Abstract

We present the results of numerical simulations of the modal properties of Photonic Band Gap Fibers (PBGFs) in which a structural distortion of the silica ring surrounding the air core is gradually introduced. We demonstrate that surface modes supported within such fibers are very sensitive to structural distortions, and that any asymmetric change in the structure can break their degeneracy resulting in associated changes in the anticrossing behavior of the orthogonally polarized core modes, and the development of polarization dependent transmission properties. Our results provide insight into recent experimental observations of wavelength dependent PDL and birefringence in PBGFs.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

IEEE Photonics Technol. Lett. (1)

K. Saitoh and M. Koshiba, �??Photonic bandgap fibers with high birefringence,�?? IEEE Photonics Technol. Lett. 14, 1291�??1293, (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. R. McIsaac, �??Symmetry-induced modal characteristics of uniform waveguides. i. summary of results,�?? IEEE Trans. Microwave Theory Tech. 23, 421�??429, (1975).
[CrossRef]

Nature (1)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, 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 (9)

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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3728">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3728</a>
[CrossRef] [PubMed]

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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-3</a>
[CrossRef] [PubMed]

G. Bouwmans, F. Luan, J. C. Knight, P. S. J. Russell, L. Farr, B. J. Mangan, and H. Sabert, �??Properties of a hollow-core photonic bandgap fiber at 850 nm wavelength,�?? Opt. Express 11, 1613�??1620 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613</a>
[CrossRef] [PubMed]

T. D. Engeness, M. Ibanescu, S. G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, �??Dispersion tailoring and compensation by modal interactions in omniguide fibers,�?? Opt. Express 11, 1175�??1196, (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1175">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1175</a>
[CrossRef] [PubMed]

G. Humbert, J. C. Knight, G. Bouwmans, P. S. Russell, D. P. Williams, P. J. Roberts, and B. J. Mangan, �??Hollow core photonic crystal fibers for beam delivery,�?? Opt. Express 12, 1477�??1484, (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477 ">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1477</a>
[CrossRef] [PubMed]

M. Wegmuller, M. Legre, N. Gisin, T. P. Hansen, C. Jacobsen, and J. Broeng, �??Experimental investigation of the polarization properties of a hollow core photonic bandgap fiber for 1550 nm,�?? Opt. Express 13, 1457�??1467 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1457">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1457</a>
[CrossRef] [PubMed]

X. Chen, M.-J. Li, N. Venkataraman, M. T. Gallagher, W. A.Wood, A. M. Crowley, J. P. Carberry, L. A. Zenteno, and K.W. Koch, �??Highly birefringent hollow-core photonic bandgap fiber,�?? Opt. Express 12, 3888�??3893 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3888">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3888</a>
[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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-236</a>
[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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1485,/a>
[CrossRef] [PubMed]

Opt. Lett. (3)

Proc. SPIE (1)

D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Muller, C. M. Smith, N. Venkataraman, J. A.West, P. Zhang, and K. W. Koch, �??Surface modes and loss in air-core photonic band-gap fibers,�?? in Photonic Crystal Materials and Devices, Proc. SPIE 5000, 161�??174, (2003).
[CrossRef]

Science (2)

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

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, �??Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,�?? Science 301, 1702�??1704, (2003).
[CrossRef] [PubMed]

Other (1)

T. J. Stephens, R. R. Maier, J. S. Barton and J. D. C. Jones, �??Fused silica hollow-core photonic crystal fibre for mid-infrared transmission,�?? presented at Conference on Lasers and Electro-Optics (CLEO); Postconference Digest, CPDD4, 16-21 May 2004, San Francisco, CA, USA, (2004).

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Figures (8)

Fig. 1.
Fig. 1.

(a) SEM image of a typical PBGF produced at our facilities; (b) idealized cross section of the PBGF under investigation; (c) main parameters for the definition of the simulated structure.

Fig. 2.
Fig. 2.

(Top) Effective index plot for the perfectly symmetric structure. The shaded area represents the bandgap as calculated for an infinite periodic cladding; (Bottom) Poynting vector of a linearly polarized mode: (a) and (h) are at the bandgap edges, while (b)→(d) and (e)→(g) show the mode evolution in the two branches of the anticrossing.

Fig. 3.
Fig. 3.

Deformation types considered: (A) overall deformation with f = 30%; (B) core deformation with an exaggerated f = 300% for illustration purposes.

Fig. 4.
Fig. 4.

Effect of deformation A with f = 5% and f = 10%. Linearly polarized modes are represented with solid lines, while dashed lines are used for any other polarization type.

Fig. 5.
Fig. 5.

Effect of deformation B, producing an increase of 5%, 10%, 20% and 30% on the thickness of vertical struts around the core.

Fig. 6.
Fig. 6.

Effect of core deformation on the mode having the transverse electric field polarized along the y (left) and x axis (right). The insets show the surface mode involved in the anticrossing.

Fig. 7.
Fig. 7.

The set of Lorentzian peaks proportional to the loss induced by avoided crossings in the two polarizations for different levels of structural deformation. The dashed lines represent single peaks while the continuous lines show the total contribution for each polarization.

Fig. 8.
Fig. 8.

Effective index (Top) and percentage of the mode in the core (Middle) for the 5 modes involved in three different anticrossings for a fiber with a 10% distortion; (Bottom) Calculated beatlength for various interactions between an x and y polarized mode.

Equations (3)

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( x , y ) ( [ 1 + f ] , y )
( x , y ) ( x · [ 1 f · ʌ d Lc ] , y )
Loss ( dB / m ) ~ γ i · κ ij 2 ( Δ β ij ) 2

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