Abstract

We report the design criteria for the use of long period gratings (LPGs) as refractive-index sensors with output power at a single interrogating wavelength as the measurement parameter. The design gives maximum sensitivity in a given refractive-index range when the interrogating wavelength is fixed. Use of the design criteria is illustrated by the design of refractive-index sensors for specific application to refractive-index variation of a sugar solution with a concentration and detection of mole fraction of xylene in heptane (paraffin).

© 2009 Optical Society of America

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References

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  1. A. M. Vengaskar, 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, 58-64 (1996).
    [CrossRef]
  2. V. Bhatia and A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692-694 (1996).
    [CrossRef] [PubMed]
  3. R. Singh, H. Kumar, and E. K. Sharma, “Design of long period gratings necessity of a three layer fiber geometry for cladding mode characteristics,” Microwave Opt. Technol. Lett. 37, 45-49 (2003).
    [CrossRef]
  4. T. Erdogan, “Cladding mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760-1773(1997).
    [CrossRef]
  5. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  6. T. Zhu, Y-J. Rao, and Q-J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 2700-2702 (2005).
    [CrossRef]
  7. V. Bhatia, “Applications of long-period gratings to single and multi-parameter sensing,” Opt. Express 4, 457-466(1999).
    [CrossRef] [PubMed]
  8. H. J. Patrick, A. D. Kersey, and F. Bucholtz, “Analysis of the response of long period fiber gratings to external index of refraction,” J. Lightwave Technol. 161606-1612(1998).
    [CrossRef]
  9. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255-266 (2002).
    [CrossRef]
  10. Corning Incorporated, “Corning SMF28e optical fiber product information,” http://www.corning.com/assets/0/433/573/583/09573389-147D-4CBC-B55F-18C817D5F800.pdf.
  11. M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
    [CrossRef]
  12. M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. 18, 533-542 (2003).
  13. A. Ghatak and K. Thyagrajan, Introduction to Fiber Optics (Cambridge U. Press, 1998), pp. 543-546.
  14. Topac, Incorporated, “Relationship between salt solution and sugar concentration (Brix) and refractive index at 20 °C,” www.topac.com/salinity_brix.html.
  15. R. C. Weast, ed., Handbook of Physics and Chemistry (CRC Press, 1982).
  16. S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).
  17. M. Bousonville and J. Rausch, “Velocity of signal delay changes in fiber optic cables,” in Proceedings of the Ninth European Workshop on Beam Diagnostics and Instrumentation for Particle Accelerators (DIPAC)( 2009).

2006 (1)

M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
[CrossRef]

2005 (1)

T. Zhu, Y-J. Rao, and Q-J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 2700-2702 (2005).
[CrossRef]

2003 (2)

R. Singh, H. Kumar, and E. K. Sharma, “Design of long period gratings necessity of a three layer fiber geometry for cladding mode characteristics,” Microwave Opt. Technol. Lett. 37, 45-49 (2003).
[CrossRef]

M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. 18, 533-542 (2003).

2002 (1)

2000 (1)

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

1999 (1)

1998 (1)

1997 (2)

1996 (2)

A. M. Vengaskar, 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, 58-64 (1996).
[CrossRef]

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

Bennion, I.

Bhatia, V.

Bousonville, M.

M. Bousonville and J. Rausch, “Velocity of signal delay changes in fiber optic cables,” in Proceedings of the Ninth European Workshop on Beam Diagnostics and Instrumentation for Particle Accelerators (DIPAC)( 2009).

Bucholtz, F.

Cabeza, O.

M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
[CrossRef]

Chang, S.

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

Chuang, W-C.

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

Domínguez-Perez, M.

M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
[CrossRef]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

T. Erdogan, “Cladding mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 14, 1760-1773(1997).
[CrossRef]

A. M. Vengaskar, 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, 58-64 (1996).
[CrossRef]

Franjo, C.

M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
[CrossRef]

Ghatak, A.

A. Ghatak and K. Thyagrajan, Introduction to Fiber Optics (Cambridge U. Press, 1998), pp. 543-546.

Hsu, C-C.

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

Huang, T-H.

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

Jiménez, E.

M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
[CrossRef]

Judkins, J. B.

A. M. Vengaskar, 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, 58-64 (1996).
[CrossRef]

Kersey, A. D.

Kumar, H.

R. Singh, H. Kumar, and E. K. Sharma, “Design of long period gratings necessity of a three layer fiber geometry for cladding mode characteristics,” Microwave Opt. Technol. Lett. 37, 45-49 (2003).
[CrossRef]

Lemaire, P. J.

A. M. Vengaskar, 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, 58-64 (1996).
[CrossRef]

Leung, C-Y.

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

Mo, Q-J.

T. Zhu, Y-J. Rao, and Q-J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 2700-2702 (2005).
[CrossRef]

Monerie, M.

M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. 18, 533-542 (2003).

Patrick, H. J.

Rao, Y-J.

T. Zhu, Y-J. Rao, and Q-J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 2700-2702 (2005).
[CrossRef]

Rausch, J.

M. Bousonville and J. Rausch, “Velocity of signal delay changes in fiber optic cables,” in Proceedings of the Ninth European Workshop on Beam Diagnostics and Instrumentation for Particle Accelerators (DIPAC)( 2009).

Segade, L.

M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
[CrossRef]

Sharma, E. K.

R. Singh, H. Kumar, and E. K. Sharma, “Design of long period gratings necessity of a three layer fiber geometry for cladding mode characteristics,” Microwave Opt. Technol. Lett. 37, 45-49 (2003).
[CrossRef]

Shieh, J-Y.

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

Shu, X.

Singh, R.

R. Singh, H. Kumar, and E. K. Sharma, “Design of long period gratings necessity of a three layer fiber geometry for cladding mode characteristics,” Microwave Opt. Technol. Lett. 37, 45-49 (2003).
[CrossRef]

Sipe, J. E.

A. M. Vengaskar, 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, 58-64 (1996).
[CrossRef]

Thyagrajan, K.

A. Ghatak and K. Thyagrajan, Introduction to Fiber Optics (Cambridge U. Press, 1998), pp. 543-546.

Tsai, Y-S.

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

Vengaskar, A. M.

A. M. Vengaskar, 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, 58-64 (1996).
[CrossRef]

Vengsarkar, A. M.

Weast, R. C.

R. C. Weast, ed., Handbook of Physics and Chemistry (CRC Press, 1982).

Zhang, L.

Zhu, T.

T. Zhu, Y-J. Rao, and Q-J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 2700-2702 (2005).
[CrossRef]

Chin. J. Phys. (1)

S. Chang, C-C. Hsu, T-H. Huang, W-C. Chuang, Y-S. Tsai, J-Y. Shieh, and C-Y. Leung, “Heterodyne interferometric measurement of the thermo-optic coefficient of single mode fiber,” Chin. J. Phys. 38, 437-442 (2000).

IEEE J. Quantum Electron. (1)

M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. 18, 533-542 (2003).

IEEE Photon. Technol. Lett. (1)

T. Zhu, Y-J. Rao, and Q-J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 2700-2702 (2005).
[CrossRef]

J. Chem. Eng. Data (1)

M. Domínguez-Perez, L. Segade , O. Cabeza, C. Franjo, and E. Jiménez, “Densities, surface tensions, and refractive indices of propyl propanoate+hexane+m-xylene at 298.15 K,” J. Chem. Eng. Data 51, 294-300 (2006).
[CrossRef]

J. Lightwave Technol. (4)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

H. J. Patrick, A. D. Kersey, and F. Bucholtz, “Analysis of the response of long period fiber gratings to external index of refraction,” J. Lightwave Technol. 161606-1612(1998).
[CrossRef]

X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol. 20, 255-266 (2002).
[CrossRef]

A. M. Vengaskar, 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, 58-64 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Microwave Opt. Technol. Lett. (1)

R. Singh, H. Kumar, and E. K. Sharma, “Design of long period gratings necessity of a three layer fiber geometry for cladding mode characteristics,” Microwave Opt. Technol. Lett. 37, 45-49 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (5)

M. Bousonville and J. Rausch, “Velocity of signal delay changes in fiber optic cables,” in Proceedings of the Ninth European Workshop on Beam Diagnostics and Instrumentation for Particle Accelerators (DIPAC)( 2009).

Corning Incorporated, “Corning SMF28e optical fiber product information,” http://www.corning.com/assets/0/433/573/583/09573389-147D-4CBC-B55F-18C817D5F800.pdf.

A. Ghatak and K. Thyagrajan, Introduction to Fiber Optics (Cambridge U. Press, 1998), pp. 543-546.

Topac, Incorporated, “Relationship between salt solution and sugar concentration (Brix) and refractive index at 20 °C,” www.topac.com/salinity_brix.html.

R. C. Weast, ed., Handbook of Physics and Chemistry (CRC Press, 1982).

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Figures (12)

Fig. 1
Fig. 1

Typical phase matching curves for the SMF28 with n amb = 1.0 .

Fig. 2
Fig. 2

Transmission spectrum of SMF28 for a grating of 320 μm with n amb = 1.0 .

Fig. 3
Fig. 3

Calculated wavelength shift in the four resonance bands of a LPG of periodicity Λ = 320 μm as a function of the ambient refractive index. The shifts are calculated with respect to the resonance wavelength for LP 05 ( 1.09 μm ), LP 06 ( 1.15 μm ), LP 07 ( 1.257 μm , and LP 08 ( 1.525 μm ) with n amb = 1.0 .

Fig. 4
Fig. 4

Transmission spectrum of the LPG with a periodicity of Λ = 320 μm and coupling to the LP 08 mode for different ambient refractive indices. The dashed line corresponds to λ = 1.525 μm and shows that, as the ambient refractive index changes from n amb = 1.0 (lowest curve) to n amb = 1.32 (highest curve), the normalized core power changes from no transmission to full transmission.

Fig. 5
Fig. 5

Variation of the normalized core power and function f ( Δ ) with Δ.

Fig. 6
Fig. 6

Variation of g m ( n amb ) with changing ambient indices for different cladding modes corresponding to λ = 1.3 μm .

Fig. 7
Fig. 7

Variation of coupling coefficient and corresponding coupling lengths for different cladding modes at n amb = 1.0 corresponding to λ = 1.3 μm .

Fig. 8
Fig. 8

Variation of d n eff cl , m / d n amb with changing ambient index, for different cladding modes. The curve on the top corresponds to LP 0 , 25 ; the LP 02 curve is almost at the origin line, corresponding to λ = 1.3 μm .

Fig. 9
Fig. 9

Variation of g m ( n amb ) with a changing ambient index for different cladding modes with an ambient index that varies from 1 to 1.4.

Fig. 10
Fig. 10

(a) Transmission spectrum of a LPG of Λ = 287.6 μm and length 12.45 cm for an ambient index that varies from 1.33 to 1.38. (b) The output power in the core for varying ambient index when the interrogating wavelength is 1.3 μm . The solid curve was obtained from our design and the symbols represent the results obtained with OptiGrating (Optiwave, Ottawa, Ontario, Canada).

Fig. 11
Fig. 11

Variation of g m ( n amb ) with changing ambient index for different cladding modes with an ambient index that varies from 1.3 to 1.4.

Fig. 12
Fig. 12

(a) Transmission spectrum of a LPG of Λ = 157.6 μm and length 15.39 cm for an ambient index that varies from 1.37 to 1.38. (b) Output power in the core for varying the mole fraction of xylene in heptane when the interrogating wavelength is 1.3 μm . The solid curve was obtained with our design, i.e., κ N ( 13 ) = 1 , the symbols represent the results obtained by use of the actual value of κ N ( 13 ) for the respective ambient index.

Tables (2)

Tables Icon

Table 1 Variation of Core Power for Different Concentrations of Sugar in Water

Tables Icon

Table 2 Variation of Power in Core Mode (Input Power of 10 mW) for Different Mole Fractions of Xylene in Hexane

Equations (13)

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λ res ( m ) = ( n eff co n eff cl , m ) Λ ,
P co ( z ) P co ( z = 0 ) = P co = 1 κ ( m ) 2 γ 2 sin 2 ( γ z ) ,
κ ( m ) = k o 4 0 a Ψ core Δ n 2 ( r ) Ψ clad ( m ) r d r ,
Δ = γ κ ( m ) = Γ 2 4 κ ( m ) 2 + 1 ,
P co = 1 sin 2 ( Δ κ ( m ) z ) Δ 2 .
P co = 1 sin 2 ( Δ π κ N ( m ) / 2 ) Δ 2 = 1 sin 2 ( Δ π / 2 ) Δ 2 ,
d P co d n amb = d P co d Δ d Δ d n amb = 2 f ( Δ ) g m ( n amb ) ,
f ( Δ ) = Δ 2 1 Δ 4 ( sin 2 ( Δ π 2 ) Δ π 4 sin ( Δ π ) ) ,
g m ( n amb ) = k 0 2 κ 0 m d n eff cl , m d n amb .
d Δ d n amb | n amb = n a = Δ 2 1 Δ g m ( n amb ) .
d Δ d n amb | n amb = n a 0.8 δ n .
g m ( n amb = n a ) 1.31 δ n .
Λ = 2 π k o Δ n eff m + 1.533 κ 0 m .

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