GB2563758B - Hollow-core photonic bandgap fibers - Google Patents

Description

The present invention relates to hollow-core photonic bandgap fibers (HC-PBGFs), for example^ for application in data transmission and high-power laser pulse delivery.

As illustrated in Figure 1, HC-PBGFs comprise an elongate fiber body having a hollow core 3 and a cladding 5 which surrounds the core 3 at a boundary 7 and comprises a silica lattice of relatively-thin struts 9 and relatively-large interstitial nodes 11, which together define an array of air holes of cavities 15 which are arranged in packed relation around the core 3, with the core 3 being formed by omitting a number of capillaries at the center of the structure. Figure 1 illustrates a prior art HC-PBGF design which is considered to be most optimized or ideal, in preserving a perfect cladding periodicity of nodes 11' at the boundary 7 of the core 3 and the cladding 5.

It is the optical resonance properties of these nodes that primarily determine the photonic bandgap or range of optical frequencies over which light can be effectively confined and guided within the core.

It is desirable in many applications to achieve a wide photonic bandgap over which light can be guided with low loss. The termination of the microstructured cladding around the core forms a continuous boundary which consists of nodes interconnected by struts. As loss is predominantly dictated by the overlap of the guided-mode field with this boundary through scattering at the air-glass interfaces, optimizing its configuration is important in loss reduction.

Owing to recent progress in the development of HC-PBGFs, these fibers are now emerging as a credible alternative to the all-solid optical fibers as used in telecom applications [1, 2]. Indeed, the highly-desifable features of iow-latency, ultraiow nonlinearity and potentially lower transmission loss make these fibers suitable for next generation data-earrying fibers. However, the attenuation levels which are fundamentally limited by scattering from surface roughness have yet to be reduced to theoretically predicted levels [3-4].

Numerous efforts in loss reduction have aimed at optimizing: the fiber design to reduce the overlap of the guided-mode field with the scattering surfaces.

Notably, the introduction of an anti-resonant core surround has led to the lowest reported loss value of 1,7 dl/km [5] Howevpf, the resulting ''thick-core supports a multitude of surface modes within the photonic bandgap, which restrict the usable bandwidth.

It has also been demonstrated that, for fibers with a seven cell (7c) core defect/ making the core wall half as thin as the struts in the cladding eliminates surface modes, thereby increasing the operational bandwidth [ΒΙΟ].

In an attempt to expand the usable bandwidth and further reduce loss p fibers vith larger core defects, a number of recently-reported HOPBGFs have been produced without a core tube. This fabrication procedure has; however, resulted in more prominent structural distortions, notably, more enlarged core defects, including oversized air holes on the six "corners" around the core and compressed claddings with different periodicity along the main symmetry axes [1,1, 11],

Significant theoretical efforts hive already been devoted to understanding and predicting the attenuation that could be obtained from a given HC-PBGF design. This work has, however; either neglected the scattering loss contribution, and hence considerably underestimated the total loss, or considered only "ideal" structures with perfectly periodic lattices, which are visibly different from fabricated lattices [12],

Another strand of activity has focused on modeling fiber geometries obtained from scanning electron micrographs of fabricated fibers; however, instrument resolution imposes a constraiiil on the accuracy of such studies [13, 14]. For a foil fiber cross-section, the width of a single glass strut is only a few pixels wide, making it difficulf for edge-detection routines to determine accurately the boundaries of the cladding air holes, and even more so to estimate thickness and impact of the metallic coating necessary to acquire the images. Good quantitative agreement between measured and simulated modal properties^ such as dispersion and mode-field diameter of current commercial HC-PBGFs, has been obtained using this approach, although any reasonable comparison of loss values is foregone by the omission of part of the cladding [15].

Contrary to the common understanding in the art, the present inventors have recognized that an exact periodicity in the cladding is not a strict requirement for air-guidance. From this recognition, the present inventors have devised improved fiber designs which are less susceptible to surface-mode induced bandwidth degradation, exhibit a considerable reduction in loss and advantageously allow the core wall thickness to be increased.

In one aspect fie present invention provides a hoifow-eore photonic bandgap fiber according to claim l.

By providing that the nodes at the core boundary are substantially equi-spaced, the modal overlap with the scattering surfaces, and hence fiber loss, is minimized.

In addition, providing the core boundary with nearly equidistant nodes is effective in eliminating surface modes, without causing significant bandwidth or loss penalty, even in fibers with a thickened core wall or which incorporate a core tube, which can present advantages in fabrication.

With the present invention, it is predicted that for a fiber With a nineteen ceil (lid) core defect, in an optimum configuration, losses can be reduced to less than 0.5 dB/km at a wavelength of 1.55 pm over a 450 nm bandwidth, with it being possible to reduce loss further, for example, by a factor greater than % by operating at a wavelength of 2 pm or by more than 2.7 times using a fiber with a thirty-seven cell (37c) or greater core defect.

Furthermore, for laser delivery applications, dispersion engineering is easily achieved through control of the size of the core nodes.

Preferred embodiments of the present invention will now be descn|ed herelnbeiow by way of example only with reference to the accompanying drawings, in which*

Figure 1 illustrates a lateral cross-section through an "ideal" HC-PBGF in accordance with the prior art;

Figure 2 illustrates a lateral cross-section through a HC-PBGF in accordance with a first design;

Figure 3 illustrates a lateral cross-section through a HC-PBGF in accordance with an embodiment of the present invention;

Figure 4 illustrates plots of the simulated losses for the "idear fiber of Figure 1, the fiber of Figure 2 and the fiber of Figure 3;

Figure 5 illustrates a plot Of the s.mutated loss as a function of core diameter for the fiber of Figure 3;

Figure 6 illustrates a plot of the simulated loss of the filer of Figure 3 as a function of a ratio of the thickness (tc) of the struts to the average spacing of the nodes;

Figure 7 illustrates plots of the simulated ^oss of the fiber of Figure 3 as a function of a ratio of the area of the struts to the area of the nodes;

Figure 8 illustrates plots of the simulated loss as a function of cladding thickness for the fiber of Figure 3;

Figure 9 illustrates plots Of the siradlated loss as a function of the size of the "corner" cavities for the fiber of Figure 3 and the "ideal" fiber of Figure 1;

Figures 10(a) and (b) illustrate contour plots of the average power flow in the z-direction from Fibers B1 and B6, respectively, of the fiber of Figure 3;

Figure 11 illustrates plots Of the simuiated ioss as a function or core wail thickness for fibers ih accordance with the embodiment of Figure 3, where each having equi-spaced core nodes and having no core tube and core tubes of the same thickness as the capillaries in the starting stack and 1.25 times the thickness of the capiiiaries in the starting stack;

Figure 12 iiiustrates plots of ioss as a function or core wai! thickness for fibers in accordance with the embodiment of Figure 3, where each having oversized "corner" cavities and having no core tube and core tubes of the same thickness as the capillaries in the starting stack and 1.25 times the thickness of the capillaries in the starting stack;

Figure 13(a) illustrates plots of the simulated dispersion for fibers in accordance with the embodiment of Figure 3, having increasing node sizes at the core boundary; and

Figure 13(b) illustrates plots of the simulated loss as a function of node size, corresponding to Figure 13(a).

In tie present embodiments the fiber loss accounts for contributions from loth leakage (or confinement) loss and scattering from surface roughness. The latter is known to impose a fundamental limit on the achievable attenuation in HC-PBGFs, and as recently shown, is the major loss contribution in libers with ~dB/km loss levels with six or more rings of air holes outside the core defect [3, 4]. For computation purposes, but without loss of generality* the scattering loss is computed here not by the rigorous treltmihtformulated in [4], but through the simplified method of calculating the normalized interface field intensity of the fiber on the air-glass interfaces [3]:

where E and H are the electric and magnetic field vectors of the fundamental mode, in addition, the scattering loss is calibrated by comparing multiple measurements and simulations So that a loss value of 3.5 dB/km around a wavelength of 1,5 ym corresponds to an interface field intensity (F) of 0,01

Figure 2 illustrates a HC-PBGF in accordance with a first design.

Tip HC-PBGF comprises an elongate fiber body having a hoiiow core 103 and a cladding 105 which surrounds the core 103 at a boundary Ilf.

In this design the core 103 is gaf lllel, here air filled. In other designs the core 103 could be filled with any of argon, xeon, helium or hydrogen.

In an alternative design the core 103 could be a vacuum.

In another alternative design the core 103 could contain a liquid,

In this design the core 103 Is substantially clrcuiar in section.

The cladding 105 comprises a lattice or network 108 of struts 109, 109' and interstitial nodes 111, 111', which together define a plurality of cavities 115, in this design extending along the length of the fiber body, which are arranged in packed relation around the core 103;

In one design different materiais, glasses or poiymers, may be used in the cladding 105 for an inner region at the core boundary 107 and for an outer region.

In one design different materiais, glasses or polymers, can be used in regions across the cross-section of the cladding 105,

In this design the cavities 115 comprise gas-fiiied holes, here air-fried holes. In other designs the cavities 115 could be filled with any of argon, xeon, helium or hydrogen.

In an alternative design the cavities 115 could be a vacuum.

In another alternative design the cavities 115 could contain a liquid.

The cavities 115 are arranged in triangular-packed relation.

In this design the struts lii' at the core boundary 107 have substantially equal length, and the nodes 111' at the core boundary 107 are substantially equi-spaced at a pitch p.

The present inventors have established that surprisingly, and contrary to the understanding in the art which requires an exact periodicity of the structure of the cladding 103, as illustrated in the "ideal" fiber of Figure 1, by arranging the core Struts Ipf' to have substantially equal length and the core nodes |ll' to be substantially equi-spaced, there is a significant reduction in fiber loss over a much broader operational bandwidth. As illustrated in Figure 4, the loss value is about 40% lower than the loss seen in the "ideal" fiber of Figure 1.

The present inventors postulate that the broader operational bandwidth is provided by improved uniformity of the core struts 109' in terms of length and mass* arising from equi-spacing of the core nodes 111', and that the reduction in Fiber loss arises as a result of the field being equally prevented from overlapping each of the core struts 109'.

In one design the core nodes 111' have substantially the same size as the nodes 111. Within the body of the cladding 105 which arrangement yields the lowest fiber loss.

In this design the core struts 109' have an average thickness (tc) of iiout 13 nm, the cladding struts |09 have an average thickness (tc) Of 47 nm, the average cladding node area is 0.47 pm2 and the overall effective fiber diameter (Deeding) Is 80 pm, which are the same as for the "ideal" fiber of Figure 1.

In this design the fiber is a nineteen cei! (19c) fiber, having an effective core diameter of 5Λ, where A is the average spacing of the cavities 115, which is the same size as the "idea!" fiber of Figure 1. in an alternative design the fiber could have a different core size, for example, a thirty-seven ceii (37c) fiber, haying an effective core diameter of 7Λ, or a sixty-one ceii (61c) having an effective core diameter of 9Λ,

Figure 3 illustrates a fiber in accordance with an embodirnent of the present invention.

The fiber of this embodirnent is quite similar to the fiber of Figure 2, and thus, in order to avoid unnecessary duplication of description, only the differences will he described in detail, with like parts being designated by like reference signs.

In this embodiment the fiber has an enlarged core 103 as compared both to the "ideal" fiber of Figure 1 and the fiber of Figure 2.

In this embodiment the core 113 has an effective diameter of 1.26 times greater than that of the "ideal® fiber of Figure 1, where the effective diameter is nA, here 5Λ, and where Λ is 4.4 pm.

In one embodiment the average cavity spacmg Λ is from about 3 pm to about 6 pm in fibers operating at a wavelength of 1.55 pm.

In another embodiment the average cavity spacing A is from about 4 pm tp abop 8 pm i| fibers operating at the minimum loss wavelength of 2 pm

As illustrated In F|gute 4, the reduction in fiber loss, as compared to the "idea!" fiber of Figure 1, is further reduced in relation to the fiber of Figure 2, here by a factor as high as 2.4 over the entire transmission bandwidth.

Figure 5 illustrates a plot of the fiiiulated loss as a function of pri eliameter for the fiber of Figure 3. As will be seen, the fiber of this embodiment has an optimum core diameter ratio of from about 1.05 to about 1.35 nA, preferably from about 1,1 to about 1.35 nA, and more preferably from about 1.15 to about 1,30 fiA,

In addition, as illustrated in Figure 6, which illustrates the simulated loss for the fiber of Fi|ure 3 as a function of a ratio of the average thickness (tc) of the struts 109 to the average spacing of the nodes 111, the present invention allows for reduction of loss by optimizing the thickness (tc) of the struts 109 in relation to the spacing of the nodes 111. In the present invention, loss is minimized by providing that the ratio of the average thickness (tc) of the struts 109 to the average spacing of the nodes 111 is less than about 5%, and optionally less than about 2%.

Furthermore, as Illustrated in Figure 7, which illustrates plots of the simulated loss for tie fiber of Figure 3 as a function of a ratio of the average area of the struts 109 to the average area of the nodes 111, the present invention allows for reduction of loss by optimizing the area of the struts 109 in relation to the area of the nodes 111; the various plots being for fibers having a ratio of the average thickness (tc) of the struts 109 to the average spacing of the nodes 111 in the range of from 1.7% to 8.6%.

For the purposes of calculation, the area of each strut 109 is the area oyer which the strut ill has a substantially uniform thickness, and the area of each node 111 is the area enclosed between three adjoining struts109 of substantially uniform thickness.

In the present invention, loss is minimized by providing that the ratio of the average area of the nodes 111 to the average area of the struts 109 is from about 1 to about 30, preferably from about 1 to about 20, still more preferably mm about 2 to about 20, yet more preferably from about 4 to about 13, yet still more preferably from about 4 to about 10, and still yet more preferably from about 6 to about 10.

Figure 8 illustrates plots pf tbesSlm plated loss as a function of wavelength for three fibers, here in accordance with the fiber of Figure 2, each having the same effective core diameter and the same effective diameter for the first two rings of cavities 115, but With a decreasing thickness to the remaining! outer rings of cavities 115, with the decreased thickness of the outer rings of caviues 115 being achieved by radial compression.

In the first fiber (Fiber Al|, the core 115 has an effective core radius (Rcore) of 13 pm, the ratio of the effective core diameter (0¾¾) to the effective cladding diameter (Ddadamg) is 0,31, whereby the thickness of the microstruetured cladding in the radial direction is 28.93 pm, the average strut thickness (tc) is 110 nm, tie IHet radius (rc/VV) is 0.21, where W is the average diameter of the cavities 115, and the photonic bandgap is centered around a wavelength of l.y pm.

In the second fiber (Fiber A2), the core 115 has an effective core radius (Rcore) of 13 pm, the thickness of the microstruetured cladding in the radial direction is 26;84 pm (95% of that of Fiber Al), the average strut thickness (tc) is 110 nrri, the filet radius (rc/W) is 0.21, and the photonic bandgap is centered around a wavelength of 1J5 pm.

In the third fiber (Fiber A3), the Pre 115 his an effective core radius (Rc) of 13 pm, the thickness of the microstruetured cladding in the radial direction is 24.74 pm (90% of that of Fiber Al), the average strut thickness (tc) is 110 nm, the fillet radius (rc/W) is 0.21, and the photonic bandgap is centered around a wavelength of 1,625 pm.

As can be seen from Figure 8, confinement loss, plotted in dotted lines, increases by more than an order of magnitude for each progressive cladding compression, and contributes to a net reduction in the overall transmission bandwidth. The narrower bandwidth resuits from more closely spaced nodes (narrowing the photonic bandgap) and a thinner air cavity region surrounding the core (Increasing the confinement loss). However, at wavelengths well within the bandgap, all fibers have essentially the same value of totai loss, which confirms that ioss is dominated by scattering from surface roughness, which is mostly unaffected by the structure beyond the second ring of cavities 115. As a result, the HC-PBGF of the present invention advantageously is robust to slight distortions beyond the second ring of air holes 115.

Figure 9 illustrates plots of simulated loss as a function of the size of the oversized "corner" cavities 115' at the core boundary 107 for six fibers ((Fibers B1 to B6) in accordance with the embodiment of Figure 3. Also superposed is the loss plot for the "ideal" fiber of Figure 1, and the cutback measurement for the fabricated "idea!" fiber [1].

Thise oversized "corner" cavities arise as a natural consequence of surface tension trying to create a circular core surround from an original hexagonal structure, and in an alternative embodiment could be undersized.

In this embodiment the fiber has an effective core diameter (DCQrs) of 26 pm, the ratio of the core diameter (DCOre = 2RC) to the cladding diameter (Dciad«nns| is 0.36 (which compares to 0.31 for the fiber of Figure 2), the average thickness (tc) of the cladding struts 111 is 110 hm, the average thickness (tc) of the core struts 111', which define the core boundary 107, is 55 nm and the fillet radius (r^W) is 0 Jl.

In this embodiment the length uniformity (0) of the pitches of the adjacent core nodes l|9' for each of the Fibers B1 to B6, which is given by a ratio between the length difference between the longest and shortest pitches |ΑΙ) and the average length of the pitches of the core nodes 109' (mean(i)), is 0,01, 0.15, 0.29, 0.45, 0,57 and 0,74, which compares to a length uniformity (§j of 0.536 for the "idea!" fiber of Figure 1,

In addition, conservation of the glass volume in the struts 109, 109' was imposed, resulting in struts 111, 111' longer than average being thinner than and vice-versa for shifter struts 109, 109'.

In Fibers B1 to B6, the size of the corner holes was increased In incremental steps from 2.8RC/(5V3) to 4.8RC/(5V3), and the mode profiles and loss computed for all wavelengths across the bandgap.

As before, the scattering loss contribution remains dominant for the six ring structures. Although the leakage loss contribution in the fiber with the most enlarged "corner" holes 115' (Fiber B6) is twice as much as for the fiber with the least enlarged "Corner" holes 115' (Fiber Bl), this still only amounts to 0.035 dB/km, which is a small fraction of the total loss.

As can be seen from Figure 9, fibers with larger corner holes 115' sutler from higher losses. The larger corner holes 115' impose larger gaps between the nodes 111' on the core boundary 107, and such gaps prompt the electric field to overlap more strongly with the scattering surfaces, generating a significantly higher scattering loss, as illustrated in the contour plots of Figures 19(a) and (b), which illustrate the contour lines for the time average power flow in the z-direction over a 30 dB range at 2 dB intervals for Fibers Bl and B6, Fiber Bl not only results in reduced overlap of the guided field with the scattering surfaces, but also avoids introducing surface modes within the photonic bandgap.

It is striking to note that the structure considered to date to be the "ideal" fiber design, as illustrated in Figure 1, is that which provides the highest loss, despite featuring a core surround that preserves the periodicity of the structure. As discussed above, this is due to a smaller core diameter (Deere), but aisp because the pitch of the nodes 111' on the core boundary 107 is not uniform* which in combination leads to the loss in this ''ideal" fiber being 2.4 times higher than that of Fiber IT, in which the nodes 111' on the core boundary are equidistant.

Figure |1 illustrates plots of loss as a function or core wall thickness for fibers (Fibers Cl to C3) in accordance with the embodiment of Figure 3, where each having equi^spaced core nodes 111' and having no core tube and core tubes of the same thickness as the capillaries in the starting stack and 1.25 times the thickness of the capillaries in the starting stack.

As will be seen, when mass conservation is applied to the wail at the core boundary 107 in the absence of core tube in the preform (Fiber Cl), the fundamental mode bandwidth is wide and ioss remains low. Additionally, the effective indices of all the guided modes are dearly separated.

When the core wall thickness is increased by, for example, introducing a core tube as thick as the cladding capillaries (Fiber C2), there is only a small bandwidth of loss penalty for fundamental mode transmission, with the minimum loss increasing from 2 to 2,4 cfB/km, with a 10 nm reduction in the bandwidth.

In this embodiment the surface modes introduced cross the fundamental mode near the short wavelength edge of the photonic bandgap, ensuring that the bandwidth for the fundamental modes remains largely unaffected, higher order modes, however; interact with these surface modes near the center of the bandgap and therefore suffer a severe reduction in bandwidth. This also confirms that the design with equal node spacing on the core boundary 107 not only provides the lowest loss but is also more tolerant to thicker in core wall,

Further increasing the core wall thickness (Fiber G3) has limiting effects on performance. As can be seen* When a core tube which is 1.25 times thicker than the capillaries is used, surface modes anti-cross with the fundamental mode near the middle of the band|ap, resulting in higher losses and severe reduction in bandwidth.

Figure 12 illustrates plots of loss as a function or core wall thickness for fibers (Fibers EJI to D3) in accordance with the embodiment of Figure 3, where each having oversized "corner" cavities 115' and having ho core tube and cone tubes of the same thickness as the capllaries in the starting stack and 1.25 times the thickness of the capillaries in the starting stack, following fibers Cl to C3.

As will b! seen, the reduction in bandwidth and increase in loss is clearly more noticeable for fibers with oversized "corner" holes 115', increasing from a minimum of 2.9 dB/km over a bandwidth of 230 nm (Fiber Dl) to 4.6 dB/km over a bandwidth of 160 nm (Fiber D2j,

Similarly to Fiber C3, further increasing the core wall thickness (Fiber D3) has significant limiting effects on performance.

Figure 13(a) illustrates plots of dispersion for fibers in accordance with the embodiment of Figure 3, with the nodes 111' at the core boundary 107 having a size of approximately 0.6 (Fiber El % 1 (Fiber E2) and 1.4 (Fiber E3) times the average size of the nodes 111 within the body of the cladding 1Q5.

In this embodiment the pitch of the cavities 115 (Λ) is 3,03 prn, d^A is 0.987 and Dc/W is 0.6, where W is the average effective internal diameter of the cavities 115.

As can be seen, the fiber of the present invention allows readily for iiigineered dispersion through adjustment ofthe size of fhl core nodes 111' at the core boundary 107.

Figure 13(b) illustrates plots of loss as a function of node size, corresponding to Figure 13(a),

As regards application, the HC-PBGF of the present invention has diverse application, including optical fiber communication systems, in particular ultrahigh capacity, ultralong haul systems and low latency short haul systems (such as of Interest to financial trading firms/banks), datacomms, in particular low latency fiber Sinks in datacentres and supercomputers, large scale high-energy physics (HEP), in particular use for low latency data transfer in detector arrays and for timing synchronisation, high-power laser delivery, in particular continuous-wave and puised radiation formats at diverse wavelengths, and gas sensing, In particular compact gas cells for environmental sensing/laser stabilisation.

Finally/ it will be understood that the present Invention has been described in its preferred embodiments and can be modified in many different ways without departing from t^e scope of the invention as defined by the appended claims.

References 1. F. Poletti, Μ* V. Wheeler, Μ, N. Petrovich, N, Baddela, E. Numkam Fokoua, 3. R. Hayes, D. R. Gray, E Li, R; Slavik, and D. J. Richardson, "Towards high-capacity fibre-optic communications at the speed of light in vacuum/' Nature Photonics 7, 279-284 (2011). 2. Y. Jung, V, A. J. M. Sleiffer, N. i|di||a, Μ. N. Petrovich, J. R. Hayes, N, V. Wheeler; D. R. Gray, E, Numkam Fokoua, J. P, Woofer, §i H.-L. Wong, F. Parmigiani, S,-U. Aiam, J. Suro| M, Kusclnerov, V, Veijanovski, H. de Waafdt, F. Poletti, and D. J. Richardson, "First demonstration of a broadband 37-celi hollow core photonic bandgap fiber and its application to high capacity mode division multiplexing**' in Brm&mtirtgs of the Optical Fiber Communications conference (2013), paper PBP5A.3 (Postdeadline). 3. 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). 4. E. Numkam Fokoua, F. Poletti, and D. J. Richardson, "Analysis of light scattering from surface roughness in hollow-core photonic bandgap fibers," Opt. Express 20, 20980-20991 (2012). 5. B. J. Mangan, L. Farr, A, Langford, P. J. Roberts, B, P. Williams, F. Couny, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/krn) hollow core photonic bandgap fiber/' in Proceedings of Optica! Fiber Communication Conference (2004), paperPDP24. 6. P. Roberts, D. Williams, B. Mangan, H. Sabert, F. Couny, W. Wadsworth, T. Birks, I. Knight; and P. Russell, "Realizing low lofs air pore photons crystal fibers by exploiting an antirespnant core surround/' Opt. Express 13, 8277-8281 (2005). 7. C. M. Smith, N. Venkata ram an, Μ. 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 |bfe," Nature 424, 657-659, (2003). 8. R. Amezcua-Correa, N. G. Broderick, ML 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), 9. |, Amezeua-forrea, N. G. R. Broderick* Μ, N, Petrovich, F. Poletti, and 0. I. Richardson, "Design of 7 and 19 ceils core air-guiding photonic crystal fibers fbr low-loss, wide bandwidth and dispersion controlled operation/ Opt* Express 15, 17577-17586 (2007), 10. R. Amezcua-Correa, F, G|rome, S. G. Leon-Saval, N. G. R. Broderick, T. A. Birks, and J. C, Knight, "Control of surface modes in low loss hollow-core phdlonic bandgap fibers/ Opt. Express 16, 1142-1149 (2008), 11. M. H. Frosz, J. Nold, T, Weiss, A, Stefani, F. Babic, S. Rammler, and P. St, J. Russell* "Five-ring hoilow-eore photonic crystal fiber with 1.8 dB/km loss," Opt. Lett. 38, 2215-2217 (2013). 12. Kunimasa Saitoh and Masanori Koshiba, "Leakage loss and group velocity dispersion In air-core photonic bandgap fibers," Opt. Express 11, 3100-3109 (2003). 13. Ming-Jun U, James A. West, and Karl W. Koch, "Modeling Effects of Structural Distortions on Air-Core Photonic Bandgap Fibers," J. Lightwave Technol. IS, 2463-2468 (2007). 14. F. Poletti, Μ. N. Petrovich, R. Amezcua-Correa, N. G. Broderick, T. M. Monro, and D. J. Richardson, '* Advances and Limitations in the Modeling qf Fabricated Photonic Bandgap Fibers," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2006), paper ©FC2. 15. Kiarash Zamani Aghaie, Michel J. F. Digonnet, and Shanhui Fan, "Experimental Assessment of the Accuracy of an Advanced Photonic-Bandgap-Fiber Model," J. Lightwave TechnoL 31, 1015-1022 (2013), 16. Franceseo Poletti, "Hollow core fiber with an octave spanning bandgsp," Opt. Lett, 3% 2837-2839 (2010). 17. F, Poietti, a|l| E, Nu|fi||m Fokoua "Understanding the Physical Origin of Surface Modes and Practical Rules for their Suppression/ accepted for oral presentation at ECOC 2013. IS.Tadashi Murao, Kunimasa Saitoh, and Masanori Koshiba, “Structural Optimization of Air-Ouidihg Photonic Bandgap Fibers for Realizing Ultimate Low Loss Waveguides/ J. Lightwave Techno!. 26, 1602-1612 (2008).

Claims (2)

1. A hollow-core photonic bandgap fiber having a hollow core a rtf a: cladding which surrounds the core at a core boundary and comprises a lattice or network of struts and interstitial nodes formed of a silicate glass, which together define an array of cavities which are triangular-packed, wherein the diameter of the core is greater than 1.05 nA, wherein the fiber has a nineteen cell (19c), a thirty-seven cell (37c) or a sixty-one cell (61c) core defect corresponding to values of n of 5, 7 and 9 respectively, and Λ is the average spacing of the cavities,

2, The fiber of claim 1, wherein the nodes at the core boundary have pitch spacings which differ with a ratio between a difference in length of a longest and shortest pitch spacing of the nodes at the core boundary to an average pitch spacing at the core boundary of less than 0,3.