Abstract

It is well known that periodic variations in refractive index can be used to create guidance in an optical fiber via photonic bandgap effects. It has also been shown that periodic structure in index-guiding microstructured fibers can lead to the guidance of additional leaky higherorder modes due to bandgap effects. Here we demonstrate that this additional guidance mechanism can have important practical implications in large mode area silica microstructured fibers. We also demonstrate that similar modes can exist when a bandgap is not present and attribute this guidance to a low density of states. Excellent agreement between theoretical predictions and experimental observations is demonstrated. We explore the impact of these additional modes on the practical operation of these fibers and explore ways of minimizing their effects via the fiber geometry.

© 2008 Optical Society of America

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References

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  1. T. M. Monro and H. Ebendorff-Heidepriem, "Progress In Microstructured Optical Fibers," Ann. Rev. Mater. Res. 36, 467-495 (2006).
    [CrossRef]
  2. K. Nakajima, J. Zhou, K. Tajima, K. Kurokawa, C. Fukai, and I. Sankawa, "Ultrawide-band single-mode transmission performance in a low-loss photonic crystal fiber," J. Lightwave Technol. 23, 7- 12 (2005).
    [CrossRef]
  3. J. C.  Baggett, T. M. Monro, and D. J. Richardson, "Mode area limits in practical single-mode fibers," CLEO 2005, Baltimore, paper CMD6 (2005).
  4. J. C. Flanagan, D. J. Richardson, M. J. Foster, and I. Bakalski, "Microstructured fibers for broadband wavefront filtering in the mid-IR," Opt. Express 14, 11773-11786 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11773.
    [CrossRef] [PubMed]
  5. J. Corbett and J. Allington-Smith, "Coupling starlight into single-mode photonic crystal fiber using a field lens," Opt. Express 13, 6527-6540 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-17-6527.
    [CrossRef] [PubMed]
  6. T. A. Birks, J. C. Knight, and P. S. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=ol-22-13-961.
    [CrossRef] [PubMed]
  7. J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic band gap guidance in optical fibers," Science 282, 1476-1478 (1998).
    [CrossRef] [PubMed]
  8. T. M. Monro, P. J. Bennett, N. G. R. Broderick, and D. J. Richardson, "Holey fibers with random cladding distributions," Opt. Lett. 25, 206-208 (2000).
    [CrossRef]
  9. R. F. Cregan B. J. Mangan, J. C. Knight, T. A. Birks, P. St. 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]
  10. T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
    [CrossRef]
  11. A. Ferrando E. Silvestre, J. J. Miret, P. AndrÃs, and M. V. Andras, "Donor and acceptor guided modes in photonic crystal fibers," Opt. Lett. 25, 1328-1330 (2000).
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  12. M. Yan and P. Shum, "Guidance varieties in photonic crystal fibers," J. Opt. Soc. Am. B 23, 1684-1691 (2006).
    [CrossRef]
  13. K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E,  58, 3896-3907 (1998)
    [CrossRef]
  14. T. D. Hedley, D. M. Bird, F. Benabid, J. C. Knight, and P. St. J Russell, "Modelling of a novel hollow-core photonic crystal fibre" QLES 2003, Baltimore, paper QTuL4 (2003)
  15. G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St. J. Russell, "Models for guidance in kagome-structured hollow-core photonic crystal fibres," Opt. Express 15, 12680-12685 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-12680.
    [CrossRef] [PubMed]
  16. J. Pottage, D. Bird, T. Hedley, J. Knight, T. Birks, P. Russell, and P. Roberts, "Robust photonic band gaps for hollow core guidance in PCF made from high index glass," Opt. Express 11, 2854-2861 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-22-2854.
    [CrossRef] [PubMed]
  17. The simulations were done using Comsol, http://www.comsol.com.
  18. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-10-3728S.
    [CrossRef] [PubMed]
  19. S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, "Complex FEM modal solver of optical waveguides with PML boundary conditions," Opt. Quantum Electron. 14, 1530 (2001).
  20. B. Kuhlmey, R. C. McPhedran, and C. Martijn de Sterke, "Modal cutoff in microstructured optical fibers," Opt. Lett. 27, 1684-1686 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=ol-27-19-1684.
    [CrossRef]
  21. Crystal fiber products website (large mode area fibers), http://www.crystal-fibre.com/products/lma.shtm.
  22. J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
    [CrossRef]
  23. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, "Grating resonances in airsilica microstructured optical fibers," Opt. Lett. 24, 1460-1462, (1999).
    [CrossRef]
  24. A. M. Grassi, F. Casagrande, M. D’Alessandro, and S. Marinoni, "Single-modeness of short large mode area fibers: An experimental study," Opt. Commun. 273, 127-132 (2007).
    [CrossRef]
  25. N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, "Improved large-mode-area endlessly single-mode photonic crystal fibers," Opt. Lett. 25, 393-395 (2003)
    [CrossRef]
  26. J. C. Baggett, T. M. Monro, J. R. Hayes, V. Finazzi, and D. J. Richardson, "Improving bending losses in holey fibers," OFC 2005, Anaheim, paper OWL4 (2005).

2007

2006

2005

2003

2002

2001

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, "Complex FEM modal solver of optical waveguides with PML boundary conditions," Opt. Quantum Electron. 14, 1530 (2001).

2000

1999

R. F. Cregan B. J. Mangan, J. C. Knight, T. A. Birks, P. St. 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]

J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T. A. Strasser, "Grating resonances in airsilica microstructured optical fibers," Opt. Lett. 24, 1460-1462, (1999).
[CrossRef]

1998

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E,  58, 3896-3907 (1998)
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic band gap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

1997

1995

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
[CrossRef]

Allington-Smith, J.

Atkin, D. M.

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
[CrossRef]

Baggett, J. C.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
[CrossRef]

Bakalski, I.

Bennett, P. J.

Bird, D.

Birks, T.

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic band gap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. S. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=ol-22-13-961.
[CrossRef] [PubMed]

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
[CrossRef]

Broderick, N. G. R.

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic band gap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Burger, S.

Busch, K.

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E,  58, 3896-3907 (1998)
[CrossRef]

Casagrande, F.

A. M. Grassi, F. Casagrande, M. D’Alessandro, and S. Marinoni, "Single-modeness of short large mode area fibers: An experimental study," Opt. Commun. 273, 127-132 (2007).
[CrossRef]

Corbett, J.

D’Alessandro, M.

A. M. Grassi, F. Casagrande, M. D’Alessandro, and S. Marinoni, "Single-modeness of short large mode area fibers: An experimental study," Opt. Commun. 273, 127-132 (2007).
[CrossRef]

Ebendorff-Heidepriem, H.

T. M. Monro and H. Ebendorff-Heidepriem, "Progress In Microstructured Optical Fibers," Ann. Rev. Mater. Res. 36, 467-495 (2006).
[CrossRef]

Eggleton, J.

Finazzi, V.

Flanagan, J. C.

Folkenberg, J. R.

Foster, M. J.

Fukai, C.

Furusawa, K.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
[CrossRef]

Grassi, A. M.

A. M. Grassi, F. Casagrande, M. D’Alessandro, and S. Marinoni, "Single-modeness of short large mode area fibers: An experimental study," Opt. Commun. 273, 127-132 (2007).
[CrossRef]

Hedley, T.

John, S.

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E,  58, 3896-3907 (1998)
[CrossRef]

Knight, J.

Knight, J. C.

Kuhlmey, B.

Kurokawa, K.

Marinoni, S.

A. M. Grassi, F. Casagrande, M. D’Alessandro, and S. Marinoni, "Single-modeness of short large mode area fibers: An experimental study," Opt. Commun. 273, 127-132 (2007).
[CrossRef]

Martijn de Sterke, C.

McPhedran, R. C.

Monro, T. M.

Mortensen, N. A.

Nakajima, K.

Nielsen, M. D.

Pearce, G. J.

Petersson, A.

Poletti, F.

Pottage, J.

Poulton, C. G.

Richardson, D. J.

Roberts, P.

Roberts, P. J.

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
[CrossRef]

Russell, P.

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, 1476-1478 (1998).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. S. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=ol-22-13-961.
[CrossRef] [PubMed]

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
[CrossRef]

Russell, P. St. J.

Sankawa, I.

Selleri,

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, "Complex FEM modal solver of optical waveguides with PML boundary conditions," Opt. Quantum Electron. 14, 1530 (2001).

Shepherd, T. J.

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
[CrossRef]

Simonsen, H. R.

Spalter, S.

Strasser, T. A.

Tajima, K.

Tse, V.

Westbrook, P. S.

Wiederhecker, G. S.

Windeler, R. S.

Zhou, J.

Ann. Rev. Mater. Res.

T. M. Monro and H. Ebendorff-Heidepriem, "Progress In Microstructured Optical Fibers," Ann. Rev. Mater. Res. 36, 467-495 (2006).
[CrossRef]

Electron. Lett.

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941 - 1943 (1995).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Commun.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. J. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
[CrossRef]

A. M. Grassi, F. Casagrande, M. D’Alessandro, and S. Marinoni, "Single-modeness of short large mode area fibers: An experimental study," Opt. Commun. 273, 127-132 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Optical and Quantum Electronics

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, "Complex FEM modal solver of optical waveguides with PML boundary conditions," Opt. Quantum Electron. 14, 1530 (2001).

Phys. Rev. E

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E,  58, 3896-3907 (1998)
[CrossRef]

Science

R. F. Cregan B. J. Mangan, J. C. Knight, T. A. Birks, P. St. 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]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, "Photonic band gap guidance in optical fibers," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

Other

J. C.  Baggett, T. M. Monro, and D. J. Richardson, "Mode area limits in practical single-mode fibers," CLEO 2005, Baltimore, paper CMD6 (2005).

T. D. Hedley, D. M. Bird, F. Benabid, J. C. Knight, and P. St. J Russell, "Modelling of a novel hollow-core photonic crystal fibre" QLES 2003, Baltimore, paper QTuL4 (2003)

The simulations were done using Comsol, http://www.comsol.com.

Crystal fiber products website (large mode area fibers), http://www.crystal-fibre.com/products/lma.shtm.

J. C. Baggett, T. M. Monro, J. R. Hayes, V. Finazzi, and D. J. Richardson, "Improving bending losses in holey fibers," OFC 2005, Anaheim, paper OWL4 (2005).

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Figures (12)

Fig. 1.
Fig. 1.

DOS maps for an infinite triangular lattice of circular air holes in silica glass (n=1.44) with (a) d/Λ=0.20, (b) d/Λ=0.33, (c) d/Λ=0.40 and (d) d/Λ=0.48.

Fig. 2.
Fig. 2.

(a) and (b) SEM images of fiber A: Λ=11.7 µm, d/Λ=0.33, N=7. (c) and (d) SEM image of fiber B: Λ=10.0 µm, d/Λ=0.48, N~8.

Fig. 3.
Fig. 3.

Main plot: color shading shows the density of states (DOS) for a triangular lattice of air holes with Λ=11.7 µm and d/Λ=0.33 in silica glass (n=1.44). Dotted black line corresponds to nFSM . Dashed blue lines indicate positions of core localized (defect) modes, shown to the right of the main plot for λ=1.064 µm.

Fig. 4.
Fig. 4.

Example near-field output intensity profile from a 50 cm straight length of fiber A at λ=1.064 µm for (a) optimized (on-axis) launch conditions and (b) detuned (off-axis) launch conditions. Corresponding predicted mode profiles are shown in inset.

Fig. 5.
Fig. 5.

(a) Color shading shows the density of states (DOS) for a triangular lattice of air holes with Λ=10.0 µm and d/Λ=0.48 in silica glass (n=1.44). Dotted black line corresponds to nFSM . Dashed blue lines indicate positions of core localized modes, shown to the right of the main plot for λ=1.064 µm.

Fig. 6.
Fig. 6.

Experimental observations at λ=1.064 µm: near-field intensity profiles of fiber B (solid core silica MOF with Λ=10.0 µm and d/Λ=0.48) for varying launch conditions. (a) bend radius≈20 cm, length=1 m, (b) straight fiber, length≈1 m, (c)–(e) straight fiber, length≈25 cm.

Fig. 7.
Fig. 7.

DOS maps for an infinite triangular lattice of circular air holes in silica glass (n=1.44) with (a) d/Λ=0.20, (b) d/Λ=0.33, (c) d/Λ=0.40 and (d) d/Λ=0.48 (shown on a smaller scale than in previous figures). Dashed blue lines correspond to mode type iii.

Fig. 8.
Fig. 8.

Calculated coupling efficiency as a function of wo for the fundamental mode and mode type iii for (a) launch centered on fiber core and (b) offset launch.

Fig. 9.
Fig. 9.

Fig. 9. (a), (e) and (i) show near-field intensity profiles from a straight 50 cm length of fiber LMA-8 at λ=633 nm, imaged on to a CCD camera. (d), (h) and (l) show predicted modal intensity profiles calculated using a FEM approach, corresponding to the FM, the mode of type iii and a 90:10 combination of these two modes, respectively. Figs (b), (f) and (j) show cross-sectional slices in the x direction through the observed (in blue) and predicted (in red) profiles shown on the same row. Figs (c), (g) and (k) show the same as Figs (b), (f) and (j) for slices in the y direction.

Fig. 10.
Fig. 10.

Confinement loss vs. number of rings of holes for Λ=11.7 µm, d/Λ=0.33 at λ=514 nm for the fundamental mode and mode type iii

Fig. 11.
Fig. 11.

Fig. 11. (a)–(c) Transverse structure, FM and mode type iii for a 5% randomization in hole position. Λ=11.7 µm, d/Λ=0.33 at λ=514 nm (N=7), shown in a 60×60 µm box.

Fig. 12.
Fig. 12.

(a) and (b) show the DOS for Λ=10.0 µm, d/Λ=0.48 and Λ=6.0 µm, d/Λ=0.20, respectively. The blue dashed lines correspond to core localized modes for (a) a single-defect core and (b) a three-defect core. Figures (c)–(e) show example modal intensity profiles for fiber C (three defect core with Λ=6.0 µm, d/Λ=0.20 and N=10) at λ=1.064 µm.

Tables (2)

Tables Icon

Table 1. mode parameters for Λ=11.7, d/Λ=0.33 at 1.064 µm (n=1.44)

Tables Icon

Table 2. mode parameters for Λ=10.0, d/Λ=0.48 at 1.064 µm (n=1.44)

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