Abstract

We investigate the phase sensitivity of the fundamental mode of hollow-core photonic bandgap fibers to strain and acoustic pressure. A theoretical model is constructed to analyze the effect of axial strain and acoustic pressure on the effective refractive index of the fundamental mode. Simulation shows that, for the commercial HC-1550-02 fiber, the contribution of mode-index variation to the overall phase sensitivities to axial strain and acoustic pressure are respectively ~-2% and ~-17%. The calculated normalized phase-sensitivities of the HC-1550-02 fiber to strain and acoustic pressure are respectively 1 ε−1 and −331.6 dB re μPa−1 without considering mode-index variation, and 0.9797 ε−1 and −333.1 dB re μPa−1 when mode-index variation is included in the calculation. The latter matches better with the experimentally measured results.

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References

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  1. C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37(18), R197–R216 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Air-core photonic-bandgap fiber-optic Gyroscope,” J. Lightwave Technol. 24(8), 3169–3174 (2006).
    [CrossRef]
  4. M. Pang and W. Jin, “Detection of acoustic pressure with hollow-core photonic bandgap fiber,” Opt. Express 17(13), 11088–11097 (2009).
    [CrossRef] [PubMed]
  5. L. J. Gibson, and M. F. Ashby, Cellular solids: structure and properties, second edition, (Cambridge University Press, New York 1997).
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    [CrossRef]
  7. S. P. Timoshenko and J. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).
  8. A. Cucnotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14(11), 1530–1532 (2002).
    [CrossRef]
  9. J. Ju, W. Jin, and M. S. Demokan, “Properties of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photon. Technol. Lett. 15(10), 1375–1377 (2003).
    [CrossRef]
  10. J. D. Shephard, P. J. Roberts, J. D. C. Jones, J. C. Knight, and D. P. Hand, “Measuring Beam Quality of Hollow Core Photonic Crystal Fibers,” J. Lightwave Technol. 24(10), 3761–3769 (2006).
    [CrossRef]
  11. Y. L. Su, Y. Q. Wang, Z. G. Zhao, and Y. L. Kang, Mechanics of Materials (Tianjin Univ. Press, China 2001).
    [PubMed]
  12. K. Saitoh, N. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12(3), 394–400 (2004).
    [CrossRef] [PubMed]
  13. C. D. Butter and G. B. Hocker, “Fiber optics strain gauge,” Appl. Opt. 17(18), 2867–2869 (1978).
    [CrossRef] [PubMed]
  14. Crystal Fiber website, http://www.nktphotonics.com/

2009 (1)

2006 (2)

2005 (1)

2004 (2)

K. Saitoh, N. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12(3), 394–400 (2004).
[CrossRef] [PubMed]

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37(18), R197–R216 (2004).
[CrossRef]

2003 (1)

J. Ju, W. Jin, and M. S. Demokan, “Properties of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photon. Technol. Lett. 15(10), 1375–1377 (2003).
[CrossRef]

2002 (1)

A. Cucnotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14(11), 1530–1532 (2002).
[CrossRef]

2000 (1)

R. M. Christensen, “Mechanics of cellular and other low-density materials,” Int. J. Solids Struct. 37(1-2), 93–104 (2000).
[CrossRef]

1978 (1)

Butter, C. D.

Christensen, R. M.

R. M. Christensen, “Mechanics of cellular and other low-density materials,” Int. J. Solids Struct. 37(1-2), 93–104 (2000).
[CrossRef]

Cucnotta, A.

A. Cucnotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14(11), 1530–1532 (2002).
[CrossRef]

Dandridge, A.

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37(18), R197–R216 (2004).
[CrossRef]

Dangui, V.

Demokan, M. S.

J. Ju, W. Jin, and M. S. Demokan, “Properties of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photon. Technol. Lett. 15(10), 1375–1377 (2003).
[CrossRef]

Digonnet, M. J. F.

Hand, D. P.

Hocker, G. B.

Jin, W.

M. Pang and W. Jin, “Detection of acoustic pressure with hollow-core photonic bandgap fiber,” Opt. Express 17(13), 11088–11097 (2009).
[CrossRef] [PubMed]

J. Ju, W. Jin, and M. S. Demokan, “Properties of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photon. Technol. Lett. 15(10), 1375–1377 (2003).
[CrossRef]

Jones, J. D. C.

Ju, J.

J. Ju, W. Jin, and M. S. Demokan, “Properties of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photon. Technol. Lett. 15(10), 1375–1377 (2003).
[CrossRef]

Kim, H. K.

Kino, G. S.

Kirkendall, C. K.

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37(18), R197–R216 (2004).
[CrossRef]

Knight, J. C.

Koshiba, M.

Mortensen, N.

Pang, M.

Roberts, P. J.

Saitoh, K.

Selleri, S.

A. Cucnotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14(11), 1530–1532 (2002).
[CrossRef]

Shephard, J. D.

Vincetti, L.

A. Cucnotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14(11), 1530–1532 (2002).
[CrossRef]

Zoboli, M.

A. Cucnotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14(11), 1530–1532 (2002).
[CrossRef]

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (2)

A. Cucnotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14(11), 1530–1532 (2002).
[CrossRef]

J. Ju, W. Jin, and M. S. Demokan, “Properties of a Highly Birefringent Photonic Crystal Fiber,” IEEE Photon. Technol. Lett. 15(10), 1375–1377 (2003).
[CrossRef]

Int. J. Solids Struct. (1)

R. M. Christensen, “Mechanics of cellular and other low-density materials,” Int. J. Solids Struct. 37(1-2), 93–104 (2000).
[CrossRef]

J. Lightwave Technol. (2)

J. Phys. D (1)

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37(18), R197–R216 (2004).
[CrossRef]

Opt. Express (3)

Other (4)

L. J. Gibson, and M. F. Ashby, Cellular solids: structure and properties, second edition, (Cambridge University Press, New York 1997).

S. P. Timoshenko and J. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).

Y. L. Su, Y. Q. Wang, Z. G. Zhao, and Y. L. Kang, Mechanics of Materials (Tianjin Univ. Press, China 2001).
[PubMed]

Crystal Fiber website, http://www.nktphotonics.com/

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Figures (12)

Fig. 1
Fig. 1

Configuration of a HC-PBF with an air-core, a honeycomb air-silica inner-cladding, a solid-silica outer-cladding and a polymer jacket.

Fig. 2
Fig. 2

(1) Profile configuration of the HC-PBF’s microstructure cladding; (2) In-profile stress σ1r on a cell of the microstructure cladding; (3) In-profile stress σ1θ on a cell of the microstructure cladding.

Fig. 3
Fig. 3

The deformation of the cell under loads ε1r|x, σ1r|y and τ1r|xy respectively.

Fig. 4
Fig. 4

Deformed profile (black) of HC-PBF, when the fiber is under the axial straining of ε1z = 0.3. For comparison, the original profile is shown in red.

Fig. 11
Fig. 11

SEM photograph of HC-PBF (HC-1550-02).

Fig. 5
Fig. 5

The calculated intensity profiles and the effective refractive indices of the fundamental mode of HC-1550-02 fiber under different axial strains.

Fig. 6
Fig. 6

HC-PBF’s fundamental mode effective index (neff) as the functions of (1) axial straining and (2) acoustic pressure.

Fig. 7
Fig. 7

Radial strain εr1 in the HC-PBF’s cladding for (1) an applied axial straining of 1με and (2) acoustic pressure of 103Pa.

Fig. 8
Fig. 8

(1) NR of HC-PBF as function of the thickness of the silica cladding (c-b) for different air filling ratios; (2) Calculated Sn/SL of the HC-PBF as the function of (c-b), while other parameters are fixed at a = 5.45μm, b = 35μm, d = 110μm, and η = 94%.

Fig. 9
Fig. 9

NR of HC-PBF to acoustic pressure with/without considering Sn.

Fig. 10
Fig. 10

SEM photograph of photonics crystal fiber (NL-3.3).

Fig. 12
Fig. 12

Experimental setup.

Tables (4)

Tables Icon

Table 1 Physical parameters of a commercial HC-PBF

Tables Icon

Table 2 Physical parameters of NL-3.3

Tables Icon

Table 3 Measured S and predicted S, SL, SN of HC-1550-02/NL-3.3 to axial strain

Tables Icon

Table 4 Measured S and predicted S, SL, SN, and NR of HC-1550-02 PBF to acoustic pressure

Equations (20)

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φ = 2 π λ n eff L
S = 1 φ d φ d X = 1 L d L d X + 1 n eff d n eff d X = S L + S n ,
S = 1 φ d φ ε = L φ d φ d L = 1 + L n eff d n eff d L = 1 + 1 n eff d n eff ε = S L + S n
{ E r = E θ = 3 2 ( 1 η ) 3 E 0 = E 1 * E z = ( 1 η ) E 0 = E 1 { v r θ = v θ r = 1 v z θ = v z r = v 1 v r z = v θ z 0 ,
{ σ r i = A i r 2 + 2 C i σ θ i = A i r 2 + 2 C i σ z i = D i ,
{ ε r 1 = 2 A 1 E 1 * r 2 v 1 D 1 E 1 ε θ 1 = 2 A 1 E 1 * r 2 v 1 D 1 E 1 ε z 1 = D 1 E 1 { ε r i = 1 E i [ ( 1 + v i ) A i r 2 + 2 ( 1 v i ) C i v i D i ] ε θ i = 1 E i [ ( 1 + v i ) A i r 2 + 2 ( 1 v i ) C i v i D i ] ε z i = 1 E i ( D i 4 v i C i ) ( i = 2 , 3 )
σ r 1 | r = b = σ r 2 | r = b ( a ) σ r 2 | r = c = σ r 3 | r = c ( b ) u r 1 | r = b = u r 2 | r = b ( c ) u r 2 | r = c = u r 3 | r = c ( d ) σ r 1 | r = a = 0 ( e ) σ r 3 | r = d = 0 ( f ) ε z 1 = ε z 2 = ε z 3 = ε ( g ) ,
u r i = ε r i d r
{ σ r 1 | x = σ r 1 cos 2 ( θ ) σ r 1 | y = σ r 1 sin 2 ( θ ) τ r 1 | xy = σ r 1 sin ( θ ) cos ( θ )
M x = 3 2 W x ' ,
V y ' , x = 3 W 2 E 0 I [ ( x ' + l / 2 ) 3 6 l ( x ' + l / 2 ) 2 4 + l 3 24 ] ,
M y = 1 2 P x '
V y ' , y = P 2 E 0 I [ ( x ' + l / 2 ) 3 6 l ( x ' + l / 2 ) 2 4 + l 3 24 ]
Δ ϕ = F l 2 24 E 0 I ,
{ M τ 1 = F x ' M τ 2 = F 2 x ' M τ 6 = F 2 x '
V y ' , τ 1 = F E 0 I [ ( x ' + l / 2 ) 3 6 l ( x ' + l / 2 ) 2 4 + l 3 24 ] V y ' τ 2 = F E 0 I [ ( x ' + l / 2 ) 3 6 l ( x ' + l / 2 ) 2 4 + l 3 24 ] V y ' , τ 6 = F E 0 I [ ( x ' + l / 2 ) 3 6 l ( x ' + l / 2 ) 2 4 + l 3 24 ]
Δ ( 1 n 2 ) i = j = 1 6 p i j [ σ r 1 E 1 v 0 σ θ 1 E 1 v 0 ε z 1 σ θ 1 E 1 v 0 σ r 1 E 1 v 0 ε z 1 ε z 1 0 0 0 ] ,
Δ n r = 1 2 n 0 3 [ ( 1 v 0 ) p 12 ε z 1 v 0 p 11 ε z 1 + σ r 1 v 0 σ θ 1 E 1 p 11 + σ θ 1 v 0 σ r 1 E 1 p 12 ] Δ n θ = 1 2 n 0 3 [ ( 1 v 0 ) p 12 ε z 1 v 0 p 11 ε z 1 + σ θ 1 v 0 σ r 1 E 1 p 11 + σ r 1 v 0 σ θ 1 E 1 p 12 ] Δ n z = 1 2 n 0 3 [ ε z 1 ( p 11 2 v 0 p 12 ) + 2 σ r 1 σ θ 1 E 1 p 12 ]
d n eff d X = ( d n eff / d X ) D + ( d n eff / d X ) N
S = 1 φ Δ φ ε = ( 1 2 ) λ N f n eff Δ L ,

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