Abstract

We present useful expressions predicting the filling time of gaseous species inside photonic crystal fibers. Based on the theory of diffusion, this gas-filling model can be applied to any given fiber geometry or length by calculating diffusion coefficients. This was experimentally validated by monitoring the filling process of acetylene gas in several fiber samples of various geometries and lengths. The measured filling times agree well, within ±15%, with the predicted values for all fiber samples. In addition, the pressure dependence of the diffusion coefficient was experimentally verified by filling a given fiber sample with acetylene gas at various pressures. Finally, optimized conditions for gas–light interaction are determined by considering the gas flow dynamics in the design of microstructured fibers for gas detection and all-fiber gas cell applications.

© 2010 Optical Society of America

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References

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    [CrossRef]
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2009

F. Couny and F. Benabid, “Optical frequency comb generation in gas-filled hollow core photonic crystal fibres,” J. Opt. A Pure Appl. Opt. 11, 103002 (2009).
[CrossRef]

P. S. Light, F. Couny, Y. Y. Wang, N. V. Wheeler, P. J. Roberts, and F. Benabid, “Double photonic bandgap hollow-core photonic crystal fiber,” Opt. Express 17, 16238–16243 (2009).
[CrossRef] [PubMed]

2008

N. Gayraud, Ł. W. Kornaszewski, J. M. Stone, J. C. Knight, D. T. Reid, D. P. Hand, and W. N. MacPherson, “Mid-infrared gas sensing using a photonic bandgap fiber,” Appl. Opt. 47, 1269–1277 (2008).
[PubMed]

J. Henningsen and J. Hald, “Dynamics of gas flow in hollow core photonic bandgap fibers,” Appl. Opt. 47, 2790–2797(2008).
[CrossRef] [PubMed]

L. Dong, B. K. Thomas, and L. Fu, “Highly nonlinear silica suspended core fibers,” Opt. Express 16, 16423–16430 (2008).
[CrossRef] [PubMed]

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

2007

2006

2005

2004

2003

2000

Barretto, E. C. S.

Benabid, F.

Beugnot, J.-C.

S. Chin, I. Dicaire, J.-C. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thévenaz, “Material slow light does not enhance Beer-Lambert absorption,” in Slow and Fast Light (Optical Society of America, 2009), paper SMA3.

Bond, K. S.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Chen, J. S. Y.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

Cheng, T.-L.

Chesini, G.

Chin, S.

S. Chin, I. Dicaire, J.-C. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thévenaz, “Material slow light does not enhance Beer-Lambert absorption,” in Slow and Fast Light (Optical Society of America, 2009), paper SMA3.

Collett, N. D.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Cordeiro, C. M. B.

Couny, F.

Cruz, C. H. B.

Cunningham, R.

R. Cunningham and R. Williams, Diffusion in Gases and Porous Media (Plenum, 1980).

Dicaire, I.

S. Chin, I. Dicaire, J.-C. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thévenaz, “Material slow light does not enhance Beer-Lambert absorption,” in Slow and Fast Light (Optical Society of America, 2009), paper SMA3.

Dong, L.

Dushman, S.

S. Dushman and J. M. Lafferty, Scientific Foundations of Vacuum Technique (Wiley, 1962).

Euser, T. G.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

Farrer, N. J.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

Fini, J. M.

J. M. Fini, “Microstructure fibres for optical sensing in gases and liquids,” Meas. Sci. Technol. 15, 1120–1128 (2004).
[CrossRef]

Foaleng-Mafang, S.

S. Chin, I. Dicaire, J.-C. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thévenaz, “Material slow light does not enhance Beer-Lambert absorption,” in Slow and Fast Light (Optical Society of America, 2009), paper SMA3.

Franco, M. A. R.

Fu, L.

Fuller, E. P.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Gayraud, N.

Gilbert, S. L.

Gonzalez-Herraez, M.

S. Chin, I. Dicaire, J.-C. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thévenaz, “Material slow light does not enhance Beer-Lambert absorption,” in Slow and Fast Light (Optical Society of America, 2009), paper SMA3.

Hald, J.

Han, Y.

Hand, D. P.

Hansen, T.

Hardwick, J. L.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Henningsen, J.

Hinds, E. E.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Ho, H. L.

Hoo, Y. L.

Hou, L.-T.

Jin, W.

Jost, W.

W. Jost, Diffusion in Solids, Liquids, Gases (Academic, 1970).

Keiber, T. W.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Kelly-Morgan, I. S. G.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Knight, J. C.

Kornaszewski, L. W.

Lafferty, J. M.

S. Dushman and J. M. Lafferty, Scientific Foundations of Vacuum Technique (Wiley, 1962).

Large, M. C. J.

Li, S.-G.

Light, P. S.

Liu, S.-Y.

Ludvigsen, H.

Lwin, R.

MacPherson, W. N.

Matthys, C. M.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

O’Hanlon, J.

J. O’Hanlon, A User’s Guide to Vacuum Technology(Wiley, 2003).
[CrossRef]

Petersen, J.

Peterson, J. C.

Pilkenton, M. J.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Poletti, F.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, “Suspended-core holey fiber for evanescent-field sensing,” Opt. Eng. 46, 010503 (2007).
[CrossRef]

Reid, D. T.

Richardson, D. J.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, “Suspended-core holey fiber for evanescent-field sensing,” Opt. Eng. 46, 010503 (2007).
[CrossRef]

Ritari, T.

Roberts, P. J.

Ruan, S. C.

Russell, P. St. J.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

Sadler, P. J.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

Sahu, J. K.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, “Suspended-core holey fiber for evanescent-field sensing,” Opt. Eng. 46, 010503 (2007).
[CrossRef]

Scharrer, M.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

Shi, C.

Simonsen, H.

Sinclair, K. W.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Song, Z.-Y.

Sørensen, T.

Stone, J. M.

Swann, W. C.

Taylor, A. A.

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

Thévenaz, L.

S. Chin, I. Dicaire, J.-C. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thévenaz, “Material slow light does not enhance Beer-Lambert absorption,” in Slow and Fast Light (Optical Society of America, 2009), paper SMA3.

Thomas, B. K.

Tuominen, J.

Wang, D. N.

Wang, Y. Y.

Webb, A. S.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, “Suspended-core holey fiber for evanescent-field sensing,” Opt. Eng. 46, 010503 (2007).
[CrossRef]

Wheeler, N. V.

Williams, R.

R. Cunningham and R. Williams, Diffusion in Gases and Porous Media (Plenum, 1980).

Yaws, C. L.

C. L. Yaws, Handbook of Transport Property Data: Viscosity, Thermal Conductivity, and Diffusion Coefficients of Liquids and Gases (Gulf, 1995).

Zhou, G.-Y.

Appl. Opt.

Appl. Phys. B

K. S. Bond, N. D. Collett, E. P. Fuller, J. L. Hardwick, E. E. Hinds, T. W. Keiber, I. S. G. Kelly-Morgan, C. M. Matthys, M. J. Pilkenton, K. W. Sinclair, and A. A. Taylor, “Temperature dependence of pressure broadening and shifts of acetylene at 1550nm by He, Ne, and Ar,” Appl. Phys. B 90, 255–262 (2008).
[CrossRef]

J. Appl. Phys.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, “Quantitative broadband chemical sensing in air-suspended solid-core fibers,” J. Appl. Phys. 103, 103108 (2008).
[CrossRef]

J. Opt. A Pure Appl. Opt.

F. Couny and F. Benabid, “Optical frequency comb generation in gas-filled hollow core photonic crystal fibres,” J. Opt. A Pure Appl. Opt. 11, 103002 (2009).
[CrossRef]

J. Opt. Soc. Am. B

Meas. Sci. Technol.

J. M. Fini, “Microstructure fibres for optical sensing in gases and liquids,” Meas. Sci. Technol. 15, 1120–1128 (2004).
[CrossRef]

Opt. Eng.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, “Suspended-core holey fiber for evanescent-field sensing,” Opt. Eng. 46, 010503 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Other

S. Dushman and J. M. Lafferty, Scientific Foundations of Vacuum Technique (Wiley, 1962).

R. Cunningham and R. Williams, Diffusion in Gases and Porous Media (Plenum, 1980).

W. Jost, Diffusion in Solids, Liquids, Gases (Academic, 1970).

C. L. Yaws, Handbook of Transport Property Data: Viscosity, Thermal Conductivity, and Diffusion Coefficients of Liquids and Gases (Gulf, 1995).

S. Chin, I. Dicaire, J.-C. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thévenaz, “Material slow light does not enhance Beer-Lambert absorption,” in Slow and Fast Light (Optical Society of America, 2009), paper SMA3.

J. O’Hanlon, A User’s Guide to Vacuum Technology(Wiley, 2003).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Calculated diffusion coefficients of acetylene gas for several capillary diameters. The various flow regimes are defined according to the two blue diagonal lines representing Knudsen numbers of 1 and 0.01.

Fig. 2
Fig. 2

Calculated diffusion coefficient of acetylene gas for several hole diameters in the slip-flow regime according to Eqs. (11, 12).

Fig. 3
Fig. 3

Measured average pressure as a function of time in A, a suspended-core PCF; B, a microstructured-core PCF; and C, a solid-core PCF. The black curves represent nonlinear fittings of Eq. (13) from which experimental diffusion coefficients can be obtained. All scale bars represent 20 μm .

Fig. 4
Fig. 4

Calculated diffusion coefficient for acetylene gas diffusing in suspended-core fibers ( 11.8 μm hole diameter; scale bar, 10 μm ) with average pressures taken as 2 / 3 of the filling pressures. The data points represent experimental diffusion coefficients obtained using Eq. (11).

Fig. 5
Fig. 5

Contours of constant filling time are plotted in the 2 a L plane for a filling pressure of 100 mbar s according to Eqs. (11, 15) ( P / P 0 = 85 % ).

Tables (1)

Tables Icon

Table 1 Characteristics of the Microstructured Fibers

Equations (18)

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

Φ = D n x ,
n t = Φ x .
K n = λ / a , λ = k B T 2 π P ¯ δ 2 ,
Φ k = 2 3 a v ¯ k B T p x ,
v ¯ = 8 k B T π m .
D k = 2 3 a v ¯ .
Φ v = a 2 n 8 η p x ,
η = v ¯ m 2 2 π δ 2 .
D v = a 2 p 8 η .
Φ = Φ v + Z ( K n ) Φ k .
D = a 2 p 8 η + Z ( K n ) 2 3 a v ¯ ,
Z = 1 + 2.507 ( a / λ ) 1 + 3.095 ( a / λ ) = 1 + 2.507 / K n 1 + 3.095 / K n .
P ( t ) P 0 = 1 8 π 2 j = 1 , 3 , 5 1 j 2 exp [ ( j π ξ L ) 2 D t ] ,
P = 85 % P 0 .
t fill = ( ξ L ) 2 π 2 D ln [ π 2 8 × P 0 P 0 P ]
D = a 2 P ¯ 8 η + Z ( K n ) 2 3 a v ¯ ,
P ( t ) P 0 = ln ( I ( t , ν ) / I 0 ( ν ) ) d ν ln ( I fill ( t fill , ν ) / I 0 ( ν ) ) d ν .
Δ ν V = 0.5346 Δ ν L + 0.2169 Δ ν L 2 + Δ ν G 2 ,

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