Abstract

The sensitivities of integrated optic pressure sensors with diaphragms theoretically are known to be strongly dependent on the position of the sensing waveguide on the diaphragm. According to the theoretical results, the diaphragm edge is the best position for the waveguide of a sensor based on the elasto-optic effect. The relationship between sensitivity and the waveguide position, however, has not been investigated experimentally, although it is important in the designing of such a sensor and in determining the misalignment tolerance of the sensing waveguide. In this study, this relationship in a glass-based integrated optic sensor by use of an intermodal interference was examined experimentally.

© 2002 Optical Society of America

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References

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  1. M. Tabib-Azar, G. Beheim, “Modern trends in microstructures and integrated optics for communication, sensing, and actuation,” Opt. Eng. 36, 1307–1318 (1997).
    [CrossRef]
  2. M. Ohkawa, M. Izutsu, T. Sueta, “Integrated optic pressure sensor on silicon substrate,” Appl. Opt. 28, 5153–5157 (1989).
    [CrossRef] [PubMed]
  3. G. N. De Brabander, G. Beheim, J. T. Boyd, “Integrated optical micromachined pressure sensor with spectrally encoded output and temperature compensation,” Appl. Opt. 37, 3264–3267 (1998).
    [CrossRef]
  4. H. Porte, V. Gorel, S. Kiryenko, J. Goedgebuer, W. Daniau, P. Blind, “Imbalanced Mach–Zehnder interferometer integrated in micromachined silicon substrate for pressure sensor,” J. Lightwave Technol. 17, 229–233 (1999).
    [CrossRef]
  5. G. N. De Brabander, J. T. Boyd, G. Beheim, “Integrated optical ring resonator with micromechanical diaphragm for pressure sensing,” IEEE Photon. Technol. Lett. 6, 671–673 (1994).
    [CrossRef]
  6. M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
    [CrossRef]
  7. Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Silicon-based integrated optical pressure sensor using intermodal interference between TM-like and TE-like modes,” in Integrated Optic Devices V, G. C. Righini, S. Honkanen, eds., Proc. SPIE4277, 411–418 (2001).
    [CrossRef]
  8. A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.
  9. S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Kogakusha, Tokyo, 1981).

2000 (1)

M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
[CrossRef]

1999 (1)

1998 (1)

1997 (1)

M. Tabib-Azar, G. Beheim, “Modern trends in microstructures and integrated optics for communication, sensing, and actuation,” Opt. Eng. 36, 1307–1318 (1997).
[CrossRef]

1994 (1)

G. N. De Brabander, J. T. Boyd, G. Beheim, “Integrated optical ring resonator with micromechanical diaphragm for pressure sensing,” IEEE Photon. Technol. Lett. 6, 671–673 (1994).
[CrossRef]

1989 (1)

Beheim, G.

G. N. De Brabander, G. Beheim, J. T. Boyd, “Integrated optical micromachined pressure sensor with spectrally encoded output and temperature compensation,” Appl. Opt. 37, 3264–3267 (1998).
[CrossRef]

M. Tabib-Azar, G. Beheim, “Modern trends in microstructures and integrated optics for communication, sensing, and actuation,” Opt. Eng. 36, 1307–1318 (1997).
[CrossRef]

G. N. De Brabander, J. T. Boyd, G. Beheim, “Integrated optical ring resonator with micromechanical diaphragm for pressure sensing,” IEEE Photon. Technol. Lett. 6, 671–673 (1994).
[CrossRef]

Blind, P.

Boyd, J. T.

G. N. De Brabander, G. Beheim, J. T. Boyd, “Integrated optical micromachined pressure sensor with spectrally encoded output and temperature compensation,” Appl. Opt. 37, 3264–3267 (1998).
[CrossRef]

G. N. De Brabander, J. T. Boyd, G. Beheim, “Integrated optical ring resonator with micromechanical diaphragm for pressure sensing,” IEEE Photon. Technol. Lett. 6, 671–673 (1994).
[CrossRef]

Daniau, W.

De Brabander, G. N.

G. N. De Brabander, G. Beheim, J. T. Boyd, “Integrated optical micromachined pressure sensor with spectrally encoded output and temperature compensation,” Appl. Opt. 37, 3264–3267 (1998).
[CrossRef]

G. N. De Brabander, J. T. Boyd, G. Beheim, “Integrated optical ring resonator with micromechanical diaphragm for pressure sensing,” IEEE Photon. Technol. Lett. 6, 671–673 (1994).
[CrossRef]

Goedgebuer, J.

Gorel, V.

Goto, T.

A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.

Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Silicon-based integrated optical pressure sensor using intermodal interference between TM-like and TE-like modes,” in Integrated Optic Devices V, G. C. Righini, S. Honkanen, eds., Proc. SPIE4277, 411–418 (2001).
[CrossRef]

Hasebe, K.

M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
[CrossRef]

Izutsu, M.

Kiryenko, S.

Nishiwaki, C.

M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
[CrossRef]

Ohkawa, M.

M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
[CrossRef]

M. Ohkawa, M. Izutsu, T. Sueta, “Integrated optic pressure sensor on silicon substrate,” Appl. Opt. 28, 5153–5157 (1989).
[CrossRef] [PubMed]

Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Silicon-based integrated optical pressure sensor using intermodal interference between TM-like and TE-like modes,” in Integrated Optic Devices V, G. C. Righini, S. Honkanen, eds., Proc. SPIE4277, 411–418 (2001).
[CrossRef]

A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.

Porte, H.

Sato, T.

M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
[CrossRef]

Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Silicon-based integrated optical pressure sensor using intermodal interference between TM-like and TE-like modes,” in Integrated Optic Devices V, G. C. Righini, S. Honkanen, eds., Proc. SPIE4277, 411–418 (2001).
[CrossRef]

A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.

Sekine, S.

M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
[CrossRef]

Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Silicon-based integrated optical pressure sensor using intermodal interference between TM-like and TE-like modes,” in Integrated Optic Devices V, G. C. Righini, S. Honkanen, eds., Proc. SPIE4277, 411–418 (2001).
[CrossRef]

A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.

Shirai, Y.

A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.

Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Silicon-based integrated optical pressure sensor using intermodal interference between TM-like and TE-like modes,” in Integrated Optic Devices V, G. C. Righini, S. Honkanen, eds., Proc. SPIE4277, 411–418 (2001).
[CrossRef]

Sueta, T.

Tabib-Azar, M.

M. Tabib-Azar, G. Beheim, “Modern trends in microstructures and integrated optics for communication, sensing, and actuation,” Opt. Eng. 36, 1307–1318 (1997).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Kogakusha, Tokyo, 1981).

Woinowsky-Krieger, S.

S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Kogakusha, Tokyo, 1981).

Yamada, A.

A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (1)

G. N. De Brabander, J. T. Boyd, G. Beheim, “Integrated optical ring resonator with micromechanical diaphragm for pressure sensing,” IEEE Photon. Technol. Lett. 6, 671–673 (1994).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Eng. (1)

M. Tabib-Azar, G. Beheim, “Modern trends in microstructures and integrated optics for communication, sensing, and actuation,” Opt. Eng. 36, 1307–1318 (1997).
[CrossRef]

Opt. Rev. (1)

M. Ohkawa, K. Hasebe, C. Nishiwaki, S. Sekine, T. Sato, “Integrated optical pressure sensor using intermodal interference between two mutual orthogonal guided-modes,” Opt. Rev. 7, 144–148 (2000).
[CrossRef]

Other (3)

Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Silicon-based integrated optical pressure sensor using intermodal interference between TM-like and TE-like modes,” in Integrated Optic Devices V, G. C. Righini, S. Honkanen, eds., Proc. SPIE4277, 411–418 (2001).
[CrossRef]

A. Yamada, Y. Shirai, T. Goto, M. Ohkawa, S. Sekine, T. Sato, “Relationship between sensitivity and waveguide position on diaphragm for silicon-based integrated optic pressure sensor,” in Technical Digest Volume I of 4th Pacific Rim Conference on Lasers and Electro-Optics (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 420–421.

S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Kogakusha, Tokyo, 1981).

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic drawing of the integrated optic pressure sensor placed between a pair of crossed polarizers and (b) its cross sectional view. The sensor has 24 waveguides on the diaphragm to determine the relationship between phase sensitivity and waveguide position.

Fig. 2
Fig. 2

Illustration of the rectangular diaphragm assumed in the calculations.

Fig. 3
Fig. 3

Relationships between normalized sensitivity and waveguide position in the y direction. Normalized waveguide positions of ±0.5 indicate that the waveguide is placed along the diaphragm edge, whereas a position of 0 corresponds to the center of the diaphragm.

Fig. 4
Fig. 4

Experimental setup to measure the output intensity as a function of the applied pressure.

Fig. 5
Fig. 5

These figures indicate the experimental results of normalized output intensity versus applied pressure difference for waveguides placed at (a) 0.35, (b) 1.35, (c) 2.35, (d) 3.35, and (e) 4.35 mm from the center of the diaphragm. Also, (f) is for a waveguide located 0.35 mm outside of the diaphragm edge.

Fig. 6
Fig. 6

Measured phase sensitivity as a function of the waveguide position on the diaphragm.

Equations (16)

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4wy4+2 4wy2z2+4wz4=qD.
w=w0+w1+w2,
w0=4qa4π5Dm=1,3,5,-1m-1/2m5×1-αm tanh αm+22 cosh αmcoshmπza+12 cosh αmmπzasinhmπzacosmπya,
w1=-a22π2Dm=1,3,5, Em-1m-1/2m2 cosh αm×mπzasinhmπza-αm tanh αm coshmπzacosmπya,
w2=-b22π2Dm=1,3,5, Fm-1m-1/2m2 cosh βm×mπybsinhmπyb-βm tanh βm coshmπybcosmπzb,
w0zz=b/2+w1z+w2zz=b/2=0,
w0yy=a/2+w1y+w2yy=a/2=0.
σx=T1=-3q423-2tx+132t x3,
σy=T2=-Yx1-ρ22wy2+ρ 2wz2,
σz=T3=-Yx1-ρ22wz2+ρ 2wy2.
Si=sijTj  i, j=1,, 6,
Δni=-12 n3pijSj  i, j=1,, 6,
ΔϕTM-b/2b/2ωε0n2-a/2a/2-t/2t/2 Exx, y×Δn1x, y, zEx*x, ydxdydz,
ΔϕTE=-b/2b/2ωε0n2-a/2a/2-t/2t/2 Eyx, y×Δn2x, y, zEy*x, ydxdydz,
Δϕ=ΔϕTM-ΔϕTE.
n=1.523, Y=7.44×1010 Pa, ρ=0.22,sij= s11s12s12000s12s11s12000s12s12s11000000s44000000s44000000s44,s11=1.37×10-11 Pa-1,s12=-2.33×10-12 Pa-1,s44=3.20×10-11 Pa-1,pij=p11p12p12000p12p11p12000p12p12p11000000p44000000p44000000p44,p11=1.21×10-1,p12=2.70×10-1,p44=7.45×10-2.

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