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]
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    [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)

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

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]

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)

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

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

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

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

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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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