Abstract

We present a theoretical method for analyzing radiation loss from surface roughness scattering in hollow-core photonic bandgap fibers (HC-PBGFs). We treat the scattering process as induced dipole radiation and combine statistical information about surface roughness, mode field distribution and fibre geometry to accurately describe the far-field scattering distribution and loss in fibers with an arbitrary cross-sectional distribution of air holes of any shape. The predicted angular scattering distribution, total scattering loss and the loss wavelength dependence are all shown to agree well with reported experimental data. Our method yields a simpler result than that obtained by more complex approaches and is to the best of our knowledge the first successful attempt to accurately describe roughness scattering in HC-PBGFs.

© 2012 OSA

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    [CrossRef] [PubMed]
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Nature (London)285, 1537–1539 (1999).
  3. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature (London)424, 657–659 (2003).
    [CrossRef]
  4. M. N. Petrovich, F. Poletti, A. van Brakel, and D. J. Richardson, “Robustly single mode hollow core photonic bandgap fiber,” Opt. Express16, 4337–4346 (2008).
    [CrossRef] [PubMed]
  5. B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.
  6. 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. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13236–244 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
    [CrossRef]
  11. V. Dangui, M. J. F. Digonnet, and G. S. Kino, “Modeling of the propagation loss and backscattering in air-core photonic-bandgap fibers,” J. Lightwave Technol.17, 3783–3789 (2009).
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    [CrossRef]
  15. S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. F. Poletti, N. G. R. Broderick, D. J. Richardson, and T. M. Monro, “The effect of core asymmetries on the polarization properties of hollow core photonic bandgap fibers,” Opt. Express139115–9124 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  21. T. Sarlat, A. Lelarge, E Søndergård, and D. Vandembroucq, “Frozen capillary waves on glass surfaces: an AFM study,” Eur. Phys. J. B54, 121–126 (2006).
    [CrossRef]
  22. N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.
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  24. F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt.2, 87–124 (2011).
    [CrossRef]
  25. R. Amezcua-Correa, N. G. R. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Design of 7 and 19 cells core air-guiding photonic crystal fibers for low-loss, wide bandwidth and dispersion controlled operation,” Opt. Express15, 17577–17586 (2007).
    [CrossRef] [PubMed]
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2012

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

2011

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt.2, 87–124 (2011).
[CrossRef]

2009

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

V. Dangui, M. J. F. Digonnet, and G. S. Kino, “Modeling of the propagation loss and backscattering in air-core photonic-bandgap fibers,” J. Lightwave Technol.17, 3783–3789 (2009).
[CrossRef]

2008

2007

2006

T. Sarlat, A. Lelarge, E Søndergård, and D. Vandembroucq, “Frozen capillary waves on glass surfaces: an AFM study,” Eur. Phys. J. B54, 121–126 (2006).
[CrossRef]

2005

2004

P. Mazumder, S. L. Logunov, and S. Raghavan, “Analysis of excess scattering in optical fibers,” J. Appl. Phys.96, 4042–4049 (2004).
[CrossRef]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

2003

P. St. J. Russell, “Photonic crystal fibers,” Science299, 358–362 (2003).
[CrossRef] [PubMed]

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

1999

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

1995

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys. Condens. Matter7, 4351–4358 (1995).
[CrossRef]

1979

1975

1974

1972

1970

A. W. Snyder, “Radiation losses due to variations of radius on dielectric or optical fibers,” IEEE Trans. Microwave Theory Tech.MT18(9) 608–615 (1970).
[CrossRef]

1969

D. Marcuse, “Mode conversion caused by surface imperfection of a dielectric slab waveguide,” Bell Syst. Tech. J.48, 3187–3215 (1969).

Allan, D. C.

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

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

Amezcua-Correa, R.

Baddela, N.

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

Benabid, F.

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt.2, 87–124 (2011).
[CrossRef]

Bennett, J. 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. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13236–244 (2005).
[CrossRef] [PubMed]

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, T. A. Birks, J. C. Knight, and P. S. Russell, “Loss in solid-core photonic crystal fibers due to interface roughness scattering,” Opt. Express13, 7779–7793 (2005).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

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

Borrelli, N. F.

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

Broderick, N. G. R.

Couny, F.

Coupland, S.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Cregan, R. F.

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

Dangui, V.

V. Dangui, M. J. F. Digonnet, and G. S. Kino, “Modeling of the propagation loss and backscattering in air-core photonic-bandgap fibers,” J. Lightwave Technol.17, 3783–3789 (2009).
[CrossRef]

Digonnet, M. J. F.

V. Dangui, M. J. F. Digonnet, and G. S. Kino, “Modeling of the propagation loss and backscattering in air-core photonic-bandgap fibers,” J. Lightwave Technol.17, 3783–3789 (2009).
[CrossRef]

Douay, M.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

Elson, J. M.

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. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13236–244 (2005).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Flea, R.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Gallagher, M. T.

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

Gray, D. R.

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

Hayes, J. R.

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

Jäckle, J.

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys. Condens. Matter7, 4351–4358 (1995).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electodynamics, 3rd ed. (John Wiley and Sons, 1998)

Jacobs, S.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

Johnson, S. G.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

Karalis, A.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
[CrossRef]

Kawasaki, K.

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys. Condens. Matter7, 4351–4358 (1995).
[CrossRef]

Kino, G. S.

V. Dangui, M. J. F. Digonnet, and G. S. Kino, “Modeling of the propagation loss and backscattering in air-core photonic-bandgap fibers,” J. Lightwave Technol.17, 3783–3789 (2009).
[CrossRef]

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. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13236–244 (2005).
[CrossRef] [PubMed]

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, T. A. Birks, J. C. Knight, and P. S. Russell, “Loss in solid-core photonic crystal fibers due to interface roughness scattering,” Opt. Express13, 7779–7793 (2005).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

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

Koch, K. W.

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

Langford, A.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Lawman, M.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Lelarge, A.

T. Sarlat, A. Lelarge, E Søndergård, and D. Vandembroucq, “Frozen capillary waves on glass surfaces: an AFM study,” Eur. Phys. J. B54, 121–126 (2006).
[CrossRef]

Levenson, J. A.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

Logunov, S. L.

P. Mazumder, S. L. Logunov, and S. Raghavan, “Analysis of excess scattering in optical fibers,” J. Appl. Phys.96, 4042–4049 (2004).
[CrossRef]

Love, J. D.

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

Mangan, B. J.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, T. A. Birks, J. C. Knight, and P. S. Russell, “Loss in solid-core photonic crystal fibers due to interface roughness scattering,” Opt. Express13, 7779–7793 (2005).
[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. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13236–244 (2005).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

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

Marcuse, D.

D. Marcuse, “Radiation losses of HE11 mode of a fiber with sinusoidally perturbed core boundary,” Appl. Opt.14, 3021–3025 (1975).
[CrossRef] [PubMed]

D. Marcuse, “Mode conversion caused by surface imperfection of a dielectric slab waveguide,” Bell Syst. Tech. J.48, 3187–3215 (1969).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic Press, 1991).

Mason, M.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Mason, M. W.

Mazumder, P.

P. Mazumder, S. L. Logunov, and S. Raghavan, “Analysis of excess scattering in optical fibers,” J. Appl. Phys.96, 4042–4049 (2004).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

Melin, G.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

Moison, J.-M.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

Monro, T. M.

Muller, D.

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

Numkam Fokoua, E.

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

Petrovich, M. N.

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

M. N. Petrovich, F. Poletti, A. van Brakel, and D. J. Richardson, “Robustly single mode hollow core photonic bandgap fiber,” Opt. Express16, 4337–4346 (2008).
[CrossRef] [PubMed]

R. Amezcua-Correa, N. G. R. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Design of 7 and 19 cells core air-guiding photonic crystal fibers for low-loss, wide bandwidth and dispersion controlled operation,” Opt. Express15, 17577–17586 (2007).
[CrossRef] [PubMed]

Phan-Huy, M.-C.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

Poletti, F.

Povinelli, M. L.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
[CrossRef]

Quiquempois, Y.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

Raghavan, S.

P. Mazumder, S. L. Logunov, and S. Raghavan, “Analysis of excess scattering in optical fibers,” J. Appl. Phys.96, 4042–4049 (2004).
[CrossRef]

Rawson, E. G.

Richard, S.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

Richardson, D. J.

Roberts, P. J.

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt.2, 87–124 (2011).
[CrossRef]

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, T. A. Birks, J. C. Knight, and P. S. Russell, “Loss in solid-core photonic crystal fibers due to interface roughness scattering,” Opt. Express13, 7779–7793 (2005).
[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. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13236–244 (2005).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

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

Russell, P. S.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, T. A. Birks, J. C. Knight, and P. S. Russell, “Loss in solid-core photonic crystal fibers due to interface roughness scattering,” Opt. Express13, 7779–7793 (2005).
[CrossRef] [PubMed]

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

Russell, P. S. J.

Russell, P. St. J.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

P. St. J. Russell, “Photonic crystal fibers,” Science299, 358–362 (2003).
[CrossRef] [PubMed]

Sabert, H.

Sarlat, T.

T. Sarlat, A. Lelarge, E Søndergård, and D. Vandembroucq, “Frozen capillary waves on glass surfaces: an AFM study,” Eur. Phys. J. B54, 121–126 (2006).
[CrossRef]

Slavík, R.

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

Smith, C. M.

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

Snyder, A. W.

A. W. Snyder, “Radiation losses due to variations of radius on dielectric or optical fibers,” IEEE Trans. Microwave Theory Tech.MT18(9) 608–615 (1970).
[CrossRef]

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

Soljacic, M.

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
[CrossRef]

Søndergård, E

T. Sarlat, A. Lelarge, E Søndergård, and D. Vandembroucq, “Frozen capillary waves on glass surfaces: an AFM study,” Eur. Phys. J. B54, 121–126 (2006).
[CrossRef]

Tomlinson, A.

van Brakel, A.

Vandembroucq, D.

T. Sarlat, A. Lelarge, E Søndergård, and D. Vandembroucq, “Frozen capillary waves on glass surfaces: an AFM study,” Eur. Phys. J. B54, 121–126 (2006).
[CrossRef]

Venkataraman, N.

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

West, J. A.

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

Wheeler, N. V.

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

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. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express13236–244 (2005).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

Appl. Opt.

Appl. Phys. B

S. G. Johnson, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Appl. Phys. B81, 283–293 (2005).
[CrossRef]

Bell Syst. Tech. J.

D. Marcuse, “Mode conversion caused by surface imperfection of a dielectric slab waveguide,” Bell Syst. Tech. J.48, 3187–3215 (1969).

Eur. Phys. J. B

T. Sarlat, A. Lelarge, E Søndergård, and D. Vandembroucq, “Frozen capillary waves on glass surfaces: an AFM study,” Eur. Phys. J. B54, 121–126 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

A. W. Snyder, “Radiation losses due to variations of radius on dielectric or optical fibers,” IEEE Trans. Microwave Theory Tech.MT18(9) 608–615 (1970).
[CrossRef]

J. Appl. Phys.

P. Mazumder, S. L. Logunov, and S. Raghavan, “Analysis of excess scattering in optical fibers,” J. Appl. Phys.96, 4042–4049 (2004).
[CrossRef]

J. Lightwave Technol.

V. Dangui, M. J. F. Digonnet, and G. S. Kino, “Modeling of the propagation loss and backscattering in air-core photonic-bandgap fibers,” J. Lightwave Technol.17, 3783–3789 (2009).
[CrossRef]

J. Lightwave. Technol.

M.-C. Phan-Huy, J.-M. Moison, J. A. Levenson, S. Richard, G. Melin, M. Douay, and Y. Quiquempois, “Surface roughness and light scattering in a small effective area microstructured fiber,” J. Lightwave. Technol.27, 1597–1604 (2009).
[CrossRef]

J. Mod. Opt.

F. Benabid and P. J. Roberts, “Linear and nonlinear optical properties of hollow core photonic crystal fiber,” J. Mod. Opt.2, 87–124 (2011).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Condens. Matter

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys. Condens. Matter7, 4351–4358 (1995).
[CrossRef]

Nature (London)

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

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

Opt. Express

Proceedings of Optical Fiber Communication Conference

N. V. Wheeler, M. N. Petrovich, R. Slavík, N. Baddela, E. Numkam Fokoua, J. R. Hayes, D. R. Gray, F. Poletti, and D. J. Richardson “Wide-bandwidth, low-loss, 19-cell hollow core photonic band gap fiber and its potential for low latency data transmission,” in Proceedings of Optical Fiber Communication Conference (2012), paper PDP5A.2.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Low loss (1.7 dB/km) hollow core photonic bandgap fiber,” in Proceedings of Optical Fiber Communication Conference (2004), paper PDP24.

Science

P. St. J. Russell, “Photonic crystal fibers,” Science299, 358–362 (2003).
[CrossRef] [PubMed]

Other

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic Press, 1991).

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

J. D. Jackson, Classical Electodynamics, 3rd ed. (John Wiley and Sons, 1998)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystal: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

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Figures (7)

Fig. 1
Fig. 1

Overlap between Ex component of the field of the fundamental guided mode and glass surfaces in HC-PBGFs with an illustration of the intrinsic roughness present at air-glass interfaces. The contour line are 2dB apart down to 30dB lower than the maximum value of the electric field at the center of the core.

Fig. 2
Fig. 2

(a) Illustration of scattering point P on a distant sphere and (b) the relative phase between a ray scattered by the dipole at (si, z) and a reference ray.

Fig. 3
Fig. 3

Normalized exponential scattering loss coefficient of the fundamental LP01 mode due to sinusoidal core diameter variations of a step-index fiber with the parameters shown in the inset.. The loss is plotted as a function of the escaping angle ϕ which is given by ϕ = cos−1((β − 2π/Λ)/n2k0). The result plotted here and obtained by solving Eq. (11) is identical to that obtained by coupled-mode theory (see [7], page 159)

Fig. 4
Fig. 4

(a)Angular scattering distribution from frozen-in surface capillary waves for a few guided modes of the HC-PBGF in [22]. (b) Measured and calculated loss contributions for the fundamental guided mode. A cut-off at κc = 0.1μm−1 has been imposed on the roughness PSD. In performing the cutback loss measurement, care was taken to predominantly excite the fundamental mode only. s2 and time of flight measurements showed an extinction higher than 22dB for all the higher order modes at the output (see [22].

Fig. 5
Fig. 5

Predicted wavelength dependence of the minimum scattering loss coefficient when the fibre in [22] is rigidly scaled to larger transverse cross-sections.

Fig. 6
Fig. 6

(a)Scattering loss as a function of the spatial frequency κc of the SCW roughness PSD at a wavelength of 1.55μm. (b) Computed total loss across the photonic bandgap for the fibre in [22] for three distinct values of the roughness frequency cut-off.

Fig. 7
Fig. 7

(a)Scattering loss from exponential and Gaussian roughness as function of correlation length.(b) Roughness PSD for frozen-in SCWs, Gaussian and exponential roughness. If exponential or gaussian roughness with the correlation lengths shown are present in the fiber, their contribution is negligible in the region where SCWs dominate.

Equations (17)

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

p = α | | d V E | | + γ d V D
p = α 0 sgn ( f ( s , z ) ) d V E 0 = α 0 f ( s , z ) d s j d z E 0
d E s ( ϑ , ϕ ) = k 0 2 4 π ε 0 R ( r × p ) × r
Φ ( ϑ , ϕ , s , z ) = β z k 0 z cos ϕ k 0 y sin ϕ
E s ( ϑ , ϕ ) = z = L L d E s ( ϑ , ϕ ) exp ( i Φ )
E s ( ϑ , ϕ ) = j z = L L d E s ( ϑ , ϕ ) exp ( i Φ ) = j k 0 2 α 0 4 π ε 0 R z = L L f ( s j , z ) ( r × E 0 ) × r exp ( i Φ ) d s j d z
L L f ( z ) e i ( β k 0 cos ϕ ) z d z F ˜ ( β k 0 cos ϕ )
E s ( ϑ , ϕ ) = k 0 2 α 0 4 π ε 0 R F ˜ ( β k 0 cos ϕ ) j e i k 0 y sin ϕ [ E 0 v + ( E 0 z sin ϕ E 0 | | cos ϕ ) u ] d s j = k 0 2 α 0 4 π ε 0 R F ˜ ( β k 0 cos ϕ ) × [ E s u u + E s v v ]
P ( ϕ ) = 1 2 π ϑ = 0 2 π 1 2 c n ε 0 | E s ( ϑ , ϕ ) | 2 R 2 sin ϕ d ϑ .
S ( κ ) = lim L [ 1 2 L | L L f ( z ) e i κ z d z | 2 ] = 1 2 L | F ˜ ( κ ) | 2 ,
P ( ϕ ) = 2 L 2 π ( k 0 2 α 0 4 π ε 0 ) 2 S ( β k 0 cos ϕ ) × ϑ = 0 2 π 1 2 c n ε 0 [ | E s u | 2 + | E s v | 2 ] sin ϕ d ϑ .
α s c 2 π 1 2 L P 0 ϕ = 0 π P ( ϕ ) L ( ϕ ) d ϕ .
S ( κ ) = b 2 4 δ ( κ 2 π Λ )
β k 0 n 2 cos ϕ 2 π Λ = 0 cos ϕ = β 2 π / Λ k 0 n 2 .
S ( κ ) = k B T g ρ g + γ | κ | 2 ,
S z ( κ ) = k B T g 4 π γ κ .
F = ( ε 0 μ 0 ) 1 2 holeperimeters | E | 2 d s cross section E × H * d A

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