WO2004057392A1

WO2004057392A1 - Photonic crystal fibre with enhanced design flexibility in core defect size

Info

Publication number: WO2004057392A1
Application number: PCT/GB2003/005611
Authority: WO
Inventors: David Philip Williams; Timothy Adam Birks; Jonathan Cave Knight
Original assignee: Crystal Fibre AS; Blazephotonics Ltd
Current assignee: Crystal Fibre AS; Blazephotonics Ltd
Priority date: 2002-12-20
Filing date: 2003-12-19
Publication date: 2004-07-08
Anticipated expiration: 2005-06-20
Also published as: AU2003290312A1

Abstract

The present invention relates to novel optical fibres that guide light in hollow core (210) by virtue of photonic band-gap. Such fibres are sometimes known as photonic crystal fibres or holey fibres. Embodiments of the present invention include fibres in which a hollow core region (210) has a rotational symmetry greater than two and a cladding region (220) surrounding the core region (210) and having a different rotational symmetry. In one example, the hollow core region (210) is generally triangular, having a three-fold rotational symmetry, and the cladding (region220) comprises a triangular array of generally hexagonal holes, which provide a six-fold rotational symmetry for the cladding.

Description

PHOTONIC CRYSTAL FIBRE WITH ENHANCED DESIGN FLEXIBILITY IN CORE DEFECT SIZE

The present invention is in the field of optical waveguides and relates in particular to optical waveguides that guide light by virtue of a photonic bandgap. Optical fibre waveguides, which are able to guide light by virtue of a so-called photonic bandgap (PBG), were first considered in 1995.

In, for example, "Full 2-D photonic bandgaps in silica/air structures", Birks et al., Electronics Letters, 26 October 1995, Vol. 31, No. 22, pp.1941-1942, it was proposed that a PBG may be created in an optical fibre by providing a dielectric cladding structure, which has a refractive index that varies periodically between high and low index regions, and a core defect in the cladding structure in the form of a hollow core. In the proposed cladding structure, periodicity was provided by an array of air holes that extended through a silica glass matrix material to provide a PBG structure through which certain wavelengths of light could not pass. It was proposed that light coupled into the hollow core defect would be unable to escape into the cladding due to the PBG and, thus, the light would remain localised in the core defect.

It was appreciated that light travelling through a hollow core defect, for example filled with air or even under vacuum, would suffer significantly less from undesirable effects, such as non-linearity and loss, compared with light travelling through a solid silica or doped silica fibre core. As such, it was appreciated that a PBG fibre may find application as a transmission fibre to transmit light between a transmitter and a receiver over extremely long distances, for example under the Atlantic Ocean, without undergoing signal regeneration, or as a high optical power delivery waveguide. In contrast, for standard index-guiding, single mode optical fibre, signal regeneration is typically required approximately every 80 kilometres.

The first hollow core PBG fibres that were attempted by the inventors had a periodic cladding structure formed by a triangular lattice of circular air holes embedded in a solid silica matrix and surrounding a central air core defect. Such fibres were formed by stacking circular or hexagonal capillary tubes, incorporating a core defect into the cladding by omitting a single, central capillary of the stack, and then heating and drawing the stack, in a one or two step process, to form a fibre having the required structure.

International patent application PCT/DK99/00193 describes various PBG fibre structures, for example having a cladding region based on a honeycomb lattice with a central air core. The air core is the same size as holes in the cladding region. The structure of the cladding produces a PBG and the air core, which creates a defect in the cladding, enables light to be guided in the glass in the locality of the air core.

International patent application PCT/GB00/01249 (The Secretary of State for Defence, UK), filed on 21 March 2000, proposed the first PBG fibre to have a so-called seven-cell core defect, surrounded by a cladding comprising a triangular lattice of air holes embedded in an all-silica matrix. The core defect was formed by omitting an inner capillary and, in addition, the six capillaries surrounding the inner capillary. This fibre structure was seen to guide one or two modes in the core defect, in contrast to the previous, single-cell core defect fibre, which appeared not to support any guided modes in the core defect.

According to PCT/GB00/01249, it appeared that the single-cell core defect fibre, by analogy to the density-of-states calculations in solid-state physics, would only support approximately 0.23 modes. That is, it was not surprising that the single-cell core defect fibre appeared to support no guided modes in its core defect. In contrast, based on the seven-fold increase in core defect area (increasing the core defect radius by a factor of v7), the seven-cell core defect fibre was predicted to support approximately 1.61 spatial modes in the core defect. This prediction was consistent with the finding that the seven-cell core defect fibre did indeed appear to support at least one guided mode in its core defect.

A preferred fibre in PCT/GB00/01249 was described as having a core defect diameter of around 15μm and an air-filling fraction (AFF) - that is, the proportion by volume of air in the cladding - of greater than 15% and, preferably, greater than 30%. Herein, AFF (or any equivalent measure for air or vacuum or other solid or gaseous materials) is intended to mean the proportion by volume of air in a microstructured, or holey, portion of the cladding, which is representative of a substantially perfect and unbounded cladding. That is, imperfect regions of the cladding, for example near to or abutting a core defect and at an outer periphery of a microstructured region, would not be used in calculating the AFF. Likewise, a calculation of AFF does not take into account over-cladding or jacketing layers, which may surround the microstructured region.

In "Analysis of air-guiding photonic bandgap fibres", Optics Letters, Vol. 25, No. 2, January 15, 2000, Broeng et al. provided a theoretical analysis of PBG fibres. For a fibre with a seven-cell core defect and a cladding comprising a triangular lattice of near-circular holes, providing an AFF of around 70%, the structure was shown to support one or two air guided modes in the core defect. This was in line with the finding in PCT/GB00/01249. In the chapter entitled "Photonic Crystal Fibers: Effective Index and Band-Gap Guidance" from the book "Photonic Crystal and Light Localization in the 21^st Century", CM. Soukoulis (ed.), ©2001 Kluwer Academic Publishers, the authors presented further analysis of PBG fibres based primarily on a seven-cell core defect fibre. The optical fibre was fabricated by stacking and drawing hexagonal silica capillary tubes. The authors suggested that a core defect must be large enough to support at least one guided mode but that, as in conventional fibres, increasing the core defect size would lead to the appearance of higher order modes. The authors also went on to suggest that there are many parameters that can have a considerable influence on the performance of bandgap fibres: choice of cladding lattice, lattice spacing, index filling fraction, choice of materials, size and shape of core defect, and structural uniformity (both in-plane and along the axis of propagation).

WO 02/075392 (Corning, Inc.) identifies a general relationship in PBG fibres between the number of so-called surface modes that exist at the boundary between the cladding and core defect of a PBG fibre and the ratio of the radial size of the core defect and a pitch of the cladding structure, where pitch is the centre to centre spacing of nearest neighbour holes in the triangular lattice of the exemplified cladding structure. It is suggested that when the core defect boundary, together with the photonic bandgap crystal pitch, are such that surface modes are excited or supported, a large fraction of the "light power" propagated along the fibre is essentially not located in the core defect. Accordingly, while surface states exist, the suggestion was that the distribution of light power is not effective to realise the benefits associated with the low refractive index core defect of a PBG crystal optical waveguide. The mode energy fraction in the core defect of the PBG fibre was shown to vary with increasing ratio of core defect size to pitch. In other words, it was suggested that the way to increase mode energy fraction in the core defect is by decreasing the number of surface modes, in turn, by selecting an appropriate ratio of the radial size of the core defect and a pitch of the cladding structure. In particular, WO 02/075392 states that, for a circular core structure, a ratio of core radius to pitch of around 1.07 to 1.08 provides a high mode power fraction of not less than 0.9 and is single mode. Other structures are considered, for example in Figure 7, wherein the core defect covers an area equivalent to 16 cladding holes. In a Post-deadline paper presented at ECOC 2002, "Low Loss (13dB) Air core defect

Photonic Bandgap Fibre", N. Venkataraman et al. reported a PBG fibre having a seven-cell core defect that exhibited loss as low as 13dB/km at 1500nm over a fibre length of one hundred metres. The structure of this fibre closely resembles the structure considered in the book chapter referenced above. The authors attribute the relatively small loss of the fibre as being due to the high degree of structural uniformity along the length of the fibre.

PBG fibre structures are typically fabricated by first forming a pre-form and then heating and drawing an optical fibre from that pre-form in a fibre-drawing tower. It is known either to form a pre-form by stacking capillaries and fusing the capillaries into the appropriate configuration of pre-form, or to use extrusion.

For example, in PCT/GB00/01249, identified above, a seven-cell core defect pre-form structure was formed by omitting from a stack of capillaries an inner capillary and, in addition, the six capillaries surrounding the inner capillary. The capillaries around the core defect boundary in the stack were supported during formation of the pre-form by inserting truncated capillaries, which did not meet in the middle of the stack, at both ends of the capillary stack. The stack was then heated in order to fuse the capillaries together into a preform suitable for drawing into an optical fibre. Clearly, only the fibre drawn from the central portion of the stack, with the missing inner seven capillaries, was suitable for use as a hollow core defect fibre.

US patent application number US 6,444,133 (Corning, Inc.), describes a technique of forming a PBG fibre pre-form comprising a stack of hexagonal capillaries in which the inner capillary is missing, thus forming a core defect of the eventual PBG fibre structure that has flat inner surfaces. In contrast, the holes in the capillaries are round. US 6,444,133 proposes that, by etching the entire pre-form, the flat surfaces of the core defect dissolve away more quickly than the curved surfaces of the outer capillaries. The effect of etching is that the edges of the capillaries that are next to the void fully dissolve, while the remaining capillaries simply experience an increase in hole-diameter. Overall, the resulting pre-form has a greater fraction of air in the cladding structure and a core defect that is closer to a seven-cell core defect than a single cell core defect.

PCT patent application number WO 02/084347 (Corning, Inc.) describes a method of making a pre-form comprising a stack of hexagonal capillaries of which the inner capillaries are preferentially etched by exposure to an etching agent. Each capillary has a hexagonal outer boundary and a circular inner boundary. The result of the etching step is that the centres of the edges of the hexagonal capillaries around the central region dissolve more quickly than the corners, thereby causing formation of a core defect. In some examples, the circular holes are offset in the inner hexagonal capillaries of the stack so that each capillary has a wall that is thinner than its opposite wall. These capillaries are arranged in the stack so that their thinner walls point towards the centre of the structure. An etching step, in effect, preferentially etches the thinner walls first, thereby forming a seven-cell core defect.

According to a first aspect, the present invention provides an optical waveguide, having a plane cross section and a length dimension, which extends perpendicular to the plane cross section, comprising: a photonic bandgap structure having an m-fold maximum rotational symmetry, where m is an integer, and comprising, in the plane cross section, relatively low refractive index regions and relatively high refractive index regions, arranged in a substantially periodic array of regions extending parallel to the length dimension; and a core having an n-fold maximum rotational symmetry, where n is an integer greater than two, and comprising a region of relatively low refractive index, which extends parallel to the length dimension and through the photonic bandgap structure, thereby forming, in the plane cross section, a defect in the substantially periodic array of regions, which, according to the periodicity of the photonic bandgap structure, is substantially centred on what would have been, were the defect absent, a region of relatively high refractive index in the photonic bandgap structure, wherein, the photonic bandgap structure provides a photonic bandgap over a range of frequencies of light such that a mode of light at one or more of those frequencies is concentrated in the relatively low refractive index region of the core defect. The array is said to be "substantially" periodic to take account of potential manufacturing imperfections or systematic distortions, for example due to the presence of a core defect and/or additional layers (over-cladding) and jacketing around the photonic band- gap structure, as well as the fact that the photonic bandgap structure is not infinite in dimension: being bounded by an outer periphery and has a core defect therein. The present invention is intended to encompass both perfect and imperfect structures. Likewise, any reference to "periodic", "lattice", or the like herein, imports the likelihood of imperfection.

The core may have a form (for example, shape, size, relationship with the photonic band-gap structure, etc.) that would be obtained by omission or removal of a region of the photonic bandgap structure that is substantially centred on a region of relatively high refractive index.

In some embodiments, m is the same as n. In other embodiments, m and n are different. For example, m may be greater than or less than n. The maximum order of rotational symmetry of the photonic bandgap structure may relate to the bounded structure in a practical waveguide or to a notionally infinite structure, which is unbounded. The bounded structure may have a maximum order of rotational symmetry that is the same as or less than the maximum order of rotational symmetry of the 5 infinite structure. For example, the maximum order of rotational symmetry of a notionally infinite regular triangular lattice of round holes is six.

If that infinite structure were bounded by a hexagonal boundary, a square boundary or a rectangular boundary, the maximum order of rotational symmetry for the structure as a whole would be six, four and two respectively. 10 The photonic bandgap structure may have a rotational symmetry, wherein m = 1, 2, 3,

4 or 6. In particular embodiments described hereinafter, m=6.

The core may have a rotational symmetry wherein n=3, 4, 5 or 6. Alternatively, n may be higher than 6. In particular embodiments described hereinafter, n=3.

The waveguide is not birefringent. It is, however, conceivable that a certain degree of 15 birefringence may arise due to imperfections in the structure. Such birefringence will be classed as unintentional and ignored for the present purposes.

The core may have an area which is significantly larger than the area of at least some of the relatively low refractive index regions of the photonic bandgap structure. For example, the core area may be greater than twice or three times the area of at least some of the 20 relatively low refractive index regions of the photonic bandgap structure. In some embodiments, the core area may be larger than the area of each of the relatively low refractive index regions of the photonic bandgap structure.

The photonic band-gap structure may have a proportion by volume of relatively low refractive index regions (for example air) exceeding 70%. Preferably, that proportion is above 25 80% and, in some embodiments, above 90%.

The relatively low refractive index regions may be voids under vacuum, or be filled with air or another gas. Alternatively, the relatively low refractive index regions comprise a material having a relatively low refractive index.

The regions of relatively high refractive index may comprise silica. This may include

30 relatively pure silica or doped silica, or other silicate glasses. Alternatively, the regions of relatively high refractive index may comprise a different inorganic glass or an organic polymer. The present invention is not limited in any way to a particular material or material system, as long as a practical structure can be made. According to a second aspect, the present invention provides a pre-form for making a photonic bandgap optical waveguide having a core region and a cladding region, which provides a photonic bandgap over a range of frequencies of light such that a mode of light of at least one of those frequencies is concentrated in the core region, the pre-form having a plane cross section and a length dimension, which extends perpendicular to the plane cross section, and comprising: a first part for forming the cladding region comprising, in the plane cross section, relatively low refractive index regions and relatively high refractive index regions, arranged in a substantially periodic array of regions, the first part extending parallel to the length dimension; and a relatively low refractive index region, for forming the core region, extending through the first part parallel to the length dimension and resulting from omission or removal of an inner region of the first part, which is substantially centred on a relatively high refractive index region of the first part. According to a third aspect, the present invention provides an optical fibre transmission system comprising at least a transmitter, a receiver and a waveguide, as described above, for transmitting light between the transmitter and the receiver.

According to a fourth aspect, the present invention provides data conditioned by having been transmitted through a waveguide, as described above. As in any transmission system, data that is carried by the system acquires a characteristic 'signature' determined by a transfer function of the system. By characterising the system transfer function sufficiently accurately, using known techniques, it is possible to match a model of the input data, operated on by the transfer function, with real data that is output (or received) from the transmission system. Other aspects and embodiments of the present invention will become apparent from reading the following description and claims and considering the following drawings.

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

Figure 1 is a diagram which illustrates a transverse cross section of a PBG fibre structure of the kind known from the prior art, with a seven-cell core defect in a triangular lattice cladding structure; Figure 2 is a diagram which illustrates a transverse cross section of an exemplary embodiment of the present invention in which a three-cell core defect is formed in a triangular lattice cladding structure;

Figure 3 is a diagram which illustrates a transverse cross section of an exemplary embodiment of the present invention in which a twelve-cell core defect is formed in a triangular lattice cladding structure;

Figure 4 is a diagram which illustrates a transverse cross section of an exemplary embodiment of the present invention in which a six-cell core defect is formed in a triangular lattice cladding structure; Figure 5 is a diagram which illustrates a transverse cross section of an exemplary embodiment of the present invention in which a ten-cell core defect is formed in a triangular lattice cladding structure;

Figure 6 is a graph of a mode spectrum for the waveguide structure illustrated in Figure 2; Figures 7a and 7b are mode diagrams for the mode identified as "F" in the graph of

Figure 6;

Figure 8 a diagram which illustrates a transverse cross section of an exemplary embodiment of the present invention in which a core defect is formed in a hexagonal lattice cladding structure; Figure 9 is a diagram which illustrates a transverse cross section of an exemplary embodiment of the present invention in which a core defect is formed in a square lattice cladding structure; and

Figure 10 is a diagram illustrating an arrangement of capillaries for use in forming a waveguide structure according to an embodiment of the present invention. Figure 1 is a diagram which illustrates the transverse cross-section of the inner region of a fibre structure 100 of the kind described in the prior art, for example in PCT/GB00/01249, which can guide light in an air-core 110 by virtue of a photonic bandgap provided by a periodic cladding structure 120. In the Figure, the dark regions represent fused silica glass and the light regions represent air holes in the glass. As illustrated, the cladding 120 comprises a triangular array of generally circular holes 1 30 in a silica matrix 140, surrounding a seven-cell core defect 110, which is formed by omitting or removing seven central cells; an inner cell and the six cells that surround the inner cell. The cells would typically have been removed or omitted from a pre-form prior to drawing the pre-form into the fibre. The omitted or removed cells remain illustrated, for ease of understanding only, as relatively faint, broken circles 150 in the core defect 110.

It is known that such a fibre structure 100 typically, in practice, has more layers of periodic cladding structure and an outer layer or layers of solid material as well as protective jacketing layers.

It is clearly seen in Figure 1 that the core defect 110 is centred about what would have been the inner hole 190 of the cladding 120. In other words, the core defect 110 is centred on, what would have been a region of relatively low refractive index; in this case air.

Another way of considering whether the core defect is centred on a region of relatively high refractive index is to extrapolate the cladding structure into the core defect.

The word "centred" is used while bearing in mind that a typical PBG optical fibre manufacturing process is likely to produce imperfect fibres, meaning the intended centre of the core defect may not exactly match the theoretical, or required, centre. However, it should be relatively clear from the size and position of the core defect, and from the form of the cladding structure, whether the core defect is, or is intended to be, centred on what would have been a relatively high refractive index region of, for example, an extrapolated cladding.

As the skilled person will appreciate, according to embodiments of the invention, although a cell comprises a region of relatively high refractive index surrounding a void, or a hole, for example filled with air or under vacuum, the voids or holes may alternatively be filled with a gas or a liquid or may instead comprise a solid material that has a different refractive index than the material that surrounds the hole. Equally, the silica glass may be doped or replaced by a different glass, or other suitable material such as a polymer, or may comprise plural materials.

For reasons of simplicity of description herein, unless otherwise stated, the following PBG fibre structures are formed from air holes in a silica matrix.

The following exemplary structures, unlike the prior art structures, have a core defect formed by removal or omission of a cladding region centred on silica rather than air. In other words, the core defects are centred on what would have been silica, in the absence of a core defect. Additionally, the core defects have a maximum order of rotational symmetry that is greater than two. In other words, the core defects would not be suitable in birefringent waveguide structures, where the maximum rotational order of symmetry of the structure needs to be two and no more than two. Figures 2 and 3 are diagrams, in transverse cross section, of exemplary embodiments of the present invention. The structures shown are PBG fibre structures that guide at least one mode of light predominantly in their core defect regions.

Where possible in the following exemplary structures, similar parts or regions are 5 identified with the same reference numeral. Additionally, as in Figure 1, dark regions represent silica and light regions represent air.

As illustrated in Figure 2, a fibre structure 200 has a cladding 220, which comprises a triangular array of generally hexagonal holes 230, surrounding a three-cell core defect 210. As in Figure 1, the omitted or removed cells are illustrated, diagrammatically, as relatively 10 feint, broken hexagons 250 in the core defect 210.

Hereafter, and with reference to Figure 2, a region of glass 240 between any two holes is referred to as a "vein" and a region of glass 260 where veins meet is referred to as a "node".

In practice, for triangular lattice structures that have a large AFF, for example above

15 75%, the cladding holes 230 tend to assume a generally hexagonal form, as shown in Figure

2, and the veins are generally straight. It has been found that increasing the AFF for a given structure tends to increase the width of the band-gap. An AFF above 85% or even 90% has been shown to provide a particularly wide band-gap.

A core defect boundary 270 comprises the inwardly-facing veins of the innermost cells 20 that surround the core defect 210. As can be seen, certain of the cells 280 surrounding the core defect 210 are pentagonal rather than hexagonal, as a result of surface tension in the silica during the drawing process, which flattens-off the respective sides.

In Figure 2, it is clear that the core defect 210 of the PBG structure 200 is substantially centred on what would have been a region of silica, specifically a node 290, in the cladding 25 structure 220.

The structure in Figure 2, and each of the following examples of different structures, is a practical optical fibre structure, which has either been made or may be made according to known processes or the processes described hereinafter. The present structures share the following common characteristics: 30 a pitch A of the cladding chosen between values of approximately 3μm and 6μm (this value may be chosen to position core-guided modes at an appropriate wavelength for a particular application); and an AFF in the cladding of approximately 87.5%. Further details relating to various characteristics of exemplary cladding structures are provided in applicant's co-pending patent application number GB0302632.5, the contents of which are hereby incorporated herein by reference.

The exemplary PBG fibre structure in Figure 3 has a twelve-cell core defect 210, made by omitting or removing a triangular arrangement of three inner cells and the nine cells that surround the three inner cells. Other than the size of the core defect 210, the structure in Figure 3 is the same as the structure in Figure 2, with the core defect 210 being centred on what would have been a region of silica, specifically a node 290, in the cladding structure 220. The exemplary PBG fibre structure in Figure 4 has a six-cell core defect 210, made by omitting or removing a triangular arrangement of six inner cells, as represented by the relatively feint, broken hexagons 250. The cladding structure 220 in the structure 200 has the same form as the cladding structures in Figures 2 and 3. Again, the core defect 210 is centred on what would have been a node region 290 of silica in the cladding structure 220. The PBG fibre structure in Figure 5 has a ten cell core defect 210, made by omitting a triangular arrangement often cells. The cladding structure 220 is the same as for the Figure 4 structure. The core defect 210 is centred on what would have been a node region 290 of silica.

It is apparent that each structure in Figures 2, 3, 4 and 5 has a three-fold rotational symmetry about a central node, whereas the cladding structures have a six-fold rotational symmetry. In contrast, prior art PBG fibre cores tend to have the same, or a higher, order of rotational symmetry as the respective cladding structures. For example, the core defect 110 of the prior art structure in Figure 1 has a six-fold rotational symmetry, which is the same as the cladding structure. Additionally, the structures in Figures 2, 3, 4 and 5 tend to have different natural sizes and shapes to those in the prior art. Typically, the more recent prior art PGB fibre structures have tended to concentrate on a seven-cell, quasi-hexagonal core defect in a triangular lattice of holes. While seven-cell core defect structures may be fabricated using known stack and draw techniques to have a small range of different core defect sizes, by shrinking or expanding the core defect transverse cross-sectional area during drawing of the fibre, it is not practical to vary core size significantly without also significantly perturbing the surrounding cladding, which is perceived to be undesirable. It would be possible to select, instead, a one- cell core defect or a nineteen-cell core defect, if there is a need to have a significantly smaller or significantly larger core defect, but such radical changes to core defect size may have attendant problems. For example, a single-cell core defect may not guide any modes at a required wavelength and a nineteen cell core defect may guide far too many modes.

One of the PBG fibre structures of Figures 2, 3, 4 or 5 may provide a desirable alternative core defect size that is practical to make, without significantly modifying a manufacturing process, and is closer to a required core defect size.

For the purposes of comparing aspects of the performance of various different structures it is useful to consider the modes that are supported in the band gap of various PBG fibre structures. This may be achieved by solving Maxwell's vector wave equation for the fibre structures, using known techniques. In brief, Maxwell's equations are recast in wave equation form and solved in a plane wave basis set using a variational scheme. An outline of the method may be found in Chapter 2 of the book "Photonic Crystals - Molding the Flow of Light", J.D. Joannopoulos et al., ©1995 Princeton University Press.

Figure 6 is a graph that shows the mode spectrum of the PBG fibre structure of Figure 2. The horizontal axis of the spectrum is normalised frequency, ωA/c, where ω is the frequency of the light, A is the pitch of the cladding structure, and c is the speed of light in a vacuum. The vertical axis of the spectrum relates to the response of the structure to a given input for a given normalised wave- vector βΛ=13, against which the spectrum is plotted, where β is the chosen propagation constant for the calculations. The spectrum is produced using a Finite-Difference Time Domain (FDTD) algorithm, which computes the time- dependent response of a given hollow core structure to a given input. This technique has been extensively used in the field of computational electrodynamics, and is described in detail in the book "Computational Electrodynamics: The Finite-Difference Time-Domain Method", A. Taflove & S.C. Hagness, ©2000 Artech House. The FDTD technique may be readily applied to the field of PBG fibres and waveguides by those skilled in the art of optical fibre modelling.

In Figure 6, each vertical spike indicates the presence of at least one mode at a corresponding normalised frequency. In some cases, multiple modes may appear as a single spike or as a relatively thicker spike compared with other spikes in a spectrum. This is due to the fact that the data used to generate the spectra is sometimes not of a high enough resolution to distinguish very closely spaced modes. As such, the mode spectrum should be taken to provide only an approximation to the actual number of modes that exist for a given structure, which is satisfactory for the present purposes. On the spectrum, a 'light line' is shown as a solid vertical line at ωΛ/c=13=βΛ, and band edges, which bound a bandgap, are represented as two dotted vertical lines, one on either side of the light line, with a lower band edge of the bandgap at around ωΛ/c=12.92 and an upper band edge of the bandgap at around ωΛ/c=T3.35. As already indicated, a bandgap is a range of frequencies of light for a given β that cannot propagate through the cladding structure. For the present example, the bandgap is slightly wider than 0.35 (in units of ωΛ/c). The inventors estimate that the minimum practical width for a PBG fibre bandgap would be around 0.05 in the present units of measure but, more preferably, would be greater than 0.1.

In general, any modes that are between the light line and the lower band edge (that is, to the left of the light line) will concentrate in the glass and be evanescent in air whereas the modes that are between the light line and the upper band edge (that is, to the right of the light line) may be air-guiding.

As shown in Figure 6, there are no modes between the light line and the lower band edge and around six modes between the light line and the upper band edge (taking the thicker spike D as two modes).

It is clear that the PBG fibre structure in Figure 2 supports a number of modes, some of which could be air-guiding; although, it is unlikely that all of these modes will be excited by a given light input. Analysis of the individual modes shown in the bandgap leads to a finding that the mode marked as F is a degenerate, air-guiding mode, which has two polarisations falling at about the same position in the bandgap, as will be shown below.

Figures 7a and 7b comprise plots, which show the mode intensity distributions, over a transverse cross-section of the PBG fibre structure shown in Figure 2, for the two polarisations of the mode marked F. These plots were produced using the results obtained by solving Maxwell's equations for the structure, as described above. The amount of light in air for both polarisations shown in Figures 7a and 7b is found to be around 93%.

The percentage of light in air for a mode is found by calculating the power propagating in the air regions of the plots in Figure 7a and 7b and normalising to the total power. Of course, the plots in Figure 7 represent the intensity across only an inner region of the various PBG fibre structures. Accordingly, the respective percentages of light in air are calculated for the inner regions only and may be slightly different if calculated across an entire PBG fibre structures. However, the intensities have typically reduced so considerably towards the edges of the plots that any light in regions outside of the inner regions, whether in air, glass or both, is unlikely to have a significant impact on the percentage of light in air values.

Although results are not presented herein, it is anticipated that the PBG fibre structure in Figure 3 is likely to support a mode with a greater portion of light in air, predominantly in the core defect, than the structure in Figure 2. This proposition is supported by reference to structures in applicant's co-pending patent application GB0229826.3, which compares modes in seven cell core defect structures with modes in nineteen-cell core defect structures. In applicant's co-pending patent application, the nineteen cell core defect structures consistently support modes with significantly more light in air than similar seven-cell core defect structures. Similarly, the PBG fibre structure in Figure 5, which has a relatively large core defect, is likely to support a mode with significantly more light in air than the PBG fibre structure in Figure 4, which has a relatively small core defect.

Alternative exemplary structures according to embodiments of the present invention are illustrated diagrammatically in Figures 8 and 9. These structures share in common with the previous exemplary embodiments the feature that the core defect is centred on what would have been, in the absence of the core defect, a relatively high refractive index region of the cladding. However, in contrast to the previous embodiments, these PBG fibre structures have core defects that have a rotational symmetry equal to or greater than the rotational symmetry of the cladding structure. Figure 8 illustrates an exemplary PBG fibre structure based on what is commonly known as a honeycomb arrangement of cells. The core defect is centred on what would have been a region of high refractive index matrix material in the cladding and is formed by removal or omission of an inner group of six holes (and associated matrix material) and the generally round region of silica that would have been surrounded by the six holes. Figure 9 illustrates an exemplary PBG fibre structure based on a square lattice of circular holes in a silica matrix. The structure is centred on what would have been a region of high refractive index matrix material and is formed by omission or removal of an inner, square group of four holes (and associated matrix material).

The cladding structures in Figures 8 and 9 are known to provide different photonic bandgap characteristics compared with the triangular lattice cladding structures described above.

There are a number of methods suitable for making PBG fibre structures according to embodiments of the present invention. Some of the known methods involve creating a pre- from from a stack of glass capillaries and, possibly, glass rods, to match the desired PBG fibre structure on a macro scale and heating and drawing-down the stack into a fibre of the required dimensions. An inner region of the stack, which becomes the core defect of the fibre, may be formed by omitting the requisite number of inner capillaries and, if present, rods from the pre- form and, for example, supporting the outer capillaries using truncated capillaries at either end of the stack, as described in PCT/GB00/01249 (described above), or by etching away glass from inner capillaries in accordance with either PCT/GB00/01249 or US 6,444,133 also mentioned above.

Alternatively, the core defect may be formed by omitting the requisite number of capillaries and rods from the inner region of the stack and supporting the outer capillaries and rods around an insert in the inner region. The insert may be a large glass capillary, which remains in-situ during the drawing process and becomes part of a core boundary. Alternatively, as shown in Figure 10, the insert may, for example, be made from graphite, platinum, tantalum, tungsten or a ceramic material, which has a higher melting point than silica glass and, preferably, a higher coefficient of thermal expansion. A stack 310 of glass capillaries 320 is formed around the insert 300. The stack is heated to allow the capillaries 320 to fuse into a pre-form. The pre-form is then allowed to cool and the insert 300 is removed. In practice, the capillaries are held in place in the stack by an outer glass tube (not shown) and the pre-form is, again, over-clad by another glass tube (not shown) before being drawn down into fibre.

An advantage of using an insert material having a higher coefficient of thermal expansion than silica is that, when the stack 310 and insert 300 are heated, the insert expands more than the silica. When permitted to cool down again, the insert 300 shrinks back down to its original size and the silica solidifies leaving an inner region that is larger than the insert. The insert, which as a result is loose-fitting in the central region, may then be removed readily from the pre-form with reduced risk of damaging or contaminating the pre-form. The resulting pre-form is then heated and drawn in the usual way to form a PBG fibre.

Claims

1. An optical waveguide, having a plane cross section and a length dimension, which extends perpendicular to the plane cross section, comprising: a photonic bandgap structure having an m-fold maximum rotational symmetry, where m is an integer, and comprising, in the plane cross section, relatively low refractive index regions and relatively high refractive index regions, arranged in a substantially periodic array of regions extending parallel to the length dimension; and a core having an n-fold maximum rotational symmetry, where n is an integer greater than two, and comprising a region of relatively low refractive index, which extends parallel to the length dimension and through the photonic bandgap structure, thereby forming, in the plane cross section, a defect in the substantially periodic array of regions, which, according to the periodicity of the photonic bandgap structure, is substantially centred on what would have been, were the defect absent, a region of relatively high refractive index in the photonic bandgap structure, wherein, the photonic bandgap structure provides a photonic bandgap over a range of frequencies of light such that a mode of light at one or more of those frequencies is concentrated in the relatively low refractive index region of the core defect.

2. The waveguide according to claim 1, wherein the core has a form that would be obtained by omission or removal of a region of the photonic bandgap structure that is substantially centred on a region of relatively high refractive index.

3. The waveguide according to^* claim 1 or claim 2, wherein m is the same as n.

4. The waveguide according to claim 1 or claim 2, wherein m and n are different.

5. The waveguide according to claim 4, wherein, m is lower than n.

6. The waveguide according to any one of the preceding claims, wherein m = 1, 2, 3, 4 or 6.

7. The waveguide according to any one of the preceding claims, wherein m=6.

8. The waveguide according to any one of the preceding claims, wherein n = 3, 4, 5 or 6.

9. The waveguide according to claim 8, wherein n=3. 5

10. The waveguide according to any one of claims 1 to 7, wherein n is higher than 6.

11. The waveguide according to any one of the preceding claims, wherein the core area is significantly larger than the area of at least some of the relatively low refractive index regions

10 of the photonic bandgap structure.

12. The waveguide according to any one of the preceding claims, wherein the core area is greater than twice the area of at least some of the relatively low refractive index regions of the photonic bandgap structure.

15

13. The waveguide according to any one of the preceding claims, wherein the core area is greater than three times the area of at least some of the relatively low refractive index regions of the photonic bandgap structure.

20 14. The waveguide according to any one of the preceding claims, wherein the core area is larger than the area of each of the relatively low refractive index regions of the photonic bandgap structure.

15. The waveguide according to any one of the preceding claims, wherein the photonic 25 band-gap structure has a proportion by volume of relatively low refractive index regions exceeding 70%.

16. The waveguide according to any one of the preceding claims, wherein the relatively low refractive index regions comprise voids under vacuum, or filled with air or another gas.

30

17. The waveguide according to any one of the preceding claims, wherein the regions of relatively high refractive index comprise silica.

18. A pre-form for making a photonic bandgap optical waveguide having a core region and a cladding region, which provides a photonic bandgap over a range of frequencies of light such that a mode of light of at least one of those frequencies is concentrated in the core region, the pre-form having a plane cross section and a length dimension, which extends 5 perpendicular to the plane cross section, and comprising: a first part for forming the cladding region comprising, in the plane cross section, relatively low refractive index regions and relatively high refractive index regions, arranged in a substantially periodic array of regions, the first part extending parallel to the length dimension; and 10 a relatively low refractive index region, for forming the core region, extending through the first part parallel to the length dimension and resulting from omission or removal of an inner region of the first part, which is substantially centred on a relatively high refractive index region of the first part.

15 19. Apre-form for making a waveguide according to any one of claims 1 to 17.

20. An optical fibre transmission system comprising a transmitter, a receiver and a waveguide, according to any one of claims 1 to 17, for transmitting light between the transmitter and the receiver.

20

21. Data conditioned by having been transmitted through a waveguide according to any one of claims 1 to 17.