WO2005083483A1

WO2005083483A1 - Birefringent optical fibre

Info

Publication number: WO2005083483A1
Application number: PCT/DK2005/000128
Authority: WO
Inventors: Ole Sigmund; Andreas Hvidtfeld Nielsen
Original assignee: Danmarks Tekniske Universitet
Current assignee: Danmarks Tekniske Universitet
Priority date: 2004-02-27
Filing date: 2005-02-25
Publication date: 2005-09-09
Anticipated expiration: 2006-08-27

Abstract

The invention relates to birefringent optical fibres, used as e.g. polarisation maintaining optical fibres. More specifically, the invention relates to distributing different material compositions in the fibre to increase the birefringence in the core of the fibre. By applying topology optimization methods based on finite element analysis, fibre designs with three different material phases are produced which significantly increase the birefringence in the fibre core. One of the phases have a lower Young’s modulus than the others and may be void such as air holes. The invention proposes alterations to standard layouts such as the bow-tie or double bow-tie. The invention may also be applied on optical crystal fibres or photonic bandgap fibres.

Description

BI EFRINGENT OPTICAL FIBRE

FIELD OF THE INVENTION

The invention relates to birefπngent optical fibres, used as e.g. polarisation maintaining optical fibres. More specifically, the invention relates to designing the material composition of the fibre to increase the birefringence in the core of the fibre.

BACKGROUND OF THE INVENTION

Optical fibres that can preserve a certain state of polarisation of the guided light are important for many applications, especially in optical fibre sensor technology. Such fibres fall into two classes. The polarisation-maintaining fibres allowing two orthogonal polarisations to propagate independently and which are designed to minimise any coupling between them. This can be achieved in a birefπngent fibre, where the optical anisotropy in two mutually perpendicular directions is large. The second class comprises single polarisation fibres. These are characterised by a large differential attenuation between orthogonal directions so that any light coupled into all but the desired state of polarisation is quickly removed.

Birefπngent fibres typically have segments with materials having different thermal expansion coefficients in the cladding. When the fibre has been drawn under high temperatures during fabrication, the different sections contract differently resulting in stress in and on the fibre core. This stress deforms the shape of the core and affects the refractive indices in different directions according to the photoelastic effect. By distributing the segments properly the stress anisotropy, and thereby the birefringence, can be controlled. Figures 1A-C shows typical cross sectional designs of birefπngent fibres, the PANDA (Polarisation-maintaining AND Absorption-reducing) (Figure 1A), bow-tie (Figure IB), and double bow-tie (Figure 1C). Another type is described in US 2003/174985.

Some polarisation-maintaining fibres are designed to be sensitive to external variations in temperature and pressure in order to act as a sensor. Here, the polarisation-maintaining fibre is used as an interferometer. Light with a certain state of polarisation is coupled into the fibre, and due to the intrinsic birefringence of the fibre, the x-component of the E field travels faster than the y-component. The net effect is a relative phase delay between the two components. The sensitivity is achieved by included stress-inducing elements in the cladding so that the degree of birefringence is a function of the change in internal energy of the fibre. By determining the change in the relative phase delay of the orthogonal components, the internal energy variations are monitored. An analytical solution for the stress-induced birefringence at the centre of various polarisation-maintaining fibres has been used to show that the double bow-tie layout shown in Figure 1C represents the optimal design for polarisation maintaining fibres, see e.g. Varnham et al (Journal of Lightwave Technology 1, 332 ( 1983)) or Tsai et al (Journal of Lightwave Technology 9, 7 ( 1991)).

SUMMARY OF THE INVENTION

It is an object of the invention to provide an improved design for birefπngent fibres that includes mechanisms for enhancing the stress-induced birefringence.

The optimal design for polarisation maintaining fibres according to the prior art typically applies two materials with different coefficients of thermal expansion. The present invention applies the novel and inventive measure of allowing a further phase, material or void, of lower stiffness to relieve mechanical bindings between the other materials. This increases the stress exerted on the fibre core by the other materials.

It is an advantage of the fibre design according to the invention that it allows for the initial strain of the material phases in the cladding to exert a larger stress on the core, thereby increasing the birefringence of the fibre.

In a first aspect, the present invention provides a birefπngent optical fibre described by cylindrical coordinates (r, θ, z) and having a waveguiding zone extending inside an outer cladding portion in the longitudinal z-direction of the fibre, the outer cladding portion comprises first and second stress-producing segments formed by first and second material compositions having different expansion coefficients, the outer cladding portion further comprises radially oblong stress-redistributing regιon(s) formed on or along at least substantially radially oriented boundary sections between the first and second segments, the stress-redistributing regιon(s) have a lower Young's modulus than the first and the second material compositions.

The waveguiding zone typically consist of a high refractive index fibre core surrounded by a low refractive index inner cladding portion ensuring total internal reflection for electromagnetic radiation propagating in the longitudinal z-direction inside the core - this is called index guiding. Index guiding can also be performed using only a single material, in which case the low-index layer consist of a pattern of microstructured air-holes running along the length of the fibre. The holes result in a low average refractive index in the inner cladding portion, thereby satisfying the conditions for total internal reflection. Such fibres are typically referred to as crystal fibres. The waveguiding zone may be based on photonic bandgap waveguiding instead of index guiding. Here, a central core part of the fibre is surrounded by a periodic microstructure (typically air holes). Light of proper wavelength will be confined in the central part since no propagation modes can exist in the periodic structure due to multiple-beam interference. Since there are no requirements on the refractive index in this case, the core may also be an air hole. Such fibres are typically referred to as photonic bandgap optical fibres Often, the distinction between crystal fibres and photonic bandgap fibres is not rigid.

The outer cladding portion surrounding the waveguiding zone primarily provides protection and mechanical stability to the waveguiding zone. However, the evanescent field from a mode propagating in the waveguiding zone may extend into the outer cladding portion, and therefore the distinction between the inner and the outer cladding portion is not exact.

By including stress-producing segments in the outer cladding portion, the waveguiding zone and especially the core part will become birefπngent due to the photoelastic effect and due to deformation of the core. The photoelastic effect is the change in refractive index due to stress on a solid material. The atoms move further apart under tensile stress, and closer together under compressive stress - this is the lattice effect Similarly, the electron shells of the atoms are distorted, known as the atomic effect. For silica-rich glass, the former effect is dominant so that the refractive index changes the most along the direction of the greatest stress. Therefore, it is reasonable to assume that the principal birefπngent axes coincide with the principal stress axes. Experiments show that, for a given wavelength, the change in refractive index is proportional by a constant C to the magnitude of the applied stress. For an EM wave propagating in a birefπngent material, the refractive index is different for different polarisation components, so that n_x ≠ n_y (for propagating along the z-direction in a Cartesian system). Therefore, the birefringence B is defined as B = n_x - n_y.

The difference in expansion coefficients means that the stress-producing segments will expand/contract differently and exert different stress under a change in an external parameter. The expansion coefficients may e.g. refer to thermal expansion coefficients in which case the external parameter is the temperature. Alternatively, the expansion coefficients may also refer to the change in the volume of a solid under variations in e.g. humidity or current conducted by the solid. The traditional way to fabricate birefπngent optical fibres relies on different thermal expansion coefficients for the various parts of the fibre (core, different segments of the cladding). As the fibres are drawn at temperatures around 2000° C, stress is produced when the parts expand/contract differently during cooling. To induce birefringence in the fibre core, there has to be some angular variation in the positioning of the stress-producing segments in the outer cladding portion. The forces exerting stress on the central fibre core should be at least substantially radially directed, and the stress-producing segments according to the invention therefore have at least substantially radially oriented boundary sections between them. The radially oblong stress- redistributing regions serve to relax radial strain formed by the mechanical binding at the boundary section. In the context of the present invention, the position of the redistributing regions on or along at least substantially radially oriented boundary sections between the first and second segments, may be defined so that a single redistributing region, in cylindrical coordinates, extends over an arc segment of maximum 10°, preferably maximum 5°, and more preferably maximum 2°; alternatively, the arc segment may be maximum 45°, preferably maximum 30°, and more preferably maximum 15°.

The stress-redistributing regions allow for the initial strain of the segments to be released as stress in the core instead of as stress or work on a neighbouring segment To have this effect, the stress-redistributing regions should have a lower stiffness than the stress- producing segments. A material's stiffness is typically quantified as its Young's modulus, E, defined as _ stress _ L₀ F strain ΔL A ' where L-o is the equilibrium length, ΔL is the length change under the applied stress, F is the force applied, and A is the area over which the force is applied. Young's modulus therefore has units of pressure. 'Strain' may be defined as the relative deformation of a physical body under the action of applied forces, and 'stress' may be defined as force per unit area that produces strain on a physical body. Stiffer materials have larger Young's modulus. Radially oblong means that the regions are elongated and that their long direction are radially aligned. In special cases, the region need not be a connected region. If e.g. a series of holes are positioned so close that their separating walls are thin enough to be flexible towards strain, such series of holes and separating walls could be considered a stress-redistributing region. In particular, the separating walls may have the form of a web, a mesh, a perforated region or similar. Preferably, the stress-redistributing regions are connected regions of voids such as air holes.

There may be stress at non-radial boundaries between the first and second stress- producing segments, and thus the stress-redistributing regιon(s) may further extend on or along such non-radially oriented boundary sections. Also, analysis has shown that it may be favourable to increase the width of the radially oblong stress-redistributing regions for decreasing radius, the width referring to the length of arc spanned by the region for a given radius. In particular, the inmost end parts of the radially oblong stress-redistributing regions may span a larger length of arc than outer part of the regions, so as to form a triangular pedestal or a T-shaped footing.

As previously mentioned, it has been shown that the double bow-tie layout shown in Figure 1C represents the optimal design for polarisation maintaining fibres. The (single) bow-tie layout may be of interest for fabrication issues as it is a simpler structure to produce. According to the present invention, this optimal layout may be significantly improved by introducing new design variables not previously considered. In a preferred layout of a birefπngent optical fibre according to the invention, the characterising elements are alterations to an underlying bow-tie or double bow-tie layout.

Thus, the first and second stress-producing segments preferably occupy alternating arc sections of at least some radial sections around the core zone, with at least four at least substantially radially oriented boundary sections. Further, the alternating arc sections may be of at least substantially the same size and at least substantially centred around 0°, 90°, 180° and 270°. These values of course depend on the orientation of the fibre in the cylindrical co-ordinate system, the important feature being their angular distance.

The feature that the underlying layout is a bow-tie or double bow-tie layout should not be too rigorously interpreted Several small or large changes can make the layout different from a bow-tie or double bow-tie layout in the strict sense, but, the underlying layout will still be recognisable to the human eye. Although a large number of smaller alterations such as stress-redistributing regions will improve the birefringence of an underlying bow-tie or double bow-tie layout, it may be preferable, from a fabrication point of view, to include only a few important alterations.

Hence, according to a second aspect, the present invention provides a method for optimising the birefringence in a polarisation maintaining optical fibre by introducing alterations to an underlying bow-tie or double bow-tie layout with a cladding layer formed by first and second stress-producing segments having different expansion coefficients, the method comprising the step of introducing radially oblong regions at the inmost part of radially oriented boundary sections between the first and second segments, the radially oblong regions having lower Young's modulus than the first and second segments.

Further alterations may be widening of the inmost end parts of the radially oblong regions and rounding off corners of boundary sections between the first and second segments.

When a ray of light travels through a birefπngent optical fibre, the anisotropy felt by the light is caused by two effects that have different physical explanations. One is the stress induced birefringence caused by the photoelastic effect, the other is the form-induced or geometric birefringence caused by asymmetric boundary conditions (e.g. asymmetric core) that encourage one polarisation state to travel faster than the other. In birefπngent crystal fibres or photonic bandgap fibres, the birefringence is traditionally form-induced birefringence. WO 00/60390 is a typical example on form-induced birefringence in crystal fibres. Here, the microstructures introduce a break in symmetry, a directionality, in the periodic microstructure leading to different propagation velocity for different states of polarisation.

According to the present invention, stress-redistributing regions such as air holes may improve the stress exerted by stress-producing segments with different expansion coefficients.

Therefore, in a third aspect, the invention provides combining crystal fibres or photonic bandgap fibres with stress-induced birefringence caused by segments with different expansion coefficients. In the third aspect, a birefπngent optical crystal fibre or photonic bandgap fibre is provided which comprise a core zone surrounded by a cladding zone having voids arranged in a periodic pattern in a material matrix, the material matrix comprises first and second material compositions of different expansion coefficients occupying alternating arc sections of at least some radial sections around the core zone, boundaries between the first and second material compositions form at least substantially radially oriented boundary sections, with some voids arranged at or along parts of the radially oriented boundary sections. Preferably, the voids arranged at or along parts of the radially oriented boundary sections are radially oblong.

The increase in the stress exerted by the stress-producing segments enhance the birefringence resulting from the photoelastic effect. The increased stress also increases the deformation of the core and thereby the form-induced birefringence. Especially for photonic bandgap fibres with hollow cores, the increased deformation and form-induced birefringence is expected to be significant. Recently, a first demonstration of a large mode area photonic crystal fibre with stress induced birefringence was disclosed in Optics Express, Vol. 12, No. 5, 8 March 2004, by Folkenberg et al. Thus, the principles of the present invention may also beneficially be implemented in future photonic crystal fibres.

Structural optimisation is a commonly used tool in material science such as building materials and within the automotive and aeronautical industry. There exist a number of numerical methods for calculating optimised structures, one of which is the topology optimisation method or the material distribution method, as described in e.g. Bendsøe and Sigmund, Topology Optimization: Theory, Methods and Applications. Spπnger-Verlag, Berlin, 2003. The topology optimisation method can, given a domain in two- or three- dimensional space with prescribed boundary conditions, distribute an amount of at least one material in a defined subdomain such that a certain scalar quantity (the objective function) is maximised or minimised.

The inventors have applied topology optimisation to the design of birefringent optical fibres to determine the distribution of three material phases in an optical fibre that results in the greatest stress-induced birefringence when the fibre is subjected to uniform heating or cooling. However, as mentioned previously, other external properties such as current or humidity may induce similar stress effects.

However, the applied topology optimisation for the design of birefringent optical fibres may advantageously be applied to more than three material phases, e.g. four, five, six etc. material phases may readily be subjected to optimisation once the principles of the present invention is understood. Furthermore, topology optimisation combining mechanical and optical field may beneficially be applied for designing birefringent optical fibres. In the context of the present invention, only mechanical fields have been optimised. However, by also considered the actual optical field intensity as weighting for maximising the birefringence one may obtain even higher birefringence. This also comprises weighting the optical field distribution as by finite element modelling.

Therefore, in a fourth aspect, the present invention provides a method for determining a design of a birefringent optical fibre, the method comprising applying a topology optimisation method based on finite-element analysis to determine a distribution of three material phases, one of which having a lower Young's modulus than the two others, in a cladding portion of a fibre, which distribution increase and/or maximise stress-induced birefringence at one or more positions in a core zone of the fibre. As the resulting distribution may be very complicated and not practically feasible, the method further comprise the step of determining a design for a birefringent optical fibre by applying at least some of the following adaptation steps to the distribution of phases resulting from the topology optimisation method remove regions of the low Young's modulus phase that impede the mechanical strength and/or stability of the fibre, and smooth edges of boundaries between regions of different phases. Preferably, the one material phase having a lower Young's modulus has a significantly lower Young's modulus. These adaptation steps serve to adapt the distribution to a simple design which can be produced while taking the improved birefringence of the final design versus the costs and complexity of the fabrication into consideration. A number of further adaptation steps may be included : - Removing regions of the low Young's modulus phase which are of lesser significance to the birefringence at the core zone, such as regions which are further away from the core zone than other regions with approximately the same cross sectional area. In general, the significance of a stress-redistributing region for the stress in the core zone decreases with its distance from the core zone. - Disregarding connected regions of one phase having a total cross sectional area smaller than a predetermined limit, such as occupying less than 5% of the total cross sectional area, such as less than 3%, less than 1%, less than 0,8%, less than 0,5% or less than 0,2%. Redistribution of other material phases in the void regions resulting from removal of a material phase in a region in the above steps.

- Varying geometrical and/or material parameters of regions of the low Young's modulus phase.

Preferably, any adaptation steps are performed in a supervised evaluation process where the effect of the adaptation step on the resulting birefringence is monitored. The supervised evaluation means that the adaptation is evaluated taking the resulting change in birefringence and the gam in design simplicity into consideration. As a result of the supervised evaluation, an adaptation step may be approved or excluded. The evaluation process is preferably based on finite element analysis but other numerical methods may be applicable e.g. finite difference, beam propagation, and weighted residual methods.

Similarly, in a fifth aspect, the invention provides a method for determining a design of a birefringent optical fibre, the method comprising the steps of

- applying a topology optimisation method based on finite-element analysis to determine a distribution of three material phases, one of which having a lower Young's modulus than the two others, in a cladding portion of a fibre, which distribution increase and/or maximise stress-induced birefringence at one or more positions in a core zone of the fibre,

- determining a design for a birefringent optical fibre by introducing alterations in a standard birefringent fibre layout, alterations comprising introducing at least one region of a phase having lower Young's modulus than the material phases of the standard birefringent fibre layout, the at least one region corresponding to at least part or at least one region of the phase with low Young's modulus from the topology optimisation. Preferably, the one material phase having a lower Young's modulus has a significantly lower Young's modulus.

In a sixth aspect, the invention provides a method for manufacturing a birefringent optical fibre, the method comprising the steps of providing a cylindrical waveguiding member comprising a core zone surrounded by an innercladding, and first and second outercladdmg rods of a first and of a second material composition having different expansion coefficients, forming a preform structure by arranging the first and second outercladdmg rods around the cylindrical waveguiding member, the first and second outercladdmg rods occupying alternating arc sections, boundaries between the first and second outercladdmg rods forming at least substantially radially oriented boundary sections forming interstices at the radially oriented boundary sections between the first and second outercladdmg rods, and - drawing the preform structure to an optical fibre with predetermined dimension under a controlled heat treatment.

In accordance with the principle of the invention, the outercladdmg rods form stress- producing segments in the drawn fibre, and the interstices are stress-redistributing regions. The interstices may be formed by several methods, e.g. by providing spacers between the first and second outercladdmg rods during the step of forming the preform structure, - forming holes in the preform structure at the radially oriented boundary sections between the first and second outercladdmg rods, or - shaping the first and second outercladdmg rods so that when arranged around the cylindrical waveguiding member, interstices are formed along parts of their radially oriented boundary sections.

As for the optical fibre of the first aspect, the waveguiding may be based on index guiding or photonic bandgap guiding. In the latter case, the cylindrical waveguiding member may comprise microstructure features arranged in a periodic pattern in the innercladding.

These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

Figures 1A - C show cross sectional views of common layouts for birefringent optical fibres.

Figure 2 shows cross sectional views of a bow-tie layout for a birefringent optical fibre. Figure 3 is a graph illustrating the shape and size of the core at various stages during fabrication.

Figures 4A-H show distributions of different phases at various stages during topology optimisation.

Figures 5A-B show two different distributions of phases resulting from topology optimisations.

Figures 6A-B are stress diagrams for two different optical fibre layouts.

Figure 7A shows a distribution resulting from topology optimisations, Figure 7B shows a design resulting from adaptation of the distribution of Figure 7A.

Figure 8A-B show alterations to an underlying PANDA fibre design altered according to the invention.

Figures 9A-G show different birefringent optical fibre designs according to the invention.

Figures 10A and B shows different birefringent crystal fibre designs according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

The present description refers to embodiments where first and second stress-producing segments have different thermal expansion coefficients. As described elsewhere, the expansion coefficients may as well refer to another external property than temperature, and the presented embodiments should not be restrictive in that sense

Figures 1A - C show cross sections of common layouts for birefringent optical fibres. There are different ways of calculating the stress-induced birefringence B in the fibre core. The stress-induced birefringence can be evaluated at the centre of the core or as a weighted average over the core. In the present description, values of B₀ represent the stress- induced birefringence in the centre of the fibre core, whereas values of Bj represent a weighted average over the core. Usually, the latter value is cited in the literature of this technical field. The birefringence of the layouts of Figures 1A-C are given in Table 1 The birefringence is calculated using the material properties and parameters listed below.

Table 1

In the following, typical design parameters for the basic single bow-tie fibre sketched in Figure 2 is given. These will later be used to describe fibre designs according to the invention. The core has radius a = 5 μm and the cladding has radius b = 60 μm. Two stress-producing regions are embedded in the cladding in the shape of cylindrical segments resembling a bow tie. Each segment spans an arc of 20_! = 90°. The outer radius of the bow-tie is r₂ = 0.76b which is commonly regarded as the optimal value of r₂. The inner radius of the segments is ^ = 7 μm. A extra bow-tie can be added at an angle 90° from the original one. In this case we have a double bow-tie fibre. The two materials of the bow-tie are made from materials with different coefficients of thermal expansion. Applicable material properties from Chu et al., Journal of Lightwave Technology, vol. LT-2, 5, October 1984, are listed in Table 2. The temperature change is T = -850 K. The stress optical coefficient is given by C = 3.36 x 10^"5 mm²/kg.

Table 2. Material properties for the bow-tie fibre.

According to a preferred method of the invention, a numerical structure optimisation method is used to increase the birefringence in an optical fibre.

The total birefringence is caused by two effects, one due to form induced birefringence, and one due to stress-induced birefringence. The stress on the core is generated during fabrication of the fibre. The stress results in both a change in the size of the core and a change in shape. The finished fibre is strictly speaking not a solid. Amorphous silica — more commonly known as glass — is an undercooled liquid with a very high viscosity at room temperature. As the material is heated, the viscosity slowly begins to drop. At the glass transition temperature, around 1270° C, and above, pure silica begins to behave more like a typical liquid, as it cannot sustain shear stresses any longer. The thermal expansion coefficient increases by a factor 3 around this temperature while the bulk modulus drops by a factor 2. This effect has some consequences for the development of thermal stresses in the fibre during and immediately after draw. In the process of cooling, the cladding sets (i.e. begins to behave like a solid material) before the core. Because the core now has a higher expansion coefficient than the cladding and is contained within the cladding, hydrostatic thermal stresses develop in the fluid core. In a simple but illustrative model, the deformation of the core is divided into three distinct stages illustrated in Figure 3.

After drawing but before cooling, the fibre core has an outline corresponding to the curve 30. First the fibre is cooled, and the material contracts freely by an amount h_τ (assuming uniform cooling). Second, because the cladding contracts less than the core, it restricts the contraction of the core by an amount h_σ. And third, because the cladding is not homogeneous the shape of core is distorted into the non-circular shape shown by curve 31, by amounts δi and δ₂ along each axis. During the first process, the mean stress experienced by the core is zero. During the second process the magnitude of mean stress is raised to a certain level by suppression of the free thermal strain. During the third process the circular shape is distorted by shear stress, which may or may not be accompanied by further changes in mean stress.

Presently, optical fibres are mainly manufactured in various silica compositions as outlined above, but alternative materials are also available, e.g. microstructured polymer optical fibres as demonstrated in Optics Express, vol. 9, no. 7, p. 319-327, 2001, by Eijkilenborg et al. The principles of present invention are also readily applied to such optical fibres compositions.

For any given volume of material around the core, some work is spent on increasing the mean stress, while some work is spent on increasing the shear stress. Therefore, the most efficient solution is characterised by zero mean stress (zero dilatational strain energy) and maximum shear stress (or maximum distortional strain energy).

In the following, the topology optimisation method described in Topology Optimization: Theory, Methods and Applications (by Bendsøe and Sigmund, Spπnger-Verlag, Berlin, 2003), hereby included by reference, is applied. The topology optimisation is used to distribute an amount of material in a defined domain so that a certain scalar quantity (the objective function) is maximised or minimised. Based on the above, the objective function is chosen to be the shear stress exerted on the core during cooling of the drawn fibre. However, other objective functions are applicable in pursuing the aim of maximising the mean value of the stress-induced birefringence over the core.

The design domain D was chosen as D = {(r, θ) I 7 μm < r < 58 μm, 0 < θ < 2π} A fixed cylindrical region of thickness 2 μm is left around the 5 μm core; another of same thickness encircles the design domain. The purpose of the inner fixed region is to ensure that the light is contained within the core by a controlled index difference. It is generally accepted that the stress producing region should be as close as possible to the core The design domain contains three material phases, one of which is void, the other two having different thermal expansion coefficients

Figure 4(a) - (h) shows the progression of the algorithm in one half of the cross-section when the initial design domain had an asymmetric distribution of material. As is illustrated, the algorithm slowly distributes the material until a symmetrical distributions is achieved. More interestingly, void regions are included at certain positions very early in the progression.

As it turns out, the inclusion of voids has a dramatic effect on the birefringence in the core. Two final structures shown in Figure 5A and B have a birefringence of 4.61 x 10 ⁴ and 4.36 x 10 ⁴, respectively, which represents an increase of roughly 63% and 54%, respectively, compared with the birefringence in the solid double bow-tie. This is an enormous improvement. For comparison, the improvement when going from a PANDA layout to the optimised solid double bow-tie layout is around 15% (please refer to table 1).

It is believed that the voids act as stress re-distπbuting regions releasing the stress from the boundary regions and increasing stress on the core. According to this point of view it is of interest to look at where in the fibre layout stress tends to build up. Figure 6A shows stress regions in a standard double bow-tie layout. Two regions 61 and 62 with high stress can be found (due to conversion from colour to grey-scale, the regions does not stand out clearly). By intuition, it is expected that region 62 has a high stress, and that this may be avoided by not having four corners meet in a single point. The distributions from the topology optimisations shown in Figures 5A and B propose to round the corners instead of introducing voids. At the region 61, a region of slightly increased stress appears at the inmost part of the radially oriented boundary. Turning to the topology optimisation shown in Figures 5A and B, it is proposed to introduce voids along the radially oriented boundaries.

These alterations have been introduced in the layout shown in Figure 6B. It can be seen that the previous high-stress region 62, now 64, have almost disappeared. More interesting, the previous high-stress region 61, now 63, have changed its shape and increased in size and amplitude. Although not clearly visible on the grey-scale illustration, it can be seen that the stress region 63 almost radiates into the core region indicating an increased shear stress on the core (lighter grey, almost white colour indicates higher stress than the grey colour in the core region in Figure 6A). This shows how the introduced alterations re-distribute the stress produced by the segments of different expansion coefficients.

In the manner shown in the above, alterations can be introduced starting from an underlying standard layout, the alterations being inspired from the distributions resulting from the topology optimisation. Inversely, it is possible to start from the distributions resulting from the topology optimisation and adapt the distribution to simplify the layout towards an underlying standard layout, ending at a design which can realistically be produced. In both cases, the alterations or adaptations along the process should be evaluated to estimate their effect of the resulting birefringence. As a result of the evaluation, the alteration or adaptation step should be approved or excluded, this is referred to as a supervised evaluation.

The above distinction between in one approach introducing alterations in a standard layout, which are inspired by the topology optimisation and in another approach adapting a distribution resulting from the topology optimisation illustrates the different lines of thought, the resulting designs are typically the same.

Figure 7A shows a distribution resulting from the topology optimisation, and Figure 7B shows a design resulting from adaptation of the distribution of Figure 7A. In order to facilitate fabrication, the design has been adapted to make the regions of the phases relatively smooth and well defined.

Figures 8A-B show an improvements of the basic PANDA layout based on the general experiences from the present topology optimisation, namely that the inclusion of oblong voids along the boundaries between segments improve the birefringence. For the design in Figure 8A, the improvement is however quite small, only around 2% relative to a double bow-tie design. In another optimisation of the modified PANDA layout shown in Figure 8B a 8% improvement was obtained. The optimised PANDA design yields a PANDA core radius of 21.5 μm and an arc length of 53° measured from the PANDA core centre for each of the four voids shown in Figure 8B. The position of the arc relative to the centre of the fibre core was also optimised. It should be noted that the stress-redistributing regions, i e. the voids, shown in Figures 8A-B are also, within the context of the present invention, understood to be positioned substantially radially with respect to the fibre core centre. This is the case, although the azimuthal angle of a void of Figure 8B, in cylindrical coordinates, extends over approximately 20° measured from the centre of the fibre core. Figures 9A-G show different designs resulting from alterations to standard layouts under supervised evaluation. The alterations are clearly inspired by the voids appearing in the distributions resulting from the topology optimisation. As can be seen, the designs shown in Figures 9 A-G may be described as alterations to an underlying bow-tie or double bow- tie layout. In the following paragraph, the design parameters are roughly specified for the fibres shown in Figures 9 A-G, using the nomenclature given for the bow-tie fibre in relation to Figure 2 Basically, all parameters may be varied, but the parameters given in relation to Figure 2 provides applicable design parameters for fibres according to the invention. The exact dimensions for the optimal air holes may vary depending on actual material properties, core material, and core and cladding dimensions

In the design shown in Figure 9A-C, the air holes are rectangular in shape, ended with semi-circles with diameters corresponding to the width w of the rectangle. In the design shown in Figure 9D-G, the air holes are also rectangular in shape, ended at the outer end of the voids with semi-circles with diameters corresponding to the width w of the rectangle, but additionally the inner end of the voids are connected to αrcumferentially extending holes so-called pedestals or T-footings. The air holes start at radius r_! and extend in the outward radial direction with angles of 45, 135, 225 and 315 degrees up to a distance of approximately b/2. For the examples in Figures 9A-B the length of the voids have been optimised to 21 μm and 22.3 μm, respectively, under a constant width w of 1 μm. See Table 3 below for further results. The width w of the voids may of course additionally be optimised, but other fixed values of the width w may be considered, such as approximate values of 1.5 μm, 2 μm, 2.5 μm, 3 μm, and so forth, Similarly, the length of the voids may be fixed while optimising the width and/or, if present, the arc span of the pedestal. Possible fixed values of the arc span of the pedestal may be approximate values of 5°, 10°, 15°, 20°, 25°, 30°', 35°, 40° , 45°, 50°, 55°, or 60°. Possible fixed values of the void length may be approximate values of 5 μm, 10 μm, 15 μm, 20 μm, 25 μm, or 30 μm.

Figure 9C shows the birefringence (B) distribution for a void without a pedestal and Figure 9D shows the birefringence distribution for a void with a pedestal, both figures for a double bow-tie fibre modified according to the invention. On the right in Figures 9C and 9D, ust a quarter of the fibre is shown due to the symmetry, and on the left in Figures 9C and 9D enlarged sections of the inner part of the fibre are shown. For the example in Figures 9C, w = lμm and the air holes extend to 0.55b. For the example in Figure 9D, circumferentially extending holes have been added to the radially extending holes. The extra holes extend through angles 45 degrees plus/minus an interval; in this case 18 degrees. The inner and outer radii are 7 and 8 μm, respectively. From Figures 9C and 9D, it is seen that in contrast to the conventional double bow-tie fibre where the B-field is almost constant (as evidenced by the B₀ value being substantially equal to B_a value in Table 3 below) the B-field increases for decreasing radius - especially for the case of the pedestal void in figure 9D. This B-distπbution may correspond to the actual optical field distribution, thus we obtain an effective birefringence distribution that lies somewhere between Bj and B₀, hence an improvement even larger than calculated may result.

An additional optimisation (not shown in the Figures) was performed on the design of Figure 9F also allowing the outer radius, r₂, of the inner bow-tie to vary. The result was a r₂ value of 48 μm, a void length of 27 μm, and a pedestal arc span of 36°. Table 3 gives values for the birefringence B and selected optimised dimensions for some of the presented designs:

Table 3

Birefπngent crystal fibres and photonic bandgap fibres typically rely only on form-induced birefringence. Figure 10A shows a birefringent crystal fibre design 80 with a combination of stress-producing segments 81 and 82 and periodic microstructure in the form of air holes 84. The effect of stress-producing segments 81 and 82 have been improved by introducing air holes 86 according to the distributions resulting from the topology optimisations.

Figure 10B shows another birefringent crystal fibre design 90 where the stress-producing segments 91 and 92 are merged with the periodic microstructure The effect of stress- producing segments 91 and 92 have been improved by introducing air holes 96 according to the distributions resulting from the topology optimisations. The air holes 96 may e.g. be formed so that they contribute to the photonic bandgap effect of the microstructure. Also, they may be formed so that they contribute to a form-induced birefringence in the fibre.

There exist hundreds of different designs for crystal fibres and photonic bandgap fibres, where the shape, size and pattern of the air holes are varied. The designs showed in Figures 10A-B therefore only represent simple examples.

In the following, the basic process for manufacturing optical fibres is described, and modifications for fabricating fibres according to the present invention are proposed.

The manufacture process consist of three mam parts: (1) laydown, (2) consolidation, and

(3) draw.

1. Laydown.

The aim of the laydown process — sometimes called preform deposition — is to build up, layer by layer, a rod of extremely pure silica or silica doped with a controlled quantity of some other material. The techniques commonly used are called Outside Vapour Deposition (OVD) and Modified Chemical Vapour Deposition (MCVD). The product at this stage is called a preform.

The traditional manufacture process allows only the production of axisymmetπcal fibres. Inherently, birefringent fibres are not axisymmetπcal. Birefringent fibres having a circumferential variation can be made by two techniques. In the first technique, an axisymmetπcal preform is made as before. Holes are then drilled into the preform and different materials are inserted into the hole. The preform is then drawn. In the second technique, a large number of prefabricated silica tubes and rods are stacked in the desired pattern. The individual rods are typically hexagonal or circular in shape, but any shape may be used. The latter technique is the one applied in the fabrication of crystal fibres and photonic bandgap fibres. After stacking the rods are held together by thin wires and fused together in a drawing process.

Obviously, it is in the laydown process that the design of the final fibre is determined. Stacking of prefabricated silica tubes and rods with different shape and material composition is the most promising technique for fabrication of birefringent fibres according to the invention. Interstices such as air holes can be formed by several methods, e.g. by providing spacers between the rods during laydown of the preform structure. Alternatively, the rods in the cladding can be shaped so that interstices are formed when they are arranged around the fibre core.

2. Consolidation.

The product of the laydown process is a translucent porous mass. The purpose of consolidation is to eliminate the gas bubbles trapped inside the deposited material, and to compact the product. This is achieved by sintering the preform. This process occurs naturally during laydown, but some aftertreatment is needed in a controlled atmosphere.

3. Draw. The preform is now suspended above a furnace located at the top of a tower. The temperature inside the furnace is between 1800 °C and 2000 °C. As the preform is lowered into the furnace, the tip of the preform begins to melt. The tip is clamped and pulled through a system capable of controlling the diameter of the fibre by adjusting the speed of the draw. Along the way the fibre is cooled and coated with a protective polymer layer. Finally, the fibre is proof tested and wound onto a drum.

Claims

1. An optical fibre described by cylindrical coordinates (r, θ, z) and having a waveguiding zone extending inside an outer cladding portion in the longitudinal z-direction of the fibre, the outer cladding portion comprising first and second stress-producing segments formed by first and second material compositions having different expansion coefficients, the outer cladding portion further comprising radially oblong stress-redistributing regιon(s) formed on or along at least substantially radially oriented boundary sections between the first and second segments, the stress-redistributing regιon(s) having a lower Young's modulus than the first and the second material compositions.

2. The optical fibre according to claim 1, wherein the first and second stress-producing segments occupy alternating arc sections of at least some radial sections around the waveguiding zone with at least four at least substantially radially oriented boundary sections, the radially oblong stress-redistributing regιon(s) being formed on or along at least part of one or more of the at least four boundary sections.

3. The optical fibre according to claim 1, wherein the alternating arc sections are of at least substantially the same size and at least substantially centred around 0°, 90°, 180° and

270°.

4. The optical fibre according to claim 1, wherein the first and second stress-producing segments at least substantially form a bow-tie or double bow-tie configuration.

5. The optical fibre according to claim 1, wherein the stress-redistributing regιon(s) are voids.

6. The optical fibre according to claim 1, wherein the stress-redistributing regιon(s) further extends on or along non-radially oriented boundary sections between the first and second stress-producing segments.

7. The optical fibre according to claim 1, wherein the width, in length of arc, of the radially oblong stress-redistributing regions increases for decreasing radius.

8. A method for optimising the birefringence in a polarisation maintaining optical fibre by introducing alterations to an underlying bow-tie or double bow-tie layout, the method comprising the steps of providing a polarisation maintaining optical fibre with an underlying bow-tie or double bow-tie layout having a cladding layer formed by first and second stress-producing segments formed by first and second material compositions having different expansion coefficients, and 5 - introducing radially oblong regions at the inmost part of radially oriented boundary sections between the first and second segments, the radially oblong regions having lower Young's modulus than the first and second material compositions.

9. The method according to claim 8, wherein the step of introducing radially oblong regions 10 comprises widening the inmost end parts of the radially oblong regions.

10. The method according to claim 8, further comprising the step of rounding off corners of boundary sections between the first and second segments.

15 11. A birefringent optical crystal fibre or photonic bandgap fibre comprising a core zone surrounded by a cladding zone having voids arranged in a periodic pattern in a material matrix, the material matrix comprising first and second material compositions of different expansion coefficients occupying alternating arc sections of at least some radial sections around the core zone, boundaries between the first and second material compositions

20 forming at least substantially radially oriented boundary sections, some voids being arranged at or along parts of the radially oriented boundary sections.

12. A method for determining a design of a birefringent optical fibre, the method comprising the steps of

25 applying a topology optimisation method based on finite-element analysis to determine a distribution of three material phases, one of which having a lower Young's modulus than the two others, in a cladding portion of a fibre, which distribution increase and/or maximise stress-induced birefringence at one or more positions in a core zone of the fibre,

30 determining a design for a birefringent optical fibre by applying at least the following adaptation steps to the distribution of phases resulting from the topology optimisation method remove regions of the low Young's modulus phase that impede the mechanical 35 strength and/or stability of the fibre, and - smooth edges of boundaries between regions of different phases.

13. The method according to claim 12, wherein the step of determining a design further comprises the adaptation step of removing regions of the low Young's modulus phase which are of lesser significance to the birefringence at the core zone.

14. The method according to claim 12, wherein the step of determining a design further comprises the adaptation step of disregarding connected regions of one phase having a total cross sectional area smaller than a predetermined limit.

15. The method according to claim 12, wherein the step of determining a design further comprises the adaptation step of varying geometrical and/or material parameters of regions of the low Young's modulus phase.

16. The method according to claim 12, wherein the step of determining a design comprises an evaluation of each adaptation step by simulating the resulting birefringence of the fibre for the adaptation step.

17. A method for determining a design of a birefringent optical fibre, the method comprising the steps of

applying a topology optimisation method based on finite-element analysis to determine a distribution of three material phases, one of which having a lower Young's modulus than the two others, in a cladding portion of a fibre, which distribution increase and/or maximise stress-induced birefringence at one or more positions in a core zone of the fibre,

determining a design for a birefringent optical fibre by introducing alterations in a standard birefringent fibre layout, the alterations comprising introducing at least one region of a phase having lower Young's modulus than the material phases of the standard birefringent fibre layout, the at least one region corresponding to at least part or at least one region of the phase with low Young's modulus from the topology optimisation.

18. A method for manufacturing a birefringent optical fibre, the method comprising the steps of

providing the following elements: - a cylindrical waveguiding member comprising a core zone surrounded by an innercladding, and - first and second outercladdmg rods of a first and of a second material composition having different expansion coefficients, forming a preform structure by arranging the first and second outercladdmg rods around the cylindrical waveguiding member, the first and second outercladdmg rods occupying alternating arc sections, boundaries between the first and second outercladdmg rods forming at least substantially radially oriented boundary sections 5 forming interstices at the radially oriented boundary sections between the first and second outercladdmg rods, and drawing the preform structure to an optical fibre with predetermined dimension under a 10 controlled heat treatment.

19. The method according to claim 18, wherein the step of forming interstices comprises providing spacers between the first and second outercladdmg rods during the step of forming the preform structure.

15 20. The method according to claim 18, wherein the step of forming interstices comprises forming holes in the preform structure at the radially oriented boundary sections between the first and second outercladdmg rods.

20 21. The method according to claim 18, wherein the step of providing the first and second outercladdmg rods comprises shaping the first and second outercladdmg rods so that when arranged around the cylindrical waveguiding member, interstices are formed along parts of their radially oriented boundary sections.

25 22. The method according to claim 18, wherein the step of providing the cylindrical waveguiding member comprises providing microstructure features arranged in a periodic pattern in the innercladding.