Abstract

The dynamics of gas flow in a hollow core photonic bandgap fiber is studied over four decades of pressure covering free molecular flow as well as hydrodynamic flow. Expressions are derived that allow for determination of the pressure inside the fiber as a function of time and position in the limits of Knudsen number Kn1 and Kn1. The expressions, which are validated by using absorption lines of acetylene as probes of the pressure inside the fiber, provide a straightforward way of predicting the temporal response for gas sensors of any fiber geometry.

© 2008 Optical Society of America

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References

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  1. P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
    [CrossRef]
  2. P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729-4749 (2006).
    [CrossRef]
  3. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
    [CrossRef]
  4. Y. Hoo, W. Jin, C. Shi, H. Ho, D. Wang, and S. Huan, “Design and modeling of a photonic crystal fiber gas sensor,” Appl. Opt. 42, 3509-3515 (2003).
    [CrossRef]
  5. T. Ritari, J. Tuominen, H. Ludvigsen, J. Petersen, T. Sorensen, T. Hansen, and H. Simonsen, “Gas sensing using air-guiding photonic bandgap fibers,” Opt. Express 12, 4080-4087 (2004).
    [CrossRef]
  6. J. Pawlat, T. Sugiyama, T. Matsuo, and T. Ueda, “Photonic bandgap fiber for a sensing device,” IEE Trans. Sensors Micromachines 127, 160-164 (2007).
  7. F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).
  8. S. Ghosh, J. Sharping, D. Ouzounov, and A. L. Gaeta, “Resonant optical interaction with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
    [CrossRef]
  9. J. Henningsen, J. Hald, and J. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13, 10475-10482 (2005).
    [CrossRef]
  10. R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L. Weaver, and K. L. Corwin, “Saturated absorption spectroscopy of acetylene gas inside large core photonic bandgap fiber,” Opt. Lett. 31, 2489-2491, (2006).
    [CrossRef]
  11. F. Couny, P. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 236, 28-31 (2006).
    [CrossRef]
  12. J. Hald, J. Henningsen, and J. Petersen, “Saturated optical absorption by slow molecules in hollow-core photonic bandgap fibers,” Phys. Rev. Lett. 98, 213902 (2007).
    [CrossRef]
  13. Y. Hoo, W. Jin, H. Ho, and D. Wang, “Measurement of gas diffusion coefficient using photonic crystal fiber,” IEEE Photon. Tecnol. Lett. 15, 1434-1436 (2003).
  14. Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).
  15. http://crystal-fibre.com
  16. M. Knudsen, “Die Gesetze der Molekularstroemung und der inneren Reibungsstroemung der Gase durch Roehren,” Ann. Phys. 333, 75-130 (1909).
  17. E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, 1938).
  18. R. Present, Kinetic Theory of Gases (McGraw-Hill, 1958).
  19. B. Lautrup, Physics of Continuous Matter (IOP Publishing Ltd., 2005).
  20. R. S. Mulliken and W. C. Ermler, Polyatomic Molecules (Academic, 1981).
  21. H. Babovsky, “On Knudsen flows within thin tubes,” J. Stat. Phys. 44, 865-878 (1986).
    [CrossRef]
  22. W. Swann and S. Gilbert, “Pressure-induced shift and broadening of 1510-1540 nm acetylene wavelength calibration lines,” J. Opt. Soc. Am. B 17, 1263-1270 (2000).
    [CrossRef]
  23. M. Kusaba and J. Henningsen, “The ν1+ν3 and the ν1+ν2+ν14+ν5-1 combination bands of 13C2H2 linestrengths, broadening parameters, and pressure shifts,” J. Mol. Spectrosc. 209, 216 (2001).
    [CrossRef]
  24. B. J. Bailey, “The viscosity of carbon dioxide and acetylene at atmospheric pressure,” J. Phys. D 3, 550-562 (1970).
  25. C. J. Hensley, D. H. Broaddus, C. B. Schaffer, and A. L. Gaeta, “Photonic band-gap fiber gas cell fabricated using femtosecond micromachining,” Opt. Express 15, 6690-6695 (2007).
    [CrossRef]
  26. A. van Brakel, C. Grivas, M. N. Petrovich, and D. J. Richardson, “Micro-channels machined in microstructured optical fibers by femtosecond laser,” Opt. Express 15, 8731-8736 (2007).
    [CrossRef]

2007 (4)

J. Pawlat, T. Sugiyama, T. Matsuo, and T. Ueda, “Photonic bandgap fiber for a sensing device,” IEE Trans. Sensors Micromachines 127, 160-164 (2007).

J. Hald, J. Henningsen, and J. Petersen, “Saturated optical absorption by slow molecules in hollow-core photonic bandgap fibers,” Phys. Rev. Lett. 98, 213902 (2007).
[CrossRef]

C. J. Hensley, D. H. Broaddus, C. B. Schaffer, and A. L. Gaeta, “Photonic band-gap fiber gas cell fabricated using femtosecond micromachining,” Opt. Express 15, 6690-6695 (2007).
[CrossRef]

A. van Brakel, C. Grivas, M. N. Petrovich, and D. J. Richardson, “Micro-channels machined in microstructured optical fibers by femtosecond laser,” Opt. Express 15, 8731-8736 (2007).
[CrossRef]

2006 (3)

R. Thapa, K. Knabe, M. Faheem, A. Naweed, O. L. Weaver, and K. L. Corwin, “Saturated absorption spectroscopy of acetylene gas inside large core photonic bandgap fiber,” Opt. Lett. 31, 2489-2491, (2006).
[CrossRef]

F. Couny, P. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 236, 28-31 (2006).
[CrossRef]

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729-4749 (2006).
[CrossRef]

2005 (4)

F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).

S. Ghosh, J. Sharping, D. Ouzounov, and A. L. Gaeta, “Resonant optical interaction with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

J. Henningsen, J. Hald, and J. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13, 10475-10482 (2005).
[CrossRef]

Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).

2004 (1)

2003 (3)

Y. Hoo, W. Jin, H. Ho, and D. Wang, “Measurement of gas diffusion coefficient using photonic crystal fiber,” IEEE Photon. Tecnol. Lett. 15, 1434-1436 (2003).

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef]

Y. Hoo, W. Jin, C. Shi, H. Ho, D. Wang, and S. Huan, “Design and modeling of a photonic crystal fiber gas sensor,” Appl. Opt. 42, 3509-3515 (2003).
[CrossRef]

2001 (1)

M. Kusaba and J. Henningsen, “The ν1+ν3 and the ν1+ν2+ν14+ν5-1 combination bands of 13C2H2 linestrengths, broadening parameters, and pressure shifts,” J. Mol. Spectrosc. 209, 216 (2001).
[CrossRef]

2000 (1)

1999 (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

1986 (1)

H. Babovsky, “On Knudsen flows within thin tubes,” J. Stat. Phys. 44, 865-878 (1986).
[CrossRef]

1970 (1)

B. J. Bailey, “The viscosity of carbon dioxide and acetylene at atmospheric pressure,” J. Phys. D 3, 550-562 (1970).

1909 (1)

M. Knudsen, “Die Gesetze der Molekularstroemung und der inneren Reibungsstroemung der Gase durch Roehren,” Ann. Phys. 333, 75-130 (1909).

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

Babovsky, H.

H. Babovsky, “On Knudsen flows within thin tubes,” J. Stat. Phys. 44, 865-878 (1986).
[CrossRef]

Bailey, B. J.

B. J. Bailey, “The viscosity of carbon dioxide and acetylene at atmospheric pressure,” J. Phys. D 3, 550-562 (1970).

Benabid, F.

F. Couny, P. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 236, 28-31 (2006).
[CrossRef]

F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).

Birks, T.

F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

Broaddus, D. H.

Corwin, K. L.

Couny, F.

F. Couny, P. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 236, 28-31 (2006).
[CrossRef]

F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

Ermler, W. C.

R. S. Mulliken and W. C. Ermler, Polyatomic Molecules (Academic, 1981).

Faheem, M.

Gaeta, A. L.

C. J. Hensley, D. H. Broaddus, C. B. Schaffer, and A. L. Gaeta, “Photonic band-gap fiber gas cell fabricated using femtosecond micromachining,” Opt. Express 15, 6690-6695 (2007).
[CrossRef]

S. Ghosh, J. Sharping, D. Ouzounov, and A. L. Gaeta, “Resonant optical interaction with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Ghosh, S.

S. Ghosh, J. Sharping, D. Ouzounov, and A. L. Gaeta, “Resonant optical interaction with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Gilbert, S.

Grivas, C.

Hald, J.

J. Hald, J. Henningsen, and J. Petersen, “Saturated optical absorption by slow molecules in hollow-core photonic bandgap fibers,” Phys. Rev. Lett. 98, 213902 (2007).
[CrossRef]

J. Henningsen, J. Hald, and J. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13, 10475-10482 (2005).
[CrossRef]

Hansen, T.

Henningsen, J.

J. Hald, J. Henningsen, and J. Petersen, “Saturated optical absorption by slow molecules in hollow-core photonic bandgap fibers,” Phys. Rev. Lett. 98, 213902 (2007).
[CrossRef]

J. Henningsen, J. Hald, and J. Petersen, “Saturated absorption in acetylene and hydrogen cyanide in hollow-core photonic bandgap fibers,” Opt. Express 13, 10475-10482 (2005).
[CrossRef]

M. Kusaba and J. Henningsen, “The ν1+ν3 and the ν1+ν2+ν14+ν5-1 combination bands of 13C2H2 linestrengths, broadening parameters, and pressure shifts,” J. Mol. Spectrosc. 209, 216 (2001).
[CrossRef]

Hensley, C. J.

Ho, H.

Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).

Y. Hoo, W. Jin, H. Ho, and D. Wang, “Measurement of gas diffusion coefficient using photonic crystal fiber,” IEEE Photon. Tecnol. Lett. 15, 1434-1436 (2003).

Y. Hoo, W. Jin, C. Shi, H. Ho, D. Wang, and S. Huan, “Design and modeling of a photonic crystal fiber gas sensor,” Appl. Opt. 42, 3509-3515 (2003).
[CrossRef]

Hoo, Y.

Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).

Y. Hoo, W. Jin, H. Ho, and D. Wang, “Measurement of gas diffusion coefficient using photonic crystal fiber,” IEEE Photon. Tecnol. Lett. 15, 1434-1436 (2003).

Y. Hoo, W. Jin, C. Shi, H. Ho, D. Wang, and S. Huan, “Design and modeling of a photonic crystal fiber gas sensor,” Appl. Opt. 42, 3509-3515 (2003).
[CrossRef]

Huan, S.

Jin, W.

Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).

Y. Hoo, W. Jin, H. Ho, and D. Wang, “Measurement of gas diffusion coefficient using photonic crystal fiber,” IEEE Photon. Tecnol. Lett. 15, 1434-1436 (2003).

Y. Hoo, W. Jin, C. Shi, H. Ho, D. Wang, and S. Huan, “Design and modeling of a photonic crystal fiber gas sensor,” Appl. Opt. 42, 3509-3515 (2003).
[CrossRef]

Ju, J.

Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).

Kennard, E. H.

E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, 1938).

Knabe, K.

Knight, J.

F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

Knudsen, M.

M. Knudsen, “Die Gesetze der Molekularstroemung und der inneren Reibungsstroemung der Gase durch Roehren,” Ann. Phys. 333, 75-130 (1909).

Kusaba, M.

M. Kusaba and J. Henningsen, “The ν1+ν3 and the ν1+ν2+ν14+ν5-1 combination bands of 13C2H2 linestrengths, broadening parameters, and pressure shifts,” J. Mol. Spectrosc. 209, 216 (2001).
[CrossRef]

Lautrup, B.

B. Lautrup, Physics of Continuous Matter (IOP Publishing Ltd., 2005).

Light, P.

F. Couny, P. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 236, 28-31 (2006).
[CrossRef]

Ludvigsen, H.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

Matsuo, T.

J. Pawlat, T. Sugiyama, T. Matsuo, and T. Ueda, “Photonic bandgap fiber for a sensing device,” IEE Trans. Sensors Micromachines 127, 160-164 (2007).

Mulliken, R. S.

R. S. Mulliken and W. C. Ermler, Polyatomic Molecules (Academic, 1981).

Naweed, A.

Ouzounov, D.

S. Ghosh, J. Sharping, D. Ouzounov, and A. L. Gaeta, “Resonant optical interaction with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Pawlat, J.

J. Pawlat, T. Sugiyama, T. Matsuo, and T. Ueda, “Photonic bandgap fiber for a sensing device,” IEE Trans. Sensors Micromachines 127, 160-164 (2007).

Petersen, J.

Petrovich, M. N.

Present, R.

R. Present, Kinetic Theory of Gases (McGraw-Hill, 1958).

Richardson, D. J.

Ritari, T.

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

Russel, P. J.

F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).

Russell, P. St. J.

P. St. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. 24, 4729-4749 (2006).
[CrossRef]

F. Couny, P. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 236, 28-31 (2006).
[CrossRef]

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

Schaffer, C. B.

Sharping, J.

S. Ghosh, J. Sharping, D. Ouzounov, and A. L. Gaeta, “Resonant optical interaction with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Shi, C.

Simonsen, H.

Sorensen, T.

Sugiyama, T.

J. Pawlat, T. Sugiyama, T. Matsuo, and T. Ueda, “Photonic bandgap fiber for a sensing device,” IEE Trans. Sensors Micromachines 127, 160-164 (2007).

Swann, W.

Thapa, R.

Tuominen, J.

Ueda, T.

J. Pawlat, T. Sugiyama, T. Matsuo, and T. Ueda, “Photonic bandgap fiber for a sensing device,” IEE Trans. Sensors Micromachines 127, 160-164 (2007).

van Brakel, A.

Wang, D.

Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).

Y. Hoo, W. Jin, H. Ho, and D. Wang, “Measurement of gas diffusion coefficient using photonic crystal fiber,” IEEE Photon. Tecnol. Lett. 15, 1434-1436 (2003).

Y. Hoo, W. Jin, C. Shi, H. Ho, D. Wang, and S. Huan, “Design and modeling of a photonic crystal fiber gas sensor,” Appl. Opt. 42, 3509-3515 (2003).
[CrossRef]

Weaver, O. L.

Ann. Phys. (1)

M. Knudsen, “Die Gesetze der Molekularstroemung und der inneren Reibungsstroemung der Gase durch Roehren,” Ann. Phys. 333, 75-130 (1909).

Appl. Opt. (1)

IEE Trans. Sensors Micromachines (1)

J. Pawlat, T. Sugiyama, T. Matsuo, and T. Ueda, “Photonic bandgap fiber for a sensing device,” IEE Trans. Sensors Micromachines 127, 160-164 (2007).

IEEE Photon. Tecnol. Lett. (1)

Y. Hoo, W. Jin, H. Ho, and D. Wang, “Measurement of gas diffusion coefficient using photonic crystal fiber,” IEEE Photon. Tecnol. Lett. 15, 1434-1436 (2003).

J. Lightwave Technol. (1)

J. Mol. Spectrosc. (1)

M. Kusaba and J. Henningsen, “The ν1+ν3 and the ν1+ν2+ν14+ν5-1 combination bands of 13C2H2 linestrengths, broadening parameters, and pressure shifts,” J. Mol. Spectrosc. 209, 216 (2001).
[CrossRef]

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

J. Phys. D (1)

B. J. Bailey, “The viscosity of carbon dioxide and acetylene at atmospheric pressure,” J. Phys. D 3, 550-562 (1970).

J. Stat. Phys. (1)

H. Babovsky, “On Knudsen flows within thin tubes,” J. Stat. Phys. 44, 865-878 (1986).
[CrossRef]

Nature (1)

F. Benabid, F. Couny, J. Knight, T. Birks, and P. J. Russel, “Compact, stable and efficient all-fiber gas cells using hollow-core photonic crystal fibers,” Nature 434, 488-491 (2005).

Opt. Commun. (1)

F. Couny, P. Light, F. Benabid, and P. St. J. Russell, “Electromagnetically induced transparency and saturable absorption in all-fiber devices based on 12C2H2-filled hollow-core photonic crystal fiber,” Opt. Commun. 236, 28-31 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

S. Ghosh, J. Sharping, D. Ouzounov, and A. L. Gaeta, “Resonant optical interaction with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

J. Hald, J. Henningsen, and J. Petersen, “Saturated optical absorption by slow molecules in hollow-core photonic bandgap fibers,” Phys. Rev. Lett. 98, 213902 (2007).
[CrossRef]

Science (2)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537-1539 (1999).
[CrossRef]

P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef]

Sens. Actuators B (1)

Y. Hoo, W. Jin, H. Ho, J. Ju, and D. Wang, “Gas diffusion measurement using hollow-core photonic bandgap fiber,” Sens. Actuators B 105, 183-186 (2005).

Other (5)

http://crystal-fibre.com

E. H. Kennard, Kinetic Theory of Gases (McGraw-Hill, 1938).

R. Present, Kinetic Theory of Gases (McGraw-Hill, 1958).

B. Lautrup, Physics of Continuous Matter (IOP Publishing Ltd., 2005).

R. S. Mulliken and W. C. Ermler, Polyatomic Molecules (Academic, 1981).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Flow regimes in terms of Knudsen number K n = λ / d .

Fig. 3
Fig. 3

Spatial variation of normalized pressure κ = p / p 0 as a function of normalized position ξ = x / L in the free molecular flow regime at dimensionless times t f = 0.001 , 0.015, 0.05, 0.1, and 0.2, for venting in the upper graph, and for filling in the lower graph.

Fig. 4
Fig. 4

Spatial variation of normalized pressure κ = p / p 0 as a function of normalized position ξ = x / L in the hydrodynamic regime at dimensionless times t h = 0.002 , 0.03, 0.10, 0.20, and 0.40, for venting in the upper graph, and for filling in the lower graph.

Fig. 5
Fig. 5

Dimensionless graphs representing the dynamics for all combinations of parameters in the free molecular flow regime (dotted lines) and the hydrodynamic regime (full lines). The more rapid temporal development in the free molecular flow regime is only apparent, since different scale factors apply in the two regimes.

Fig. 6
Fig. 6

Measured temporal dependence for filling and venting of three different fibers with 10 μm core in the free molecular flow regime (upper graph). The lower graph displays the results for the 3.66 m fiber together with the sum of the filling and venting recordings.

Fig. 7
Fig. 7

Filling curves (open) and venting curves (filled) for 10 m fiber with 20 μm core at 6.3 kPa (squares) and 54 kPa (circles) compared with predictions of the hydrodynamic model (solid lines) and the free molecular flow model (dotted lines). Note that for the latter case only one set of curves is given, since the dynamics is pressure independent.

Fig. 8
Fig. 8

Measured scale factors K f for free molecular flow plotted as a function of the values calculated from Eq. (8) with the known fiber parameters. Results for filling are shown with circles, and results for venting with squares.

Fig. 9
Fig. 9

Scale factors as a function of pressure for L = 10 m and d = 20 μm , circles derived from the free flow model and squares from the hydrodynamic model. The theoretical scale factor K f from Eq. (8) for the free molecular flow regime is shown as the dotted line and K h from Eq. (15) for the hydrodynamic regime as the solid line.

Equations (34)

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

n t = Φ x ,
λ = k T 2 π d m o l 2 p ,
Φ = D n x .
D = 1 3 < v > d ,
< v > = 8 k T π m
n t = D 2 n x 2 .
κ t f = 2 κ ξ 2 ,
t = 3 L 2 < v > d t f K f t f .
f i l l i n g { κ = 0 for 0 < ξ < 1 κ = 1 elsewhere ,
v e n t i n g { κ = 1 for 0 < ξ < 1 κ = 0 elsewhere .
κ v e n t ( ξ , t f ) = 4 π μ = 0 sin ( ( 2 μ + 1 ) π ξ 2 μ + 1 exp { ( 2 μ + 1 ) 2 π 2 t f } ,
κ f i l l ( ξ , t f ) = 1 κ v e n t ( ξ , t f ) .
Q = π d 4 128 η p x ,
Φ = Q n A ,
p t = d 2 32 η x ( p p x ) ,
κ t h = ξ ( κ κ ξ ) ,
t = 32 η L 2 d 2 p 0 t h K h t h .
1 n 0 L 0 L n ( x , t f , h ) d x = 0 1 κ ( ξ , t f , h ) d ξ F ( t f , h ) .
α ( x , t f , h , ν ν 0 ) = S n ( x , t f , h ) g ( ν ν 0 ) ,
g V ( ν ν 0 ) = 1 Δ ν D ln 2 π Re [ w ( x + i y ) ] ,
w ( z ) = exp ( z 2 ) erfc ( i z ) ,
x = ν ν 0 Δ ν D ln 2 ,
y = Δ ν L Δ ν D ln 2 ,
P ( x ) P ( x + d x ) = α f P ( x ) d x + d x 0 d / 2 I ( r , x ) S n ( x , t f , h ) g ( ν ν 0 ) 2 π r d r ,
ρ 0 I ( r , x ) 2 π r d r 0 d / 2 I ( r , x ) 2 π r d r ,
d P d x = P ( x ) [ α f + ρ S g V ( ν ν 0 ) n ( x , t f , h ) ] ,
ln P ( L ) P ( 0 ) = α f L ρ S g V ( ν ν 0 ) 0 L n ( x , t f , h ) d x .
ln P off ( L ) P ( 0 ) = α f L ,
A ( ν , t f , h ) ln P ( L ) P off ( L ) = ρ S g V ( ν ν 0 ) 0 L n ( x , t f , h ) d x .
g V ( ν ν 0 ) d ν = 1 ,
A ( ν , t f , h ) d ν = S ρ 0 L n ( x , t f , h ) d x .
A ( ν , t f , h ) d ν A e q ( ν , t f , h ) d ν = 0 1 κ ( ξ , t f , h ) d ξ = F ( t f , h ) .
F vent ( t f ) = 8 π 2 μ = 0 exp { ( 2 μ + 1 ) 2 π 2 t f } ( 2 μ + 1 ) 2 ,
F fill ( t f ) = 1 F vent ( t f ) .

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