Abstract

Modeling of microstructure fibers often involves severe computational bottlenecks, in particular when a design space with many degrees of freedom must be analyzed. Perturbative versions of numerical mode-solvers can substantially reduce the computational burden of problems involving automated optimization or irregularity analysis, where perturbations arise naturally. A basic theory is presented for perturbative multipole and boundary element methods, and the speed and accuracy of the methods are demonstrated. The specific optimization results in an elliptical-hole birefringent fiber design, with substantially higher birefringence than the intuitive unoptimized design.

© 2004 Optical Society of America

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  1. P. Kaiser and H. W. Astle. “Low-loss single-matrial fibres made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–39 (1974).
  2. S. A. Diddams and D. J. Jones, et al. “Direct link between microwave and optical frequencies with a 300THz femtosecond laser comb,” Phys. Rev. Lett.,  84, 5102–5 (2000).
    [CrossRef] [PubMed]
  3. S. G. Johnson and M. Ibanescu, et al. “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–79 (2001).
    [CrossRef] [PubMed]
  4. John Fini and Ryan Bise. “Progress in fabrication and modeling of microstructured optical fiber,” Jap. J. App. Phys. 43, 5717–5730 (2004).
    [CrossRef]
  5. A. Ferrando and E. Silvestre, et al. “Full vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–8 (1999).
    [CrossRef]
  6. T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. deSterke. “Calculations of air-guiding modes in photonic crystal fibers using the multipole method,” Opt. Express, 9, 721–32 (2001).
    [CrossRef]
  7. F. Brechet and J. Marcou, et al. “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Tech. 6, 181–191 (2000).
    [CrossRef]
  8. N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada. “Boundary element method for analysis of holey optical fibers,” J. Lightwave. Technol. 21, 1787–92 (2003).
    [CrossRef]
  9. 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). software available at http://ab-initio.mit.edu/mpb.
    [CrossRef] [PubMed]
  10. T. A. Birks, J. C. Knight, and P. S. J. Russell. “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–3 (1997).
    [CrossRef] [PubMed]
  11. T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya. “Bend-insensitive single-mode holey fibre with SMF compatibility for optical wiring applications,” In European Conference on Optical Communications, paper We2.7.3, (2003).
  12. James A. West, Charlene M. Smith, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Surface modes in air-core photonic band-gap fibers,” Opt. Express, 12, 1485–96 (2004).
    [CrossRef]
  13. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli. “Perturbation analysis of dispersion properties in photonic crystal fibers through the finite element method,” J. Lightwave Technol. 20, 1433–42 (2002).
    [CrossRef]
  14. A. Peyrilloux, T. Chartier, L. Berthelot, A. Hideur, G. Mélin, S. Lempereur, D. Pagnoux, and P. Roy. “Thoeretical and experimental study of the birefringence of a photonic crystal fiber,” J. Lightwave Technol. 21, 536–9(2003).
    [CrossRef]
  15. I. K. Hwang, Y. J. Lee, and Y. H. Lee. “Birefringence induced by irregular structure in photonic crystal fiber,” Opt. Express 11, 2799–2806 (2003).
    [CrossRef] [PubMed]
  16. Steven G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink. “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
    [CrossRef]
  17. M. J. Steel, T. P. White, C.Martijn de Sterke, R. C. McPhedran, and L. C. Botten. “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–91 (2001).
    [CrossRef]
  18. J. M. Fini. “Improved symmetry analysis of many-moded microstructure optical fibers,” J. Opt. Soc. Am. B, 21, 1431–6 (2004).
    [CrossRef]
  19. J. M. Fini. “Perturbative modeling of irregularities in microstructure optical fibers,” In Conference on Lasers and Electro-Optics (CLEO), TOPS vol. 96, paper CThX6, (Optical Society of America, Washington, D.C.,2004).
  20. M. Koshiba and K. Saitoh. “Polarization-dependent confinement losses in actual holey fibers,” Photon. Technol. Lett. 15, 691–3 (2003).
    [CrossRef]
  21. Paul R. McIsaac. “Symmetry-induced modal characteristics of uniform waveguides-I: Summary of results,” Microwave Theory and Techniques 23, 421–9 (1975).
    [CrossRef]
  22. M. J. Steel and R. M. Osgood. “Elliptical-hole photonic crystal fibers,” Opt. Lett. 26, 229–31 (2001).
    [CrossRef]
  23. M. J. Steel and R. M. Osgood. “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19, 495–503 (2001).
    [CrossRef]
  24. Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
    [CrossRef]
  25. William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical recipes in C, the art of scientific computing. (Cambridge University Press, New York,1992).
  26. C. C. Su. “A surface integral equations method for homogeneous optical fibers and coupled image lines of arbitrary cross sections,” Microwave. Theory and Technol.,  33, 1114–9, (1985).
    [CrossRef]
  27. R. Bise and R. S. Windeler, et al. “Tunable photonic band gap fiber,” In Optic al Fiber Communications Conference (OFC), TOPS vol. 70, paper ThK3, (Optical Society of America, Washington, D.C., 2002).
  28. R. Bise and D. Trevor. “Sol-gel-derived microstructured fibers: fabrication and characterization,” To appear in Optical Fiber Communications Conference (OFC), (Optical Society of America, Washington, D.C.,2005).
  29. T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba. “Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss,” Opt. Express 9, 681–6, (2001).
    [CrossRef] [PubMed]
  30. Alexander Argyros, Ian M. Bassett, Martijn A. van Eijkelenborg, M.C.J. Large, Joseph Zagari, N.A.P. Nicorovici, Ross C. McPhedran, and C.Martijn de Sterke. “Ring structures in microstructured polymer optical fibres,” Opt. Express 9, 813–20, (2001).
    [CrossRef] [PubMed]

2004 (3)

John Fini and Ryan Bise. “Progress in fabrication and modeling of microstructured optical fiber,” Jap. J. App. Phys. 43, 5717–5730 (2004).
[CrossRef]

James A. West, Charlene M. Smith, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Surface modes in air-core photonic band-gap fibers,” Opt. Express, 12, 1485–96 (2004).
[CrossRef]

J. M. Fini. “Improved symmetry analysis of many-moded microstructure optical fibers,” J. Opt. Soc. Am. B, 21, 1431–6 (2004).
[CrossRef]

2003 (5)

M. Koshiba and K. Saitoh. “Polarization-dependent confinement losses in actual holey fibers,” Photon. Technol. Lett. 15, 691–3 (2003).
[CrossRef]

A. Peyrilloux, T. Chartier, L. Berthelot, A. Hideur, G. Mélin, S. Lempereur, D. Pagnoux, and P. Roy. “Thoeretical and experimental study of the birefringence of a photonic crystal fiber,” J. Lightwave Technol. 21, 536–9(2003).
[CrossRef]

I. K. Hwang, Y. J. Lee, and Y. H. Lee. “Birefringence induced by irregular structure in photonic crystal fiber,” Opt. Express 11, 2799–2806 (2003).
[CrossRef] [PubMed]

N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada. “Boundary element method for analysis of holey optical fibers,” J. Lightwave. Technol. 21, 1787–92 (2003).
[CrossRef]

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

2002 (3)

R. Bise and R. S. Windeler, et al. “Tunable photonic band gap fiber,” In Optic al Fiber Communications Conference (OFC), TOPS vol. 70, paper ThK3, (Optical Society of America, Washington, D.C., 2002).

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

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli. “Perturbation analysis of dispersion properties in photonic crystal fibers through the finite element method,” J. Lightwave Technol. 20, 1433–42 (2002).
[CrossRef]

2001 (8)

M. J. Steel, T. P. White, C.Martijn de Sterke, R. C. McPhedran, and L. C. Botten. “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–91 (2001).
[CrossRef]

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). software available at http://ab-initio.mit.edu/mpb.
[CrossRef] [PubMed]

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. deSterke. “Calculations of air-guiding modes in photonic crystal fibers using the multipole method,” Opt. Express, 9, 721–32 (2001).
[CrossRef]

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba. “Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss,” Opt. Express 9, 681–6, (2001).
[CrossRef] [PubMed]

Alexander Argyros, Ian M. Bassett, Martijn A. van Eijkelenborg, M.C.J. Large, Joseph Zagari, N.A.P. Nicorovici, Ross C. McPhedran, and C.Martijn de Sterke. “Ring structures in microstructured polymer optical fibres,” Opt. Express 9, 813–20, (2001).
[CrossRef] [PubMed]

S. G. Johnson and M. Ibanescu, et al. “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–79 (2001).
[CrossRef] [PubMed]

M. J. Steel and R. M. Osgood. “Elliptical-hole photonic crystal fibers,” Opt. Lett. 26, 229–31 (2001).
[CrossRef]

M. J. Steel and R. M. Osgood. “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19, 495–503 (2001).
[CrossRef]

2000 (2)

F. Brechet and J. Marcou, et al. “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Tech. 6, 181–191 (2000).
[CrossRef]

S. A. Diddams and D. J. Jones, et al. “Direct link between microwave and optical frequencies with a 300THz femtosecond laser comb,” Phys. Rev. Lett.,  84, 5102–5 (2000).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

1985 (1)

C. C. Su. “A surface integral equations method for homogeneous optical fibers and coupled image lines of arbitrary cross sections,” Microwave. Theory and Technol.,  33, 1114–9, (1985).
[CrossRef]

1975 (1)

Paul R. McIsaac. “Symmetry-induced modal characteristics of uniform waveguides-I: Summary of results,” Microwave Theory and Techniques 23, 421–9 (1975).
[CrossRef]

1974 (1)

P. Kaiser and H. W. Astle. “Low-loss single-matrial fibres made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–39 (1974).

Allan, Douglas C.

James A. West, Charlene M. Smith, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Surface modes in air-core photonic band-gap fibers,” Opt. Express, 12, 1485–96 (2004).
[CrossRef]

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

Argyros, Alexander

Astle, H. W.

P. Kaiser and H. W. Astle. “Low-loss single-matrial fibres made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–39 (1974).

Bassett, Ian M.

Berthelot, L.

Birks, T. A.

Bise, R.

R. Bise and R. S. Windeler, et al. “Tunable photonic band gap fiber,” In Optic al Fiber Communications Conference (OFC), TOPS vol. 70, paper ThK3, (Optical Society of America, Washington, D.C., 2002).

R. Bise and D. Trevor. “Sol-gel-derived microstructured fibers: fabrication and characterization,” To appear in Optical Fiber Communications Conference (OFC), (Optical Society of America, Washington, D.C.,2005).

Bise, Ryan

John Fini and Ryan Bise. “Progress in fabrication and modeling of microstructured optical fiber,” Jap. J. App. Phys. 43, 5717–5730 (2004).
[CrossRef]

Borrelli, Nicholas F.

James A. West, Charlene M. Smith, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Surface modes in air-core photonic band-gap fibers,” Opt. Express, 12, 1485–96 (2004).
[CrossRef]

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

Botten, L. C.

M. J. Steel, T. P. White, C.Martijn de Sterke, R. C. McPhedran, and L. C. Botten. “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–91 (2001).
[CrossRef]

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. deSterke. “Calculations of air-guiding modes in photonic crystal fibers using the multipole method,” Opt. Express, 9, 721–32 (2001).
[CrossRef]

Brechet, F.

F. Brechet and J. Marcou, et al. “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Tech. 6, 181–191 (2000).
[CrossRef]

Chartier, T.

Cucinotta, A.

de Sterke, C.Martijn

deSterke, C. M.

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. deSterke. “Calculations of air-guiding modes in photonic crystal fibers using the multipole method,” Opt. Express, 9, 721–32 (2001).
[CrossRef]

Diddams, S. A.

S. A. Diddams and D. J. Jones, et al. “Direct link between microwave and optical frequencies with a 300THz femtosecond laser comb,” Phys. Rev. Lett.,  84, 5102–5 (2000).
[CrossRef] [PubMed]

Eijkelenborg, Martijn A. van

Ferrando, A.

Fini, J. M.

J. M. Fini. “Improved symmetry analysis of many-moded microstructure optical fibers,” J. Opt. Soc. Am. B, 21, 1431–6 (2004).
[CrossRef]

J. M. Fini. “Perturbative modeling of irregularities in microstructure optical fibers,” In Conference on Lasers and Electro-Optics (CLEO), TOPS vol. 96, paper CThX6, (Optical Society of America, Washington, D.C.,2004).

Fini, John

John Fini and Ryan Bise. “Progress in fabrication and modeling of microstructured optical fiber,” Jap. J. App. Phys. 43, 5717–5730 (2004).
[CrossRef]

Fink, Y.

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

Flannery, Brian P.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical recipes in C, the art of scientific computing. (Cambridge University Press, New York,1992).

Gallagher, Michael T.

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

Guan, N.

N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada. “Boundary element method for analysis of holey optical fibers,” J. Lightwave. Technol. 21, 1787–92 (2003).
[CrossRef]

Habu, S.

N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada. “Boundary element method for analysis of holey optical fibers,” J. Lightwave. Technol. 21, 1787–92 (2003).
[CrossRef]

Hasegawa, T.

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba. “Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss,” Opt. Express 9, 681–6, (2001).
[CrossRef] [PubMed]

T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya. “Bend-insensitive single-mode holey fibre with SMF compatibility for optical wiring applications,” In European Conference on Optical Communications, paper We2.7.3, (2003).

Hideur, A.

Himeno, K.

N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada. “Boundary element method for analysis of holey optical fibers,” J. Lightwave. Technol. 21, 1787–92 (2003).
[CrossRef]

Hosoya, T.

T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya. “Bend-insensitive single-mode holey fibre with SMF compatibility for optical wiring applications,” In European Conference on Optical Communications, paper We2.7.3, (2003).

Hwang, I. K.

Ibanescu, M.

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

S. G. Johnson and M. Ibanescu, et al. “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–79 (2001).
[CrossRef] [PubMed]

Joannopoulos, J. D.

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

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). software available at http://ab-initio.mit.edu/mpb.
[CrossRef] [PubMed]

Johnson, S. G.

Johnson, Steven G.

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

Jones, D. J.

S. A. Diddams and D. J. Jones, et al. “Direct link between microwave and optical frequencies with a 300THz femtosecond laser comb,” Phys. Rev. Lett.,  84, 5102–5 (2000).
[CrossRef] [PubMed]

Kaiser, P.

P. Kaiser and H. W. Astle. “Low-loss single-matrial fibres made from pure fused silica,” Bell Syst. Tech. J. 53, 1021–39 (1974).

Knight, J. C.

Koch, Karl W.

James A. West, Charlene M. Smith, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Surface modes in air-core photonic band-gap fibers,” Opt. Express, 12, 1485–96 (2004).
[CrossRef]

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

Koshiba, M.

Large, M.C.J.

Lee, Y. H.

Lee, Y. J.

Lempereur, S.

Marcou, J.

F. Brechet and J. Marcou, et al. “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Tech. 6, 181–191 (2000).
[CrossRef]

McIsaac, Paul R.

Paul R. McIsaac. “Symmetry-induced modal characteristics of uniform waveguides-I: Summary of results,” Microwave Theory and Techniques 23, 421–9 (1975).
[CrossRef]

McPhedran, R. C.

M. J. Steel, T. P. White, C.Martijn de Sterke, R. C. McPhedran, and L. C. Botten. “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–91 (2001).
[CrossRef]

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. deSterke. “Calculations of air-guiding modes in photonic crystal fibers using the multipole method,” Opt. Express, 9, 721–32 (2001).
[CrossRef]

McPhedran, Ross C.

Mélin, G.

Müller, Dirk

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

Nicorovici, N.A.P.

Nishimura, M.

Nishioka, D.

T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya. “Bend-insensitive single-mode holey fibre with SMF compatibility for optical wiring applications,” In European Conference on Optical Communications, paper We2.7.3, (2003).

Onishi, M.

Osgood, R. M.

Pagnoux, D.

Peyrilloux, A.

Press, William H.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical recipes in C, the art of scientific computing. (Cambridge University Press, New York,1992).

Roy, P.

Russell, P. S. J.

Saitoh, K.

M. Koshiba and K. Saitoh. “Polarization-dependent confinement losses in actual holey fibers,” Photon. Technol. Lett. 15, 691–3 (2003).
[CrossRef]

Saitoh, T.

T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya. “Bend-insensitive single-mode holey fibre with SMF compatibility for optical wiring applications,” In European Conference on Optical Communications, paper We2.7.3, (2003).

Sasaoka, E.

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba. “Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss,” Opt. Express 9, 681–6, (2001).
[CrossRef] [PubMed]

T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya. “Bend-insensitive single-mode holey fibre with SMF compatibility for optical wiring applications,” In European Conference on Optical Communications, paper We2.7.3, (2003).

Selleri, S.

Silvestre, E.

Skorobogatiy, M. A.

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

Smith, Charlene M.

James A. West, Charlene M. Smith, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Surface modes in air-core photonic band-gap fibers,” Opt. Express, 12, 1485–96 (2004).
[CrossRef]

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

Smith, G. H.

T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. deSterke. “Calculations of air-guiding modes in photonic crystal fibers using the multipole method,” Opt. Express, 9, 721–32 (2001).
[CrossRef]

Steel, M. J.

Su, C. C.

C. C. Su. “A surface integral equations method for homogeneous optical fibers and coupled image lines of arbitrary cross sections,” Microwave. Theory and Technol.,  33, 1114–9, (1985).
[CrossRef]

Takenaga, K.

N. Guan, S. Habu, K. Takenaga, K. Himeno, and A. Wada. “Boundary element method for analysis of holey optical fibers,” J. Lightwave. Technol. 21, 1787–92 (2003).
[CrossRef]

Teukolsky, Saul A.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical recipes in C, the art of scientific computing. (Cambridge University Press, New York,1992).

Trevor, D.

R. Bise and D. Trevor. “Sol-gel-derived microstructured fibers: fabrication and characterization,” To appear in Optical Fiber Communications Conference (OFC), (Optical Society of America, Washington, D.C.,2005).

Tsuji, Y.

Venkataraman, Natesan

Charlene M. Smith, Natesan Venkataraman, Michael T. Gallagher, Dirk Müller, James A. West, Nicholas F. Borrelli, Douglas C. Allan, and Karl W. Koch. “Low loss hollow-core silica/air photonic bandgap fibre,” Nature, 424657–9, (2003).
[CrossRef]

Vetterling, William T.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical recipes in C, the art of scientific computing. (Cambridge University Press, New York,1992).

Vincetti, L.

Wada, A.

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Figures (7)

Fig. 1.
Fig. 1.

For many realistic fibers, irregularity in hole geometry is small, but large enough to seriously impact optical properties such as birefringence. A perturbative approach is then natural.

Fig. 2.
Fig. 2.

Standard multipole and boundary-element methods require many large-matrix operations for each geometry, since there are many effective index values in the search. A perturbative approach needs very few large-matrix operations for each perturbed geometry.

Fig. 3.
Fig. 3.

Test of perturbative method for random hole irregularities. The fiber has three rings of cladding holes with spacing 2 microns, diameter 1 micron, and index 1. The wavelength was 1630 nm and the substrate index was set to 1.45. The geometric perturbations consisted of independently displacing six holes (σx =σy = .02Λ), and placing the remaining 30 holes to preserve sixfold rotational symmetry. Dashed lines indicate expected error trends (blue and pink), the unperturbed loss value (red), and ideal agreement between standard and perturbative methods (black).

Fig. 4.
Fig. 4.

For a birefringent fiber with elliptical holes, four holes of the inner ring were initially misaligned. An automated optimization of birefringence adjusts orientations of these four holes, ultimately aligning them with the orientation of the fixed holes. This is an optimization test with an intuitive optimum design. Modes are calculated at wavelength λ = 1.17Λ.

Fig. 5.
Fig. 5.

A consistency check confirms that the estimates of birefringence perturbation agree with non-perturbative results at each step in the optimization.

Fig. 6.
Fig. 6.

Birefringence is plotted for two optimizations where all 18 holes are free to rotate. Both initially x-oriented and y-oriented holes arrive at equivalent fiber geometries with a substantial improvement in birefringence. Again λ = 1.17Λ.

Fig. 7.
Fig. 7.

Orientation angles for the six inner holes are plotted versus optimization step. All holes are initially oriented to ϕj = 90° and ϕj = 0 for the left and right optimizations respectively. Both optimizations are converging to equivalent geometries, rotated 120 degrees from each other. The optimal perturbations at each step approximately maintain point-reflection symmetry about the origin (from which “hidden” curves can be inferred).

Equations (21)

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M ( n eff , λ ) v = 0 .
M ( n ) = M ( n eff = n ; λ , p )
M ( n ) = M 0 ( n ) + δ M 1 ( n ) + δ 2 M 2 ( n ) +
M 1 ( n ) = M δ M ( n ; λ , p 0 + ε p 1 ) M ( n ; λ , p 0 ε p 1 ) 2 ε .
v = v 0 + δ v 1 + δ 2 v 2 +
n = n 0 + δ n 1 + δ 2 n 2 +
[ M 0 ( n 0 + δ n 1 + ) + M 1 ( n 0 + ) + ] [ v 0 + δ v 1 + ] = 0 ,
δ n 1 = u 0 δ M 1 ( n 0 ) v 0 u 0 M 0 ( n 0 ) v 0
M 0 ( n 0 ) v 0 = 0 .
M 0 ( n 0 ) δ v 1 + [ δ n 1 M 0 ( n 0 ) + δ M 1 ( n 0 ) ] v 0 = 0 ,
u 0 [ δ n 1 M 0 ( n 0 ) + δ M 1 ( n 0 ) ] v 0 = 0 .
M 0 p M 0 ( n 0 ) = I v ̂ 0 v ̂ 0 .
δ v 1 = M 0 p [ δ n 1 M 0 ( n 0 ) + δ M 1 ( n 0 ) ] v 0 .
[ M 0 ( n 0 ) ] [ δ 2 v 2 ] + [ δ n 1 M 0 ( n 0 ) + δ M 1 ( n 0 ) ] [ δ v 1 ] + [ M 2 ] [ v 0 ] = 0
M 2 = ( δ 2 v 2 ) M 0 ( n 0 ) + 1 2 ( δ n 1 ) 2 M 0 ( n 0 ) + δ M 1 ( n 0 ) ( δ n 1 ) + δ 2 M 2 ( n 0 )
v 0 = Bx .
A [ δ n 1 M 0 ( n 0 ) + δ M 1 ( n 0 ) ] Bx = 0 ,
A δ M 1 ( n 0 ) Bx = δ n 1 A M 0 ( n 0 ) Bx ,
[ p n Bi ] j = n slow ϕ j n fast ϕ j .
p m + 1 = p m + [ Δ p ] m .
[ Δ p ] m = δ p n Bi p n Bi .

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