Abstract

A theoretical model based on the ray-transfer-matrix method is developed for explaining the principle of a graded-index multimode fiber (GI-MMF) based hybrid fiber Fabry-Perot (GI-FFP) sensor. It is verified by the numerical simulations and experimental results that the high fringe contrast of the reflective spectrum of the sensor is due to the periodic self-focusing effect of the GI-MMF. The influence of the GI-MMF length on the shape of reflective spectrum and corresponding maximum fringe contrast are investigated. Experimental results are in good agreement with the theory. A typical GI-FFP sensor is fabricated and its response to the external refractive index is measured with a maximum sensitivity of ~160 dB/RIU (Refractive Index Unit).

© 2010 OSA

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References

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2010 (2)

2009 (4)

2008 (2)

2005 (1)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[CrossRef]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

1996 (1)

1987 (1)

W. L. Emkey and C. A. Jack, “Analysis and evaluation of graded-index fiber-lenses,” J. Lightwave Technol. 5(9), 1156–1164 (1987).
[CrossRef]

Andrés, M. V.

Bhatia, V.

Chiang, K. S.

Choi, H. Y.

Cruz, J. L.

Eggleton, B. J.

Emkey, W. L.

W. L. Emkey and C. A. Jack, “Analysis and evaluation of graded-index fiber-lenses,” J. Lightwave Technol. 5(9), 1156–1164 (1987).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Han, Y.

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Huang, W. P.

Huang, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[CrossRef]

Jack, C. A.

W. L. Emkey and C. A. Jack, “Analysis and evaluation of graded-index fiber-lenses,” J. Lightwave Technol. 5(9), 1156–1164 (1987).
[CrossRef]

Jian, S. S.

Kapoor, A.

Kuhlmey, B. T.

Lee, B. H.

Lee, R. K.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[CrossRef]

Li, Y.

Liang, W.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[CrossRef]

Liao, X.

Liu, W. J.

Liu, Z.

Lu, Y.

Mosquera, L.

Mudhana, G.

Paek, U. C.

Park, K. S.

Ran, Z.

Ran, Z. L.

Rao, Y. J.

Sáez-Rodriguez, D.

Sharma, E. K.

Tsai, H. L.

Vengsarkar, A. M.

Wei, T.

Wu, D. K. C.

Xiao, H.

Xu, B.

Xu, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[CrossRef]

Yariv, A.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[CrossRef]

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

Zhang, J.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005).
[CrossRef]

J. Lightwave Technol. (3)

Opt. Express (3)

Opt. Lett. (3)

Sens. Actuators B Chem. (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Beam propagation in the hybrid GI-FFP cavity; (b) schematic diagram of the three-beam interference model and (c) the microscopic image of the GI-FFP sensor.

Fig. 2
Fig. 2

(a) Beam radius at the GI-MMF end and R I I I , and (b) the maximum fringe contrast of the reflective spectra of the GI-FFP sensors in air (dots) and calculated R I I I e f f (line), as a function of GI-MMF length.

Fig. 3
Fig. 3

Calculated and experimental reflective spectra of the GI-FFP snesors with GI-MMF length of ~515μm and ~610μm. The reflective spectra from the air gap and the SMF end are also given.

Fig. 4
Fig. 4

The reflective spectra of the sensor in air and deionized water.

Fig. 5
Fig. 5

(a) Refractive index and (b) temperature responses of the GI-FFP sensor. The measurement sensitivity of the refractive index is also given in (a).

Tables (1)

Tables Icon

Table 1 Values of parameters used in the simulations

Equations (14)

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E ( r , z ) = A 0 w exp ( i Φ i n k r 2 2 q ) .
1 q = 1 ρ i λ n π w 2 .
q = A q + B C q + D .
R I I = 0 w I I r | E I I r ( r ) | 2 R ( r ) r d r / 0 w I I i | E I I i ( r ) | 2 r d r ,
n ( r ) = n 1 1 g 2 r 2 , r < a .
R I I e f f = 0 a s | E I I ( r ) | 2 r d r 0 a s | E 0 ( r ) | 2 r d r
R I I I = 0 w I I I i | E I I I r ( r ) | 2 R ( r ) r d r / 0 w I I I i | E I I I i ( r ) | 2 r d r .
M 23 = [ 1 0 ( n 0 n 1 ) / ρ 1 n 1 n 0 / n 1 ] , M 34 = [ cos ( g L ) sin ( g L ) / g - g sin ( g L ) cos ( g L ) ] ,
M 33 ' = [ cos ( 2 g L ) sin ( 2 g L ) / g - g sin ( 2 g L ) cos ( 2 g L ) ] , M 3 ' 2 ' = [ 1 0 ( n 1 n 0 ) / ρ 1 n 0 n 1 / n 0 ] .
R I I I e f f = 0 a s | E I I I ( r ) | 2 r d r / 0 a s | E 0 ( r ) | 2 r d r .
I ( λ ) = 0 a s | E I + E I I + E I I I | 2 r d r
V = 10 log ( I max ( λ ) I min ( λ ) ) .
I ( λ ) = R I + R I I e f f + R I I I e f f 2 R I R I I e f f cos Φ I I 2 R I I e f f R I I I e f f cos ( Φ I I I Φ I I ) + 2 R I R I I I e f f cos Φ I I I .
1 R I + R I I e f f R I I I e f f 2 R I R I I e f f 1

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