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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 2 — Jan. 22, 2007
  • pp: 316–324
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Solid photonic bandgap fiber assisted by an extra air-clad structure for low-loss operation around 1.5 μm

A. Bétourné, V. Pureur, G. Bouwmans, Y. Quiquempois, L. Bigot, M. Perrin, and M. Douay  »View Author Affiliations


Optics Express, Vol. 15, Issue 2, pp. 316-324 (2007)
http://dx.doi.org/10.1364/OE.15.000316


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Abstract

We demonstrate that our previous loss results [1] in an all-solid photonic bandgap fiber were in fact limited by bend loss. A new design, based on the addition of an extra ring of air holes on the outside of the all-solid photonic bandgap structure, is then proposed, realized and characterized. We demonstrate that it significantly reduces both the fiber diameter and its sensitivity to bend loss.

© 2007 Optical Society of America

1. Introduction

In the large family of Photonic Crystal Fibers (PCFs) [1

1. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and 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 13,8452–8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]

-4

4. W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron .41,1558–1564 (2005). [CrossRef]

], Photonic BandGap Fibers (PBGFs) are probably the most original ones as the light in these structures is confined in a low index core conversely to all the other fibers. Such confinement leads to very unusual and interesting dispersive and spectral properties [5

5. G. Bouwmans, F. Luan, J.C. Knight, P.St.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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613 [CrossRef]

-8

8. F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, “Singlemode propagation into depressed-core-index photonic-bandgap fiber designed for zero-dispersion propagation at short wavelengths,” Electron. Lett. 36 :514–515 (2000). [CrossRef]

]. Among these PBGFs, the totally solid ones [1

1. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and 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 13,8452–8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]

,8

8. F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, “Singlemode propagation into depressed-core-index photonic-bandgap fiber designed for zero-dispersion propagation at short wavelengths,” Electron. Lett. 36 :514–515 (2000). [CrossRef]

,9

9. F. Luan, A.K. George, T.D. Hedley, G.J. Pearce, D.M. Bird, J.C .Knight, and P.St.J. Russell, “All solid photonic bandgap fiber,” Opt. Lett .29,2369–2371 (2004). [CrossRef] [PubMed]

], made of pure and doped silica, are particularly interesting as they present the great benefit to associate the original properties of PBGFs (in terms of chromatic dispersion and spectral filtering) with the advantages of all-solid fibers (relatively easy to fabricate, to splice, to actively dope and to insolate for Bragg gratings realization). Since the first realization of 2D all-solid PBGFs in 2004 [9

9. F. Luan, A.K. George, T.D. Hedley, G.J. Pearce, D.M. Bird, J.C .Knight, and P.St.J. Russell, “All solid photonic bandgap fiber,” Opt. Lett .29,2369–2371 (2004). [CrossRef] [PubMed]

], significant progress have been made, both in terms of attenuation [1

1. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and 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 13,8452–8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]

] and comprehension of these fibers properties [10

10. A. Argyros, T.A. Birks, S.G. Leon-Saval, C.B. Cordeiro, F. Luan, and P.St.J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13,309–314 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309 [CrossRef] [PubMed]

-12

12. T.A. Birks, F. Luan, G.J. Pearce, A. Wang, J.C. Knight, and D.M. Bird, “Bend loss in all-solid bandgap fibres,” Opt. Express 14,5688 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5688 [CrossRef] [PubMed]

].

In this paper, we propose to further investigate experimentally the quantitative importance of bend loss in these fibers. We also propose and realize a new fiber design that allows a decrease of the bend sensitivity for these low index contrast PBGFs.

2. Bend loss: a limiting factor?

In Ref. [1

1. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and 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 13,8452–8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]

] we reported the lowest loss obtained in 2D all-solid PBGFs. However the measured total loss (around 18 dB/km) was about 20 times higher than the one predicted by numerical simulation using a commercial vectorial Finite Element Method (FEM) with Perfectly Matched Layers (PML) (COMSOL 3.2b software) [13

13. J. Jin, “The Finite Element Method in Electromagnetics” (John Wiley & Sons, Inc., New York, 2002).

]. The effect responsible for this discrepancy could be the appearance of important bend losses. In order to investigate the relative importance of such losses, we performed series of cut-back measurements for the fiber described in Ref. [1

1. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and 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 13,8452–8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]

] wrapped on spools of different radii. The results are summarized on Fig. 1(a) (limited to the 3rd PBG window of our fiber) and Fig. 1(b) (overview from the 3rd to 6th PBG). On both graphs, the green, red and blue curves were obtained for respectively 7.9, 10.5 and 15.8 cm spools radii.

Fig. 1. Loss spectra obtained by cut-back measurements of the all-solid PBGF [1] wrapped on spools of different radius R: R=7.9 cm (green), R=10.5 cm (red) and R=15.8 cm (blue). a) zoom on the 3rd bandgap; b) overview from the 6th to the 3rd bandgap.

Finally, let’s mention that we also observed, as T.A. Birks et al. [12

12. T.A. Birks, F. Luan, G.J. Pearce, A. Wang, J.C. Knight, and D.M. Bird, “Bend loss in all-solid bandgap fibres,” Opt. Express 14,5688 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5688 [CrossRef] [PubMed]

] did recently albeit on a different fiber with significantly larger bend loss, i) that bending our all-solid PBGF reduces more the transmission window on the shorter wavelength side of the PBG than on the longer wavelength side ii) that even PBGs are more sensitive to bend loss than odd ones. For example, the estimated extra losses due to a decrease of R from 15.8 to 7.9 cm are of 740 dB/km for the 4th PBG whereas they are “only” of 12 dB/km and 170 dB/km for the 3rd and 5th PBGs (cf. Fig. 1(b)). An interpretation of these surprising results can be found in Ref. [12

12. T.A. Birks, F. Luan, G.J. Pearce, A. Wang, J.C. Knight, and D.M. Bird, “Bend loss in all-solid bandgap fibres,” Opt. Express 14,5688 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5688 [CrossRef] [PubMed]

].

3. New design

As bend loss appears to have a major impact on the transmission properties of low index contrast PBGFs, we investigated a new design to reduce the fiber bend sensitivity.

3.1 Principle

A well-known solution to reduce bend loss for conventional fiber is to add a low index region in the fiber cladding [14

14. S. Tomljenovic-Hanic, J.D. Love, and A. Ankiewicz, “Low-loss singlemode waveguide and fibre bends,” Electron. Lett. 38,220–222 (2002). [CrossRef]

]. This low index region acts as a barrier to avoid coupling of the light between the core region and the effective higher index cladding (due to the bend [14

14. S. Tomljenovic-Hanic, J.D. Love, and A. Ankiewicz, “Low-loss singlemode waveguide and fibre bends,” Electron. Lett. 38,220–222 (2002). [CrossRef]

]) on the outside of the bend. We thus propose the new design shown in Fig. 2. It is based on both the reduction of the number of doped rings and the addition of an extra holey ring to help the confinement of the core mode both for the straight and bent fiber. The number of doped rings will come from a compromise between a large number that will reduce the confinement losses of the straight fiber but lead to a thicker fiber and a small number that is likely to present the disadvantage of diminishing the PBG effect in favor of the more conventional Total Internal Reflection (TIR) due to the proximity of the core and the holey region. In the case of a large number of doped rings, the bend sensitivity reduction is also anticipated to be less efficient as the low index region is further away from the core. More precisely, it is expected that a larger inner cladding will support cladding modes with effective indices more “affected” by the bend (for a fixed R) as the perturbation increases away from the core. This will lead to an increase of the coupling between the core mode and inner cladding modes and thus produces bend loss either on the outside or inside of the bend as explained in Ref. [12

12. T.A. Birks, F. Luan, G.J. Pearce, A. Wang, J.C. Knight, and D.M. Bird, “Bend loss in all-solid bandgap fibres,” Opt. Express 14,5688 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5688 [CrossRef] [PubMed]

].

Fig. 2. Schematic representation of the proposed double-clad PBGF. (a) transversal cut (b) index profile along axis x with the definition of the pitch Λ, the doped region diameter d and the hole diameter dH.

Note that, for simplicity of fabrication, we kept the same pitch, Λ, for the doped and air hole rings but allowed the doped region diameter, d, and the holes diameter, dH, to be different.

This new design, called hereafter Double-Clad (DC) PBGF, appears as an alternative to the one proposed recently by J.M. Stone et al. consisting in using annular doped rods [15

15. J.M. Stone, G.J. Pearce, F. Luan, T.A. Birks, J.C. Knight, A.K. George, and D.M. Bird, “An improved photonic bandgap fiber based on an array of rings,” Opt. Express 14,6291–6296 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6291 [CrossRef] [PubMed]

], but the two solutions are not incompatible and can indeed be implemented together.

3.2 Modeling

Our new design has the obvious advantage to reduce the number of doped rods from 168 (7 rings) to 36 (3 rings) whereas keeping the confinement loss to a low level. As a direct consequence, the fiber diameter (generally rather large to insure low loss transmission in these class of low index contrast PBGFs) is then also significantly reduced. The advantage of this new design against bend loss will be demonstrated experimentally in section 5.

Fig. 3. Theoretical plot of the bandgaps (white). For simplicity, the silica refractive index is kept constant and equal to 1.45 (upper blue curve). Also shown the fundamental space filling mode of the air clad (nFSM, lower blue curve) and the effective index of the fundamental core mode in the 3rd and 4th bandgap (dark lines).

To predict the optical properties of such fibers, the PBGs for a triangular lattice of parabolic high index rods embedded in a silica background have been calculated using a Plane Wave Expansion method developed at the MIT (MPB) [16

16. S.G. Johnson and J.D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in planewave basis,” Opt. Express 8,173–190 (2001). http://www.opticsexpress.org/abstract.cfm?id=63584. [CrossRef] [PubMed]

] with the above opto-geometrical parameters (but without the holey ring). The PBGs are displayed in Fig. 3 assuming a constant refractive index for the background.

The second clad (i.e. the holey ring) will act as a lower index region compare to the inner cladding. The effective index of this region will be, for simplicity, approximated in the following by the effective index of the fundamental space filling mode (nFSM) calculated using the analytical relationships given in Ref. [17

17. K. Saitoh and M. Koshiba, “Empirical Relations for simple design of photonic crystal fibers,” Opt. Express 13,267–274 (2005). http://www.opticsexpress.org/abstract.cfm?id=82269 [CrossRef] [PubMed]

]. Its evolution against wavelength has been plotted in blue on Fig. 3 (lower blue curve). Also shown are the fundamental modes for the band gaps # 3 and # 4 (dark curves). In the high effective index region (above nsilica), the mode of the whole ensemble of rods gather into a discrete ensemble of single rod modes. A label placed above Fig. 3, gives the nature of these LPlm modes.

A possible drawback of this new fiber is that higher order core modes will also be better confined in the ‘defect’ core by the depressed cladding, as long as their effective indices are higher than nFSM. However, we verified numerically that, for the design described above, the differential loss between the first higher order mode and the fundamental mode is still significantly large (> 2 orders of magnitude between 1400-1600 nm) to practically ensure singlemode operation. Note also that it is possible theoretically to modify nFSM (by simply changing dH) in order to adjust it between the fundamental and the first higher order core mode effective indices. Doing this, one can expect to increase the differential loss between these two modes as the depressed cladding will act as a conventional confinement layer only for the fundamental core mode. However this may work efficiently only for some specific wavelengths and will add strict requirements on the holes diameters. As we want to keep the fabrication as simple as possible we have discarded such possibility.

4. Fabrication

Fig. 4. Scanning Electron Micrograph (SEM) of the DC PBGF. The fiber diameter is 187 μm for a core diameter of 20 μm, a pitch, Λ, of 15 μm and an average hole diameter dH of 10.6 μm.

5. Experimental characterization of DC PBGF.

In order to facilitate the study of the air-clad addition impact, we used the same set-up as in [1

1. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and 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 13,8452–8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]

] to characterize our new fiber. In particular, all the spectra described below were obtained by butt-coupling a super continuum source to the input of the fiber under test whereas the fiber output was butt-coupled to a standard telecom single mode fiber (∼ 10 m of SMF28) connected to an Optical Spectrum Analyser (OSA) with a 1 nm resolution.

5.1 Preliminary results

Fig. 5. (a) Transmission spectrum of the DC PBGF through 460 m (blue) and 10 m (red) with the bandgap number. (c) and (d) are the mode profiles observed at 1150 nm for respectively L = 10 m and L = 460 m. e) and g) are the mode profiles observed for L = 460 m at respectively 1190 et 1500 nm. Note that if (d) and (e) show all the solid microstructured cladding, (c) and (g) are zoomed on the core mode, whereas (b) and (f) are zooms on few doped rods respectively at 950 and 1190 nm.

This phenomenom is even more dramatic in the vicinity of the 5th bandgap where only the cladding modes can be observed through the 460 m piece with LP03-like modes in the high index region (cf. Fig. 5(b)). In opposite, the fundamental core mode of the 3rd bandgap is clearly observed (Fig. 5(g)) for L = 460 m and the cladding modes contribute significanlty to this transmission spectrum only for wavelength higher than 1615 nm (Fig. 5(a)).

Note that the bandgap-like transmission of these cladding modes (for example the transmission window from 922 to 952 nm for L= 460 m), poorly excited at the fiber input, can be understood as a consequence of i) an efficient power coupling from the core mode to these modes only for wavelengths around the cut-off of the isolated rods and ii) an increase of their losses with the wavelength as their effective index become closer to nFSM (cf. Fig. 3).

5.2 Validation of bend losses reduction

We now focus on the 3rd bandgap centered around 1550 nm. Figure 6 shows the total loss spectra obtained by cutting back the DC PBGF from around 500 m to 10 m for two bend radius, R = 7.9 cm (dark green curve) and R= 15.8 cm (dark blue curve). In order to facilitate the comparison between the two designs we also add to this graph, in bright colors, the corresponding loss spectra for the all-solid PBGF described in section 2.

Fig. 6. Loss spectra of the DC PBGF obtained by the cut back technique for bend radius of 15.8 cm (dark blue curve) and 7.9 cm (dark green curve). The red circle points out an artifact due to the existence of extra confined modes. The corresponding spectra for the all-solid PBGF are represented in bright colors.

Except for this particularity, the loss spectra for the largest bend radius (R= 15.8 cm, blue curves) are very similar for both fibers, demonstrating experimentally the confinement properties of the extra air holes ring. Note that the experimental minimum losses of our new design are about 10 times higher than the one expected from confinement loss calculations done for the ideal structure described in section 3. The exact origin (OH contaminations, transverse and longitudinal defect of the structure…) of this discrepancy is under current investigations.

However, the advantage of the new design clearly appears for R = 7.5 cm. Thus, while the impact of bend loss is obvious for the all-solid PBGF (increase by a factor of 3 of the minimum loss, narrowing by roughly 50% of bandgap width), the transmission of the DC PBGF is not significantly affected by this reduction of R: no visible effect on the minimum loss and only a slight narrowing (< 10%) on the red side of the bandgap.

To demonstrate further the advantage of the new fiber design, we studied the sensitivity of the transmission spectra to sharper bends for shorter fiber length. The results are summarized on Fig. 7-a (all-solid PBGF) and 7-b (DC PBGF), both fibers lengths being around 4.5 m. The blue curves were obtained for the fibers bent on 3 loops of diameter larger than 35 cm and by taking care that the rest of the fiber was as straight as possible. These spectra will be referred in the following as the ‘straight’ fiber transmission spectra as this experimental condition should not lead to any significant bend loss, at least in the wavelength range of interest here. All the other transmission spectra were obtained for 10 loops of fiber wrapped on a mandrel of diameter R (6, 4.5, 3.75, 3 cm) whereas the rest of the fiber was maintained as straight as possible.

Fig. 7. Transmission spectra of the all-solid PBGF (a) and of the DC PBGF (b) for different bend radii: 6 cm (pink), 4.5 cm (yellow), 3.75 cm (cyan) and 3 cm (purple). For each of these spectra 10 turns of the fiber were wrapped on a mandrel of the corresponding radius. The dark blue curves, referred as ‘straight fiber’, were obtained for 3 very large loops of diameter higher than 35 cm.

The decrease of sensitivity to bend loss of our new design is obvious when comparing Fig. 7(a) and 7(b). For the larger bend radius (R= 6 cm, pink curve), 10 loops are enough to significantly reduce the transmission of the all-solid PBGF (compared to the ‘straight’ case) whereas the output power of the DC PBGF is not modified on most (1450 to 1600 nm) of the bandgap transmission range. This improvement is even more visible in the case of 10 loops of 4.5 cm bend radius (yellow curve): the output transmission of the all-solid PBGF decreases by 12 dB for the less affected wavelength (∼ 1572 nm) while the DC PBGF transmission decreases at most of 1.5 dB on a large wavelength range (∼1460 to 1600 nm). For the smaller studied bend radii, R= 3.75 and 3 cm, only the DC PBGF has a significant transmission, represented on Fig. 7(b) respectively in cyan and purple.

Comparisons with the results obtained by other authors [15

15. J.M. Stone, G.J. Pearce, F. Luan, T.A. Birks, J.C. Knight, A.K. George, and D.M. Bird, “An improved photonic bandgap fiber based on an array of rings,” Opt. Express 14,6291–6296 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6291 [CrossRef] [PubMed]

,18

18. S. Février, R. Jamier, J-M. Blondy, S.L. Semjonov, M.E. Likhachev, M.M. Bubnov, E.M. Dianov, V.F. Khopin, M.Y. Salganskii, and A.N. Guryanov, “Low-loss singlemode large mode area all-silica photonic bandgap fiber,” Opt. Express 14,562–569 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-2-562. [CrossRef] [PubMed]

] with low index contrast PBGFs are not straight forward either because their designs do not lead to a bandgap at 1550 nm or by lack of information. However, we believe that our new design significantly improves the fiber properties against bend loss especially for relatively long wavelength (1.5μm) and for reasonable value of pitch and Λn.

6. Conclusion

Acknowledgments

The authors would like to thank Karen Delplace and Antoine Lerouge for providing technical supports.

This work was supported in part by the “Conseil Régional Nord Pas de Calais”, the “Fonds Européen de Développement Economique des Régions”, the “Centre National de la Recherche Scientifique” (ATIP FIBI) and the “Agence Nationale de la Recherche” (ANR-05-BLAN-0080).

References and Links

1.

G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino, and 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 13,8452–8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]

2.

J.C. Knight, “Photonic crystal fibres, ” Nature 424,847–851 (2003). [CrossRef] [PubMed]

3.

A. Bjarklev, J. Broeng, and A.S. Bjarklev, “Photonic Crystal Fibres” (Kluwer Academic Publishers, Boston, 2003).

4.

W. Belardi, G. Bouwmans, L. Provino, and M. Douay, “Form-induced birefringence in elliptical hollow photonic crystal fiber with large mode area,” IEEE J. Quantum Electron .41,1558–1564 (2005). [CrossRef]

5.

G. Bouwmans, F. Luan, J.C. Knight, P.St.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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613 [CrossRef]

6.

J Riishede, J. Laegsgaard, J. Broeng, and A. Bjarklev, “All-silica photonic bandgap fibre with zero dispersion and a large mode area at 730 nm,” J. Opt. A: Pure Appl. Opt. 6,667–670 (2004). [CrossRef]

7.

N.M. Litchinistser, A.K. Abeeluck, C. Headdley, and B.J. Eggleton, “Antiresonant reflecting photonic crystal optical waveguides,” Opt. Lett. 27,1592–1594 (2002). [CrossRef]

8.

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, “Singlemode propagation into depressed-core-index photonic-bandgap fiber designed for zero-dispersion propagation at short wavelengths,” Electron. Lett. 36 :514–515 (2000). [CrossRef]

9.

F. Luan, A.K. George, T.D. Hedley, G.J. Pearce, D.M. Bird, J.C .Knight, and P.St.J. Russell, “All solid photonic bandgap fiber,” Opt. Lett .29,2369–2371 (2004). [CrossRef] [PubMed]

10.

A. Argyros, T.A. Birks, S.G. Leon-Saval, C.B. Cordeiro, F. Luan, and P.St.J. Russell, “Photonic bandgap with an index step of one percent,” Opt. Express 13,309–314 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309 [CrossRef] [PubMed]

11.

G. Renversez, P. Boyer, and A. Sagrini, “Antiresonant reflecting optical waveguide microstructured fibers revisited: a new analysis based on leaky mode coupling,” Opt. Express 14,5682–5687 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5682 [CrossRef] [PubMed]

12.

T.A. Birks, F. Luan, G.J. Pearce, A. Wang, J.C. Knight, and D.M. Bird, “Bend loss in all-solid bandgap fibres,” Opt. Express 14,5688 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5688 [CrossRef] [PubMed]

13.

J. Jin, “The Finite Element Method in Electromagnetics” (John Wiley & Sons, Inc., New York, 2002).

14.

S. Tomljenovic-Hanic, J.D. Love, and A. Ankiewicz, “Low-loss singlemode waveguide and fibre bends,” Electron. Lett. 38,220–222 (2002). [CrossRef]

15.

J.M. Stone, G.J. Pearce, F. Luan, T.A. Birks, J.C. Knight, A.K. George, and D.M. Bird, “An improved photonic bandgap fiber based on an array of rings,” Opt. Express 14,6291–6296 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6291 [CrossRef] [PubMed]

16.

S.G. Johnson and J.D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in planewave basis,” Opt. Express 8,173–190 (2001). http://www.opticsexpress.org/abstract.cfm?id=63584. [CrossRef] [PubMed]

17.

K. Saitoh and M. Koshiba, “Empirical Relations for simple design of photonic crystal fibers,” Opt. Express 13,267–274 (2005). http://www.opticsexpress.org/abstract.cfm?id=82269 [CrossRef] [PubMed]

18.

S. Février, R. Jamier, J-M. Blondy, S.L. Semjonov, M.E. Likhachev, M.M. Bubnov, E.M. Dianov, V.F. Khopin, M.Y. Salganskii, and A.N. Guryanov, “Low-loss singlemode large mode area all-silica photonic bandgap fiber,” Opt. Express 14,562–569 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-2-562. [CrossRef] [PubMed]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2400) Fiber optics and optical communications : Fiber properties

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 11, 2006
Revised Manuscript: October 25, 2006
Manuscript Accepted: October 25, 2006
Published: January 22, 2007

Citation
A. Bétourné, V. Pureur, G. Bouwmans, Y. Quiquempois, L. Bigot, M. Perrin, and M. Douay, "Solid photonic bandgap fiber assisted by an extra air-clad structure for low-loss operation around 1.5 µm," Opt. Express 15, 316-324 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-316


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References

  1. G. Bouwmans, L. Bigot, Y. Quiquempois, F. Lopez, L. Provino and 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, 8452-8459 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8452 [CrossRef] [PubMed]
  2. J.C. Knight, "Photonic crystal fibres, " Nature 424, 847-851 (2003). [CrossRef] [PubMed]
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