Abstract

We study the sensitivity of fiber grating sensors in the applications of strain, temperature, internal label-free biosensing, and internal refractive index sensing. New analytical expressions for the sensitivities, valid for photonic crystal fibers are rigorously derived. These are generally valid, and we identify a previously unaccounted term for temperature and strain sensing. It is shown that dispersion plays a central role in determining the sensitivity, and that dispersion may enhance or suppress sensitivity as well as change the sign of the resonant wavelength shifts. We propose a quality factor, Q, for characterizing long period gratings sensors.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  33. H. Dobb, K. Kalli, and D. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fibre,” Opt. Commun. 260, 184-191 (2006).
    [CrossRef]
  34. C. Martelli, J. Canning, N. Groothoff, and K. Lyytikainen, “Strain and temperature characterization of photonic crystal fiber Bragg gratings,” Opt. Lett. 30, 1785-1787 (2005).
    [CrossRef] [PubMed]
  35. Y. Park, T.-J. Ahn, Y. H. Kim, W.-T. Han, U.-C. Paek, and D. Y. Kim, “Measurement method for profiling the residual stress and the strain-optic coefficient of an optical fiber,” Appl. Opt. 41, 21-26 (2002).
    [CrossRef] [PubMed]
  36. J. S. Petrovic, H. Dobb, V. K. Mezentsev, K. Kalli, D. J. Webb, and I. Bennion, “Sensitivity of LPGs in PCFs fabricated by an electric arc to temperature strain and external refractive index,” J. Lightwave Technol. 25, 1306-1312 (2007).
    [CrossRef]
  37. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

2007

2006

H. Dobb, K. Kalli, and D. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fibre,” Opt. Commun. 260, 184-191 (2006).
[CrossRef]

L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Hoiby, and O. Bang, “Biochemical sensing using photonic crystal fiber long-period gratings,” Opt. Express 14, 8824-8831 (2006).
[CrossRef]

M. C. P. Huy, G. Laffont, Y. Frignac, V. Dewynter-Marty, P. Ferdinand, P. Roy, J.-M. Blondy, D. Pagnoux, W. Blanc, and B. Dussardier, “Fibre Bragg grating photowriting in microstructured optical fibres for refractive index measurement,” Meas. Sci. Technol. 17, 992-997 (2006).
[CrossRef]

L. Rindorf, P. E. Hoiby, J. B. Jensen, L. H. Pedersen, O. Bang, and O. Geschke, Towards biochips using microstructured optical fiber sensors,” Anal. Bioanal. Chem. 385, 1370-1375 (2006).
[CrossRef] [PubMed]

M. P. Hiscocks, M. A. van Eijkelenborg, A. Argysor, and M. C. J. Large, “Stable imprinting of long-period gratings in microstructured polymer optical fibre,” Opt. Express 14, 4644-4649 (2006).
[CrossRef] [PubMed]

H. R. Sorensen, J. Canning, J. Laegsgaard, and K. Hansen, “Control of the wavelength dependent thermo-optic coefficients in structured fibres,” Opt. Express 14, 6428-6433 (2006).
[CrossRef] [PubMed]

2005

O. Frazao, J. P. Carvalho, L. A. Ferreira, F. M. Araujo, and J. L. Santos, “Discrimination of strain and temperature using Bragg gratings in microstructured and standard optical fibres,” Meas. Sci. Technol. 16, 2109-2113 (2005).
[CrossRef]

Z. Li, Y. Tam, L. Xu, and Q. Zhang, “Fabrication of long-period gratings in poly(methyl methacrylate-co-methyl vinyl ketone-co-benzyl methacrylate)-core polymer optical fiber by use of a mercury lamp,” Opt. Lett. 30, 1117-1119 (2005).
[CrossRef] [PubMed]

H. Dobb, D. Webb, K. Kalli, A. Argyros, M. Large, and M. van Eijkelenborg, “Continuous wave ultraviolet light-induced fiber Bragg gratings in few- and single-mode microstructured polymer optical fibers,” Opt. Lett. 30, 3296-3298 (2005).
[CrossRef]

S. Ramachandran, “Dispersion-tailored few-mode fibers: a versatile platform for in-fiber photonic devices,” J. Lightwave Technol. 23, 3426-3443 (2005).
[CrossRef]

C. Martelli, J. Canning, N. Groothoff, and K. Lyytikainen, “Strain and temperature characterization of photonic crystal fiber Bragg gratings,” Opt. Lett. 30, 1785-1787 (2005).
[CrossRef] [PubMed]

J. B. Jensen, P. E. Hoiby, G. Emiliyanov, O. Bang, L. H. Pedersen, and A. Bjarklev, “Selective detection of antibodies in microstructured polymer optical fibers,” Opt. Express 13, 5883-5889 (2005).
[CrossRef] [PubMed]

N. Burani and J. Laegsgaard, “Perturbative modeling of Bragg-grating-based biosensors in photonic-crystal fibers,” J. Opt. Soc. Am. B 22, 2487-2493 (2005).
[CrossRef]

2004

2003

C. Kerbage and B. Eggleton, “Tunable microfluidic optical fiber gratings,” Appl. Phys. Lett. 82, 1338-1340 (2003); erratum ibid., 1059 (2007).
[CrossRef]

M. D. Nielsen, G. Vienne, J. R. Folkenberg, and A. Bjarklev, “Investigation of microdeformation-induced attenuation spectra in a photonic crystal fiber,” Opt. Lett. 28, 236-238 (2003).
[CrossRef] [PubMed]

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9, 57-79 (2003).
[CrossRef]

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 4, 349-350 (2003).
[CrossRef]

X. Daxhelet and M. Kulishov, “Theory and practice of long-period gratings: when a loss becomes a gain,” Opt. Lett. 28, 686-688 (2003).
[CrossRef] [PubMed]

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, “Modal cutoff and the v parameter in photonic crystal fibers,” Opt. Lett. 28, 1879-1881 (2003).
[CrossRef] [PubMed]

B. R. Acharya, T. Krupenkin, S. Ramachandran, Z. Wang, C. C. Huang, and J. A. Rogers, “Tunable optical fiber devices based on broadband long-period gratings and pumped microfluidics,” Appl. Phys. Lett. 83, 4912-4914 (2003).
[CrossRef]

2002

2001

2000

M. P. DeLisa, Z. Zhang, M. Shiloach, S. Pilevar, C. C. Davis, J. S. Sirkis, and W. E. Bentley, “Evanescent wave long-period fiber Bragg grating as an immobilized antibody biosensor,” Anal. Chem. 72, 2895-2900 (2000).
[CrossRef] [PubMed]

1999

B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spälter, and T. A. Strasser, “Grating resonances in air-silica microstructured optical fibers,” Opt. Lett. 24, 1460-1462 (1999).
[CrossRef]

G. D. Peng, Z. Xiong, and P. L. Chu, “Photosensitivity and gratings in dye-doped polymer optical fibers,” Opt. Fiber Technol. 5, 242-251 (1999).
[CrossRef]

1997

Anal. Bioanal. Chem.

L. Rindorf, P. E. Hoiby, J. B. Jensen, L. H. Pedersen, O. Bang, and O. Geschke, Towards biochips using microstructured optical fiber sensors,” Anal. Bioanal. Chem. 385, 1370-1375 (2006).
[CrossRef] [PubMed]

Anal. Chem.

M. P. DeLisa, Z. Zhang, M. Shiloach, S. Pilevar, C. C. Davis, J. S. Sirkis, and W. E. Bentley, “Evanescent wave long-period fiber Bragg grating as an immobilized antibody biosensor,” Anal. Chem. 72, 2895-2900 (2000).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

B. R. Acharya, T. Krupenkin, S. Ramachandran, Z. Wang, C. C. Huang, and J. A. Rogers, “Tunable optical fiber devices based on broadband long-period gratings and pumped microfluidics,” Appl. Phys. Lett. 83, 4912-4914 (2003).
[CrossRef]

C. Kerbage and B. Eggleton, “Tunable microfluidic optical fiber gratings,” Appl. Phys. Lett. 82, 1338-1340 (2003); erratum ibid., 1059 (2007).
[CrossRef]

Electron. Lett.

H. Dobb, K. Kalli, and D. Webb, “Temperature-insensitive long period grating sensors in photonic crystal fibre,” Electron. Lett. 11, 657-658 (2004).
[CrossRef]

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 4, 349-350 (2003).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Meas. Sci. Technol.

O. Frazao, J. P. Carvalho, L. A. Ferreira, F. M. Araujo, and J. L. Santos, “Discrimination of strain and temperature using Bragg gratings in microstructured and standard optical fibres,” Meas. Sci. Technol. 16, 2109-2113 (2005).
[CrossRef]

M. C. P. Huy, G. Laffont, Y. Frignac, V. Dewynter-Marty, P. Ferdinand, P. Roy, J.-M. Blondy, D. Pagnoux, W. Blanc, and B. Dussardier, “Fibre Bragg grating photowriting in microstructured optical fibres for refractive index measurement,” Meas. Sci. Technol. 17, 992-997 (2006).
[CrossRef]

Opt. Commun.

H. Dobb, K. Kalli, and D. Webb, “Measured sensitivity of arc-induced long-period grating sensors in photonic crystal fibre,” Opt. Commun. 260, 184-191 (2006).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9, 57-79 (2003).
[CrossRef]

G. D. Peng, Z. Xiong, and P. L. Chu, “Photosensitivity and gratings in dye-doped polymer optical fibers,” Opt. Fiber Technol. 5, 242-251 (1999).
[CrossRef]

Opt. Lett.

Z. Li, Y. Tam, L. Xu, and Q. Zhang, “Fabrication of long-period gratings in poly(methyl methacrylate-co-methyl vinyl ketone-co-benzyl methacrylate)-core polymer optical fiber by use of a mercury lamp,” Opt. Lett. 30, 1117-1119 (2005).
[CrossRef] [PubMed]

H. Dobb, D. Webb, K. Kalli, A. Argyros, M. Large, and M. van Eijkelenborg, “Continuous wave ultraviolet light-induced fiber Bragg gratings in few- and single-mode microstructured polymer optical fibers,” Opt. Lett. 30, 3296-3298 (2005).
[CrossRef]

T. A. Birks, J. C. Knight, and P. S. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

G. Kakarantzas, T. A. Birks, and P. S. J. Russell, “Structural long-period gratings in photonic crystal fibers,” Opt. Lett. 27, 1013-1015 (2002).
[CrossRef]

M. D. Nielsen, G. Vienne, J. R. Folkenberg, and A. Bjarklev, “Investigation of microdeformation-induced attenuation spectra in a photonic crystal fiber,” Opt. Lett. 28, 236-238 (2003).
[CrossRef] [PubMed]

B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spälter, and T. A. Strasser, “Grating resonances in air-silica microstructured optical fibers,” Opt. Lett. 24, 1460-1462 (1999).
[CrossRef]

G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjaer, and L. Lindvold, “Localized biosensing with topas microstructured polymer optical fiber,” Opt. Lett. 32, 460-462 (2007).
[CrossRef] [PubMed]

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. Folkenberg, J. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett. 29, 1974-1976 (2004).
[CrossRef] [PubMed]

B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal cutoff in microstructured optical fibers,” Opt. Lett. 27, 1684-1686 (2002).
[CrossRef]

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, “Modal cutoff and the v parameter in photonic crystal fibers,” Opt. Lett. 28, 1879-1881 (2003).
[CrossRef] [PubMed]

C. Martelli, J. Canning, N. Groothoff, and K. Lyytikainen, “Strain and temperature characterization of photonic crystal fiber Bragg gratings,” Opt. Lett. 30, 1785-1787 (2005).
[CrossRef] [PubMed]

X. Daxhelet and M. Kulishov, “Theory and practice of long-period gratings: when a loss becomes a gain,” Opt. Lett. 28, 686-688 (2003).
[CrossRef] [PubMed]

Other

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

Comsol Multiphysics, http://www.comsol.com.

The International Association for the Properties of Water and Steam, http://www.iapws.org/relguide/rindex.pdf.

A. Yariv and P. Yeh, Photonics (Oxford U. Press, 2007).

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Figures (17)

Fig. 1
Fig. 1

PCF grating attenuates the incident power ( P in ) at the resonant wavelength λ r . The grating is characterized by its pitch, Λ G , resonant wavelength, λ r , and the FWHM of the dip, λ FWHM . The PCF grating may be exposed to different measurands to cause a shift, Δ λ , in the resonant wavelength, λ r .

Fig. 2
Fig. 2

PCF with triangular cladding structure. The structure is characterized by the lattice vectors, R 1 and R 2 , the hole size, d, and the pitch, Λ. The refractive indices n h and n b are the hole and base material refractive indices.

Fig. 3
Fig. 3

Effective indices for the core (top) and the FSM modes for triangular PCFs. The curves indicate different values of the hole diameter relative to the pitch. The curves correspond to different values of d Λ , increasing by 0.1.

Fig. 4
Fig. 4

Definition of the FWHM in detuning, δ FWHM = δ + δ , and in wavelength, λ FWHM = Δ λ + Δ λ .

Fig. 5
Fig. 5

Beat length as a function of the wavelength over pitch, λ Λ , for an LPG. The gray area indicates negative group index mismatch n ¯ g < 0 . The wavelength is λ = 1 μ m .

Fig. 6
Fig. 6

FWHM as a function of the wavelength over pitch, λ Λ for an LPG.

Fig. 7
Fig. 7

Field energy intensity fraction in the air filled holes for the FSM. The curves indicate different values of the hole diameter relative to the pitch: 0.15–0.95 in steps of 0.10.

Fig. 8
Fig. 8

Field energy intensity fraction in the water filled holes for the core mode. The curves indicate different values of the hole diameter relative to the pitch: 0.15–0.95 in steps of 0.10 increasing from below.

Fig. 9
Fig. 9

Field energy intensity fraction in the water filled holes for the FSM. The curves indicate different values of the hole diameter relative to the pitch: 0.15–0.95 in steps of 0.10 increasing from below.

Fig. 10
Fig. 10

Quality factor Q RI for LPG refractive index sensing. The curves indicate different values of the hole diameter relative to the pitch: 0.25–0.95 in steps of 0.10. The gray area indicates negative group index mismatch n ¯ g < 0 . The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = π 2 .

Fig. 11
Fig. 11

γ RI for BG refractive index sensing. The curves indicate different values of the hole diameter relative to the pitch: 0.15–0.95 in steps of 0.10. The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = 4 .

Fig. 12
Fig. 12

Sensitivity, γ Bio , for BG biosensing. The curves indicate different values of the hole diameter relative to the pitch: 0.15–0.95 in steps of 0.10. The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = 4 .

Fig. 13
Fig. 13

Quality factor, Q Bio , for LPG biosensing. The curves indicate different values of the hole diameter relative to the pitch: 0.25–0.95 in steps of 0.10. The gray area indicates negative group index mismatch n ¯ g < 0 . The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = π 2 .

Fig. 14
Fig. 14

Sensitivity, γ T , for BG temperature sensing. The curves indicate different values of the hole diameter relative to the pitch: 0.15–0.95 in steps of 0.10. The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = 4 .

Fig. 15
Fig. 15

Quality factor, Q T , for LPG temperature sensing. The curves indicate different values of the hole diameter relative to the pitch: 0.25–0.95 in steps of 0.10. The gray area indicates negative group index mismatch n ¯ g < 0 . The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = π 2 .

Fig. 16
Fig. 16

Sensitivity, γ ε s , for BG strain sensing. The curves indicate different values of the hole diameter relative to the pitch: 0.15–0.95 in steps of 0.10. The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = 4 .

Fig. 17
Fig. 17

Quality factor, Q ε s , for LPG strain sensing. The curves indicate different values of the hole diameter relative to the pitch: 0.25–0.95 in steps of 0.10. The gray area indicates negative group index mismatch n ¯ g < 0 . The wavelength is 1 μ m , the length of the gratings is L = 30 mm , and κ L = π 2 .

Tables (2)

Tables Icon

Table 1 Comparison of Sensitivity and the Quality Factor for PCF Biosensors and Refractive Index Sensors for both LPGs and BGs at Different Wavelengths for Two Different PCFs: A Large Core of 11 μ m and a Small Core PCF of 2.5 μ m

Tables Icon

Table 2 Comparison of Sensitivity and the Quality Factor for PCF Temperature and Strain Sensors for both LPGs and BGs at Different Wavelengths for Two Different PCFs: A Large Core of 11 μ m and a Small Core PCF of 2.5 μ m

Equations (37)

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

× × E ω ( r , z ) = ω 2 c 2 ε ( r ) E ω ( r , z ) ,
PCF d r E m ( r ) ε ( r ) E n ( r ) = δ m n ,
[ a co ( z , δ i ) z a i ( z , δ i ) z ] = i [ 0 κ i e i δ i z κ i * e i δ i z 0 ] [ a co ( z , δ i ) a i ( z , δ i ) ] ,
δ i β co β i 2 π Λ G ,
κ i = k 2 2 β co β i PCF d r E co ( r ) Δ ε ̃ ( r ) E i ( r ) ,
Δ ε ( r , z ) = m = Δ ε ̃ m ( r ) exp ( i m ( 2 π Λ G ) z ) .
λ r = ( n co ( λ r ) n i ( λ r ) ) Λ G n ¯ f ( λ r ) Λ G ,
δ ( λ r + Δ λ ) = β co ( λ r + Δ λ ) β i ( λ r + Δ λ ) 2 π Λ G β ¯ k k λ λ r Δ λ = n ¯ g ( λ r ) 2 π λ r 2 Δ λ .
λ FWHM λ r = 1 2 π λ r δ FWHM n ¯ g ( λ r ) ,
T ( δ ) = 1 1 1 + δ 2 4 κ 2 sin 2 ( κ L 1 + δ 2 4 κ 2 ) .
λ FWHM λ r 0.80 1 n ¯ g ( λ r ) λ r L .
T ( δ ) = 1 sinh 2 ( κ L 1 δ 2 4 κ 2 ) cosh 2 ( κ L 1 δ 2 4 κ 2 ) δ 2 4 κ 2 .
δ FWHM 4.0 κ L + 3.4 L .
λ FWHM λ r 0.64 λ r κ n ¯ g ( λ r ) .
λ r + Δ λ r = [ n ¯ f ( λ r , α ) + n ¯ f λ r Δ λ r + n ¯ f α Δ α ] Λ G .
γ = 1 λ r d λ r d α = 1 n ¯ g ( λ r ) n ¯ f α = { 1 n g , co n g , cl ( n co n cl ) α , LPG 1 n g , co n co α BG .
Q = 1 λ FWHM d λ r d α { 1 0.80 L λ r ( n co n cl ) α , LPG 1 0.64 1 λ r κ n co α , BG .
f u 0 for λ Λ 0 ,
f u f for λ Λ ,
n ¯ f n h = 2 n g , co n h f u , co ,
n ¯ f n h = n g , co n h f u , co n g , cl n h f u , cl .
n eff t Bio = 2 n eff d ,
n ¯ f t Bio = { 2 ( n co d n cl d ) , LPG 4 n co d , BG ) .
n eff T λ r = d n eff ( L ( T ) , Λ ( T ) , n r ( T ) ) d T = n eff L L T + n eff Λ Λ T + n eff n b n b T .
n eff L = n eff L .
n ¯ f T λ r = 2 α ( n co + Λ n co Λ ) + 2 C T n n b ( 1 f u , co ) n g , co .
n ¯ f T λ r = α ( n ¯ f + Λ n ¯ f Λ ) + C b , T n n b [ ( 1 f u , co ) n g , co ( 1 f u , cl ) n g , cl ] .
n eff ε s λ r = d n eff ( L ( ε s ) , Λ ( ε s ) , n r ( ε s ) ) d ε s = n eff L L ε s + n eff Λ Λ ε s + n eff n r n r ε s .
n eff L = n eff L ,
n f ε s λ r = 2 n co 2 ν Λ n co Λ + η ε n b 2 n g , co ( 1 f u , co ) ,
n ¯ f ε s λ r = ( n co n cl ) ν Λ ( n co n cl ) Λ + η ε n b ( n g , co ( 1 f u , co ) n g , cl ( 1 f u , cl ) ) .
Δ β m = ω 2 β ω PCF d r Δ ε ( r ) E m ( r ) 2 PCF d r ε ( r ) E m ( r ) 2 .
PCF d r E m ( r ) ε ( r ) E n ( r ) = δ m n ,
Δ n eff , m = n g , m 2 PCF d r Δ ε ( r ) E m ( r ) 2 ,
f u , m holes d r D m ( r ) E m ( r ) PCF d r D m ( r ) E m ( r ) ,
n eff , m n h = n g , m n h f u , m ,
n eff , m n b = n g , m n b ( 1 f u , m ) ,

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