Abstract

We make the case for minimizing cavity length of extrinsic Fabry-Pérot (FP) cavities for use in fiber-tip sensors. Doing so mitigates multiple challenges that arise from using multimode fibers: mode averaging, phase uncertainty, amplitude reduction, and spectral modal noise. We explore these effects in detail using modal simulations, and construct pressure sensors based on this principle. We discuss the multimodal effects that we observe in our fiber sensors, and use simple filtering of the spectral signal to more easily measure pressure sensitivity. The concept of short-cavity FP interferometry is important for ensuring high quality and performance of multimode fiber sensors.

© 2013 OSA

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References

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    [CrossRef]
  2. Y. Gong, T. Zhao, Y. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Phot. Tech. L.23(11), 679–681 (2011).
    [CrossRef]
  3. Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
    [CrossRef]
  4. É. Pinet, E. Cibula, and D. Donlagic, “Ultra-miniature all-glass Fabry-Perot pressure sensor manufactured at the tip of a multimode optical fiber,” Proc. SPIE6770, 67700U, 67700U-8 (2007).
    [CrossRef]
  5. X. Wu and O. Solgaard, “Overcoming multimodal effects in optical fiber tip CMOS-compatible Fabry-Pérot sensors,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2012), paper JW2A.68. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2012-JW2A.68
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. C. Kao and P. Russell, Fundamentals of Photonics, B. E. A. Saleh and M. C. Teich, eds. (John Wiley & Sons, Inc., 2007), Chap. 9.
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    [CrossRef]
  15. Agilent Technologies white paper, “Optical spectrum analysis” (Agilent Technologies). http://cp.literature.agilent.com/litweb/pdf/5963-7145E.pdf
  16. Opsens inc. white paper, “Opsens white-light polarization interferometry technology” (Opsens inc.) http://www.opsens.com/pdf/WLPIREV2.3.pdf
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. W. C. Young and R. G. Budynas, Roarkʼs Formulas for Stress and Strain, Warren C. Young and Richard G. Budynas, eds. (McGraw-Hill, Boston, Mass., 2002).

2011 (3)

Y. Gong, T. Zhao, Y. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Phot. Tech. L.23(11), 679–681 (2011).
[CrossRef]

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

É. Pinet, “Pressure measurement with fiber-optic sensors: commercial technologies and applications,” Proc. SPIE7753, 775304, 775304-4 (2011).
[CrossRef]

2010 (1)

2007 (1)

É. Pinet, E. Cibula, and D. Donlagic, “Ultra-miniature all-glass Fabry-Perot pressure sensor manufactured at the tip of a multimode optical fiber,” Proc. SPIE6770, 67700U, 67700U-8 (2007).
[CrossRef]

2006 (3)

2004 (1)

1999 (1)

1998 (1)

1990 (1)

S. Shaklan, “Measurement of intermodal coupling in weakly multimode fibre optics,” Electron. Lett.26(24), 2022–2024 (1990).
[CrossRef]

1980 (1)

1978 (1)

Beard, P. C.

Chen, C.-H.

Cibula, E.

É. Pinet, E. Cibula, and D. Donlagic, “Ultra-miniature all-glass Fabry-Perot pressure sensor manufactured at the tip of a multimode optical fiber,” Proc. SPIE6770, 67700U, 67700U-8 (2007).
[CrossRef]

Cooper, K.

Cox, J. A.

Donlagic, D.

É. Pinet, E. Cibula, and D. Donlagic, “Ultra-miniature all-glass Fabry-Perot pressure sensor manufactured at the tip of a multimode optical fiber,” Proc. SPIE6770, 67700U, 67700U-8 (2007).
[CrossRef]

Gong, Y.

Y. Gong, T. Zhao, Y. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Phot. Tech. L.23(11), 679–681 (2011).
[CrossRef]

Han, M.

Hill, K. O.

Kawasaki, B. S.

Kost, A.

Kutz, J. N.

Liu, Z.

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Mafi, A.

Marcuse, D.

Mills, T. N.

Pérennès, F.

Pickrell, G.

Pinet, É.

É. Pinet, “Pressure measurement with fiber-optic sensors: commercial technologies and applications,” Proc. SPIE7753, 775304, 775304-4 (2011).
[CrossRef]

É. Pinet, E. Cibula, and D. Donlagic, “Ultra-miniature all-glass Fabry-Perot pressure sensor manufactured at the tip of a multimode optical fiber,” Proc. SPIE6770, 67700U, 67700U-8 (2007).
[CrossRef]

Ran, Z.

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Rao, Y.

Y. Gong, T. Zhao, Y. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Phot. Tech. L.23(11), 679–681 (2011).
[CrossRef]

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Reynolds, R. O.

Shaklan, S.

S. Shaklan, “Measurement of intermodal coupling in weakly multimode fibre optics,” Electron. Lett.26(24), 2022–2024 (1990).
[CrossRef]

Smith, D.

Sun, D.

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Tremblay, Y.

Wang, A.

Wu, Y.

Y. Gong, T. Zhao, Y. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Phot. Tech. L.23(11), 679–681 (2011).
[CrossRef]

Xu, B.

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Xu, F.

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Yu, X.

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Zhang, J.

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

Zhao, T.

Y. Gong, T. Zhao, Y. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Phot. Tech. L.23(11), 679–681 (2011).
[CrossRef]

Zhu, Y.

Appl. Opt. (3)

Electron. Lett. (1)

S. Shaklan, “Measurement of intermodal coupling in weakly multimode fibre optics,” Electron. Lett.26(24), 2022–2024 (1990).
[CrossRef]

IEEE Phot. Tech. L. (1)

Y. Gong, T. Zhao, Y. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Phot. Tech. L.23(11), 679–681 (2011).
[CrossRef]

IEEE Sens. J. (1)

Z. Ran, Z. Liu, Y. Rao, F. Xu, D. Sun, X. Yu, B. Xu, and J. Zhang, “Miniature fiber-optic tip high pressure sensors micromachined by 157 nm laser,” IEEE Sens. J.11(5), 1103–1106 (2011).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Proc. SPIE (2)

É. Pinet, E. Cibula, and D. Donlagic, “Ultra-miniature all-glass Fabry-Perot pressure sensor manufactured at the tip of a multimode optical fiber,” Proc. SPIE6770, 67700U, 67700U-8 (2007).
[CrossRef]

É. Pinet, “Pressure measurement with fiber-optic sensors: commercial technologies and applications,” Proc. SPIE7753, 775304, 775304-4 (2011).
[CrossRef]

Other (6)

W. C. Young and R. G. Budynas, Roarkʼs Formulas for Stress and Strain, Warren C. Young and Richard G. Budynas, eds. (McGraw-Hill, Boston, Mass., 2002).

Agilent Technologies white paper, “Optical spectrum analysis” (Agilent Technologies). http://cp.literature.agilent.com/litweb/pdf/5963-7145E.pdf

Opsens inc. white paper, “Opsens white-light polarization interferometry technology” (Opsens inc.) http://www.opsens.com/pdf/WLPIREV2.3.pdf

C. Kao and P. Russell, Fundamentals of Photonics, B. E. A. Saleh and M. C. Teich, eds. (John Wiley & Sons, Inc., 2007), Chap. 9.

X. Wu and O. Solgaard, “Overcoming multimodal effects in optical fiber tip CMOS-compatible Fabry-Pérot sensors,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2012), paper JW2A.68. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2012-JW2A.68

R. E. Epworth, “The phenomenon of modal noise in fiber systems,” in Optical Fiber Communication (Optical Society of America, 1979), paper ThD1.

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Figures (14)

Fig. 1
Fig. 1

The top plot shows mode averaging effects on the reflectance of an ideal Fabry-Pérot cavity for beams with different numerical apertures assuming equal distribution across angles up to the NA for cavity lengths of 0.5λ to 3.25λ. The bottom plot shows sensitivity defined as the slope of the reflectance. The NAs were chosen to represent common multimode fibers. The case where NA = 0 represents an ideal plane wave. FP mirror reflectances were assumed to be 0.8. The maximum sensitivity drops rapidly as cavity length increases.

Fig. 2
Fig. 2

Fabry-Pérot resonances for low-reflectivity mirror (R = 0.04).

Fig. 3
Fig. 3

Left: Dependence of φeff of the reflected light from the distal mirror on the cavity length L for different MPDs inside graded-index multimode fiber with core diameter of 62.5 µm and NA of 0.275, for λ = 1550 nm. Right: Modal components of the different MPDs.

Fig. 4
Fig. 4

Plot showing the phase accumulation of a plane wave with (dash-dot) and without (dash) Gouy phase, assuming a Gaussian beam waist calculated using Marcuse’s equation in [14] for our model 62.5-µm core graded index fiber used in simulations. The phase accumulation of the fundamental mode of a graded index fiber is also plotted (solid) to show that our freespace propagation simulation takes into account Gouy phase. The cavity plotted is about 12.5 wavelengths long, with λ = 1550 nm.

Fig. 5
Fig. 5

Fringe visibility as a function of cavity length for different NA. Mirror reflectances assumed to be 0.04. For the wave simulation, the fibers were assumed to be step index fibers of 50-µm diameter core with the following parameters: NA = 0.2, ncore = 1.454, nclad = 1.440; NA = 0.27, ncore = 1.465, nclad = 1.440; NA = 0.39, ncore = 1.492, nclad = 1.440.

Fig. 6
Fig. 6

Spectrum of low-finesse EFPI with cavity lengths 10 µm (left) and 40 µm (right). This spectral modal noise is caused by intermodal coupling of the reflected wave from the distal mirror of the FP back into the fiber. The SMF fundamental mode waist size depends on wavelength and ranges from 4.1 µm to 4.3 µm in our simulation. We swept the wavelength in 0.5 nm increments, which limits the perceived frequency of the noise in our spectra.

Fig. 7
Fig. 7

The magnitude of modal coupling from back-reflection at the distal mirror (sensor membrane) at different cavity lengths (columns). Five Laguerre-Gaussian modes are shown as examples of increased mode coupling at longer cavity lengths. The operating wavelength is 1550 nm.

Fig. 8
Fig. 8

(A) A 1521 nm laser beam is launched through a single mode fiber with an optical isolator into a multimode fiber. After propagating through the MM 1x2 50/50 coupler and through ~100 m of fiber, the mode profile remained in the lower few modes (B). Applying lateral pressure using the Newport FM-1 Mode Scrambler induced mode coupling. (B-E) Mode profiles of fiber under different mode power distributions. (B) Mode profile without applying lateral pressure. (C) Mode profile with the mode scrambler knob turned 6 minor tick marks from initial position. (D) Mode profile with the mode scrambler knob turned 7 minor tick marks from initial position. (E) Mode profile with the mode scrambler knob turned 8 minor tick marks from initial position; most of the lower order modes have been coupled into the higher order modes.

Fig. 9
Fig. 9

Cross-sectional view of the two sensor package types. (A) Backside fiber insertion: 125 µm-diameter fiber is inserted into the backside of the chip and is affixed using epoxy. (B) Fiber insertion through ferrule: A ferrule was aligned to a membrane and bonded to the chip using epoxy before the fiber was adjusted and bonded.

Fig. 10
Fig. 10

Membrane fabrication processing steps. (A) Start with SOI wafer with device layer thickness of 2 ± 1 µm and buried oxide thickness of 2 µm. (B) Thin the sensor area using reactive ion etching (RIE) to a nominal thickness of 0.5 µm. (C) Perform deep RIE using the Bosch process; the buried oxide acts as the etch stop. (D) Buried oxide etching with 6:1 buffered oxide etchant (BOE) for 10 min to thin the oxide to about 1 µm.

Fig. 11
Fig. 11

Experimental Setup.

Fig. 12
Fig. 12

Unfiltered and filtered spectra of two sensors with cavity lengths ~30 λ and ~6 λ. The OSA resolution used was 0.5 nm. For both spectra, the Fast Fourier Transform (FFT) was taken and truncated to what corresponds to a frequency of 0.03 nm–1, and then the inverse FFT was taken to get the filtered spectrum.

Fig. 13
Fig. 13

Unfiltered and filtered spectra of a sensor using short and long lead-in fibers, where the round-trip fiber length was about 10 m and 150 m, respectively. The OSA resolutions used were 0.5 nm and 0.1 nm, respectively. Both spectra were low-pass filtered at 0.075 nm–1.

Fig. 14
Fig. 14

(Top left) Unfiltered pressure spectra for sensor MMF-2 (OSA resolution of 0.2 nm). (Bottom left) Spectra filtered at 0.0625 nm–1. (Right) Shift of the filtered spectra vs. pressure at 30% reflectance point from 1345 nm to 1370 nm. For MMF-2, the sensitivity is about –1.5 nm/psi.

Tables (1)

Tables Icon

Table 1 Performance summary of five multimode fiber-tip pressure sensors (MMF 1 through 5) and four single mode fiber-tip pressure sensors (SMF 1 through 4). The spectral shift sensitivity and the mechanical sensitivity change depending on the low-pass filter (LPF) cut-off as well as the reflectance at which the spectral shift is measured. The reflectance sensitivity can also change depending on the LPF cut-off and the operating wavelength.

Equations (1)

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η eff =| η eff |exp(i φ eff )= k=1 N | p k | 2 η k

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