Abstract

In this paper, we study the novel propagation properties of an improved triangular-type air-core photonic bandgap fiber (PBGF) structured with an anti-resonant silica core surround, through a full-vector modal solver based on the finite-element method (FEM). At first, to realize a single-mode operation over a wide wavelength range, the fiber whose core is constructed by removing 1 air-hole and expanded is proposed and structurally-optimized. In particular, the structural parameters for the fiber that prevent the narrow-band transmission due to the existence of the surface modes and enhance the confinement of the power in the air-core are presented. For the realization of an ultimate low loss transmission, a 7-unit-cell PBGF is analyzed and we show that the 7-unit-cell PBGF can achieve not only lower confinement loss than that of regular-type 7-unit-cell PBGF, but also lower power fraction in the silica-ring when compared with the regular 19-unit-cell PBGF with an anti-resonant core surround, exhibiting an effectively single-mode operation.

© 2007 Optical Society of America

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  1. P. J. Roberts, T. A. Birks, P. St. J. Russell, T. J. Shepherd, and D. M. Atkin, "Two-dimensional photonic band-gap structures as quasi-metals," Opt. Lett. 21, 507-509 (1996).
    [CrossRef] [PubMed]
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
    [CrossRef] [PubMed]
  3. J. Broeng, S. E. Barkou, T. Sφndergaard, and A. Bjarklev, "Analysis of air-guiding photonic bandgap fibers," Opt. Lett. 25, 96-98 (2000).
    [CrossRef]
  4. K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11, 3100-3109 (2003).
    [CrossRef] [PubMed]
  5. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
    [CrossRef] [PubMed]
  6. K. Saitoh, N. A. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12, 394-400 (2004).
    [CrossRef] [PubMed]
  7. 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).
    [CrossRef] [PubMed]
  8. H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
    [CrossRef]
  9. H. K. Kim, M. J. F. Digonnet, G. S. Kino, J. Shin, and S. Fan, "Simulations of the effect of the core ring on surface and air-core modes in photonic bandgap fibers," Opt. Express 12, 3436-3442 (2004).
    [CrossRef] [PubMed]
  10. M. Yan and P. Shum, "Air guiding with honeycomb photonic bandgap fiber," IEEE Photon. Technol. Lett. 17, 64-66 (2005).
    [CrossRef]
  11. M. Yan, P. Shum, and J. Hu, "Design of air-guiding honeycomb photonic bandgap fiber," Opt. Lett. 30, 465-467 (2005).
    [CrossRef] [PubMed]
  12. T. Haas, S. Belau, and T. Doll, "Realistic monomode air-core honeycomb photonic bandgap fiber with pockets," J. Lightwave Technol. 23, 2702-2706 (2005).
    [CrossRef]
  13. 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. Express 13, 236-244 (2005).
    [CrossRef] [PubMed]
  14. P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, W. J. Wadsworth, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Realizing low loss air core photonic crystal fibers by exploiting an antiresonant core surround," Opt. Express 13, 8277-8285 (2005).
    [CrossRef] [PubMed]
  15. N. J. Florous, K. Saitoh, T. Murao, and M. Koshiba, "Non-proximity resonant tunneling in multi-core photonic band gap fibers: An efficient mechanism for engineering highly-selective ultra-narrow band pass splitters," Opt. Express 14, 4861-4872 (2006).
    [CrossRef] [PubMed]
  16. L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
    [CrossRef]
  17. T. Murao, K. Saitoh, and M. Koshiba, "Design of air-guiding modified honeycomb photonic band-gap fibers for effectively single-mode operation," Opt. Express 14, 2404-2412 (2006).
    [CrossRef] [PubMed]
  18. P. J. Roberts, D. P. Williams, H. Sabert, B. J. Mangan, D. M. Bird, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Design of low-loss and highly birefringent hollow-core photonic crystal fiber," Opt. Express 14, 7329-7341 (2006).
    [CrossRef] [PubMed]
  19. T. Murao, K. Saitoh, and M. Koshiba, "Realization of single-moded broadband air-guiding photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 1666-1668 (2006).
    [CrossRef]
  20. R. Amezcua-Correa, N. G. R. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, "Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers," Opt. Express 14, 7974-7985 (2006).
    [CrossRef] [PubMed]
  21. K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
    [CrossRef]
  22. K. Saitoh, N. J. Florous, T. Murao, and M. Koshiba, "Design of photonic band gap fibers with suppressed higher-order modes: Towards the development of effectively single mode large hollow-core fiber platforms," Opt. Express 14, 7342-7352 (2006).
    [CrossRef] [PubMed]
  23. M. Yan and P. Shum, "Improved air-silica photonic crystal with a triangular airhole arrangement for hollow-core photonic bandgap fiber design," Opt. Lett. 30, 1920-1922 (2005).
    [CrossRef] [PubMed]
  24. M. J. F. Digonnet, H. K. Kim, G. S. Kino, and S. Fan, "Understanding air-core photonic-bandgap fibers: Analogy to conventional fibers," J. Lightwave Technol. 23, 4169-4177 (2005).
    [CrossRef]
  25. M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
    [CrossRef]
  26. N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
    [CrossRef] [PubMed]

2006 (7)

N. J. Florous, K. Saitoh, T. Murao, and M. Koshiba, "Non-proximity resonant tunneling in multi-core photonic band gap fibers: An efficient mechanism for engineering highly-selective ultra-narrow band pass splitters," Opt. Express 14, 4861-4872 (2006).
[CrossRef] [PubMed]

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

T. Murao, K. Saitoh, and M. Koshiba, "Design of air-guiding modified honeycomb photonic band-gap fibers for effectively single-mode operation," Opt. Express 14, 2404-2412 (2006).
[CrossRef] [PubMed]

P. J. Roberts, D. P. Williams, H. Sabert, B. J. Mangan, D. M. Bird, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Design of low-loss and highly birefringent hollow-core photonic crystal fiber," Opt. Express 14, 7329-7341 (2006).
[CrossRef] [PubMed]

T. Murao, K. Saitoh, and M. Koshiba, "Realization of single-moded broadband air-guiding photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 1666-1668 (2006).
[CrossRef]

R. Amezcua-Correa, N. G. R. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, "Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers," Opt. Express 14, 7974-7985 (2006).
[CrossRef] [PubMed]

K. Saitoh, N. J. Florous, T. Murao, and M. Koshiba, "Design of photonic band gap fibers with suppressed higher-order modes: Towards the development of effectively single mode large hollow-core fiber platforms," Opt. Express 14, 7342-7352 (2006).
[CrossRef] [PubMed]

2005 (7)

2004 (4)

2003 (3)

2002 (1)

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

2000 (1)

1999 (1)

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

1996 (1)

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Allan, D. C.

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).
[CrossRef] [PubMed]

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

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

Amezcua-Correa, R.

Atkin, D. M.

Barkou, S. E.

Belau, S.

Bird, D. M.

Birks, T. A.

Borrelli, N. F.

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).
[CrossRef] [PubMed]

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

Broderick, N. G. R.

Broeng, J.

Couny, F.

Cregan, R. F.

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

de Sterke, C. M.

Digonnet, M. J. F.

Doll, T.

Duguay, M. A.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Dunn, S. C.

Eggleton, B. J.

Fan, S.

Farr, L.

Florous, N. J.

Gallagher, M. T.

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

Haas, T.

Hu, J.

Kim, H. K.

Kino, G. S.

Knight, J. C.

Koch, K. W.

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).
[CrossRef] [PubMed]

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

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Kokubun, Y.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Koshiba, M.

Litchinitser, N. M.

Mangan, B. J.

Mason, M. W.

McPhedran, R. C.

Mortensen, N. A.

Müller, D.

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

Murao, T.

Petrovich, M. N.

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Poletti, F.

Poli, F.

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

Richardson, D. J.

Roberts, P. J.

Russell, P. S. 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. S. J. Russell, "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005).
[CrossRef] [PubMed]

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

Russell, P. St. J.

Sabert, H.

Saitoh, K.

Selleri, S.

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

Shepherd, T. J.

Shin, J.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

H. K. Kim, M. J. F. Digonnet, G. S. Kino, J. Shin, and S. Fan, "Simulations of the effect of the core ring on surface and air-core modes in photonic bandgap fibers," Opt. Express 12, 3436-3442 (2004).
[CrossRef] [PubMed]

Shum, P.

Smith, C. M.

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).
[CrossRef] [PubMed]

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

Tomlinson, A.

Usner, B.

Venkataraman, N.

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

Vincetti, L.

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

Wadsworth, W. J.

West, J. A.

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).
[CrossRef] [PubMed]

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

White, T. P.

Williams, D. P.

Yan, M.

Appl. Phys. Lett. (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. Yan and P. Shum, "Air guiding with honeycomb photonic bandgap fiber," IEEE Photon. Technol. Lett. 17, 64-66 (2005).
[CrossRef]

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

T. Murao, K. Saitoh, and M. Koshiba, "Realization of single-moded broadband air-guiding photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 1666-1668 (2006).
[CrossRef]

J. Lightwave Technol. (2)

Nature (1)

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

Opt. Express (12)

K. Saitoh, N. A. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12, 394-400 (2004).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

H. K. Kim, M. J. F. Digonnet, G. S. Kino, J. Shin, and S. Fan, "Simulations of the effect of the core ring on surface and air-core modes in photonic bandgap fibers," Opt. Express 12, 3436-3442 (2004).
[CrossRef] [PubMed]

K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11, 3100-3109 (2003).
[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. Express 13, 236-244 (2005).
[CrossRef] [PubMed]

P. J. Roberts, D. P. Williams, B. J. Mangan, H. Sabert, F. Couny, W. J. Wadsworth, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Realizing low loss air core photonic crystal fibers by exploiting an antiresonant core surround," Opt. Express 13, 8277-8285 (2005).
[CrossRef] [PubMed]

N. J. Florous, K. Saitoh, T. Murao, and M. Koshiba, "Non-proximity resonant tunneling in multi-core photonic band gap fibers: An efficient mechanism for engineering highly-selective ultra-narrow band pass splitters," Opt. Express 14, 4861-4872 (2006).
[CrossRef] [PubMed]

T. Murao, K. Saitoh, and M. Koshiba, "Design of air-guiding modified honeycomb photonic band-gap fibers for effectively single-mode operation," Opt. Express 14, 2404-2412 (2006).
[CrossRef] [PubMed]

P. J. Roberts, D. P. Williams, H. Sabert, B. J. Mangan, D. M. Bird, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Design of low-loss and highly birefringent hollow-core photonic crystal fiber," Opt. Express 14, 7329-7341 (2006).
[CrossRef] [PubMed]

N. M. Litchinitser, S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. M. de Sterke, "Resonances in microstructured optical waveguides," Opt. Express 11, 1243-1251 (2003).
[CrossRef] [PubMed]

R. Amezcua-Correa, N. G. R. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, "Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers," Opt. Express 14, 7974-7985 (2006).
[CrossRef] [PubMed]

K. Saitoh, N. J. Florous, T. Murao, and M. Koshiba, "Design of photonic band gap fibers with suppressed higher-order modes: Towards the development of effectively single mode large hollow-core fiber platforms," Opt. Express 14, 7342-7352 (2006).
[CrossRef] [PubMed]

Opt. Lett. (4)

Science (1)

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

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Figures (14)

Fig. 1.
Fig. 1.

A portion of the 1/6 region in the unit cell of the improved triangular lattice which consists of air and silica, (b) cladding structure with structural parameters of d/Λ= 0.98, r/Λ= 0.085, θ = 80.0°, and (c) PBG diagram for the prescribed structural parameters.

Fig. 2.
Fig. 2.

Cross sections of the proposed PBGFs whose defected cores are realized (a) by removing 1 air hole and expanded (core radius R ≈ 3.2 μm), and (b) by removing 7 air-holes (R ≈ 6.4 μm). In both cases, the structural parameters of the cladding are d/Λ = 0.98, r/Λ = 0.085, θ = 80.0°, and Λ = 4.0 μm.

Fig. 3.
Fig. 3.

(a). Effective refractive indices of the guided modes as a function of normalized wavelength for the fiber whose core is realized by removing 1 air-hole and expanded, with normalized silica-ring thickness t/Λ = 0.01. The black solid curves represent the PBG boundaries. The fundamental mode is represented by the red curve, the second-order mode by the blue curve, and the third-order mode by the green curve. (b) Surface plots for the z-component of the Poynting vector for the fundamental-like mode at normalized wavelength of λ/Λ = 0.4.

Fig. 4.
Fig. 4.

Confinement losses of the fiber whose core is realized by removing 1 air-hole and expanded for (a) 6 rings (b) 10 rings. In both cases, t = 0.01Λ and Λ = 4.0 μm.

Fig. 5.
Fig. 5.

The wavelength dependence of the power fraction in the air-core of the fundamentallike mode for PBGF with t = 0.01Λ (red curve), and t = 0.02Λ (blue curve), where Λ = 4.0 μm.

Fig. 6.
Fig. 6.

(a) Effective refractive indices of the guided modes as a function of the normalized wavelength for the fiber whose core is realized by removing 1 air-hole and expanded, where t/Λ = 0.095, satisfying the first anti-resonant condition. (b) Surface plot for the z-component of the Poynting vector for the fundamental-like mode at a normalized wavelength of λ/Λ = 0.4.

Fig. 7.
Fig. 7.

Confinement losses of the fiber whose core is realized by removing 1 air-hole and expanded for (a) 6 rings (b) 10 rings. In both cases, t = 0.095Λ and Λ = 4.0 μm.

Fig. 8.
Fig. 8.

The wavelength-dependence of the power fraction in (a) the air-core, and (b) the silica-ring for the fundamental-like mode of the proposed PBGF whose core is realized by removing 1 air-hole and expanded, with d/Λ = 0.98, r/Λ = 0.085, θ = 80.0°, t = 0.095Λ, and Λ = 4.0 μm.

Fig. 9.
Fig. 9.

Variation color-map of the power fraction in (a) the air-core, and (b) the silica-ring for the fundamental-like mode of the PBGF, with d/Λ = 0.98, r/Λ = 0.085, θ = 80.0°, and Λ = 4.0μm.

Fig. 10.
Fig. 10.

(a). Effective refractive indices of the guided modes as a function of normalized wavelength for the fiber whose core is realized by removing 7 air-holes, where t/Λ = 0.095 to satisfy the anti-resonant condition. (b) Surface plots for the z-component of the Poynting vector for the fundamental-like mode at normalized wavelength of λ/Λ = 0.4.

Fig. 11.
Fig. 11.

Confinement losses of the fiber whose core is realized by removing 7 air-holes for 6 rings for (a) the fundamental-like and EH11-like modes, and (b) for the HE21-like, TE01-like, and HE31-like modes, where Λ = 4.0 μm and t/Λ = 0.095 to satisfy the anti-resonant condition.

Fig. 12.
Fig. 12.

The wavelength dependence of the power fraction (a) in the air-core, and (b) in the silica-ring for the fundamental-like mode of the proposed PBGF whose core is realized by removing 7 air-holes with d/Λ = 0.98, r/Λ = 0.085, θ = 80.0°, t = 0.095Λ, and Λ = 4.0 μm.

Fig. 13.
Fig. 13.

The wavelength dependence of the power fraction (a) in the air-core, and (b) in the silica-ring for the fundamental-like mode of the proposed PBGF whose core is realized by removing 7 air-holes with d/Λ = 0.98, r/Λ = 0.085, θ = 80.0°, t = 0.088Λ, and Λ = 4.0 μm.

Fig. 14.
Fig. 14.

Confinement losses of the fiber whose core is realized by removing 7 air-holes, and having 5 air-hole rings for the fundamental-like (red, blue, green, purple, cyan, and yellow curves) and second-order modes (black curves), where Λ = 4.0 μm and t/Λ = 0.088 to satisfy the anti-resonant condition at the wavelength of 1.48 μm.

Equations (7)

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s = Λ d ,
θ = 30 ° + θ 2 ,
r = r cos θ s 2 1 cos θ ,
O 1 x = d 2 r ,
O 1 y = Λ 2 3 ( r + s 2 ) tan θ .
t = ( 2 N + 1 ) λ 4 n 2 2 1 + ( λ 4 R ) 2 , N = 0,1,2 , .
η = glass annulus dA E × H * z cross section dA E × H * z .

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