Abstract

A long period fiber grating (LPFG) temperature sensor system based on intensity modulation is developed. The LPFG employed is fabricated by the use of a focused CO2 laser beam to carve periodic grooves on the fiber. The temperature measurement resolution of up to 0.1°C has been obtained within the temperature range between 20 °C and 100  °C. The system uses a simple intensity measurement method and exhibits the advantages of convenient intensity measurement, double temperature sensitivity, high resolution, simple configuration, and low cost.

© 2006 Optical Society of America

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  1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
    [CrossRef]
  2. V. Bhatia and A. M. Vengsarkar, "Optical fiber long-period grating sensors," Opt. Lett. 21, 692-694 (1996).
    [CrossRef] [PubMed]
  3. S. Khaliq, S. W. James, and R. P. Tatam, "Enhanced sensitivity fibre optic long period grating temperature sensor," Meas. Sci. Technol. 13, 792-795 (2002).
    [CrossRef]
  4. B. H. Lee and J. Nishii, "Self-interference of long-period fibre grating and its application as temperature sensor," Electron. Lett. 34, 2059-2060 (1998).
    [CrossRef]
  5. Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
    [CrossRef]
  6. R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
    [CrossRef]
  7. D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
    [CrossRef]
  8. Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, "Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses," J. Lightwave Technol. 21, 1320-1327 (2003).
    [CrossRef]
  9. Y. P. Wang and Y. J. Rao, "A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously," IEEE Sens. J. 5, 839-843 (2005).
    [CrossRef]
  10. C. Y. Lin, L. A. Wang, and G. W. Chern, "Corrugated long-period fiber gratings as strain, torsion, and bending sensors," J. Lightwave Technol. 19, 1159-1168 (2001).
    [CrossRef]
  11. Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
    [CrossRef]
  12. T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
    [CrossRef]
  13. G. W. Yoffe, P. A. Krug, F. Ouellette, and D. A. Thorncraft, "Passive temperature-compensating package for optical-fiber gratings," Appl. Opt. 34, 6859-6861 (1995).
    [CrossRef] [PubMed]
  14. C. S. Shin, C. C. Chiang, and S. K. Liaw, "Comparison of single and double cladding long period fiber grating sensor using an intensity modulation interrogation system," Opt. Commun. 258, 23-29 (2006).
    [CrossRef]
  15. G. Rego, O. Okhotnikov, E. Dianov, and V. Sulimov, "High-temperature stability of long-period fiber gratings produced using an electric arc," J. Lightwave Technol. 19, 1574-1579 (2001).
    [CrossRef]

2006 (1)

C. S. Shin, C. C. Chiang, and S. K. Liaw, "Comparison of single and double cladding long period fiber grating sensor using an intensity modulation interrogation system," Opt. Commun. 258, 23-29 (2006).
[CrossRef]

2005 (1)

Y. P. Wang and Y. J. Rao, "A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously," IEEE Sens. J. 5, 839-843 (2005).
[CrossRef]

2004 (1)

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

2003 (2)

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
[CrossRef]

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, "Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses," J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

2002 (1)

S. Khaliq, S. W. James, and R. P. Tatam, "Enhanced sensitivity fibre optic long period grating temperature sensor," Meas. Sci. Technol. 13, 792-795 (2002).
[CrossRef]

2001 (2)

1998 (3)

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

B. H. Lee and J. Nishii, "Self-interference of long-period fibre grating and its application as temperature sensor," Electron. Lett. 34, 2059-2060 (1998).
[CrossRef]

1997 (1)

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
[CrossRef]

1996 (2)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

V. Bhatia and A. M. Vengsarkar, "Optical fiber long-period grating sensors," Opt. Lett. 21, 692-694 (1996).
[CrossRef] [PubMed]

1995 (1)

Bennion, I.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

V. Bhatia and A. M. Vengsarkar, "Optical fiber long-period grating sensors," Opt. Lett. 21, 692-694 (1996).
[CrossRef] [PubMed]

Cai, H. W.

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

Chern, G. W.

Chiang, C. C.

C. S. Shin, C. C. Chiang, and S. K. Liaw, "Comparison of single and double cladding long period fiber grating sensor using an intensity modulation interrogation system," Opt. Commun. 258, 23-29 (2006).
[CrossRef]

Davis, D. D.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Dianov, E.

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Everall, L. A.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
[CrossRef]

Fallon, R. W.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
[CrossRef]

Fang, Z. J.

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

Gaylord, T. K.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Glytsis, E. N.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Hattori, Y.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
[CrossRef]

Hu, A. Z.

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
[CrossRef]

Inoue, A.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
[CrossRef]

Iwashima, T.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
[CrossRef]

James, S. W.

S. Khaliq, S. W. James, and R. P. Tatam, "Enhanced sensitivity fibre optic long period grating temperature sensor," Meas. Sci. Technol. 13, 792-795 (2002).
[CrossRef]

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Khaliq, S.

S. Khaliq, S. W. James, and R. P. Tatam, "Enhanced sensitivity fibre optic long period grating temperature sensor," Meas. Sci. Technol. 13, 792-795 (2002).
[CrossRef]

Kosinski, S. G.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Krug, P. A.

Lee, B. H.

B. H. Lee and J. Nishii, "Self-interference of long-period fibre grating and its application as temperature sensor," Electron. Lett. 34, 2059-2060 (1998).
[CrossRef]

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Liaw, S. K.

C. S. Shin, C. C. Chiang, and S. K. Liaw, "Comparison of single and double cladding long period fiber grating sensor using an intensity modulation interrogation system," Opt. Commun. 258, 23-29 (2006).
[CrossRef]

Lin, C. Y.

Mettler, S. C.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Nishii, J.

B. H. Lee and J. Nishii, "Self-interference of long-period fibre grating and its application as temperature sensor," Electron. Lett. 34, 2059-2060 (1998).
[CrossRef]

Nishimura, M.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
[CrossRef]

Okhotnikov, O.

Ouellette, F.

Qu, R. H.

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

Ran, Z. L.

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, "Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses," J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
[CrossRef]

Rao, Y. J.

Y. P. Wang and Y. J. Rao, "A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously," IEEE Sens. J. 5, 839-843 (2005).
[CrossRef]

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, "Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses," J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
[CrossRef]

Rego, G.

Shigematsu, M.

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
[CrossRef]

Shin, C. S.

C. S. Shin, C. C. Chiang, and S. K. Liaw, "Comparison of single and double cladding long period fiber grating sensor using an intensity modulation interrogation system," Opt. Commun. 258, 23-29 (2006).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

Sulimov, V.

Tatam, R. P.

S. Khaliq, S. W. James, and R. P. Tatam, "Enhanced sensitivity fibre optic long period grating temperature sensor," Meas. Sci. Technol. 13, 792-795 (2002).
[CrossRef]

Thorncraft, D. A.

Vengsarkar, A. M.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, "Long-period fiber gratings as band-rejection filters," J. Lightwave Technol. 14, 58-65 (1996).
[CrossRef]

V. Bhatia and A. M. Vengsarkar, "Optical fiber long-period grating sensors," Opt. Lett. 21, 692-694 (1996).
[CrossRef] [PubMed]

Wang, L. A.

Wang, X. Z.

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

Wang, Y. P.

Y. P. Wang and Y. J. Rao, "A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously," IEEE Sens. J. 5, 839-843 (2005).
[CrossRef]

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, "Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses," J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
[CrossRef]

Williams, J. A. R.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
[CrossRef]

Xiang, S. Q.

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

Yoffe, G. W.

Zhan, Y. G.

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

Zhang, L.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
[CrossRef]

Zhu, T.

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, "Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses," J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (3)

T. Iwashima, A. Inoue, M. Shigematsu, M. Nishimura, and Y. Hattori, "Temperature compensation technique for fibre Bragg gratings using liquid crystalline polymer tubes," Electron. Lett. 33, 417-419 (1997).
[CrossRef]

B. H. Lee and J. Nishii, "Self-interference of long-period fibre grating and its application as temperature sensor," Electron. Lett. 34, 2059-2060 (1998).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, "Long-period fibre grating fabrication with focused CO2 laser pulses," Electron. Lett. 34, 302-303 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. P. Wang, Y. J. Rao, Z. L. Ran, T. Zhu, and A. Z. Hu, "A novel tunable gain equalizer based on a long-period fiber grating written by high-frequency CO2 laser pulses," IEEE Photon. Technol. Lett. 15, 251-253 (2003).
[CrossRef]

IEEE Sens. J. (1)

Y. P. Wang and Y. J. Rao, "A novel long period fiber grating sensor measuring curvature and determining bend-direction simultaneously," IEEE Sens. J. 5, 839-843 (2005).
[CrossRef]

J. Lightwave Technol. (4)

Meas. Sci. Technol. (2)

S. Khaliq, S. W. James, and R. P. Tatam, "Enhanced sensitivity fibre optic long period grating temperature sensor," Meas. Sci. Technol. 13, 792-795 (2002).
[CrossRef]

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, "All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating," Meas. Sci. Technol. 9, 1969-1973 (1998).
[CrossRef]

Opt. Commun. (1)

C. S. Shin, C. C. Chiang, and S. K. Liaw, "Comparison of single and double cladding long period fiber grating sensor using an intensity modulation interrogation system," Opt. Commun. 258, 23-29 (2006).
[CrossRef]

Opt. Eng. (1)

Y. G. Zhan, H. W. Cai, R. H. Qu, S. Q. Xiang, Z. J. Fang, and X. Z. Wang, "Fiber Bragg grating temperature sensor for multiplexed measurement with high resolution," Opt. Eng. 43, 2358-2361 (2004).
[CrossRef]

Opt. Lett. (1)

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Figures (6)

Fig. 1
Fig. 1

Photograph of a CO 2 laser-grooved LPFG with a grating pitch of 400   μm observed by the CCD camera. Typical depth and width of the groove are approximately 15 and 50   μm , respectively.

Fig. 2
Fig. 2

Transmission spectrum of the CO 2 laser-grooved LPFG with a grating pitch of 400   μm and a number of grating periods of 20.

Fig. 3
Fig. 3

Transmission spectra evolution of the LPFG when the temperature is increased from 20   ° C to 100   ° C in steps of 10   ° C .

Fig. 4
Fig. 4

Changes of the resonant wavelength and the transmission loss at the resonant wavelength of the LPFG when the temperature is increased from 20   ° C to 100   ° C in steps of 10   ° C .

Fig. 5
Fig. 5

Changes of the LPFG-induced loss at wavelengths of 1500, 1504, 1508, 1512, 1516, 1523, 1527, 1531, 1535, and 1539   nm when the temperature is increased from 20   ° C to 100   ° C in steps of 10 ° C .

Fig. 6
Fig. 6

Schematic of the CO 2 laser-grooved LPFG temperature sensor system based on the intensity modulation. PD 1 and PD 2 are photodetectors. C 0 , C 1 , C 2 , C 3 , and C 4 are 3   dB couplers.

Tables (1)

Tables Icon

Table 1 Measurement Results Using the Proposed LPFG Temperature Sensor System

Equations (5)

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

Δ n = Δ n residual + Δ n groove ,
I 1 = k 1 ( T T 0 ) + I 10 + Δ ( λ 1 ) ,
I 2 = k 2 ( T T 0 ) + I 20 + Δ ( λ 2 ) ,
I 2 I 1 = ( T T 0 ) ( k 2 k 1 ) + ( I 20 I 10 ) .
T = T 0 + I 2 I 1 I 20 + I 10 k 2 k 1 .

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