Abstract

In this article, we deal with new properties of a Solid Core Photonic Bandgap (SC-PBGF) fiber with intersticial air holes (IAHs) in its transverse structure. It has been shown recently, that IAH enlarges its bandgaps (BG), compared to what is observed in a regular SC-PBGF. We shall describe the mechanisms that account for this BG opening, which has not been explained in detail yet. It is then interesting to discuss the role of air holes in the modification of the Bloch modes, at the boundaries of the BG. In particular, we will use a simple method to compute the exact BG diagrams in a faster way, than what is done usually, drawing some parallels between structured fibers and physics of photonic crystals. The very peculiar influence of IAHs on the upper/lower boundaries of the bandgaps will be explained thanks to the difference between mode profiles excited on both boundaries, and linked to the symmetry / asymmetry of the modes. We will observe a modification of the highest index band (n FSM) due to IAHs, that will enable us to propose a fiber design to guide by Total Internal Reflection (TIR) effect, as well as by a more common BG confinement. The transmission zone is deeply enlarged, compared to regular photonic bandgap fibers, and consists in the juxtaposition of (almost non overlapping) BG guiding zones and TIR zone.

© 2007 Optical Society of America

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  1. F. Couny, F. Benabid, P. J. Roberts, M. T. Burnett, S. A. Maier, "Identification of Bloch-modes in hollow-core photonic crystal fiber cladding," Opt. Express 15, 325 (2007).
    [CrossRef] [PubMed]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: molding the flow of light, (Princeton: Princeton University Press).
  3. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. B. Cordeiro, F. Luan, and Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309 (2005).
    [CrossRef] [PubMed]
  4. N. M. Litchinister, 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 (2003).
    [CrossRef]
  5. A. K. Abeeluck, N. M. Litchinitser, C. Headley, B. J. Eggleton, "Analysis of spectral characteristics of photonic bandgap waveguides," Opt. Express 10, 1320 (1999).
  6. T. P. White, R. C. McPhedran, C. Martijn de Sterke, N. M. Litchinister, and B. J. Eggleton, "Resonance and scattering in microstructured optical fibres," Opt. Lett. 27, 1977 (2002).
    [CrossRef]
  7. T. A. Birks, G. J. Pearce, D.M. Bird, "Approximate band structure calculation for photonic bandgap fibres," Opt. Express 14, 9483 (2006).
    [CrossRef] [PubMed]
  8. G. Renversez, P. Boyer and A. Sagrini, "Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling," Opt. Express 14, 5682 (2006).
    [CrossRef] [PubMed]
  9. B. T. Kuhlmey, K. Pathmanandavel, R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10851 (2006).
    [CrossRef] [PubMed]
  10. J. M. Stone, G. J. Pearce, F. Luan, T. A. Birks, J. C. Knight, A. K. George, D. M. Bird, "An improved photonic bandgap fiber based on an array of rings," Opt. Express 14, 6291 (2006).
    [CrossRef] [PubMed]
  11. G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
    [CrossRef]
  12. A. Betourne, V. Pureur, G. Bouwmans, Y. Quiquempois, L. Bigot, M. Perrin, M. Douay, "Solid photonic bandgap fiber assisted by and extra air-clad structure for low-loss operation around 1.5 ?m," Opt. Express 15, 316 (2007).
    [CrossRef] [PubMed]
  13. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, M. Douay, "Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm," Opt. Express 13, 8452 (2005).
    [CrossRef] [PubMed]
  14. A. Cerqueira S. Jr., F. Luan, C. M. B. Cordeiro, A. K. George, J. C. Knight, "Hybrid Photonic crystal fiber," Opt. Express 14, 926 (2006).
    [CrossRef] [PubMed]
  15. A. Betourne, G. Bouwmans, Y. Quiquempois, M. Perrin, M. Douay, "Improvements of solid core photonic bandgap fibers by means of interstitial air holes," Opt. Lett.  32, N 12 (2007).
    [CrossRef]
  16. J. Laegsgaard and A. Bjarklev, "Doped photonic bandgap fibers for short-wavelength nonlinear devices," Opt. Lett. 28, 783 (2003).
    [CrossRef] [PubMed]
  17. MPB software, URL: http://ab-initio.mit.edu/mpb/>
  18. J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
    [CrossRef]
  19. J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic Band Gap Guidance in Optical Fibers," Science 282, 1476 (1998).
    [CrossRef] [PubMed]
  20. J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Solid Photonic Badgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059 (2006).
    [CrossRef]
  21. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688 (2006).
    [CrossRef] [PubMed]
  22. A. Yariv, Quantum Electronics, 3rd ed., (John Wiley & Sons 1988) Chap. 22.8 627-640.
  23. C. Kittel, Introduction to Solid State Physics, (Wiley, 2004).
  24. J. P. B’erenger,"A perfectly matched layer for the absorption of electomagnetic waves," J. Comp. Phys. 114, 185 (1994).
    [CrossRef]
  25. A. Bjarklev, J. Broeng, A. S. Bjarklev, "Photonic Crystal Fibers," (Kluwer Academic Publishers, see section 6.4.2.2).
  26. M. J. F. Digonnet, H. K. Kim, J. Shin, S. Fan, G. S. Kino, " Simple geometric criterion to predict the existence of surface modes in air-core photonic-bandgap fibers," Opt. Express 12, 1864 (2004).
    [CrossRef] [PubMed]

2007 (3)

2006 (8)

2005 (2)

2004 (1)

2003 (2)

2002 (1)

1999 (2)

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
[CrossRef]

A. K. Abeeluck, N. M. Litchinitser, C. Headley, B. J. Eggleton, "Analysis of spectral characteristics of photonic bandgap waveguides," Opt. Express 10, 1320 (1999).

1998 (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic Band Gap Guidance in Optical Fibers," Science 282, 1476 (1998).
[CrossRef] [PubMed]

1994 (1)

J. P. B’erenger,"A perfectly matched layer for the absorption of electomagnetic waves," J. Comp. Phys. 114, 185 (1994).
[CrossRef]

Abeeluck, A. K.

Argyros, A.

Barbeito, P. M.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
[CrossRef]

Barkou, S. E.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
[CrossRef]

Benabid, F.

Bigot, L.

Bird, D. M.

Bird, D.M.

Birds, D. M.

J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Solid Photonic Badgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059 (2006).
[CrossRef]

T. A. Birks, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688 (2006).
[CrossRef] [PubMed]

Birks, T. A.

Bjarklev, A.

J. Laegsgaard and A. Bjarklev, "Doped photonic bandgap fibers for short-wavelength nonlinear devices," Opt. Lett. 28, 783 (2003).
[CrossRef] [PubMed]

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
[CrossRef]

Bouwmans, G.

Boyer, P.

Broeng, J.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic Band Gap Guidance in Optical Fibers," Science 282, 1476 (1998).
[CrossRef] [PubMed]

Burnett, M. T.

Cordeiro, C. B.

Couny, F.

de Sterke, C. M.

Digonnet, M. J. F.

Douay, M.

Dunn, S. C.

Eggleton, B. J.

Fan, S.

George, A. K.

Headley, C.

Kim, H. K.

Kino, G. S.

Knight, J. C.

J. M. Stone, G. J. Pearce, F. Luan, T. A. Birks, J. C. Knight, A. K. George, D. M. Bird, "An improved photonic bandgap fiber based on an array of rings," Opt. Express 14, 6291 (2006).
[CrossRef] [PubMed]

J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Solid Photonic Badgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059 (2006).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic Band Gap Guidance in Optical Fibers," Science 282, 1476 (1998).
[CrossRef] [PubMed]

Kuhlmey, B. T.

Laegsgaard, J.

Leon-Saval, S. G.

Litchinister, N. M.

Litchinitser, N. M.

Lopez, F.

Luan, F.

Luo, J.

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

Maier, S. A.

Martijn de Sterke, C.

McPhedran, R. C.

Pathmanandavel, K.

Pearce, G. J.

Provino, L.

Quiquempois, Y.

Ren, G.

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

Renversez, G.

Roberts, P. J.

Russell, P. S. J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic Band Gap Guidance in Optical Fibers," Science 282, 1476 (1998).
[CrossRef] [PubMed]

Sagrini, A.

Shin, J.

Shum, P.

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

Sondergaard, T.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
[CrossRef]

Stone, J. M.

Tong, W.

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

Usner, B.

Wang, A.

J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Solid Photonic Badgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059 (2006).
[CrossRef]

T. A. Birks, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688 (2006).
[CrossRef] [PubMed]

White, T. P.

Yan, M.

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

Yu, X.

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

Zhang, L.

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. Ren, P. Shum, L. Zhang, M. Yan, X. Yu, W. Tong, J. Luo, " Design of all-solid Bandgap fiber with improved confinement and bend losses," IEEE Photon. Technol. Lett.  18, 24 (2006).
[CrossRef]

J. Comp. Phys. (1)

J. P. B’erenger,"A perfectly matched layer for the absorption of electomagnetic waves," J. Comp. Phys. 114, 185 (1994).
[CrossRef]

J. Opt. A : Pure Appl. Opt. (1)

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, A. Bjarklev, "Waveguidance by the photonic bandgap effect in optical fibres," J. Opt. A : Pure Appl. Opt. 1, 477 (1999).
[CrossRef]

Jpn. J. Appl. Phys. (1)

J. C. Knight, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Solid Photonic Badgap Fibres and Applications," Jpn. J. Appl. Phys. 45, 6059 (2006).
[CrossRef]

Opt. Express (13)

T. A. Birks, F. Luan, G. J. Pearce, A. Wang, T. A. Birks and D. M. Birds, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688 (2006).
[CrossRef] [PubMed]

M. J. F. Digonnet, H. K. Kim, J. Shin, S. Fan, G. S. Kino, " Simple geometric criterion to predict the existence of surface modes in air-core photonic-bandgap fibers," Opt. Express 12, 1864 (2004).
[CrossRef] [PubMed]

F. Couny, F. Benabid, P. J. Roberts, M. T. Burnett, S. A. Maier, "Identification of Bloch-modes in hollow-core photonic crystal fiber cladding," Opt. Express 15, 325 (2007).
[CrossRef] [PubMed]

A. Betourne, V. Pureur, G. Bouwmans, Y. Quiquempois, L. Bigot, M. Perrin, M. Douay, "Solid photonic bandgap fiber assisted by and extra air-clad structure for low-loss operation around 1.5 ?m," Opt. Express 15, 316 (2007).
[CrossRef] [PubMed]

G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, M. Douay, "Fabrication and characterization of an all-solid 2D photonic bandgap fiber with a low-loss region (< 20 dB/km) around 1550 nm," Opt. Express 13, 8452 (2005).
[CrossRef] [PubMed]

A. Cerqueira S. Jr., F. Luan, C. M. B. Cordeiro, A. K. George, J. C. Knight, "Hybrid Photonic crystal fiber," Opt. Express 14, 926 (2006).
[CrossRef] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. B. Cordeiro, F. Luan, and Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309 (2005).
[CrossRef] [PubMed]

N. M. Litchinister, 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 (2003).
[CrossRef]

A. K. Abeeluck, N. M. Litchinitser, C. Headley, B. J. Eggleton, "Analysis of spectral characteristics of photonic bandgap waveguides," Opt. Express 10, 1320 (1999).

T. A. Birks, G. J. Pearce, D.M. Bird, "Approximate band structure calculation for photonic bandgap fibres," Opt. Express 14, 9483 (2006).
[CrossRef] [PubMed]

G. Renversez, P. Boyer and A. Sagrini, "Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling," Opt. Express 14, 5682 (2006).
[CrossRef] [PubMed]

B. T. Kuhlmey, K. Pathmanandavel, R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10851 (2006).
[CrossRef] [PubMed]

J. M. Stone, G. J. Pearce, F. Luan, T. A. Birks, J. C. Knight, A. K. George, D. M. Bird, "An improved photonic bandgap fiber based on an array of rings," Opt. Express 14, 6291 (2006).
[CrossRef] [PubMed]

Opt. Lett. (3)

Science (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic Band Gap Guidance in Optical Fibers," Science 282, 1476 (1998).
[CrossRef] [PubMed]

Other (5)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: molding the flow of light, (Princeton: Princeton University Press).

MPB software, URL: http://ab-initio.mit.edu/mpb/>

A. Bjarklev, J. Broeng, A. S. Bjarklev, "Photonic Crystal Fibers," (Kluwer Academic Publishers, see section 6.4.2.2).

A. Yariv, Quantum Electronics, 3rd ed., (John Wiley & Sons 1988) Chap. 22.8 627-640.

C. Kittel, Introduction to Solid State Physics, (Wiley, 2004).

Supplementary Material (1)

» Media 1: AVI (1342 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Panel (a) shows the cladding we study. In an elementary cell (inside the white bordered parallelogram), two IAHs (in blue) surround a parabolic radial index profile, that model a high index rod (in dark red), with d/Λ = 0.725. The maximum index gradient, between the rod center and the background is Δn = 3.2∙10-2. IAHs have a diameter dair /Λ = 0.152. Panel (b) shows the BG diagram for the cladding with IAHs (full thick black line and dashed thick black line, which represents the FSM line), and without IAH (grey line with symbols). The thin horizontal black line represents the silica index nc = 1.45.

Fig. 2.
Fig. 2.

Band diagram for structure B cladding. Only the lines corresponding to Γ, M or K have been represented. The BG have been shaded, and isolated rod LP modes are labeled. An insert represents the Brillouin zone of an hexagonal lattice. Particular values of β have been pointed out, in units of Λ-1.

Fig. 3.
Fig. 3.

Intensity and field profile for both borders of the first beam of permitted modes, associated to the LP01 mode, computed near the tip of first BG, at βΛ = 3, cf. Fig. 2, for structure B. Color bar at the right of the panels refer to the normalized field or intensity value. A contour plot on Fig. 3(b) shows iso-intensity lines, in logarithmic scale. The corresponding color bar is on the left of panel (b). On every panel, the dotted circles represent the high index inclusions. The arrow on Fig. 3(c) indicate ΓK direction.

Fig. 4.
Fig. 4.

Real part of one transverse component of the electric field, for both borders of the second beam of permitted mode, associated to the LP11 mode, computed at βΛ = 7, cf. Fig. 2, for structure B. The arrow on Fig. 4(b) indicates the ΓM direction.

Fig. 5.
Fig. 5.

Real part of one transverse component of electric field, Ex , for both borders of the second beam of permitted mode, associated to the LP11 mode, computed at βΛ = 7, cf. Fig. 2, for structure A and B. The dotted circles represent the geometry of the structure.

Fig. 6.
Fig. 6.

Panel (a) shows a zone around the core of the fibre we study. The color code refers to the different index of the constituent – Ge-doped silica, silica, air. The boundaries are those of the periodic cladding without defect. On panel(b), one can see (lines without symbols) the dispersion diagram of the lowest frequency band index – n FSM – of the cladding structure. Different sizes of IAH have been used. From top to bottom, the dashed lines correspond to IAH radius of rIAH = 2.5.10-2 and rIAH = 4.5.10-2, in Λ units. The full black line corresponds to structure A, rIAH = 7.5.10-2, as used in section (2). The line with symbols corresponds to the TIR mode observed in the fiber we study.

Fig. 7.
Fig. 7.

Modes intensity profiles at different values of λ/Λ, for an 8 rings structure. In each panel, two insets represents a transverse and a unidimensional cut view. [Media 1]

Tables (2)

Tables Icon

Table 1. Summary of the characteristics of the first four BG boundaries.

Tables Icon

Table 2. Synthetic presentation of the properties of permitted mode borders. The nature of the border, as well as the influence of the presence (or absence) of IAH have been mentioned, due to constructive (or destructive) interference between the rods.

Metrics