Abstract

The loss resulting from roughness scattering at hole interfaces within solid core photonic crystal fibers is theoretically analyzed and compared with measurements on fabricated fibers. It is found that a model roughness spectrum corresponding to frozen in capillary waves gives results in reasonably good agreement with experiments on small core fibers. In particular, the roughness scattering loss is shown to be only weakly dependent on wavelength. Agreement at a larger core size requires a long length-scale cut-off to be introduced to the roughness spectrum. Due to the long range nature of the roughness correlations, the scattering is non Rayleigh in character and cannot be interpreted in terms of a local photon density of states.

© 2005 Optical Society of America

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References

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    [PubMed]
  14. S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
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    [Crossref] [PubMed]
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  18. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers: 1. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002)
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2005 (3)

2004 (2)

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

D. P. Fussell, R. C. McPhedran, and C. M. de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004)
[Crossref]

2002 (3)

2001 (2)

1999 (1)

R. F. Cregan, J. C. Knight, P. St.J. Russell, and P. J. Roberts 1999, “Distribution of spontaneous emission from anEr3+-doped photonic crystal fiber,” J. Lightwave Tech. 17, 2138–2141 (1999)
[Crossref]

1998 (1)

1995 (1)

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys.: Condens. Matter 7, 4351–4358 (1995)
[Crossref]

1987 (1)

J. Meunier, “Liquids interfaces: role of the fluctuations and analysis of ellipsometry and reflectivity measurements,” J. Phys. France 48, 1819–1831 (1987)
[Crossref]

Allan, D. C.

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 fibers,” Opt. Express 13, 236–244 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

Birks, T.A.

Borrelli, N. F.

Botten, L. C.

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 fibers,” Opt. Express 13, 236–244 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

Cregan, R. F.

R. F. Cregan, J. C. Knight, P. St.J. Russell, and P. J. Roberts 1999, “Distribution of spontaneous emission from anEr3+-doped photonic crystal fiber,” J. Lightwave Tech. 17, 2138–2141 (1999)
[Crossref]

de Sterke, C. M.

D. P. Fussell, R. C. McPhedran, and C. M. de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004)
[Crossref]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers: 1. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002)
[Crossref]

Duraiswami, R.

F. Seydou, O. Ramahi, R. Duraiswami, and T. Seppanen, “Computation of Green’s Function for Finite-Size Photonic Crystals by Boundary Element Method,” in IEEE Antennas and Propagation Society Symposium (Monterey, USA, June 20-25, 2004), Vol. 4, pp. 4320–4323

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 fibers,” Opt. Express 13, 236–244 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

L. Farr, J. C. Knight, B. J. Mangan, and P. J. Roberts, “Low loss photonic crystal fiber,” in European Conference on Optical Communication (Copenhagen, 2002), post-deadline paper PD13

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
[Crossref]

M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, and Y. Fink, “Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates,” Opt. Express 10, 1227–1243 (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227
[PubMed]

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

Fussell, D. P.

D. P. Fussell, R. C. McPhedran, and C. M. de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004)
[Crossref]

Hasegawa, T.

Hughes, S.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005)
[Crossref] [PubMed]

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
[Crossref]

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Jäckle, J.

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys.: Condens. Matter 7, 4351–4358 (1995)
[Crossref]

Jacobs, S.

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Jacobs, S. A.

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
[Crossref]

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
[Crossref]

M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, and Y. Fink, “Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates,” Opt. Express 10, 1227–1243 (2002) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227
[PubMed]

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Karalis, A.

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Kawasaki, K.

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys.: Condens. Matter 7, 4351–4358 (1995)
[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. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibers,” Opt. Express 13, 236–244 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[Crossref] [PubMed]

R. F. Cregan, J. C. Knight, P. St.J. Russell, and P. J. Roberts 1999, “Distribution of spontaneous emission from anEr3+-doped photonic crystal fiber,” J. Lightwave Tech. 17, 2138–2141 (1999)
[Crossref]

L. Farr, J. C. Knight, B. J. Mangan, and P. J. Roberts, “Low loss photonic crystal fiber,” in European Conference on Optical Communication (Copenhagen, 2002), post-deadline paper PD13

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

Knight, J.C.

Koch, K. W.

Koshiba, M.

Kuhlmey, B. T.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Oxford: Pergamon, 1970)

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline 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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Oxford: Pergamon, 1970)

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and 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 fibers,” Opt. Express 13, 236–244 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

L. Farr, J. C. Knight, B. J. Mangan, and P. J. Roberts, “Low loss photonic crystal fiber,” in European Conference on Optical Communication (Copenhagen, 2002), post-deadline paper PD13

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

Mason, M. W.

Maystre, D.

McPhedran, R. C.

D. P. Fussell, R. C. McPhedran, and C. M. de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004)
[Crossref]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers: 1. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002)
[Crossref]

Meunier, J.

J. Meunier, “Liquids interfaces: role of the fluctuations and analysis of ellipsometry and reflectivity measurements,” J. Phys. France 48, 1819–1831 (1987)
[Crossref]

Nishimura, M.

Onishi, M.

Povinelli, M. L.

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Ramahi, O.

F. Seydou, O. Ramahi, R. Duraiswami, and T. Seppanen, “Computation of Green’s Function for Finite-Size Photonic Crystals by Boundary Element Method,” in IEEE Antennas and Propagation Society Symposium (Monterey, USA, June 20-25, 2004), Vol. 4, pp. 4320–4323

Ramunno, L.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005)
[Crossref] [PubMed]

Rarity, J.G.

Renversez, G.

Roberts, P. J.

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[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 fibers,” Opt. Express 13, 236–244 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[Crossref] [PubMed]

P. J. Roberts and T. J. Shepherd, “The guidance properties of multi-core photonic crystal fibres,” J. Optics A: Pure and applied 3, S133–S140 (2001)
[Crossref]

R. F. Cregan, J. C. Knight, P. St.J. Russell, and P. J. Roberts 1999, “Distribution of spontaneous emission from anEr3+-doped photonic crystal fiber,” J. Lightwave Tech. 17, 2138–2141 (1999)
[Crossref]

L. Farr, J. C. Knight, B. J. Mangan, and P. J. Roberts, “Low loss photonic crystal fiber,” in European Conference on Optical Communication (Copenhagen, 2002), post-deadline paper PD13

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

Roundy, D.

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Russell, P. St. J.

Russell, P. St.J.

R. F. Cregan, J. C. Knight, P. St.J. Russell, and P. J. Roberts 1999, “Distribution of spontaneous emission from anEr3+-doped photonic crystal fiber,” J. Lightwave Tech. 17, 2138–2141 (1999)
[Crossref]

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

Russell, P.St.J.

Sabert, H.

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[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 fibers,” 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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

Sasaoka, E.

Schroeder, J.

J. Schroeder, “Light scattering in glass,” in Treatise on Materials Science and Technology Vol. 12, M. Tomozawa and R. H. Doremus, eds. (Academic Press, 1977)

Seppanen, T.

F. Seydou, O. Ramahi, R. Duraiswami, and T. Seppanen, “Computation of Green’s Function for Finite-Size Photonic Crystals by Boundary Element Method,” in IEEE Antennas and Propagation Society Symposium (Monterey, USA, June 20-25, 2004), Vol. 4, pp. 4320–4323

Seydou, F.

F. Seydou, O. Ramahi, R. Duraiswami, and T. Seppanen, “Computation of Green’s Function for Finite-Size Photonic Crystals by Boundary Element Method,” in IEEE Antennas and Propagation Society Symposium (Monterey, USA, June 20-25, 2004), Vol. 4, pp. 4320–4323

Shepherd, T. J.

P. J. Roberts and T. J. Shepherd, “The guidance properties of multi-core photonic crystal fibres,” J. Optics A: Pure and applied 3, S133–S140 (2001)
[Crossref]

Sipe, J. E.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005)
[Crossref] [PubMed]

Skorobogatiy, M.

Skorobogatty, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
[Crossref]

Smith, C. M.

Snyder, A. W.

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

Soljacic, M.

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

Tomlinson, A.

Tsuji, Y.

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
[Crossref]

West, J. A.

White, T. P.

Williams, D. P.

F. Couny, H. Sabert, P. J. Roberts, D. P. Williams, A. Tomlinson, B. J. Mangan, L. Farr, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Visualization of the photonic band gap in hollow core photonic crystal fibers using side scattering,” Opt. Express 13, 558–563 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-558
[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 fibers,” Opt. Express 13, 236–244 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236
[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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

Young, J. F.

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005)
[Crossref] [PubMed]

Appl. Opt. (1)

J. Lightwave Tech. (1)

R. F. Cregan, J. C. Knight, P. St.J. Russell, and P. J. Roberts 1999, “Distribution of spontaneous emission from anEr3+-doped photonic crystal fiber,” J. Lightwave Tech. 17, 2138–2141 (1999)
[Crossref]

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

J. Optics A: Pure and applied (1)

P. J. Roberts and T. J. Shepherd, “The guidance properties of multi-core photonic crystal fibres,” J. Optics A: Pure and applied 3, S133–S140 (2001)
[Crossref]

J. Phys. France (1)

J. Meunier, “Liquids interfaces: role of the fluctuations and analysis of ellipsometry and reflectivity measurements,” J. Phys. France 48, 1819–1831 (1987)
[Crossref]

J. Phys.: Condens. Matter (1)

J. Jäckle and K. Kawasaki, “Intrinsic roughness of glass surfaces,” J. Phys.: Condens. Matter 7, 4351–4358 (1995)
[Crossref]

Opt. Express (5)

Phys. Rev. E (2)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatty, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equation with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002)
[Crossref]

D. P. Fussell, R. C. McPhedran, and C. M. de Sterke, “Three-dimensional Green’s tensor, local density of states, and spontaneous emission in finite two-dimensional photonic crystals composed of cylinders,” Phys. Rev. E 70, 066608 (2004)
[Crossref]

Phys. Rev. Lett. (1)

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: Role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005)
[Crossref] [PubMed]

Other (8)

F. Seydou, O. Ramahi, R. Duraiswami, and T. Seppanen, “Computation of Green’s Function for Finite-Size Photonic Crystals by Boundary Element Method,” in IEEE Antennas and Propagation Society Symposium (Monterey, USA, June 20-25, 2004), Vol. 4, pp. 4320–4323

S. G. Johnson, M. Ibanescu, M. L. Povinelli, M. Soljacic, A. Karalis, S. Jacobs, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Anomalous loss and propagation in photonic-crystal waveguides,” presented at PECS-VI, Aghia Pelaghia, Crete, June 2005

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

L. Farr, J. C. Knight, B. J. Mangan, and P. J. Roberts, “Low loss photonic crystal fiber,” in European Conference on Optical Communication (Copenhagen, 2002), post-deadline paper PD13

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 band gap fibre,” in Proc. Optical Fiber Commun. Conf. (Los Angeles, 2004), post-deadline paper PDP24

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,” in Proc. CLEO 2005 (Baltimore, 2005), paper CWA7

L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Oxford: Pergamon, 1970)

J. Schroeder, “Light scattering in glass,” in Treatise on Materials Science and Technology Vol. 12, M. Tomozawa and R. H. Doremus, eds. (Academic Press, 1977)

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Figures (5)

Fig. 1.
Fig. 1.

(a) The measured scattered power as a function of effective index n for a PCF with pitch approximately 2.85 μm and core diameter about 2.8 μm at a wavelength of 1.55 μm. A SEM of the structure are included as an inset. In (b), the calculated scattered power due to SCW roughness is shown for a PCF with pitch 2.85 μm composed of circular holes of diameter 2.74 μm. The wavelength is again 1.55 μm.

Fig 2.
Fig 2.

Calculated angular distribution of power scattered due to surface roughness from a solid core PCF with pitch Λ=2.0 μm and hole diameter 1.96 μm. The wavelength is 1.55 μm.

Fig. 3.
Fig. 3.

The wavelength dependence of roughness loss calculated for a solid core PCF with pitch 1.5μm and circular holes of diameter 1.44 μm. A curve with 1/λ 4 dependence, approximately 50 times the strength of the bulk Rayleigh scattering contribution, is included for comparison.

Fig. 4.
Fig. 4.

The measured loss vs. wavelength for a fabricated PCF with a core diameter of around 1.5 μm. A SEM of the structure is included as an inset. The dashed curve has a dependence of λ -1.24.

Fig. 5.
Fig. 5.

A plot of the complex plane schematically showing the analytic structure of the integrand in Eq. (5). The poles associated with the Green tensor are shown by crosses and those of the roughness function Ψ͂(s,s';β - β 1) by dots. The Green tensor poles due to forward propagating modes 1 and 2 are shown in grey and have been subtracted. The thick continuous lines indicate branch cuts. β cl is the β-value of the cladding cut-off and β g=n g k. The path of integration is deformed from the real β-axis to the dashed curve shown.

Equations (39)

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E = 1 4 A 2 σ k SCW 2 ,
Ψ ͂ ( k SCW ) = k B T g σ 1 k SCW 2
Ψ ͂ m ( β ) = k B T g σ 1 S 1 [ k s ( m ) 2 + β 2 ] ,
h ( s , z ) h ( s + Δ s , z + Δ z ) = 1 2 π m = exp ( i m Δ s ) d β exp ( i β Δ z ) Ψ m ( β ) ,
γ 1 = k 3 4 π ( ε 0 μ 0 ) 1 2 ( n g 2 1 ) 2 Im [ j = 1 N holes
j 'th hole perimeter d s j 'th hole perimeter d s ' d β e ̂ 1 H ( r j ( s ' ) ) G 2 D ( r j + ( s ' ) , r j + ( s ) ; k , β ) e ̂ 1 ( r j ( s ) ) Ψ ͂ j ( s , s ' ; β 1 β ) ] ,
1 2 A d 2 r [ e ̂ 1 ( r ) × h ̂ 1 * ( r ) ] · z ̂ = 1 ,
Ψ ͂ j ( s , s ' ; Δ β ) = k B T g σ 1 S j m = exp [ i k s ( m ) ( s s ' ) ] [ k s ( m ) 2 + Δ β 2 ]
Ψ ͂ ( s , s ' ; Δ β ) = k B T g σ 1 2 Δ β exp ( Δ β ( s s ' ) ) .
β = n m k cos θ ,
Ψ ' ͂ m ( β ) = k B T g σ 1 S 1 [ k s ( m ) 2 + β 2 + k cut 2 ] ,
d b p d z i β p b p = q ζ p C pq b q ,
C pq ( z ) = k 4 ( ε 0 μ 0 ) 1 2 1 Δ β pq x section d 2 r { [ e ̂ p * · e ̂ q ( e ̂ p * · n ̂ ) ( e ̂ q · n ̂ ) ] n 2 z ( n 2 e ̂ p * · n ̂ ) ( n 2 e ̂ q · n ̂ ) z ( 1 n 2 ) } ,
b 1 ( L ) = b 1 ( 0 ) exp ( i β 1 L ) { 1 + q 0 L d z ' z ' L z ' d z d η q ( z d ) C 1 q ( z ' ) C q 1 ( z ' z d ) exp [ i ( β q β 1 ) z d ] } .
γ 1 = 1 L ( 1 b 1 2 ( L ) 2 b 1 ( 0 ) 2 ) = 2 L Re [ q 0 L d z ' z ' d z d η q ( z d ) C 1 q ( z ' ) C q 1 ( z ' z d ) exp [ i ( β q β 1 ) z d ] ] ,
γ 1 = 2 Re [ q d z d η q ( z d ) C 1 q ( 0 ) C q 1 ( z d ) exp [ i ( β q β 1 ) z d ] ] .
n p ( r , z ) z = n 0 p ( r ) r = r + u ( r , z ) · u ( r , z ) z
( n g p 1 ) j = 1 N holes j th hole interface d s δ ( r r j ( s ) ) h j ( s , z ) z ( p = 2 , 2 ) ,
C pq ( z ) = k 4 ( ε 0 μ 0 ) 1 2 1 Δ β pq j = 1 N holes j th hole interface d s { ( n g 2 1 ) [ e ̂ p * · e ̂ q ( e ̂ p * · n ̂ j ( s ) ) ( e ̂ q · n ̂ j ( s ) ) ] ( n g 2 1 ) ( n 0 2 e ̂ p * · n ̂ j ( s ) ) ( n 0 2 e ̂ q · n ̂ j ( s ) ) } h j ( s , z ) z .
{ ( n g 2 1 ) [ e ̂ p * · e ̂ q ( e ̂ p * · n ̂ j ( s ) ) ( e ̂ q · n ̂ j ( s ) ) ] ( n g 2 1 ) ( n 0 2 e ̂ p * · n ̂ j ( s ) ) ( n 0 2 e ̂ q · n ̂ j ( s ) ) } = ( n g 2 1 ) I j ( pq ) ( s ) ,
I j ( pq ) ( s ) = { e ̂ p * ( r j + ( s ) ) · e ̂ q ( r j + ( s ) ) + [ e ̂ p * ( r j ( s ) ) · n ̂ j ( s ) e ̂ p * ( r j + ( s ) ) · n ̂ j ( s ) ] [ e ̂ q ( r j + ( s ) ) · n ̂ j ( s ) ] } .
γ 1 = k 2 8 ( ε 0 μ 0 ) ( n g 2 1 ) 2 q 1 Δ β 1 q 2 Re [ j = 1 N holes k = 1 N holes j 'th hole perimeter d s I j ( 1 q ) ( s ) k 'th hole perimeter d s I k ( q 1 ) ( s ) ×
d z d η q ( z d ) exp ( i Δ β q 1 z d ) 2 2 z d Ψ jk ( s , s ; z d ) ] ,
Ψ jk ( s , s ; z d ) = h j ( s , 0 ) h k ( s , z d )
h j ( s , z ) z z = 0 h k ( s , z ) z z = z d = 2 2 z d Ψ jk ( s , s ; z d ) .
Ψ jk ( s , s ; z d ) = Ψ j ( s , s ; z d ) δ jk ,
γ 1 = k 2 8 ( ε 0 μ 0 ) ( n g 2 1 ) 2 Re [ j = 1 N holes j 'th hole perimeter d s j 'th hole perimeter d s d z d
q I j ( 1 q ) ( s ) I j ( q 1 ) ( s ) exp ( i Δ β q 1 z d ) η q ( z d ) Ψ j ( s , s ; z d ) ] .
q η q ( z d ) e ̂ q ( r ) e ̂ q H ( r ) exp ( i β q z d ) = 4 i k ( μ 0 ε 0 ) 1 2 G 3 D ( r + z d z ̂ , r + 0 z ̂ ; k )
q I j ( 1 q ) ( s ) I j ( q 1 ) ( s ) η q ( z d ) exp ( i β q z q ) = 4 i k ( μ 0 ε 0 ) 1 2 ×
e ̂ 1 H ( r j ( s ) ) G 3 D ( r j + ( s ) + z d z ̂ , r j + ( s ) + 0 z ̂ ; k ) e ̂ 1 ( r j ( s ) ) .
γ 1 = k 3 4 π ( ε 0 μ 0 ) 1 2 ( n g 2 1 ) 2 Im [ j = 1 N holes
j 'th hole perimeter d s j 'th hole perimeter d s d β e ̂ 1 H ( r j ( s ) ) G 2 D ( r j + ( s ) , r j + ( s ) ; k , β ) e ̂ 1 ( r j ( s ) ) Ψ ͂ j ( s , s , β 1 β ) ] ,
G 2 D ( r , r ; k , β ) = d z d exp ( β z d ) G 3 D ( r + z d z ̂ , r + 0 z ̂ ; k )
Ψ ̂ j ( s , s ; Δ β ) = d z d exp ( i Δ β z d ) Ψ j ( s , s ; z d ) .
γ 1 ( θ , ϕ ) = 1 4 π ( ε 0 μ 0 ) 1 2 k 5 n g ( n g 2 1 ) 2 sin θ Re lim R R Re j j 'th hole perimeter d s j 'th hole perimeter d s Ψ ͂ ( s , s ; β 1 β ) ×
e ̂ 1 H ( r j ( s ) ) G 2 D H ( R o ̂ , r j + ( s ) ; k , β ) G 2 D ( R o ̂ , r j + ( s ) ; k , β ) e ̂ 1 ( r j ( s ) )
β = β 1 + i 2 π m S j ,
G 2 D ( r , r ; k ; β ) G 2 D ( r , r ; k , β ) ( ε 0 μ 0 ) 1 2 1 4 π q = 1 2 e ̂ q ( r ) e ̂ q H ( r ) β q β .

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