Abstract

A straightforward theory is presented to accurately model the light inferences in a low-finesse multimode fiber extrinsic Fabry-Perot (FP) interferometer. The effect on the fringe visibility of the gap length, sensor structure imperfections, and modal power distributions is explored. The analysis is particularly useful in the design and optimization of sensors that use an extrinsic FP cavity as the sensing element.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. A. Wang, H. Xiao, J. Wang, Z. Wang, W. Zhao, R. G. May, “Self-calibrated interferometric-intensity-based optical fiber sensors,” J. Lightwave Technol. 19, 1495–1501 (2001).
    [CrossRef]
  4. Y. Kim, D. P. Neikirk, “Micromachined Fabry-Perot cavity pressure transducer,” IEEE Photon. Technol. Lett. 7, 1471–1473 (1995).
    [CrossRef]
  5. N. Furstenau, M. Schmidt, H. Horack, W. Goetze, W. Schmidt, “Extrinsic Fabry-Perot interferometer vibration and acoustic sensor systems for airport ground traffic monitoring,” IEE Proc. Optoelectron. 144, 134–144 (1997).
    [CrossRef]
  6. H. Xiao, J. Deng, G. Pickrell, R. G. May, A. Wang, “Single-crystal sapphire fiber-based strain sensor for high-temperature applications,” J. Lightwave Technol. 21, 2276–2283 (2003).
    [CrossRef]
  7. A. K. Murphy, M. F. Gunter, A. M. Vengsarker, R. O. Claus, “Quadrature phase-shifted, extrinsic Fabry-Perot optical fiber sensors,” Opt. Lett. 16, 273–275 (1991).
    [CrossRef] [PubMed]
  8. V. Arya, M. J. de Vries, K. A. Murphy, A. Wang, R. O. Claus, “Exact analysis of the EFPI optical fiber sensor using Kirchhoff’s diffraction formalism,” Opt. Fiber Technol. 1, 380–384 (1995).
    [CrossRef]
  9. F. Pérennès, P. C. Beard, T. N. Mills, “Analysis of a low-finesse Fabry-Perot sensing interferometer illuminated by a multimode optical fiber,” Appl. Opt. 38, 7026–7034 (1999).
    [CrossRef]
  10. C. M. Miller, S. C. Mettler, I. A. White, Optical Fiber Splices and Connectors: Theory and Methods (Marcel Dekker, New York, 1986).
  11. G. Keiser, Optical Fiber Communications (McGraw-Hill, Boston, Mass., 2000).
  12. T.-C. Poon, P. R. Banerjee, Contemporary Optical Image Processing with MATLAB (Elsevier Science, New York, 2001).
  13. A. Safaaii-Jazi, “Optical waveguides,” Lecture notes (Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va., 2002).
  14. J. N. Kutz, J. A. Cox, D. Smith, “Mode mixing and power diffusion in multimode optical fibers,” J. Lightwave Technol. 16, 1195–1202 (1998).
    [CrossRef]
  15. D. T. Neilson, “Tolerance of optical interconnections to misalignment,” Appl. Opt. 38, 2282–2290 (1999).
    [CrossRef]

2003

2001

1999

1998

1997

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

1995

V. Arya, M. J. de Vries, K. A. Murphy, A. Wang, R. O. Claus, “Exact analysis of the EFPI optical fiber sensor using Kirchhoff’s diffraction formalism,” Opt. Fiber Technol. 1, 380–384 (1995).
[CrossRef]

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

1993

1991

C. E. Lee, H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” J. Lightwave Technol. 9, 129–134 (1991).
[CrossRef]

A. K. Murphy, M. F. Gunter, A. M. Vengsarker, R. O. Claus, “Quadrature phase-shifted, extrinsic Fabry-Perot optical fiber sensors,” Opt. Lett. 16, 273–275 (1991).
[CrossRef] [PubMed]

Arya, V.

V. Arya, M. J. de Vries, K. A. Murphy, A. Wang, R. O. Claus, “Exact analysis of the EFPI optical fiber sensor using Kirchhoff’s diffraction formalism,” Opt. Fiber Technol. 1, 380–384 (1995).
[CrossRef]

Banerjee, P. R.

T.-C. Poon, P. R. Banerjee, Contemporary Optical Image Processing with MATLAB (Elsevier Science, New York, 2001).

Beard, P. C.

Belleville, C.

Claus, R. O.

V. Arya, M. J. de Vries, K. A. Murphy, A. Wang, R. O. Claus, “Exact analysis of the EFPI optical fiber sensor using Kirchhoff’s diffraction formalism,” Opt. Fiber Technol. 1, 380–384 (1995).
[CrossRef]

A. K. Murphy, M. F. Gunter, A. M. Vengsarker, R. O. Claus, “Quadrature phase-shifted, extrinsic Fabry-Perot optical fiber sensors,” Opt. Lett. 16, 273–275 (1991).
[CrossRef] [PubMed]

Cox, J. A.

de Vries, M. J.

V. Arya, M. J. de Vries, K. A. Murphy, A. Wang, R. O. Claus, “Exact analysis of the EFPI optical fiber sensor using Kirchhoff’s diffraction formalism,” Opt. Fiber Technol. 1, 380–384 (1995).
[CrossRef]

Deng, J.

Duplain, G.

Furstenau, N.

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

Goetze, W.

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

Gunter, M. F.

Horack, H.

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

Keiser, G.

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

Kim, Y.

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

Kutz, J. N.

Lee, C. E.

C. E. Lee, H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” J. Lightwave Technol. 9, 129–134 (1991).
[CrossRef]

May, R. G.

Mettler, S. C.

C. M. Miller, S. C. Mettler, I. A. White, Optical Fiber Splices and Connectors: Theory and Methods (Marcel Dekker, New York, 1986).

Miller, C. M.

C. M. Miller, S. C. Mettler, I. A. White, Optical Fiber Splices and Connectors: Theory and Methods (Marcel Dekker, New York, 1986).

Mills, T. N.

Murphy, A. K.

Murphy, K. A.

V. Arya, M. J. de Vries, K. A. Murphy, A. Wang, R. O. Claus, “Exact analysis of the EFPI optical fiber sensor using Kirchhoff’s diffraction formalism,” Opt. Fiber Technol. 1, 380–384 (1995).
[CrossRef]

Neikirk, D. P.

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

Neilson, D. T.

Pérennès, F.

Pickrell, G.

Poon, T.-C.

T.-C. Poon, P. R. Banerjee, Contemporary Optical Image Processing with MATLAB (Elsevier Science, New York, 2001).

Safaaii-Jazi, A.

A. Safaaii-Jazi, “Optical waveguides,” Lecture notes (Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va., 2002).

Schmidt, M.

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

Schmidt, W.

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

Smith, D.

Taylor, H. F.

C. E. Lee, H. F. Taylor, “Fiber-optic Fabry-Perot temperature sensor using a low-coherence light source,” J. Lightwave Technol. 9, 129–134 (1991).
[CrossRef]

Vengsarker, A. M.

Wang, A.

Wang, J.

Wang, Z.

White, I. A.

C. M. Miller, S. C. Mettler, I. A. White, Optical Fiber Splices and Connectors: Theory and Methods (Marcel Dekker, New York, 1986).

Xiao, H.

Zhao, W.

Appl. Opt.

IEE Proc. Optoelectron.

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

IEEE Photon. Technol. Lett.

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

J. Lightwave Technol.

Opt. Fiber Technol.

V. Arya, M. J. de Vries, K. A. Murphy, A. Wang, R. O. Claus, “Exact analysis of the EFPI optical fiber sensor using Kirchhoff’s diffraction formalism,” Opt. Fiber Technol. 1, 380–384 (1995).
[CrossRef]

Opt. Lett.

Other

C. M. Miller, S. C. Mettler, I. A. White, Optical Fiber Splices and Connectors: Theory and Methods (Marcel Dekker, New York, 1986).

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

T.-C. Poon, P. R. Banerjee, Contemporary Optical Image Processing with MATLAB (Elsevier Science, New York, 2001).

A. Safaaii-Jazi, “Optical waveguides,” Lecture notes (Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va., 2002).

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Figures (12)

Fig. 1
Fig. 1

Schematic of a low-finesse MMF EFPI sensor.

Fig. 2
Fig. 2

Schematic of the calculation of η R 2 and η k . Fiber F′ is the mirror image of the lead-in fiber F with respect to the reflection surface plane R 2.

Fig. 3
Fig. 3

Diagram of a cross section of the fiber geometry considered here.

Fig. 4
Fig. 4

Fringe visibility versus gap length for fibers 1, 2, and 3. All modes in the MMFs are equally excited.

Fig. 5
Fig. 5

Schematic of a MMF illuminated by a SMF output.

Fig. 6
Fig. 6

Fringe visibility versus gap length for fibers 1, 2, and 3. The MMF are illuminated by a SMF output.

Fig. 7
Fig. 7

Illustration of a MMF EFPI sensor with a wedge between the two reflection surfaces R 1 and R 2. Fiber F′ is the mirror image of fiber F with respect to surface plane R 2.

Fig. 8
Fig. 8

Fringe visibility versus wedge angle for fiber 1 at a gap length d = 20, 30, and 40 μm. All modes in the MMFs are equally excited.

Fig. 9
Fig. 9

Fringe visibility versus wedge angle for fibers 1, 2, and 3. All modes in the MMFs are equally excited.

Fig. 10
Fig. 10

Fringe visibility versus wedge angle for fibers 1, 2, and 3. The MMFs are illuminated by a SMF output.

Fig. 11
Fig. 11

Experimental setup to measure the fringe visibility as a function of wedge angle. OSA, optical spectrum analyzer.

Fig. 12
Fig. 12

Comparison between the theoreticals and the experimental results on the fringe visibility versus wedge angle.

Tables (1)

Tables Icon

Table 1 Fiber Parameters Used in the Simulation

Equations (26)

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Etotal=k=1N pkϕk exp-jβkzeˆk=k=1N |pk|expjφpkϕk exp-jβkzeˆk,
I=Etotal·Etotal*=k=1Npkϕkpkϕk*eˆk·eˆk*=k=1N pkpk*=k=1N Ik.
E=k=1N qkϕk exp-jβkzeˆk,
IR=E·E*=k=1N qkqk*=k=1N Ik.
qkϕk=rpkϕk+ηkrpkϕk expiφ0+ckϕk expiφrk.
Ik=qkqk* =rpk+ηkrpk expiφ0+ck expiφrk×rpk*+ηk*rpk* exp-iφ0+ck exp-iφrk =r2|pk|2+r2|ηk|2|pk|2+ck2+2r2|ηkpk|2×cosφ0+φk+2r|pk|ck cosφrk-φpk+2r|ηkpk|ck cosφ0+φk+φpk-φrk.
IR=k=1N Ik =k=1Nr2|pk|2+r2|ηk|2|pk|2+ck2+2r2|ηkpk|2 cosφ0+φk+2r|pk|ck×cosφrk-φpk+2r|ηkpk|ck×cosφ0+φk+φpk-φrk.
IR=r2k=1N |pk|21+|ηk|2+ck2+2|ηk|cosφ0+φk.
IR/φ0=0.
φ01=-tan-1k=1N |pk|2|ηk|sin φkk=1N |ηk|cos φk,
φ02=π-tan-1k=1N |pk|2|ηk|sin φkk=1N |ηk|cos φk,
Imax=r2k=1N |pk|21+|ηk|2+ck2+2|ηk×cosφ01+φk|,
Imin=r2k=1N |pk|21+|ηk|2+ck2-2|ηk×cosφ01+φk|.
Vb=2 k=1N |pk|2|ηkcosφ01+φk|k=1N |pk|2+k=1N |pk|2|ηk|2+ck2.
I=k=1N |pk|2=1.
Vb=2 k=1N |pk|2|ηkcosφ01+φk|/1+ηR2,
ηR2=k=1N |pk|2|ηk|2+ck2.
ηR2=a2/a+2d tan θc2,
ηk=R1 ϕkϕk*dxdy.
ϕkx, y=Fxy-1Fxyϕkx, yHkx, ky; z|z=2d,
Hkx, ky; z=exp-jk0z1-kx2+ky2/k021/2.
Jlu/uJl-1u+Klw/wKl-1w=0,
ϕk=AJlur/a/Jlusinlφ+φ0, r<aAKlur/a/Klusinlφ+φ0, r>a.
Jl-1V<0JlV0.
|pk|2=BRi ϕsϕk*dxdy2,
ϕk,δθx, y=ϕkx-2d tan θ, y×expjk0x tan2δθ.

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