Bending-loss insensitive single mode fibre, with a shallow trench, and corresponding optical system

Abstract

The invention concerns a bending-loss single mode optical fibre having a Mode Field Diameter at 1310 nm greater than or equal to 9 microns and having a core and a cladding, the core refractive index profile having a trapezoid-like shape. According to an aspect of the invention, the cladding comprises a shallow trench with a refractive index difference Ant between 210.sup.3; and 0.910.sup.3, and: the trapezoid ratio r.sub.0/r.sub.1 of the core is between 0.1 and 0.6, preferably, between 0.2 and 0.5, more preferably between 0.25 and 0.45; the core surface integral Formula (I) is between 20.10 3 m and 24.10.sup.3 m and the cladding surface integral Formula (II) is between 2510.sup.3 m and 910.sup.3 m, where n(r) is the refractive-index difference with respect to said outer cladding as a function of the radius r, and said single mode optical fibre fulfils the following criterion: 25.710.sup.3V.sub.010.2326V.sub.0226.810.sup.3.

Claims

1. A bending-loss insensitive single mode optical fibre having a Mode Field Diameter greater than or equal to 9.0 m at a 1310 nm wavelength, said optical fibre having a core surrounded by a cladding, the core refractive index profile having a trapezoid-like shape, wherein a centre part of said core has a radius r.sub.0 and a refractive index n.sub.0 and a transition part of the trapezoid-like core refractive index profile ranges from radius r.sub.0 to a radius r.sub.1>r.sub.0 with a trapezoid ratio r.sub.0/r.sub.1 of said centre part of said core's radius r.sub.0 to said transition part's radius r.sub.1 between 0.1 and 0.6, wherein said cladding comprises at least one trench, which comprises a region of depressed refractive index, ranging from radius r.sub.2r.sub.1 to radius r.sub.3>r.sub.2 and having a refractive index n.sub.t, and an outer cladding ranging from radius r.sub.3 to the end of a glass part of the single mode fibre and having a refractive index n.sub.4, wherein the refractive-index difference of said trench with respect to said outer cladding n.sub.t=n.sub.tn.sub.4 is between 210.sup.3 and 0.910.sup.3, wherein said core has a surface integral V.sub.01 of between 2010.sup.3 m and 2410.sup.3 m, the surface integral being defined according to the following equation: V.sub.01=.sub.0.sup.r.sup.1n(r).Math.dr, where n(r) is the refractive-index difference of said core with respect to said outer cladding as a function of the radius r, wherein said cladding has a surface integral Vol of between 2510.sup.3 m and 910.sup.3 m, the surface integral being defined according to the following equation: V.sub.02=.sub.r.sub.1.sup.n(r).Math.dr, where n(r) is the refractive-index difference of said cladding with respect to said outer cladding as a function of the radius r, and wherein said single mode optical fibre fulfils the following criterion:
25.710.sup.3V.sub.010.23261V.sub.0226.810.sup.3.

2. The bending-loss insensitive single mode optical fibre of claim 1, wherein said trapezoid ratio r.sub.0/r.sub.1 of said centre part of said core's radius r.sub.0 to said transition part's radius r.sub.1 is between 0.2 and 0.5.

3. The bending-loss insensitive single mode optical fibre of claim 1, wherein said trapezoid ratio r.sub.0/r.sub.1 of said centre part of said core's radius r.sub.0 to said transition part's radius r.sub.1 is between 0.25 and 0.45.

4. The bending-loss insensitive single mode optical fibre of claim 1, wherein said cladding comprises an intermediate cladding ranging from radius r.sub.1 to radius r.sub.2>r.sub.1 and having a refractive index n.sub.2, and wherein said trench surrounds said intermediate cladding.

5. The bending-loss insensitive single mode optical fibre of claim 4, wherein said core surface integral $V_{01}\frac{n_0\left(r_1+r_0\right)+n_2\left(r_1-r_0\right)}{2},$ where n.sub.0=n.sub.0n.sub.4 is the refractive-index difference of said centre part of said core with respect to said outer cladding and where n.sub.2=n.sub.2n.sub.4 is the refractive-index difference of said intermediate cladding with respect to said outer cladding, and wherein said cladding surface integral V.sub.02(r.sub.2r.sub.1)n.sub.2+(r.sub.3r.sub.2)n.sub.t.

6. The bending-loss insensitive single mode optical fibre of claim 5, wherein the refractive-index difference of said intermediate cladding with respect to said outer cladding n.sub.2=0.

7. The bending-loss insensitive single mode optical fibre of claim 1, wherein r.sub.2=r.sub.1 and wherein said core surface integral $V_{01}\frac{n_0\left(r_1+r_0\right)+n_t\left(r_1-r_0\right)}{2},$ where n.sub.0=n.sub.0n.sub.4 is the refractive-index difference of said centre part of said core with respect to said outer cladding, and wherein said cladding surface integral V.sub.02(r.sub.3r.sub.2)n.sub.t.

8. The bending-loss insensitive single mode optical fibre of claim 1, wherein the core outer radius r.sub.1 is between 5.4 m and 8.0 m.

9. The bending-loss insensitive single mode optical fibre of claim 1, wherein the trench outer radius r.sub.3 is between 16 m and 22 m.

10. The bending-loss insensitive single mode optical fibre of claim 1, wherein the refractive-index difference of said centre part of said core with respect to said outer cladding n.sub.0=n.sub.0n.sub.4 is between 510.sup.3 and 610.sup.3.

11. The bending-loss insensitive single mode optical fibre of claim 1, wherein said optical fibre has a maximum cable cut-off wavelength of 1240 nm.

12. The bending-loss insensitive single mode optical fibre of claim 1, wherein said optical fibre has a Mode Field Diameter at 1310 nm between 9.0 m and 9.2 m.

13. The bending-loss insensitive single mode optical fibre of claim 1, wherein said optical fibre complies with the requirements of the ITU-T G.657.A2 standard.

14. Optical fibre transmission system comprising at least one single mode fibre according to claim 1.

15. A bending-loss insensitive single mode optical fibre having a Mode Field Diameter greater than or equal to 9.0 m at a 1310 nm wavelength, said optical fibre having a core surrounded by a cladding, the core refractive index profile having a trapezoid-like shape, wherein a centre part of said core has a radius r.sub.0 and a refractive index n.sub.0 and a transition part of the trapezoid-like core refractive index profile ranges from radius r.sub.0 to a radius r.sub.1>r.sub.0 with a trapezoid ratio r.sub.0/r.sub.1 of said centre part of said core's radius r.sub.0 to said transition part's radius r.sub.1 between 0.1 and 0.6, and wherein the core outer radius r.sub.1 is between 5.4 m and 8.0 m, wherein said cladding comprises at least one trench, which comprises a region of depressed refractive index, ranging from radius r.sub.2r.sub.1 to radius r.sub.3>r.sub.2 and having a refractive index n.sub.t, and an outer cladding ranging from radius r.sub.3 to the end of a glass part of the single mode fibre and having a refractive index n.sub.4, and wherein the trench outer radius r.sub.3 is between 16 m and 22 m, wherein the refractive-index difference of said centre part of said core with respect to said outer cladding n.sub.0=n.sub.0n.sub.4 is between 510.sup.3 and 610.sup.3, wherein the refractive-index difference of said trench with respect to said outer cladding n.sub.t=n.sub.tn.sub.4 is between 210.sup.3 and 0.910.sup.3, wherein said core has a surface integral V.sub.01 of between 2010.sup.3 m and 2410.sup.3 m, the surface integral being defined according to the following equation: V.sub.01=.sub.0.sup.r.sup.1n(r).Math.dr, where n(r) is the refractive-index difference of said core with respect to said outer cladding as a function of the radius r, wherein said cladding has a surface integral V.sub.02 of between 2510.sup.3 m and 910.sup.3 m, the surface integral being defined according to the following equation: V.sub.02=.sub.r.sub.1.sup.n(r).Math.dr, where n(r) is the refractive-index difference of said cladding with respect to said outer cladding as a function of the radius r, and wherein said single mode optical fibre fulfils the following criterion:
25.710.sup.3V.sub.010.23261V.sub.0226.810.sup.3.

16. The bending-loss insensitive single mode optical fibre of claim 15, wherein said cladding comprises an intermediate cladding ranging from radius r.sub.1 to radius r.sub.2>r.sub.1 and having a refractive index n.sub.2, and wherein said trench surrounds said intermediate cladding.

17. The bending-loss insensitive single mode optical fibre of claim 16, wherein said core surface integral $V_{01}\frac{n_0\left(r_1+r_0\right)+n_2\left(r_1-r_0\right)}{2},$ where n.sub.0=n.sub.0n.sub.4 is the refractive-index difference of said centre part of said core with respect to said outer cladding and where n.sub.2=n.sub.2n.sub.4 is the refractive-index difference of said intermediate cladding with respect to said outer cladding, and wherein said cladding surface integral V.sub.02(r.sub.2r.sub.1)n.sub.2+(r.sub.3r.sub.2)n.sub.t.

18. The bending-loss insensitive single mode optical fibre of claim 15, wherein r.sub.2=r.sub.1 and wherein said core surface integral $V_{01}\frac{n_0\left(r_1+r_0\right)+n_t\left(r_1-r_0\right)}{2},$ where n.sub.0=n.sub.0n.sub.4 is the refractive-index difference of said centre part of said core with respect to said outer cladding, and wherein said cladding surface integral V.sub.02(r.sub.3r.sub.2)n.sub.t.

19. The bending-loss insensitive single mode optical fibre of claim 15, wherein said optical fibre complies with the requirements of the ITU-T G.657.A2 standard.

20. Optical fibre transmission system comprising at least one single mode fibre according to claim 15.

Description

4. BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features and advantages of embodiments of the invention shall appear from the following description, given by way of an indicative and non-exhaustive example and from the appended drawings, of which:

(2) FIG. 1 schematically depicts an isometric view of an exemplary single mode optical fiber according to one or more embodiments described herein;

(3) FIG. 2 graphically provides the illustrative refractive index profile of single mode optical fibers according to a first embodiment of the present disclosure;

(4) FIG. 3 graphically provides the illustrative refractive index profile of single mode optical fibers according to a second embodiment of the present disclosure;

(5) FIGS. 4A, 4B and 4C provide simulation results for macrobending losses and cable cut-off wavelength of exemplary fibers expressed as a function of f=V.sub.01;

(6) FIGS. 5A, 5B and 5C provide simulation results for macrobending losses and cable cut-off wavelength of exemplary fibers expressed as a function of f=V.sub.01V.sub.02;

(7) FIGS. 6A to 6G provide simulation results for macrobending losses and cable cut-off wavelength of exemplary fibers expressed as a function of f=V.sub.010.2326V.sub.02;

(8) FIG. 7 illustrates an optical link according to an embodiment of the present disclosure.

(9) The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

5. DETAILED DESCRIPTION

(10) Reference will now be made in detail to embodiments of single mode optical fibers, examples of which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts.

(11) One embodiment of a bending-loss insensitive single mode optical fiber according to the present disclosure is schematically depicted in isometric view in FIG. 1. The optical fiber 10 generally has a glass core 101 surrounded by a glass cladding. More precisely, the optical fiber 10 comprises three or four abutting concentric regions, namely: a trapezoid core 101, with an outer radius r.sub.1; an optional intermediate cladding 102, with an inner radius r.sub.1 and an outer radius r.sub.2; a trench, or depressed cladding, 103, with an inner radius r.sub.2 and an outer radius r.sub.3; an outer cladding 104, ranging from an inner radius r.sub.3 to the end of the glass part of the fiber, with a refractive index n.sub.Cl.

(12) In embodiments of the present disclosure with no intermediate cladding 102, the trench 130 directly abuts the core 101, and ranges from an inner radius r.sub.1 to an outer radius r.sub.3.

(13) In embodiments of the present disclosure, the glass core 101 generally has an outer radius r.sub.1 between 5.4 m and 8.0 m. Moreover, the depressed cladding 103 has an outer radius r.sub.3 between 16 m and 22 m. The core 101 has a trapezoid shape, with a small basis radius r.sub.0 and a large basis radius r.sub.1. The small basis over large basis trapezoid ratio r.sub.0/r.sub.1 is ranging from 0.1 to 0.6, typically ranging from about 0.2 to about 0.5, preferably from about 0.25 to about 0.45.

(14) In the embodiments shown and described herein, the core 101 and the cladding generally comprise silica, specifically silica glass. The cross-section of the optical fiber 10 may be generally circular-symmetric with respect to the center of the core 101. In some embodiments described herein, the radius of the glass portion of the optical fiber 10 is about 62.5 m. However, it should be understood that the dimensions of the cladding may be adjusted so that the radius of the glass portion of the optical fiber may be greater than or less than 62.5 m. The optical fiber 10 also comprises a coating surrounding the cladding. Such a coating may comprise several layers, and it may notably be a dual-layer coating, although these different layers are not shown on FIG. 1.

(15) The different portions in the cladding may comprise pure silica glass (SiO.sub.2), silica glass with one or more dopants, which increase the index of refraction (e.g. GeO.sub.2 or any other known dopant), such as when the portion of the cladding is up-doped (e.g. for the intermediate cladding 102), or silica glass with a dopant, which decreases the index of refraction, such as fluorine, such as when the portion of the cladding is down-doped (e.g. for the trench 103).

(16) The trapezoid shape of the core 101 may be obtained by gradually adjusting the concentration of at least two dopants in the center part of the core.

(17) FIGS. 2 and 3 show diagrams of the index profile of a fibre constituting a first (referenced as Ex1) and a second (referenced as Ex3) embodiment of the invention.

(18) In the first embodiment illustrated by FIG. 2, the index profile is a trapezoid type index profile with a trench, and it presents, starting from the centre of the fibre: a centre part of the core having a substantially constant refractive index n.sub.0 greater than that of the cladding n.sub.4; a first annular portion of the core, in which the index decreases in substantially linear manner, from the index n.sub.0 of the centre part of the core to the index n.sub.t of the depressed cladding 103. Such an annular portion of the core is also called transition part of the core's trapezoid-like index profile, throughout the present document; a depressed cladding, or trench 103; an outer cladding 104.
The fibre as a whole thus constitutes a fibre having a so-called trapezoid-like profile.

(19) The centre part of the core 101 has a radius r.sub.0 and an index difference n.sub.0 relative to the outer cladding. In the transition part of the core, the refractive index difference decreases substantially linearly. The refractive index of the core typically has a trapezoid shape. Accordingly, the refractive-index difference n(r) between the central core and the outer cladding depends on the distance r from the centre of the optical fibre (e.g. decreasing as the distance from the centre of the optical fibre increases). As used herein, the term refractive-index difference does not exclude a refractive-index difference of zero.

(20) The depressed cladding, or buried trench, 103 has a radius r.sub.3 and a refractive-index difference n.sub.t with respect to the outer cladding that is typically constant. As used herein, the term buried trench is used to designate a radial portion of the optical fibre having a refractive index lower than the refractive index of the outer cladding.

(21) The outer cladding 104 ranges from a radius r.sub.3 to the end of the glass part of the single mode fibre.

(22) In the second embodiment illustrated by FIG. 3, the index profile is a trapezoid type index profile with a trench, and it presents, starting from the centre of the fibre: a centre part of the core having a substantially constant refractive index n.sub.0 greater than that of the cladding n.sub.4; a first annular portion of the core, in which the index decreases in substantially linear manner, from the index n.sub.0 of the centre part of the core to the index n.sub.2 of the intermediate cladding 102. Such an annular portion of the core is also called transition part of the core's trapezoid-like index profile, throughout the present document; an intermediate cladding 102; a depressed cladding, or trench 103; an outer cladding 104.
The fibre as a whole thus constitutes a fibre having a so-called trapezoid-like profile.

(23) Like in the embodiment of FIG. 2, the centre part of the core 101 has a radius r.sub.0 and an index difference n.sub.0 relative to the outer cladding. In the transition part of the core, the refractive index difference decreases substantially linearly. The refractive index of the core typically has a trapezoid shape. Accordingly, the refractive-index difference n(r) between the central core and the outer cladding depends on the distance r from the centre of the optical fibre (e.g. decreasing as the distance from the centre of the optical fibre increases). As used herein, the term refractive-index difference does not exclude a refractive-index difference of zero.

(24) The intermediate cladding 102 has a radius r.sub.2 and a refractive-index difference n.sub.e with respect to the outer cladding that is typically constant. In the peculiar embodiment illustrated by FIG. 3, n.sub.2=0. However, in other embodiments, this refractive-index difference may be different from zero (see exemplary embodiment Ex4 described later on in this document). The depressed cladding, or buried trench, 103 has a radius r.sub.3 and a refractive-index difference n.sub.t with respect to the outer cladding that is typically constant. As used herein, the term buried trench is used to designate a radial portion of the optical fibre having a refractive index lower than the refractive index of the outer cladding.

(25) The outer cladding 104 ranges from a radius r.sub.3 to the end of the glass part of the single mode fibre.

(26) FIGS. 2 and 3 differ from each other by the presence of an intermediate cladding 102 between the trapezoid core and the trench.

(27) In both FIGS. 2 and 3, refractive indexes n(r) are given at a 633 nm wavelength (i.e. the wavelength at which the profile is measured thanks to commercial apparatus) relatively to the outer cladding index n.sub.4. These indexes are thus also called index delta. More generally, throughout the present document, all refractive indices are given at a wavelength =633 nm.

(28) Table 2 below draws a comparison of the refractive index designs of two exemplary embodiments Ex1 and Ex2 of FIG. 2 with an equivalent step index single mode fibre Comp Ex. The values in Table 2 correspond to the theoretical refractive-index profiles.

(29) TABLE-US-00002 TABLE 2 ratio r1 r3 n.sub.0 n.sub.t r0/r1 (m) (m) 1000 1000 Comp Ex 1 4.34 17.50 5.29 0.16 Ex1 0.35 6.90 17.50 5.54 1.23 Ex2 0.35 6.88 20.00 5.41 1.35

(30) The first column of Table 2 lists the exemplary and comparative optical fibres. The following columns provide, for each single mode fibre listed in the first column: the ratio r.sub.0/r.sub.1 of the centre part of the core radius to the transition part of the core outer radius; the outer radius r.sub.1 of the transition part of the core, expressed in m; the outer radius r.sub.3 of the trench, expressed in m; the index delta n.sub.0 of the centre part of the core; the index delta n.sub.t of the trench.

(31) The refractive index differences in Table 2 (as well as in all the other tables throughout the present document) have been multiplied by 1000, as are the ordinate values in FIGS. 2 and 3 (for example, for the first exemplary embodiment of the invention Ex1, the index delta of the centre part of the core is 5.2910.sup.3). The refractive-index values were measured at a wavelength of 633 nanometres.

(32) Table 3 below details the refractive index design of exemplary embodiments Ex3 and Ex4 of FIG. 3. The values in Table 3 correspond to the theoretical refractive-index profiles. It must be noted that the overall refractive-index profile of exemplary embodiment Ex4 corresponds to the one depicted in FIG. 3, except for the fact that the refractive index difference of the intermediate cladding is not zero.

(33) TABLE-US-00003 TABLE 3 Ratio r.sub.1 r.sub.2 r.sub.3 n.sub.0 n.sub.2 n.sub.t r.sub.0/r.sub.1 (m) (m) (m) 1000 1000 1000 Ex3 0.35 5.91 10.00 17.50 5.77 0.00 1.75 Ex4 0.35 5.78 10.00 17.50 5.87 0.20 2.00

(34) The first column of Table 3 gives the reference of the exemplary optical fibres. The following columns provide for the single mode fibres listed in the first column: the ratio r.sub.0/r.sub.1 of the centre part of the core radius to the transition part of the core outer radius; the outer radius r.sub.1 of the transition part of the core, expressed in m; the outer radius r.sub.2 of the intermediate cladding, expressed in m; the outer radius r.sub.3 of the trench, expressed in m; the index delta n.sub.0 of the centre part of the core; the index delta n.sub.2 of the intermediate cladding; the index delta n.sub.t of the trench.

(35) Both in the embodiments of FIGS. 2 and 3, the core index n.sub.0 is typically ranging from about 5.010.sup.3 to about 6.010.sup.3; the trench index n.sub.t is typically ranging from about 2.010.sup.3 to about 0.910.sup.3.

(36) Table 4 (below) shows optical transmission characteristics for optical single mode fibres having the refractive-index profiles depicted in Table 2 and Table 3, compared with the optical transmission characteristics recommended in the ITU-T G.657.A2 standard. The first column identifies the minimum and maximum G.657.A2 recommended range, and the exemplary and comparative optical fibres. The next columns provide, for each optical fibre: the Cable Cut-off wavelength (CCO) expressed in nm; the Mode Field Diameter at 1310 nm (MFD 1310) expressed in m; the Mode Field Diameter at 1550 nm (MFD 1550) expressed in m; the Zero chromatic Dispersion Wavelength (ZDW) expressed in nm; the Zero Dispersion Slope (ZDS) expressed in ps/nm.sup.2-km; the Chromatic Dispersion at respective 1550 nm (DC 1550) and 1625 nm (DC 1625) wavelength expressed in ps/nm-km.

(37) TABLE-US-00004 TABLE 4 CCO MFD 1310 MFD 1550 ZDW ZDS DC 1550 DC 1625 (nm) (m) (m) (nm) (ps/nm.sup.2-km) (ps/nm-km) (ps/nm-km) G.657.A2 8.6 1300 13.3 17.2 min G.657.A2 1260 9.2 1324 0.092 18.6 23.7 max Comp Ex 1210 9 10.11 1312 0.086 16.5 20.7 Ex1 1210 9 10.05 1312 0.090 17.4 21.7 Ex2 1210 9 10.06 1312 0.090 17.4 21.7 Ex3 1210 9 10.23 1317 0.090 17.2 21.8 Ex4 1228 9 10.25 1320 0.090 17.1 21.7

(38) The comparative example Comp Ex, corresponding to a step-index single mode fibre, presents the same MFD at 1310 nm and Cable Cut-off as examples Ex1 to Ex3. However, examples Ex1 to Ex4 are all compliant with ITU-T G.657.A2 Recommendation, which is not the case of the comparative example Comp Ex.

(39) It must be noted that the cable cutoff target needs to be significantly below the maximum accepted level of 1260 nm. Targeting a cable cutoff at 1260 nm is not robust as it will by definition induce 50% of the production out of the ranges of values recommended by the G.657.A2 standard. In the above examples, the cable cutoff wavelength is targeted to be around 1210 nm that is ensuring robust production, i.e nearly all fibers can pass the cable cutoff recommendation. More generally, targeting cable cutoff below 1240 nm is recommended to ensure a robust production.

(40) As may be observed in Table 4, all the exemplary fibers Ex1 to Ex4 target a nominal Mode Field Diameter at 1310 nm of 9 microns.

(41) Table 5 (below) shows macrobending losses for optical fibres having the refractive-index profiles depicted in Tables 2 and 3 for the wavelengths of 1550 nanometres and 1625 nanometres for radii of curvature of 15 millimetres, 10 millimetres, 7.5 millimetres and 5 millimetres, such as: R15 mm Macro bend loss at 1550 nm (R15BL at 1550), expressed in dB/10T, where 10T stands for 10 turns; R10 mm Macro bend loss at 1550 nm (R10BL at 1550), expressed in dB/1T, where 1T stands for 1 turn; R7.5 mm Macro bend loss at 1550 nm (R7.5BL at 1550), expressed in dB/1T, where 1T stands for 1 turn; R5 mm Macro bend loss at 1550 nm (R5BL at 1550), expressed in dB/1T, where 1T stands for 1 turn; R15 mm Macro bend loss at 1625 nm (R15BL at 1625), expressed in dB/10T, where 10T stands for 10 turns; R10 mm Macro bend loss at 1625 nm (R10BL at 1625), expressed in dB/1T, where 1T stands for 1 turn; R7.5 mm Macro bend loss at 1625 nm (R7.5BL at 1625), expressed in dB/1T, where 1T stands for 1 turn; R5 mm Macro bend loss at 1625 nm (R5BL at 1625), expressed in dB/1T, where 1T stands for 1 turn.

(42) Table 5 also provides the maximum recommended value by the ITU-T G.657.A2 standard.

(43) TABLE-US-00005 TABLE 5 R15BL R10BL R7.5BL R5BL R15BL R10BL R7.5BL R5BL at 1550 at 1550 at 1550 at 1550 at 1625 at 1625 at 1625 at 1625 (dB/10T) (dB/1T) (dB/1T) (dB/1T) (dB/10T) (dB/1T) (dB/1T) (dB/1T) G.657.A2 0.03 0.1 0.5 0.1 0.2 1.0 max Comp Ex 0.022 0.17 1.3 10 0.14 0.55 3.0 16 Ex1 0.013 0.05 0.3 1.4 0.08 0.17 0.6 2.6 Ex2 0.016 0.04 0.1 1.0 0.08 0.10 0.3 1.8 Ex3 0.016 0.06 0.3 1.3 0.08 0.16 0.6 2.4 Ex4 0.009 0.04 0.2 0.9 0.05 0.11 0.4 1.7

(44) In accordance with Tables 4 and 5 (above), the optical fibres according to embodiments of the invention show bending losses, which are less than the comparative optical fibre, which has a step-index profile.

(45) The four refractive index profile examples Ex1, Ext, Ex3 and Ex4 according to embodiments of the invention, described in Tables 2 to 5, as well as in FIGS. 1 and 2, comply with the ITU-T G. 657.A2 Recommendation.

(46) Table 6 below provides the features of three other exemplary optical fibres Ex5 to Ex7, which refractive index profile corresponds to the one depicted in FIG. 2, but which, contrarily to the exemplary fibres of Table 2, target a MFD at 1310 nm of 9.2 microns.

(47) TABLE-US-00006 TABLE 6 ratio r1 r3 n.sub.0 n.sub.t r0/r1 (m) (m) 1000 1000 Ex5 0.35 7.00 17.50 5.5 0.93 Ex6 0.35 6.99 20.00 5.41 1 Ex7 0.35 6.97 20.00 5.29 1.1
The structure and units of Table 6 is identical to that of Table 2 and is therefore not detailed here. Similarly, Table 7 below corresponds to Table 4 above and provides the optical characteristics of exemplary optical fibres Ex5-Ex7; Table 8 below corresponds to Table 5 above and provides the macrobending losses of exemplary optical fibres Ex5-Ex7.

(48) TABLE-US-00007 TABLE 7 CCO MFD 1310 MFD 1550 ZDW ZDS DC 1550 DC 1625 (nm) (m) (m) (nm) (ps/nm.sup.2-km) (ps/nm-km) (ps/nm-km) G.657.A2 8.6 1300 13.3 17.2 min G.657.A2 1260 9.2 1324 0.092 18.6 23.7 max Ex5 1236 9.2 10.29 1312 0.090 17.4 21.8 Ex6 1235 9.2 10.29 1312 0.090 17.4 21.8 Ex7 1214 9.2 10.29 1312 0.090 17.4 21.7

(49) TABLE-US-00008 TABLE 8 R15BL R10BL R7.5BL R5BL R15BL R10BL R7.5BL R5BL at 1550 at 1550 at 1550 at 1550 at 1625 at 1625 at 1625 at 1625 (dB/10T) (dB/1T) (dB/1T) (dB/1T) (dB/10T) (dB/1T) (dB/1T) (dB/1T) G.657.A2 0.03 0.1 0.5 0.1 0.2 1.0 max Ex5 0.012 0.07 0.4 2.4 0.07 0.20 0.9 4.1 Ex6 0.013 0.05 0.2 1.7 0.07 0.14 0.5 3.2 Ex7 0.025 0.06 0.3 1.8 0.12 0.17 0.6 3.3

(50) We now present interesting tools and methods for defining acceptable profile ranges for single mode optical fibres according to the present disclosure.

(51) Each section of the optical fibre profile may be defined using surface integrals. The term surface should not be understood geometrically but rather should be understood as a value having two dimensions.

(52) Accordingly, the central core may define a surface integral V.sub.01 and the cladding may define a surface integral V.sub.02 respectively defined by the following equations:

(53) $V_{01}={}_0^{r_1}n\left(r\right).Math.\mathrm{dr}\frac{n_0\left(r_1+r_0\right)+n_2\left(r_1-r_0\right)}{2}$$V_{02}={}_{r_1}^{}n\left(r\right).Math.\mathrm{dr}\left(r_2-r_1\right)n_2+\left(r_3-r_2\right)n_t$

(54) For exemplary optical fibres which refractive index profile corresponds to the first embodiment of FIG. 2, the cladding surface integral may be expressed as:
V.sub.02(r.sub.3r.sub.2)n.sub.t

(55) Table 9 (below) completes Tables 2, 3 and 6 (above) with the values of the surface integrals V.sub.01 and V.sub.02 described above for the exemplary embodiments of the invention Ex1 to Ex7, as well as for their comparative step index single mode fibre Comp Ex. All the examples in Table 9 are hence the same as in Tables 2, 3 and 6. The values in Table 9 correspond to the theoretical refractive-index profiles.

(56) The first column in Table 9 lists the exemplary and comparative optical fibres. The three other columns provide respective values for the surface integrals V.sub.01 and V.sub.02, as well as for the polynomial V.sub.010.2326V.sub.02. The integrals in Table 9 have been multiplied by 1000.

(57) TABLE-US-00009 TABLE 9 (V.sub.01 V.sub.01 V.sub.02 0.2326V.sub.02) 1000 1000 1000 (m) (m) (m) Comp Ex 22.96 2.11 23.45 Ex1 23.04 13.04 26.08 Ex2 22.11 17.71 26.23 Ex3 23.02 13.13 26.07 Ex4 23.27 14.16 26.56 Ex5 23.87 9.77 26.14 Ex6 23.25 13.01 26.28 Ex7 22.40 14.33 25.73

(58) Tables 10 to 13 (below) provide the features of further exemplary optical fibres Ex8 to Ex35, according to embodiments of the present disclosure, which refractive index profile corresponds to the one depicted in FIG. 2. More precisely, Table 10 corresponds to Table 6, and provides: the ratio r.sub.0/r.sub.1 of the centre part of the core radius to the transition part of the core outer radius; the outer radius r.sub.1 of the transition part of the core, expressed in m; the outer radius r.sub.3 of the trench, expressed in m; the index delta n.sub.0 of the centre part of the core; the index delta n.sub.t of the trench.

(59) TABLE-US-00010 TABLE 10 ratio r1 r3 n.sub.0 n.sub.t r0/r1 (m) (m) 1000 1000 Ex8 0.20 8.00 20.00 5.59 1.91 Ex9 0.20 7.90 21.43 5.61 1.65 Ex10 0.25 7.65 17.30 5.70 1.48 Ex11 0.25 7.85 18.12 5.55 1.62 Ex12 0.25 7.43 21.49 5.61 1.13 Ex13 0.25 7.95 16.05 5.80 1.99 Ex14 0.25 7.33 18.16 5.79 1.31 Ex15 0.30 7.21 17.94 5.56 1.19 Ex16 0.30 7.56 20.73 5.12 1.84 Ex17 0.30 7.42 17.03 5.49 1.78 Ex18 0.30 7.06 19.52 5.70 1.15 Ex19 0.35 7.06 20.80 5.35 1.38 Ex20 0.35 6.78 21.74 5.48 0.92 Ex21 0.35 6.91 19.96 5.39 0.94 Ex22 0.35 7.25 18.93 5.28 1.98 Ex23 0.35 6.90 21.93 5.28 1.49 Ex24 0.40 6.67 19.57 5.33 1.06 Ex25 0.40 6.98 18.60 5.21 1.37 Ex26 0.40 7.01 16.51 5.42 1.70 Ex27 0.40 6.43 21.55 5.43 0.91 Ex28 0.45 6.42 19.71 5.33 0.91 Ex29 0.45 6.55 18.98 5.26 0.97 Ex30 0.45 6.68 19.60 5.06 1.83 Ex31 0.45 6.35 20.79 5.24 1.16 Ex32 0.50 6.23 19.23 5.19 1.02 Ex33 0.50 6.37 20.49 5.01 1.18 Ex34 0.50 6.34 18.48 5.11 1.50 Ex35 0.50 6.10 21.63 5.33 0.93

(60) Similarly, Table 11 below corresponds to Table 4 above and provides the optical characteristics of exemplary optical fibres Ex8-Ex35; Table 12 below corresponds to Table 5 above and provides the macrobending losses of exemplary optical fibres Ex8-Ex35. Last, Table 13 below corresponds to Table 9 above and provides the values of the surface integrals V.sub.01 and V.sub.02 described above for the exemplary embodiments of the invention Ex8 to Ex35. The structure and units in Tables 10-13 are the same as in the previously described corresponding tables.

(61) TABLE-US-00011 TABLE 11 CCO MFD 1310 MFD 1550 ZDW ZDS DC 1550 DC 1625 (nm) (m) (m) (nm) (ps/nm.sup.2-km) (ps/nm-km) (ps/nm-km) G.657.A2 8.6 1300 13.3 17.2 min G.657.A2 1260 9.2 1324 0.092 18.6 23.7 max Ex8 1223 9.12 10.23 1318 0.091 17.3 21.7 Ex9 1240 9.18 10.32 1319 0.091 17.1 21.5 Ex10 1219 9.11 10.21 1316 0.091 17.3 21.7 Ex11 1228 9.20 10.29 1314 0.091 17.5 21.9 Ex12 1234 9.19 10.34 1318 0.090 17 21.4 Ex13 1231 9.01 10.05 1313 0.092 17.6 22 Ex14 1202 9.00 10.12 1319 0.090 17 21.3 Ex15 1214 9.11 10.21 1315 0.090 17.3 21.6 Ex16 1234 9.19 10.26 1310 0.091 17.7 22.1 Ex17 1197 9.01 10.05 1311 0.091 17.6 22 Ex18 1224 9.00 10.10 1316 0.090 17.1 21.4 Ex19 1239 9.11 10.16 1310 0.091 17.6 21.9 Ex20 1230 9.10 10.22 1315 0.089 17.1 21.4 Ex21 1225 9.20 10.31 1313 0.090 17.3 21.6 Ex22 1230 9.00 10.00 1306 0.092 18 22.4 Ex23 1231 9.00 10.06 1311 0.090 17.4 21.7 Ex24 1222 9.11 10.17 1310 0.090 17.5 21.8 Ex25 1234 9.20 10.22 1305 0.091 18 22.3 Ex26 1235 9.01 9.98 1303 0.092 18.2 22.6 Ex27 1215 9.00 10.10 1314 0.089 17.1 21.4 Ex28 1232 9.11 10.16 1308 0.090 17.5 21.8 Ex29 1238 9.20 10.24 1306 0.090 17.8 22.1 Ex30 1232 9.01 9.96 1301 0.092 18.3 22.6 Ex31 1216 9.01 10.05 1308 0.089 17.5 21.8 Ex32 1224 9.10 10.12 1305 0.090 17.7 22 Ex33 1231 9.20 10.21 1303 0.091 18 22.3 Ex34 1216 9.00 9.97 1301 0.091 18.2 22.5 Ex35 1236 9.00 10.03 1307 0.089 17.5 21.8

(62) TABLE-US-00012 TABLE 12 R15BL R10BL R7.5BL R5BL R15BL R10BL R7.5BL R5BL at 1550 at 1550 at 1550 at 1550 at 1625 at 1625 at 1625 at 1625 (dB/10T) (dB/1T) (dB/1T) (dB/1T) (dB/10T) (dB/1T) (dB/1T) (dB/1T) G.657.A2 0.03 0.1 0.5 0.1 0.2 1.0 max Ex8 0.021 0.03 0.1 0.5 0.10 0.07 0.19 0.89 Ex9 0.016 0.02 0.1 0.6 0.07 0.06 0.18 1.19 Ex10 0.014 0.05 0.2 1.2 0.08 0.15 0.53 2.11 Ex11 0.014 0.04 0.2 0.9 0.07 0.12 0.38 1.58 Ex12 0.015 0.04 0.2 1.5 0.07 0.10 0.37 2.79 Ex13 0.005 0.03 0.1 0.7 0.03 0.09 0.34 1.29 Ex14 0.016 0.05 0.2 1.3 0.09 0.16 0.54 2.42 Ex15 0.017 0.06 0.3 1.7 0.10 0.19 0.67 2.94 Ex16 0.023 0.02 0.1 0.5 0.10 0.06 0.18 0.97 Ex17 0.018 0.05 0.2 0.9 0.10 0.15 0.44 1.58 Ex18 0.009 0.04 0.2 1.2 0.05 0.11 0.41 2.18 Ex19 0.010 0.02 0.1 0.8 0.05 0.07 0.23 1.47 Ex20 0.012 0.04 0.2 2.1 0.07 0.12 0.47 3.92 Ex21 0.019 0.06 0.3 2.2 0.10 0.18 0.66 3.90 Ex22 0.011 0.02 0.1 0.4 0.06 0.06 0.17 0.70 Ex23 0.014 0.02 0.1 0.7 0.07 0.06 0.19 1.44 Ex24 0.016 0.05 0.2 1.6 0.09 0.15 0.55 2.93 Ex25 0.013 0.04 0.2 1.0 0.07 0.12 0.41 1.88 Ex26 0.006 0.03 0.2 0.8 0.04 0.09 0.36 1.43 Ex27 0.015 0.04 0.2 2.2 0.08 0.13 0.51 4.16 Ex28 0.011 0.05 0.2 1.9 0.07 0.15 0.59 3.48 Ex29 0.012 0.05 0.3 1.9 0.07 0.16 0.63 3.34 Ex30 0.013 0.02 0.1 0.4 0.07 0.06 0.17 0.79 Ex31 0.017 0.04 0.2 1.3 0.09 0.11 0.38 2.54 Ex32 0.016 0.06 0.3 1.7 0.09 0.17 0.61 3.13 Ex33 0.019 0.04 0.2 1.4 0.10 0.13 0.42 2.57 Ex34 0.017 0.04 0.2 0.8 0.09 0.12 0.37 1.59 Ex35 0.008 0.03 0.2 1.6 0.05 0.09 0.38 3.20

(63) TABLE-US-00013 TABLE 13 (V.sub.01 V.sub.01 V.sub.02 0.2326V.sub.02) 1000 1000 1000 (m) (m) (m) Comp Ex 22.96 2.11 23.45 Ex8 20.72 22.92 26.05 Ex9 21.38 22.32 26.57 Ex10 23.01 14.28 26.33 Ex11 22.46 16.64 26.33 Ex12 22.90 15.89 26.60 Ex13 22.89 16.12 26.64 Ex14 22.92 14.19 26.22 Ex15 23.05 12.77 26.02 Ex16 20.29 24.23 25.93 Ex17 21.86 17.11 25.83 Ex18 23.32 14.33 26.65 Ex19 22.33 18.96 26.74 Ex20 23.05 13.76 26.25 Ex21 23.03 12.27 25.88 Ex22 21.17 23.13 26.55 Ex23 21.25 22.39 26.46 Ex24 22.76 13.67 25.95 Ex25 22.59 15.92 26.29 Ex26 23.02 16.15 26.78 Ex27 22.69 13.76 25.89 Ex28 23.20 12.09 26.01 Ex29 23.23 12.06 26.04 Ex30 21.14 23.64 26.64 Ex31 22.10 16.75 25.99 Ex32 22.66 13.26 25.75 Ex33 22.06 16.66 25.93 Ex34 21.92 18.21 26.16 Ex35 22.97 14.44 26.33

(64) Optical fibres according to embodiments of the invention typically target a MFD at 1310 nm greater than or equal to 9 microns, and have the following properties: a ratio r.sub.0/r.sub.1 of the centre part of the core's radius to the transition part of the core's radius ranges between 0.10 and 0.60 (which is required to keep the Zero chromatic Dispersion Wavelength ZDW between 1300 and 1324 nm), preferably ranging between 0.20 and 0.50, more preferably between 0.25 and 0.45 (which provides a robust working range); a core surface integral V.sub.01 preferably ranging between about 2010.sup.3 m and about 2410.sup.3 m; a cladding surface integral V.sub.02 preferably ranging between 2510.sup.3 m and 910.sup.3 m; the relationship V.sub.010.2326V.sub.02 between the core surface integral and the cladding surface integral preferably ranging between 25.710.sup.3 m and 26.810.sup.3 m.

(65) Actually, it is known that macrobending losses decrease when the core surface integral V.sub.01 increases and when the cladding surface integral V.sub.02 decreases. The inventors have hence worked out that there must be a positive number k, which allows describing macrobending losses by a mathematical function of the type:
f=V.sub.01kV.sub.02.
The same reasoning applies with the cable cutoff wavelength, which tends to increase when the core surface integral V.sub.01 increases and when the cladding surface integral V.sub.02 decreases. Hence, there must also be a positive number g, which allows describing the behaviour of the cable cut off wavelength by a mathematical function of the type:
f=V.sub.01gV.sub.02.
By trial and error, the inventors have found out that for k=g=0.2326, there is a strong correlation between the f function and the macrobending losses at bending radii of 15 mm and 10 mm on the one hand, and the cable cut-off wavelength on the other hand.

(66) FIGS. 4 to 6 allow illustrating this finding. More precisely, FIGS. 4A and 4B respectively illustrate on the y-axis, the macrobending losses, for optical fibres according to embodiments of the present disclosure targeting a MFD at 1310 nm of 9 microns for the wavelength of 1550 nanometres for radii of curvature of 15 millimetres and 10 millimetres (R15BL at 1550 and R10BL at 1550), expressed in dB/10T, where 10T stands for 10 turns, as a function of the above-expressed f function, when k=0, on the x-axis. FIG. 4C illustrates the cable cut-off wavelength (CCO), expressed in nm, for optical fibres according to embodiments of the present disclosure targeting a MFD at 1310 nm of 9 microns, as a function of the above-expressed f function, when g=0, on the x-axis.

(67) As may be observed, the values of macrobending losses and cable cut-off wavelength are dispersed.

(68) The same may be observed on FIGS. 5A to 5C, which are similar to FIGS. 4A to 4C, except for the fact that the k and g parameters are set to 1.

(69) However, FIGS. 6A to 6G illustrate the fact that there is a strong correlation between the above-expressed f function and both the macrobending losses and the cable cut-off wavelength when k=g=0.2326. All these figures are plotted through simulations carried out for exemplary optical fibres according to the present disclosure, both targeting a MFD at 1310 nm of 9 or 9.2 microns, corresponding to the lower and upper limits of the present disclosure.

(70) FIG. 6A provides the macrobending losses for such optical fibres for the wavelength of 1550 nanometres for a radius of curvature of 15 millimetres (R15 mm BL at 1550), expressed in dB/10T, where 10T stands for 10 turns, as a function of the above-expressed f function, when k=0.2326, on the x-axis.

(71) FIG. 6B provides the macrobending losses for such optical fibres for the wavelength of 1550 nanometres for a radius of curvature of 10 millimetres (R10 mm BL at 1550), expressed in dB/10T, where 10T stands for 10 turns, as a function of the above-expressed f function, when k=0.2326, on the x-axis.

(72) FIG. 6C provides the macrobending losses for such optical fibres for the wavelength of 1550 nanometres for a radius of curvature of 7.5 millimetres (R7.5 mm BL at 1550), expressed in dB/10T, where 10T stands for 10 turns, as a function of the above-expressed f function, when k=0.2326, on the x-axis.

(73) FIG. 6D provides the macrobending losses for such optical fibres for the wavelength of 1625 nanometres for a radius of curvature of 15 millimetres (R15 mm BL at 1625), expressed in dB/10T, where 10T stands for 10 turns, as a function of the above-expressed f function, when k=0.2326, on the x-axis.

(74) FIG. 6E provides the macrobending losses for such optical fibres for the wavelength of 1625 nanometres for a radius of curvature of 10 millimetres (R10 mm BL at 1625), expressed in dB/10T, where 10T stands for 10 turns, as a function of the above-expressed f function, when k=0.2326, on the x-axis.

(75) FIG. 6F provides the macrobending losses for such optical fibres for the wavelength of 1625 nanometres for a radius of curvature of 7.5 millimetres (R7.5 mm BL at 1625), expressed in dB/10T, where 10T stands for 10 turns, as a function of the above-expressed f function, when k=0.2326, on the x-axis.

(76) FIG. 6G provides the cable cut-off wavelength for such optical fibres, expressed in nanometers, as a function of the above-expressed f function, when g=0.2326, on the x-axis.

(77) Hence, as may be observed on FIGS. 6D and 6E, for a nominal MFD at 1310 nm between 9.0 and 9.2 m, it is necessary to have 25.710.sup.3V.sub.010.2326V.sub.02, in order to achieve macrobending losses at bending radii of 15 mm and 10 mm compliant with the requirements of the ITU-T G. 657.A2 Recommendation, which maximum accepted level is showed by the horizontal dashed line.

(78) FIG. 7 illustrates an optical link 70 according to an embodiment of the present disclosure. Such an optical link comprises p spans of optical fibers, with p2, which are spliced together. FIG. 7 only shows optical fiber 70.sub.1 and optical fiber 70.sub.p, all the other potential optical fibers in the optical link being symbolized by dashed lines. At least one of the optical fibers in optical link 70 is such that it comprises the features of one embodiment described above. In other words, at least one of the optical fibers complies with the requirements of ITU-T G.657.A2 Recommendation, targets a Mode Field Diameter at 1310 nm greater than or equal to 9 microns and shows the specific design of the refractive index profile described above in relation to FIGS. 2 and 3, and notably, a trapezoid core, with a large but shallow trench. This optical fiber may be spliced in optical link 70 with a standard single-mode optical fiber compliant with the requirements of ITU-T.G. 652.D recommendation.

(79) We now describe an exemplary method of manufacturing an optical fibre according to embodiments of the present disclosure. Such a manufacturing method comprises a first step of Chemical Vapour Deposition to form a core rod. During the Chemical Vapour Deposition doped or non-doped glass layers are deposited. The deposited glass layers form the core refractive index profile of the final optical. In a second step the core rod is provided with an external overcladding for increasing its diameter to form a preform. The overcladding may be derived from pre-formed silica tubes or by deposition of glass layers on the outer circumference of the core rod. Various techniques could be used for providing an overcladding by deposition of glass layers, such as Outside Vapour Deposition (OVD) or Advanced Plasma and Vapour Deposition (APVD). In a third step, the optical fibre is obtained by drawing the preform in a fibre drawing tower.

(80) In order to fabricate the core-rod, a tube or substrate is generally mounted horizontally and held in a glass-making lathe. Thereafter, the tube or substrate is rotated and heated or energised locally for depositing components that determine the composition of the core-rod. Those of ordinary skill in the art will appreciate that the composition of the core-rod determines the optical characteristics of the fibre.

(81) In this regard, both the centre part and the transition part of the core, the intermediate cladding and the trench are typically obtained using plasma chemical vapour deposition (PCVD) or furnace chemical vapour deposition (FCVD), which enable large quantities of fluorine and germanium to be incorporated into the silica and which enable a gradual change of their concentrations in the transition part of the core. The PCVD technique is for example described in patent document U.S. Pat. No. Re30,635 or U.S. Pat. No. 4,314,833.

(82) Other techniques could also be used to form the core-rod, such as vapour axial deposition (VAD) or outside vapour deposition (OVD).

(83) Optical fibres in accordance with the present invention are well suited for use in various optical communication systems. They are particularly suited for terrestrial transmission systems, as well as for fibre-to-the-home (FTTH) systems.

(84) Moreover, they are typically compatible with conventional optical fibres, which make them appropriate for use in many optical communication systems. For example, the optical fibres according to embodiments of the invention are typically compatible with conventional optical fibres with respect to mode field diameter, thereby facilitating good fibre-to-fibre coupling.

(85) In the specification and/or figure, typical embodiments of the invention have been disclosed. The present invention is not limited to such exemplary embodiments.