WO2004027475A1

WO2004027475A1 - Improvements in and relating to photonic-band-gap guidance in photonic-crystal fibres

Info

Publication number: WO2004027475A1
Application number: PCT/GB2003/004011
Authority: WO
Inventors: Timothy Adam Birks; Peter John Roberts; Philip St.John Russell; Jonathan Cave Knight; Brian Joseph Mangan
Original assignee: Crystal Fibre A/S
Priority date: 2002-09-19
Filing date: 2003-09-18
Publication date: 2004-04-01
Also published as: GB0221812D0; AU2003271846A1

Abstract

In order to increase the frequency range guided in the core of a photonic crystal fibre, the photonic crystal cladding structure is optimised with respect to an increased overlap of the band gaps (120, 110, 130) with the light line (100) of the fibre core. For a fibre with a hollow core and a cladding consisting of cylindrical air rods in a silica matrix arranged in a triangular lattice, this overlap can be optimised by increasing the air filling factor which 'tilts' the band gaps towards the core light line.

Description

Improvements in and relating to photonic-band-gap guidance in photonic-crystal fibres

This invention relates to the field of optical fibres and, in particular, to examples of optical fibres that guide light by photonic-band-gap guidance.

Microstructured fibres are relatively new forms of optical fibres. They are also known as photonic crystal fibres (PCFs) or holey fibres. Microstructured fibres are similar to 'standard' optical fibres of the type well known in the telecommunications industry. Like standard fibres, microstructured fibres are elongate filaments having, in transverse cross-section, at least one area identifiable as a core region that is surrounded by a cladding region. In a standard fibre, the core region is of a higher refractive index than the cladding region and light is confined to and guided in the core region by total internal reflection at the interface between the core and the cladding. However, a microstructured fibre comprises a plurality of elongate cylindrical elements, such as holes, that are distributed in at least the cladding region and run parallel to the longitudinal axis of the fibre. In a microstructured fibre, the core region and the matrix regions surrounding the elongate elements may be of the same material. Guidance in a standard fibre in which the core and the cladding were . the same material would clearly be impossible, because - there would be no refractive-index difference to provide the total -internal reflection.

Two classes of microstructured fibres may be . identified: those in which the elongate elements are cylindrically arranged in a lattice pattern and those in which the elongate elements are shells that are concentric with the core of the fibre (examples of this latter class are given in Y. Fink et al . , Science, Vol. 282, pp 1679-1682 (1998); Y. Fink et al . , J. Lightwave Technology, Vol. 17, No. 11, pp 2039-2041 (1999); F. Brechet et al . , Electronics Letters, Vol. 36, No. 6, pp 514-515 (2000); Jianqiu Xu et al . , Opt. Comm. , Vol. 182, pp 343-348 (2000); P. Yeh et al . , J. Optical Society of America, Vol. 68, No. 9, pp 1196-1201 (1978); Yong Xu et al., Optics Letters, Vol. 25, No. 24, pp 1756-1758 (2000) ) . There are two mechanisms by which the presence of the elongate elements may enable guidance of light in the core region of a microstructured fibre. In one

I mechanism, the elongate elements and the matrix material surrounding them in the cladding region together have an 'effective' refractive index that is lower than the refractive index of the core region. Thus, for example, a cladding region of holes (refractive index n = 1) defined by a matrix of silica (n = 1.54) would have a lower effective refractive index than a core of just silica (the exact value of the effective refractive index of the cladding region may be calculated but clearly falls between that of air and that of silica) . The fibre thus guides, like a standard fibre, by a form of total internal reflection at the interface between the core region and the cladding region. We therefore refer to such a fibre as index-guiding' .

-In an index-guiding microstructured fibre, parameters such as the cross-sectional area of the elongate regions and their positions in the cross-section of the fibre can take any of a wide range of values, provided that the effective refractive index of the cladding region is less than that of the core region.

In the second mechanism, guidance of light in the core results from the properties of the elongate regions in a far more specific sense. In this second kind of microstructured fibre, the elongate regions are arranged to form a structure, such as a photonic crystal, having a photonic bandgap. The core region acts as a defect (usually a low-index defect) in the photonic crystal and results in a defect state in the bandgap. Light is guided in the fibre in the defect state. We refer to such a fibre as photonic-bandgap (PBG) -guiding.

The basic physics of photonic-crystal structures is well known; for example, John D. Joannopoulos et al . , 'Photonic Crystals - Moulding the Flow of Light', Princeton University Press, 1995 provides a useful introduction. A discussion of the physics of PBG-guiding PCFs can be found for example in R.F. Cregan et al . , Science, Vol. 285, pp 1537-1539 (1999) and T.A. Birks et al., Electronics Letters, Vol. 31, pp 1941-1943 (1995).

Briefly, the mechanism can be understood as follows. In a vacuum or other homogeneous medium, light has the property that its angular frequency ω (k) = ck/n, where k is the light's wavevector, n is the refractive index of the medium and c is the speed of light in a vacuum. A plot of ω against k is thus a straight line (the 'light line' ) and, more importantly, for every frequency co there is a corresponding k; in other words, light of any frequency can propagate in a homogeneous medium.

Ctmsirder-, howev-e-r-, -a- -ea-s-e- in- which the light is propagating in a medium consisting of alternate layers of higher and lower refractive indices, each layer being of thickness a and arranged perpendicular to the direction of propagation. The cumulative effect of interference between reflections from the interfaces between the regions of higher and lower refractive index is that light of wavevector k = π/a forms a standing wave of wavelength 2a in the medium. Now, as Joannopoulos explains on page 41 of his book, the standing wave may have its nodes centred either in the high-index layers or in the low-index layers. Centering in the high-index layers results in a lower-frequency mode and centering in the low-index layers results in a higher frequency mode. Thus a plot of ω against k for this structure has two different values for ω at k = π/a. Moreover, there are frequencies between those two values that have no corresponding k's. There is thus a gap in the frequencies that can propagate in the structure.

This one-dimensional model may readily be extended to take account of structures that are periodic in two or three dimensions. A microstructured fibre may be arranged to form a two-dimensional photonic crystal in which the elongate elements form a periodic disturbance in the transverse plane that results in a bandgap for propagation in directions other than parallel to the longitudinal axis of the crystal (and hence the elongate elements; there is no periodic structure in this direction) . Several such arrangements are known for microstructured fibres, and examples are described in International Patent Application Nos . PCT/GB98/01782 and PCT/GB00/01249 (Secretary of State for Defence) and in R.F. Cregan et al, Science, Vol. 285, ppl537 - 1539 (19.99) and J.C. Knight et al, Science, Vol. 282, ppl476 - 1478 C19-S-8-} •

The core region of a microstructured fibre may take the form of an 'extra' elongate element, such that the periodicity of the photonic crystal is locally disrupted. Such a disruption allows formation of a 'defect' mode, that is a light wave with a frequency and propagation constant that fall within the bandgap of the cladding but which correspond to an allowed propagating state in the core. Thus light guided in the core of the fibre may be regarded as existing in this defect mode.

In the early years of photonic crystal structures, a close analogy between the behaviour of photons in photonic-crystal structures and the behaviour of electrons in (standard) crystals was identified. As is well known, the periodic potential caused by the atoms of a crystal causes a bandgap to form in the energies of electrons allowed to propagate in the crystal. Inclusion of 'defects' such as donors or acceptors results in the creation of allowed defect states within the bandgap. To some extent, the history of photonic crystal structures has been guided by that analogy with semiconductor physics. In developing new materials, various infinite, periodic structures having a bandgap have been identified and, to the extent that any optimisation has taken place, it has been optimisation of the width of that bandgap. The core has been considered to be a "defect" state in the bandgap of that theoretical infinite cladding structure. The bandgap of the cladding structure may be maximised by any appropriate method. For example, the behaviour of the photonic crystal forming the cladding may be modelled in a computer program and parameters (such as the refractive index of the matrix material and the refractive index, the cross-sectional area, and the pitch of the elongate cylindrical elements) may be varied according to any appropriate optimisation algorithm, such as simulated annealing (The pitch is the centre-to-centre spacing between an elongate cylindrical element and its nearest neighbour) .

Although there are many applications for microstructured fibres in which narrow bandwidths are acceptable or even advantageous, often it would be desirable if a fibre could be designed to have as wide a band of frequencies as possible confined to the core region.

An object of the invention is to provide a photonic- bandgap guiding optical fibre that guides light over a wider range of frequencies than prior art microstructured fibres.

According to the invention there is provided an optical fibre comprising: (a) a core region; (b) a cladding region comprising a plurality of elongate cylindrical elements arranged in a matrix material to form a structure, having a bandgap, that guides light in the core region; characterised in that the elongate cylindrical elements fill the cladding region to a higher filling fraction than the filling fraction that maximises the frequency width of the bandgap, at a wavevector at which the light line is in the bandgap.

The fibre may thus be able to guide in its core a larger range of light frequencies than could be guided if the elongate cylindrical elements filled the cladding region to said filling fraction that maximises the frequency width of the bandgap.

(The filling fraction is the ratio of the total area of the elongate regions in the cladding region to the total area of the cladding region, in a transverse cross- section of the fibre.)

If the bandgap can be widened by adding more silica to the fibre's structure in some way, thus decreasing the filling fraction of the elongate cylindrical elements, then the filling fraction is clearly higher than that which maximises the frequency width of the bandgap.

If one regards the core region as being a region of homogeneous, rather than periodic, material one can see that the range of frequencies that can propagate is described by the light line (also known as the air line) ; that is to say, potentially any frequency ω (k) = ck/n can propagate. However, only frequencies falling within the bandgap of the photonic crystal forming the cladding will be confined to the core region by the cladding and hence only those frequencies can be guided in the fibre. We have discovered the surprising result that maximising the bandgap of the cladding material does not necessarily maximise the range of wavelengths guided in the fibre. That result can be understood as follows. The wavelengths guided in the fibre may correspond to more than one wavevector. In a plot of ω against k for a PCF, the bandgap regions of the cladding are elongate areas ("fingers") in the plane, extending over a range of wavevectors and a range of frequencies. We have discovered that, as the filling fraction of the cladding region is increased, the bandgap areas in the ω-k plane begin to tilt relative to the axes so that they become more aligned with the light line corresponding to propagation in the core. As the filling -fraction is increased past the value that produces the largest bandgap for any single wavevector at which the light line is in the bandgap, more and more of that light line falls within the bandgap area. Thus although the bandgap area shrinks in width at any single wavevector, as it shrinks it tilts to take in more and more of the light line. Thus a larger range of light frequencies can be guided if the filling fraction is larger than the filling fraction that would give a wider bandgap at a given wavevector.

The tilting of the bandgap area in the ω-k plane can be understood as follows. Consider the example of a PCF having an air core and elongate cylindrical regions in the form of air-filled holes embedded in a matrix region of silica. The light line for the core is approximately that of free-propagation in air, which is, of course, a straight line of slope c in the ω-k plane. (In fact the line for light propagating in a hollow core is slightly different from that for free propagation in air, due to confinement by the waveguide. That is well known in the art and has been described in D.C. Allan et al . , "Photonic Crystal Fibres: Effective-Index and Band-Gap Guidance", Photonic Crystals and Light Localisation in the 21st Century, pp 305-320, CM. Soukoulis (ed.),

Kluwer Academic Publishers, Netherlands (2001) , but the discrepancy is often negligible and for the purposes of our explanations here it will be neglected.) As the filling fraction of holes in the cladding is increased, the cladding behaves more and more like air; for a filling fraction of 1, the cladding (and, indeed, the fibre) would be all air and no silica and so its ω-k relationship would be the light line. For filling fractions in which the holes are large (but not so large that adjacent holes touch) , the ω-k relationship is a bandgap area that lies approximately over the light line but which still has a finite frequency width for any given wavevector within its wavevector spread.

As discussed above, a major theme in the prior art has been the analogy between PCFs and semiconductors .

The approach to photonic crystal design suggested by that analogy has been to optimise the bandgap of the cladding structure (as an infinite lattice without a core) and then to add a core to provide a "defect" state in the bandgap, in analogy with the addition of donor or acceptor ions in a semiconductor. That approach however does not take full advantage of the flexibility available in designing a microstructured fibre. In particular, it does not recognise that the range of frequencies guided in the fibre may be increased by increasing the filling fraction beyond the value that gives the widest bandgap to the cladding structure .

The fibre according to the invention may be compared with a hypothetical fibre having the same pitch and symmetry and made of the same material but having a filling fraction optimised to maximise the frequency width of the fibre's bandgap. The fibre according to the invention has a higher filling fraction than that filling fraction and guides light over a wider range of frequencies than that hypothetical fibre. In moving from the hypothetical fibre to the fibre according to the invention, any suitable parameter may be adjusted, although the pitch, symmetry and material of the fibre will remain the same.

The elongate elements may have a cross-sectional area that is larger than the cross-sectional area that would maximise the frequency width of the bandgap if all other properties of the fibre remained the same. Preferably, the filling fraction exceeds said filling fraction that maximises the frequency width of the bandgap by at least 0.05, more preferably by at least 0.10, still more preferably by at least 0.25.

Preferably, the elongate regions are substantially parallel to the longitudinal axis of the fibre.

Preferably, the elongate elements are cylinders that are arranged in a lattice pattern. Preferably, the elongate elements are arranged in a triangular lattice in the cladding region. Alternatively, the cylindrical elements are arranged in a hexagonal lattice in the cladding region. Alternatively, the elongate elements are arranged on a square lattice in the cladding region. Alternatively, the elongate elements are arranged on a quasicrystallic lattice. Alternatively, the elongate elements are shells that are concentric about the core region.

Preferably, the core region has a lower refractive index than the matrix material. Preferably, the elongate cylindrical elements have a lower refractive index than the matrix material . Preferably, the core region and the elongate cylindrical elements have the same refractive index; in that case, the overlap of the cladding bandgap with the core light line may be optimised in comparison with other cases because, in the extreme of a filling fraction of 1 (which is of course not attainable) the light lines of the core and the cladding will be coincident .

Preferably, the core region comprises an air hole. More preferably, the core region is an air hole.

Preferably, the elongate cylindrical elements are air holes .

The elongate elements may be of circular cross- section. Alternatively, the elongate elements may be of non-circular cross-section.

Also according to the invention there is provided a method of manufacturing an optical fibre having a core region and a cladding region, comprising:

(a) selecting one or more properties that characterise the core region;

(b) selecting, for the cladding region, a structure having a bandgap that guides light in the core region, the structure comprising a plurality of elongate elements arranged in a matrix material ; (c) using a numerical optimisation procedure to determine a preferred filling fraction for the elongate elements in the cladding region;

(d) fabricating the optical fibre such that the core region has the selected core properties and the cladding region has the selected structure and the determined filling fraction; characterised in that the preferred filling fraction is determined by optimising, in the numerical optimisation procedure, overlap of the bandgap of the cladding region with the light line of the core region so as to maximise the range of light frequencies that can be guided in the core region, for the selected core properties and cladding region structure. The properties of the fibre that are selected may comprise the lattice structure (for example, it may be triangular or hexagonal) , the refractive indices of the core region, the elongate cylindrical elements and matrix material and the size of the core region. Calculation of the optimal filling fraction may require calculation of, for example, the optimal cross-sectional area of the elongate elements .

The optimal filling fraction may be calculated using any suitable method, for example a numerical optimisation method such as simulated annealing. Simulated annealing is the safest approach, in that it (essentially) always goes to the global maximum of the optimisation function. In the present case the optimisation function would be the frequency range over which the light line exists within the bandgap. However, simulated annealing is slow, particularly if many optimisation parameters are being varied. Other methods can be far quicker, but they may find a local rather than a global optimum or sometimes they can diverge. These other methods generally involve finding partial derivatives and sometimes double derivatives (the Hessian) of the optimisation function. A suitable well-known class of algorithm that can be used is based on the quasi-Newton scheme. "Genetic" algorithms for optimisation are another possibility. Also according to the invention there is provided an optical fibre having a core region and a cladding region, the cladding region comprising a plurality of elongate elements arranged in a structure having a bandgap that guides light in the core region characterised in that the elongate elements fill the cladding region to a filling fraction that provides substantially optimal overlap, according to a numerical optimisation procedure, of the bandgap of the cladding region with the light line of the core, such that the range of light frequencies that can be guided in the core are maximised, according to the optimisation procedure.

In the optimisation procedure, "optimal" overlap will generally be determined by minimising a cost function; an "optimal" overlap may correspond to a value of that cost function to within, say, ±10%, more preferably +5%, still more preferably ±1% of the minimum value of that cost function.

Also according to the invention there is provided an optical fibre (PCF) comprising:

(a) a core region;

(b) a cladding region comprising a plurality of elongate cylindrical elements arranged in a matrix material to form a structure having a bandgap that guides light in the core region; characterised in that the overlap of the bandgap with the light line of guided light is maximised.

Also according to the invention, there is provided an optical fibre having a bandgap region that is substantially aligned in the ω-k plane with the light line of the fibre.

Also according to the invention there is provided a method of manufacturing an optical fibre, comprising: selecting a filling fraction for the fibre that maximises the overlap of the bandgap with the light line of guided light and making a fibre having a cladding region having that filling fraction.

Also according to the invention, there is provided a method of manufacturing an optical fibre having a bandgap region comprising: selecting a filling fraction that substantially aligns in the ω-k plane the bandgap region with the light line of the fibre and making a fibre having a cladding region having that filling fraction. Also according to the invention there is provided a method comprising manufacturing an optical fibre comprising:

(a) a core region;

(b) a cladding region comprising a plurality of elongate cylindrical elements arranged in a matrix material to form a structure having a bandgap that guides light in the core region; characterised in that the method includes the step of selecting the arrangement of elongate cylindrical elements so that they fill the cladding region to a higher filling fraction than the highest filling fraction that would, if all other properties of the fibre remained the same, maximise the frequency width of the bandgap at a wavevector at which the light line is in the bandgap; such that the fibre is able to guide in its core a larger range of light frequencies than could be guided if the elongate cylindrical elements filled the cladding region to said highest filling fraction.

Also according to the invention there is provided a method of manuf cturing an optical fibre, comprising:

(a) selecting properties that characterise a core region of the fibre;

(b) selecting, for a cladding region of the fibre, a structure having a bandgap that guides light in the core region of the fibre, the structure comprising a plurality of elongate cylindrical elements arranged in a matrix material ;

(c) calculating the filling fraction of cylindrical elements in the cladding region that maximises the range of light frequencies that can be guided in the core region if all other properties of the fibre remain constant and;

(d) constructing the fibre having the selected properties and having elongate cylindrical elements having the calculated filling fraction.

The filling fraction that maximises the range of light frequencies guided in the fibre may be calculated using any suitable method, for example a numerical optimisation method such as simulated annealing.

Also according to the invention there is provided a method of manufacturing an optical fibre, comprising: (a) selecting properties of a core region of the fibre; (b) selecting, for a cladding region of the fibre, a structure having a bandgap that guides light in the core region of the fibre, the structure comprising a plurality of elongate cylindrical elements arranged in a matrix material ; (c) calculating the filling fraction of cylindrical elements in the cladding region that, if all other properties of the fibre remain the same, maximises the frequency width of the bandgap of the structure at a wavevector at which the light line is in the bandgap; characterised in that the method further comprises the steps of

(d) selecting a filling fraction larger than the calculated filling fraction; and

(e) constructing the fibre having the selected properties; such that the fibre guides in its core a larger range of light frequencies than could be guided if the filling fraction were to be that filling fraction that would give the maximum bandgap at that wavevector.

In any of the above-described methods, the microstructured fibre is preferably constructed by providing a preform comprising a bundle of rods or of rods and tubes arranged to form the cladding region and the core region and drawing the preform into the fibre. Alternative methods of manufacture are known, such as extruding material through a die or manufacturing from a sol-gel .

An embodiment of the invention will now be described, by way of example only, with reference to the accompanying drawings, of which:

Fig. 1 is a schematic transverse cross-section through a photonic crystal fibre according to the invention. Fig. 2 is a dispersion diagram for a prior art fibre.

Fig. 3 is a flow-chart for optimising the fibre of Fig. 1 by a method according to the invention.

Fig. 4 is a dispersion diagram for the fibre of Fig. 1, optimised by the method of Fig. 3.

Fibre 10 of Fig. 1 is a photonic crystal fibre having a cladding region 30 comprising matrix material 50 defining elongate elements in the form of holes 40. At the centre of the fibre 10 the matrix material 50 defines a core region in the form of large hole 20.

The holes 40 in the cladding region 30 are arranged to form a photonic crystal in the transverse plane of the fibre. The crystal is based on a simple triangular lattice. Hole 20 forms a defect in the lattice. The fibre has an external diameter of 100 microns and the core has a diameter of 15 microns . The diameter of holes 40 is d (cross-sectional area A) and the pitch is Λ. The filling fraction FF of the holes 40 in the cladding region 30 is given by

FF =

**cell where the summation is carried out over all holes in a unit cell and A_ceιι is the total area of that unit cell . Matrix material 50 is silica, which has a refractive index of 1.54.

Fig. 2 is a plot having axes showing normalised frequency ωΛ/c versus normalised waveconstant k₀nΛ, where k₀ is the wavevector in free space. The light line ω(k₀) = cko/n for propagation in the core region is shown by straight line 100. A number of bandgap areas 110, 120, 130 result from the photonic crystal structure of the cladding. Light can be guided in the core of fibre 10 only at frequencies for which a portion of the light line 100 lies within one of the bandgaps . Fig. 2 shows the bandgaps 110, 120, 130 obtained by maximising the frequency width Δi of bandgap 110 at a single wavevector k_n which method reflects the prior art approach to microstructured fibre technology. In that method, a wavelength in bandgap 110 is selected and the corresponding wavevector k_n calculated. Parameters of the photonic crystal are then selected, by any suitable numerical optimisation method, to maximise the frequency width (vertical extent) Δi of the bandgap at that wavevector. In fact, light is not restricted to a single wavevector and any frequency for which there is a corresponding wavevector in the bandgap will be guided.

Thus frequencies in the range labelled Δ₂ will be guided in the example of Fig. 2. However, the overlap has not been optimised for Δ₂ and it has a similar value to Δ_x in this example.

In an example of a method according to the invention (Fig. 3) , the lattice geometry, core refractive index, hole refractive index, matrix material refractive index and core size are selected (step 1) . (In this case, those parameters take the values triangular, 1, 1, 1.54 and 15 microns diameter, respectively, as described above.) An initial guess of three microns is made for the optimum hole diameter and a pitch of 5 microns for the optimum pitch (step 2) . The bandgap structure of a fibre having the selected characteristics is calculated by a computer program (step 3) , using well-known techniques. The range of frequencies for which bandgap 110 overlaps light line 100 is recorded.

A simulated annealing optimisation method is then adopted. The computer program randomly alters the hole size and the pitch by fixed amounts Δa, ΔΛ (step 4) . The overlap of the bandgap 110 with the light line 100 is recalculated (step 5) . If the range of frequencies for which there is overlap has increased, the random increments Δa, ΔΛ are reduced by a small amount in the next iteration (step 6) . If the range has not increased, the random increments Δa, ΔΛ remain the same. The method is repeated from step 4, until the random increments Δa, ΔΛ have been reduced to such an extent that the solution for hole size and pitch (and therefore filling fraction) is stable. The bandgap structure of the fibre having the filling fraction optimised as described is shown in Fig. 4. Bandgap areas 210, 220 and 230 can be seen to be narrower than bandgap areas 110, 120 and 130 of Fig. 2 and to be more tilted relative to the axes. Despite the narrowing, the overlap of bandgap 210 with the light line 100 is greatly improved compared to that of bandgap 110. For a given wavevector k_n, bandgap 210 overlaps the light line for a narrower range of frequencies Δi than the range Δi for bandgap 110 in the previous example. However, removing the restriction to keeping light at a single wavevector during optimisation allows the total overlap of bandgap 260 with the light line 100 to extend over a much wider range of frequencies Δ₂ than the range Δ₂ in the previous example .

Finally, the PCF 10 is manufactured to have the calculated hole size and pitch. The fibre 10 is drawn from a bundle of rods and tubes, in a manner well known in the art .

Claims

1. An optical fibre comprising:

(a) a core region;

(b) a cladding region comprising a plurality of elongate cylindrical elements arranged in a matrix material to form a structure, having a bandgap, that guides light in the core region; characterised in that the elongate cylindrical elements fill the cladding region to a higher filling fraction than the filling fraction that maximises the frequency width of the bandgap, at a wavevector at which the light line is in the bandgap.

2. A fibre as claimed in claim 1 which is able to guide in its core a larger range of light frequencies than could be guided if the elongate cylindrical elements filled the cladding region to said filling fraction that maximises the frequency width of the bandgap.

3. A fibre as claimed in claim 1 or claim 2, in which the filling fraction exceeds by at least 0.05 said filling fraction that maximises the frequency width of the bandgap .

4. A fibre as claimed in any preceding claim, in which the elongate elements are cylinders that are arranged in a lattice pattern.

5. A fibre as claimed in claim 4, in which the elongate elements are arranged on a triangular lattice in the cladding region.

6. A fibre as claimed in claim 4, in which the elongate elements are arranged on a hexagonal lattice in the cladding region.

7. A method as claimed in claim 4, in which the elongate elements are arranged on a square lattice in the cladding region.

8. A fibre as claimed in any of claims 1 to 3, in which the elongate elements are arranged on a quasicrystallic lattice .

9. A fibre as claimed in claim 1 or claim 2, in which the elongate elements are shells that are concentric about the core region.

10. A fibre as claimed in any preceding claim, in which the core region has a lower refractive index than the matrix material .

11. A fibre as claimed in any preceding claim, in which the elongate elements have a lower refractive index than the matrix material .

12. A fibre as claimed in any preceding claim, in which the core region and the elongate elements have the same refractive index.

13. A fibre as claimed in any preceding claim, in which the core region comprises an air hole.

14. A fibre as claimed in claim 13, in which the core region is an air hole.

15. A fibre as claimed in any preceding claim, in which the elongate elements are air holes.

16. A fibre as claimed in any preceding claim, in which the elongate cylindrical elements are of circular cross- section.

17. An optical fibre having a core region and a cladding region, the cladding region comprising a plurality of elongate elements arranged in a structure having a bandgap that guides light in the core region characterised in that the elongate elements fill the cladding region to a filling fraction that provides substantially optimal overlap, according to a numerical optimisation procedure, of the bandgap of the cladding region with the light line of the core, such that the range of light frequencies that can be guided in the core are maximised, according to the optimisation procedure.

18. A fibre as claimed in claim 17, in which a cost function is minimised in the optimisation procedure and the overlap corresponds to a value of that cost function that is within +10% of the minimum value of that cost function.

19. A method of manufacturing an optical fibre having a core region and a cladding region, comprising:

(a) selecting one or more properties that characterise the core region;

(d) fabricating the optical fibre such that the core region has the selected core properties and the cladding region has the selected structure and the determined filling fraction; characterised in that the preferred filling fraction is determined by optimising, in the numerical optimisation procedure, overlap of the bandgap of the cladding region with the light line of the core region so as to maximise the range of light frequencies that can be guided in the core region, for the selected core properties and cladding region structure.