Abstract

A major limitation to attaining low-loss single-mode guidance in hollow core photonic crystal fibre (PCF) is surface guided modes that are trapped in the core surround. This is particularly severe when high index (n > 2) glasses are used. By modelling a structure that has the characteristic features of a realistic fibre we show that, by tuning the thickness of the core wall, the influence of these ‘surface’ modes can be minimised. For a refractive index of 2.4 we predict power-in-air fractions of over 95% over a fractional bandwidth of ~ 5%, peaking at over 98%. The designs are appropriate for mid- to far-IR PCFs for which suitable glasses (e.g., tellurites and chalcogenides) have high refractive indices.

© 2005 Optical Society of America

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    [Crossref] [PubMed]
  3. F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
    [Crossref] [PubMed]
  4. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers,” Phys. Rev. Lett. 94, 093902 (2005).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2005 (3)

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

G. J. Pearce, T. D. Hedley, and D. M. Bird, “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals,” Phys. Rev. B 71, 195108 (2005).
[Crossref]

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

2004 (7)

J. A. West, C. M. Smith, N. F. Borrelli, D. C. Allen, and K. W. Koch, “Surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1485–1496 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

K. Saitoh, N. A. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12, 394–400 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394
[Crossref] [PubMed]

M. J. F. Digonnet, H. K. Kim, J. Shin, S. Fan, and G. S. Kino, “Simple geometric criterion to predict the existence of surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1864–1872 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1884
[Crossref] [PubMed]

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing Air-Core Photonic-Bandgap Fibers Free of Surface Modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[Crossref]

H. K. Kim, M. J. F. Digonnet, G. S. Kino, J. Shin, and S. Fan, “Simulations of the effect of the core ring on surface and air-core modes in photonic bandgap fibers,” Opt. Express 12, 3436–3442 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3436
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
[Crossref] [PubMed]

2003 (5)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2854
[Crossref] [PubMed]

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

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

R. Guobin, W. Zhi, L. Shuqin, and J. Shuisheng, “Mode classification and degeneracy in photonic crystal fibers,” Opt. Express ur 11, 1310–1321 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1310
[Crossref] [PubMed]

2002 (1)

2001 (1)

2000 (1)

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[Crossref]

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, 1537–1439 (1999).
[Crossref] [PubMed]

1994 (1)

J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3, 187–203 (1994).
[Crossref]

Abeeluck, A. K.

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (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, 1537–1439 (1999).
[Crossref] [PubMed]

Allen, D. C.

Barrett, R.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Benabid, F.

F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
[Crossref] [PubMed]

Berry, M.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Bird, D. M.

Birks, T. A.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2854
[Crossref] [PubMed]

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, 1537–1439 (1999).
[Crossref] [PubMed]

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

Borrelli, N. F.

J. A. West, C. M. Smith, N. F. Borrelli, D. C. Allen, and K. W. Koch, “Surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1485–1496 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Bouwmans, G.

F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

Broderick, N. G. R.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[Crossref]

Chan, T. F.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Couny, F.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
[Crossref] [PubMed]

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 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, 1537–1439 (1999).
[Crossref] [PubMed]

Demmel, J.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Digonnet, M. J. F.

Donato, J.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Dongarra, J.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Eggleton, B. J.

Eijkhout, V.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Fan, S.

Farr, L.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

Gaeta, A. L.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

Ghosh, S.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Guobin, R.

Headley, C.

Hedley, T. D.

Hewak, D. W.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[Crossref]

Humbert, G.

Joannopoulos, J. D.

Johnson, S. G.

Kim, H. K.

Kino, G. S.

Knight, J. C.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
[Crossref] [PubMed]

J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2854
[Crossref] [PubMed]

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, 1537–1439 (1999).
[Crossref] [PubMed]

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

Koch, K. W.

J. A. West, C. M. Smith, N. F. Borrelli, D. C. Allen, and K. W. Koch, “Surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1485–1496 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Koshiba, M.

Litchinitser, N. M.

Love, J. D.

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

Mangan, B. J.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

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, 1537–1439 (1999).
[Crossref] [PubMed]

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

Mason, M. W.

Monro, T. M.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[Crossref]

Mortensen, N. A.

Müller, D.

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Ouzounov, D. G.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Pearce, G. J.

G. J. Pearce, T. D. Hedley, and D. M. Bird, “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals,” Phys. Rev. B 71, 195108 (2005).
[Crossref]

Pottage, J. M.

Pozo, R.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Richardson, D. J.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[Crossref]

Roberts, P. J.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2854
[Crossref] [PubMed]

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, 1537–1439 (1999).
[Crossref] [PubMed]

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

Romine, C.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Russell, P. St.J.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

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

J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2854
[Crossref] [PubMed]

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, 1537–1439 (1999).
[Crossref] [PubMed]

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

Saad, Y.

Y. Saad, Iterative methods for sparse linear systems (PWS, Boston, 1996).

Sabert, H.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

Saitoh, K.

Sharping, J. E.

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Shin, J.

Shuisheng, J.

Shuqin, L.

Smith, C. M.

J. A. West, C. M. Smith, N. F. Borrelli, D. C. Allen, and K. W. Koch, “Surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1485–1496 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Snitzer, E.

J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3, 187–203 (1994).
[Crossref]

Snyder, A. W.

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

Tomlinson, A.

van der Vorst, H.

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

Venkataraman, N.

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Vogel, E. M.

J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3, 187–203 (1994).
[Crossref]

Wang, J. S.

J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3, 187–203 (1994).
[Crossref]

West, J. A.

J. A. West, C. M. Smith, N. F. Borrelli, D. C. Allen, and K. W. Koch, “Surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1485–1496 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

West, Y. D.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[Crossref]

Williams, D. P.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

Zhang, P.

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

Zhi, W.

Electron. Lett. (1)

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing Air-Core Photonic-Bandgap Fibers Free of Surface Modes,” IEEE J. Quantum Electron. 40, 551–556 (2004).
[Crossref]

Nature (1)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003).
[Crossref] [PubMed]

Opt. Express (9)

R. Guobin, W. Zhi, L. Shuqin, and J. Shuisheng, “Mode classification and degeneracy in photonic crystal fibers,” Opt. Express ur 11, 1310–1321 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-11-1310
[Crossref] [PubMed]

J. M. Pottage, D. M. Bird, T. D. Hedley, T. A. Birks, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express 11, 2854–2861 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2854
[Crossref] [PubMed]

K. Saitoh, N. A. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express 12, 394–400 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394
[Crossref] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. St.J. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, “Hollow core photonic crystal fibers for beam delivery,” Opt. Express 12, 1477–1484 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477
[Crossref] [PubMed]

J. A. West, C. M. Smith, N. F. Borrelli, D. C. Allen, and K. W. Koch, “Surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1485–1496 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485
[Crossref] [PubMed]

M. J. F. Digonnet, H. K. Kim, J. Shin, S. Fan, and G. S. Kino, “Simple geometric criterion to predict the existence of surface modes in air-core photonic-bandgap fibers,” Opt. Express 12, 1864–1872 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1884
[Crossref] [PubMed]

H. K. Kim, M. J. F. Digonnet, G. S. Kino, J. Shin, and S. Fan, “Simulations of the effect of the core ring on surface and air-core modes in photonic bandgap fibers,” Opt. Express 12, 3436–3442 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3436
[Crossref] [PubMed]

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, D. P. Williams, L. Farr, M. W. Mason, A. Tomlinson, T. A. Birks, J. C. Knight, and P. St.J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[Crossref] [PubMed]

Opt. Lett. (1)

Opt. Mater. (1)

J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3, 187–203 (1994).
[Crossref]

Phys. Rev. B (1)

G. J. Pearce, T. D. Hedley, and D. M. Bird, “Adaptive curvilinear coordinates in a plane-wave solution of Maxwell’s equations in photonic crystals,” Phys. Rev. B 71, 195108 (2005).
[Crossref]

Phys. Rev. Lett. (2)

F. Benabid, G. Bouwmans, J. C. Knight, P. St.J. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93, 123903 (2004).
[Crossref] [PubMed]

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant Optical Interactions with Molecules Confined in Photonic Band-Gap Fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref] [PubMed]

Proc. SPIE (1)

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic band-gap fibres,” in Photonic Crystal Materials and Devices, A. Adibi, A. Scherer, and S. Y. Lin, eds., Proc. SPIE 5000 (2003).
[Crossref]

Science (2)

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

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, 1537–1439 (1999).
[Crossref] [PubMed]

Other (5)

P. J. Roberts, F. Couny, T. A. Birks, J. C. Knight, P. St.J. Russell, B. J. Mangan, H. Sabert, D. P. Williams, and L. Farr, “Achieving low loss and low nonlinearity in hollow core photonic crystal fibers,” paper CWA7 presented at CLEO 2005 Baltimore USA, May 2005.

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St.J. Russell are preparing a manuscript to be called “Realizing low loss air core photonic crystal fibres by exploiting an antiresonant core surround.”

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

Y. Saad, Iterative methods for sparse linear systems (PWS, Boston, 1996).

R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1.

Core design of high-index PCF using geometrical shapes, showing air regions in grey (different shades of which are shown for clarity) and glass in white. For simplicity, only the unique 1 12 of the design is given; the remainder may be obtained by applying C 6v symmetry operations. The two large circles lie on the cladding lattice, and the radius s is chosen such that the corresponding circle touches arc A and line B. The adjustable parameters are the cladding hole radius r and the core wall thickness t, which is controlled by the radius R of the central hole; in this paper we consider a fixed hole radius r = 0.4Λ and vary R.

Fig. 2.
Fig. 2.

(a) An SEM image of a typical silica hollow-core fibre (fabricated by Blaze Photonics), and (b) the model design for high-index glass created using geometrical shapes. The core wall thickness in the model design is t = 0.05Λ.

Fig. 3.
Fig. 3.

Mode trajectories for a range of three core wall thicknesses of the PCF design shown in Figs. 1 and 2. The modes are labelled by symmetry according to the notation of [24]; the key to symmetry types is given in Fig. 4. The fundamental air-guided mode is shown by an arrow in each figure.

Fig. 4.
Fig. 4.

Modes of the PCF structure with core wall thickness t = 0.05Λ. The red shaded regions in the top-left and lower-right corners show the band edges, and the air-line is marked with a vertical black line. The fundamental air-guided mode is shown by an arrow.

Fig. 5.
Fig. 5.

Plots of the axial Poynting vector (normalised to unity over the supercell, and shown on a linear scale) for selected surface modes near to the air-line, at frequencies above and below the ‘clean’ region of Fig. 4. Each row of the figure shows two modes of the same symmetry type. The two modes of each doubly-degenerate pair have been added in intensity to show their structure more clearly.

Fig. 6.
Fig. 6.

Plots of the axial Poynting vector (normalised to unity over the supercell, and shown on a linear scale) for the lowest-order air-guided modes of the PCF structure with core wall thickness t = 0.05Λ at frequency k 0Λ = 5.5. The two modes of each doubly-degenerate pair (at βΛ = -0.266,-0.105) have been added in intensity, and the colour scale used is the same as that in Fig. 5.

Equations (4)

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{ t 2 + n 2 k 0 2 + t ln n 2 × t × } h t = β 2 h t ,
P ( M σ I ) w = Pu .
Q ( M ˜ σ I ) y = Qx ,
P air = air S . z ̂ d A S . z ̂ d A ,

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