of two EFPIs. Due to its smaller output divergence angle, an MMF-EFPI illuminated by halogen lamp shows better fringe visibility than a SMF-EFPI illuminated by a highly-coherent laser.

Tables (1)

Tables Icon

Table 1 MMF Parametersa

Equations (36)

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

Φ=kOPD+ φ 0
FV= I max I min I max + I min
P= S 0 ( E 1 + E 2 ) * ( E 1 + E 2 )ds
S 0 E 1 E 1 * ds = P 1
S 0 E 2 E 2 * ds =ν P 1
S 0 E 1 E 2 * ds = E 1 E 2 * ds
S 0 E 2 E 1 * ds = ( S 0 E 1 E 2 * ds ) *
E 1 ( x,y,0 )= E( k x , k y )exp[ i( k x x+ k y y ) ]d k x d k y
E 2 ( x,y,Δ )= E( k x , k y )exp[ i( k x x+ k y y k z Δπ ) ]d k x d k y
E 1 E 2 * ds = E( k x , k y ) E * ( k x ', k y ' ) exp{ i[ ( k x k x ' )x+( k y k y ' )y+ k z Δ+π ] }d k x d k y d k x 'd k y 'dxdy
exp[ i( k μ k μ ' )μ ]dμ =δ( k μ k μ ' )
E 1 E 2 * ds = | E( k x , k y ) | 2 exp[ i( k z Δ+π ) ]d k x d k y
S 0 ( E 1 E 2 * + E 2 E 1 * )ds =2 | E( k x , k y ) | 2 cos( k z Δ )d k x d k y
S 0 ( E 1 E 2 * + E 2 E 1 * )ds =2 I( k r )cos( k z Δ ) k r d k r
P=( 1+ν ) P 1 2 0 k I( k z )cos( k z Δ ) k z d k z
P( Δ )= C 0 0 I( k z )[ 1cos( k z z ) ]d k z
P( Δ )=( 1+ν ) P 1 2 0 k I( k z )cos( ( k z k )Δ+kΔ ) k z d k z
P( Δ )=Q( Δ )[ 1+ C 2 ( Δ )+ S 2 ( Δ ) Q( Δ ) cos( kΔ+θ( Δ )+π ) ]
θ( Δ )= tan 1 ( C( Δ ) S( Δ ) )+ π 2
FV( Δ )= C 2 ( Δ )+ S 2 ( Δ ) Q( Δ )
C( Δ )=2 0 k I( k z )cos( ( k z k )Δ ) k z d k z
S( Δ )=2 0 k I( k z )sin( ( k z k )Δ ) k z d k z
Q( Δ )=( 1+ν ) P 1
E( x,y )=exp[ ( x 2 + y 2 ) / w 0 2 ]
E( k x , k y )= w 0 2 8 π 2 exp[ w 0 2 ( k x 2 + k y 2 ) /4 ]
I( k z )= I 0 exp[ w 0 2 ( k 2 k z 2 ) /2 ]
I( k z )d k z =2πkI( θ )d k z
I( k z )=2πkI( θ )=2πkI[ acos( k z /k ) ]
θ= λ π w 0
I( k z )={ constant, 0<acos( k z /k )<asin( NA ) 0, others
FV( Δ )= C 2 ( Δ )+ S 2 ( Δ ) P( Δ ) = | 0 k I( k z ) e j k z Δ d k z | 0 k I( k z )d k z
C( Δ )=2 0 k I( k z )cos( ( k z k )Δ )d k z
S( Δ )=2 0 k I( k z )sin( ( k z k )Δ )d k z
P( Δ )=2 0 k I( k z )d k z
FV( Δ )= | kcos θ d k e j k z Δ d k z | k( 1cos θ d ) =| sinc( ϕ 2 ) |
ν= a 2 / ( a+Δtan θ d ) 2

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