Weakly-coupled few mode optical fibers for mode division multiplexing and corresponding optical transmission system

Abstract

A few-mode optical fiber including a core's refractive-index profile n(r) of trapezoid-like shape. The optical core having a center part of radius R1 and a transition part ranges from the radius R1 to a radius R2, such that R2>R1 with R2 between 6.8 and 11.5 m, said refractive-index profile being defined by a surface integral of the core index profile of between 18010.sup.3 and 27010.sup.3 m; a transition slope S of between 1.710.sup.3 and 1210.sup.3 m.sup.1; with n1 and n2 the refractive-index difference respectively of the center part of the optical core and of the cladding part adjacent to the optical core, with respect to the outer optical cladding.

Claims

1. An optical fiber comprising an optical core surrounded by an optical cladding, wherein the optical core has a refractive-index profile n(r) of trapezoid-like shape, as a function of a radial distance r from the center of the optical core, the optical core having a center part of radius R1 and a transition part ranges from the radius R1 to a radius R2, such that R2>R1, said refractive-index profile being defined by: a surface integral A.sub.core defined as follows: A.sub.core=2.sub.0.sup.R2n(r).Math.dr a transition slope S defined as follows: $S=.Math.\frac{n2-n1}{R2-R1}.Math.$ with: n1, the refractive-index difference of the center part of the optical core with respect to the outer optical cladding; n2, the refractive-index difference of a cladding part, adjacent to the optical core, with respect to the outer optical cladding; and wherein: the surface integral A.sub.core is between 18010.sup.3 and 27010.sup.3 m; the radius R2 is between 6.8 and 11.5 m; the transition slope S is between 1.710.sup.3 and 1210.sup.3 m.sup.1; the center part of the optical core comprises a region of depressed refractive index, called inner depressed core, ranging from the center of the optical core to radius R0 and having a refractive-index difference with respect to the outer optical cladding n0 such that n1>n0(n1610.sup.3), said inner depressed core having a surface integral A.sub.0 and assuming a surface integral A.sub.trap as the surface integral of depressless core's refractive-index profile, said surface integrals A.sub.0 and A.sub.trap being defined as follows:
A.sub.0=2.sub.0.sup.R0(n1n(r))dr
A.sub.trap=2(n1.Math.R1+.sub.R1.sup.R2n(r)dr) with a ratio A.sub.0/A.sub.trap lower than or equal to 0.01.

2. The optical fiber according to claim 1, wherein the refractive-index difference n1 is between 1310.sup.3 and 1810.sup.3.

3. The optical fiber according to claim 1, wherein a ratio R1/R2 of said center part's radius to said transition part's radius is between 0.30 and 0.85.

4. The optical fiber according to claim 1, wherein the refractive-index difference n2 is between 110.sup.3 and 110.sup.3.

5. The optical fiber according to claim 1, wherein the transition slope S satisfies the following inequality: $S{J\left(\frac{A_0}{A_{\mathrm{trap}}}\right)}^2+K\left(\frac{A_0}{A_{\mathrm{trap}}}\right)+L$ with J=65010.sup.3 m.sup.1, K=7810.sup.3 m.sup.1 and L=4.010.sup.3 m.sup.1.

6. The optical fiber according to claim 1, wherein the transition slope S satisfies the following inequality: $S{J\left(\frac{A_0}{A_{\mathrm{trap}}}\right)}^2+K\left(\frac{A_0}{A_{\mathrm{trap}}}\right)+L$ with J=190010.sup.3 m.sup.1, K=20910.sup.3 m.sup.1 and L=7.610.sup.3 m.sup.1.

7. The optical fiber according to claim 1, wherein the transition slope S satisfies the following inequality: $S{J\left(\frac{A_0}{A_{\mathrm{trap}}}\right)}^2+K\left(\frac{A_0}{A_{\mathrm{trap}}}\right)+L$ with J=580010.sup.3 m.sup.1, K=58010.sup.3 m.sup.1 and L=1710.sup.3 m.sup.1.

8. The optical fiber according to claim 1, wherein each Linear Polarization mode guided by said optical fiber has an effective area A.sub.eff, such that A.sub.eff>80 m.sup.2.

9. The optical fiber according to claim 1, wherein at least five linear polarization modes are guided.

10. The optical fiber according to claim 1, wherein a differential mode attenuation, DMA, for all the modes guided by said optical fiber is such that: DMA0.050 dB/km.

11. The optical fiber according to claim 1, wherein a transition part of the trapezoid-like core refractive-index profile comprises at least one dopant material of concentration gradually changing as a function of the radial distance r from a concentration in the center part of the optical core to a concentration in said cladding part adjacent to the optical core.

12. The optical fiber according to claim 11, wherein said at least one dopant material comprises at least one of: Germanium oxide, Phosphorus oxide, Boron oxide, and Fluorine.

13. The optical fiber according to claim 1, wherein the optical cladding has a refractive index between 1.437 and 1.458.

14. An optical transmission system comprising at least one optical fiber according to claim 1.

15. The optical fiber according to claim 1, wherein the refractive-index difference n2 is between 0.510.sup.3 and 0.510.sup.3.

16. The optical fiber according to claim 1, wherein a differential mode attenuation, DMA, for all the modes guided by said optical fiber is such that: DMA0.020 dB/km.

Description

4. LIST OF FIGURES

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

(2) FIG. 1 graphically depicts the refractive-index profile of an exemplary weakly-coupled FMF according to a first embodiment of the present disclosure;

(3) FIG. 2 graphically depicts the refractive-index profile of an exemplary weakly-coupled FMF according to a second embodiment of the present disclosure;

(4) FIG. 3 illustrates a graphic showing the impact of the transition slope of the trapezoid index profile and of the ratio A.sub.0/A.sub.trap on the inter-mode index difference n.sub.eff min of the FMF.

5. DETAILED DESCRIPTION

(5) The general principle of the present disclosure relies on a novel and inventive approach of designing FMFs with soft transition of the refractive-index profile from the optical core to the cladding, so that the extra light scattering losses in the FMF is significantly reduced while keeping a weakly-couple FMF. More precisely, the purpose of such a design is to optimize the refractive-index profile of the optical core, in order that the FMF is able to guide a plurality of weakly-couple spatial modes (typically at least five LP modes with a minimal inter-mode effective refractive-index difference n.sub.eff min equal to or greater than 0.910.sup.3) while having less DMA over prior art FMFs (typically DMA lower than 0.05 dB/km).

(6) Light travelling in an optical fiber actually forms hybrid-type modes, which are usually referred to as LP (linear polarization) modes. The LP.sub.0p modes have two polarization degrees of freedom and are two-fold degenerate, the LP.sub.mp modes with m1 are four-fold degenerate. These degeneracies are not counted when designating the number of LP modes propagating in the fiber. Hence, a few-mode optical fiber having two LP modes supports the propagation of all of the LP.sub.01 and LP.sub.11 modes, or a few-mode fiber guiding six LP modes supports the propagation of all of the LP.sub.01, LP.sub.11, LP.sub.02, LP.sub.21, LP.sub.12 and LP.sub.31 modes.

(7) Reference will now be made in detail to embodiments of few-mode optical fibers according to the invention, 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.

(8) The description therefore proposes two exemplary embodiments to obtain the desired trade-off between n.sub.eff min and DMA: a trapezoid index profile weakly-coupled FMF and a weakly-coupled FMF assisted by an inner depressed core. The second embodiment is detailed later in the description.

(9) As used herein, n.sub.eff min means the minimum value of effective index difference, in absolute value, in between two subsequent LP modes guided in the optical fiber, and n.sub.eff is the effective index difference of a given LP mode with respect to the cladding refraction index.

(10) Depressless Core Weakly-Coupled FMF

(11) FIG. 1 depicts the refractive index profile n(r) of an optical fiber according to a first embodiment of the present invention. It describes the relationship between the refractive-index difference n as a function of the radial distance r, expressed in micrometers, from the center of the optical fiber. The x-axis represents radial position with x=0 representing the center of the optical core, and the y-axis represents refractive index, expressed as a refractive-index difference n. As used herein, the term refractive-index difference does not exclude a refractive-index difference of zero.

(12) The optical fiber has an optical core surrounded by an optical cladding, and a coating surrounding the cladding. The coating may comprise several layers; for instance, the coating may be a dual-layer coating. The cladding is formed of two portions: an intermediate portion adjacent to the optical core and outer portion (also referred to as intermediate cladding and outer cladding respectively).

(13) In this particular embodiment, the refractive-index profile has a trapezoid shape, and it presents (starting from the center of the fibre): a center part of the optical core having a radius R1 and a substantially constant refractive-index difference n1 with respect to the outer cladding; an annular part of the optical core, in which the refractive-index decreases, in substantially linear manner, up to the radial distance R2 from the index of the center part of the optical core to the index of the intermediate cladding; an intermediate cladding having a radius R3 and a substantially constant refractive-index difference n2 with respect to the outer cladding; an outer cladding ranging from the radius R3 to the end of the glass part of the FMF.

(14) Throughout the present document, the aforesaid annular portion of the optical core is also called transition part of the core's trapezoid-like index profile.

(15) The fibre as a whole thus constitutes a fibre having a so-called trapezoid-like profile.

(16) As the cross-section of the FMF shown in FIG. 1 is circular-symmetric with respect to the center of the optical core, the resulting core's refractive-index profile has an isosceles trapezoid shape (the index profile is of symmetrical shape with respect to the center of the optical core (y-axis)).

(17) As stated above, the center part of the core's profile has a substantially constant refractive-index difference n1 with respect to the outer cladding (n.sub.cl), the transition part of the core's profile has a refractive-index difference which decreases substantially linearly with respect to the radial distance. This linear decrease is defined according to a slope S, so called transition slope, defined by the following equation:

(18) $S=.Math.\frac{n2-n1}{R2-R1}.Math.$

(19) Hereafter each section or part of the optical fibre profile is defined using surface integrals. The term surface should not be understood geometrically but rather should be understood as the area under the profile curve having two dimensions (expressed here in micrometers).

(20) According the invention, the center part of the optical core is defined by a surface integral A.sub.core, defined by the following equations:
A.sub.core=2.sub.0.sup.R2n(r).Math.dr=(n1n2)(R1+R2)

(21) The fiber parameters, such as radius R1 and R2, the refractive-index differences n1 and n2, are chosen to have a surface integral A.sub.core ranging in a predetermined range of values.

(22) The FMF according to this exemplary embodiment typically has further the following properties: a surface integral A.sub.core of the core's index profile ranging between 18010.sup.3 and 27010.sup.3 m; a ratio R1/R2 of the center part's radius to the transition part's radius ranging between 0.30 and 0.85; a transition part's radius R2 ranging between 6.8 and 11.5 m; a refractive-index difference n1 ranging between 1310.sup.3 and 1810.sup.3; a refractive-index difference n2 ranging between 110.sup.3 and 110.sup.3 and more particularly between 0.510.sup.3 and 0.510.sup.3; a transition slope S ranging between 1.710.sup.3 and 1210.sup.3 m.sup.1.

(23) Thanks to these profile parameters, FMFs according the invention are able to guide at least five LP modes while exhibiting an optimized trade-off between n.sub.eff min and DMA. Here the inventors of the present invention discovered that such a profile parameter allow getting a low mode coupling (i.e. an increased minimal inter-mode effective refractive index difference n.sub.eff min) and a DMA low as well.

(24) By low mode coupling, it means the minimal inter-mode effective refractive index difference n.sub.eff min0.910.sup.3 and by low DMA, it means the differential mode attenuation DMA0.050 dB/km.

(25) Such a trapezoid profile shape is achieved through a gradual change in the concentration of one or several dopant materials in the transition part of the optical core from R1 to R2. The gradual change in the dopant concentration is based on the desired value of the transition slope S (defined above). Many dopants may be used in the context of the present invention, such as, for example, Germanium and Phosphorus, which both allow increasing the refractive index, and Bore and Fluorine, which both allow decreasing the refractive index. The person skilled in the art will easily understand that these dopants (except for Fluorine) are present in the silica matrix in the form of Oxides. Hence, the use of Germanium as dopant means, for example, the use of Germanium Dioxide (GeO.sub.2).

(26) Weakly-Coupled FMF with Inner Depressed Core

(27) FIG. 2 depicts the refractive index profile n(r) of an optical fiber according to a second embodiment of the present invention. FIG. 2 differs from FIG. 1 by the presence of an inner depressed core astutely sized in the refractive-index profile of the FMF, in order to guaranty an adequate separation between LP modes guided in the fiber.

(28) As shown in the figure, the center part of the core profile comprises a region of depressed refractive index, called inner depressed core, ranging from the center of the optical core to the radius R0 and having a substantially constant refractive-index difference n0 with respect to the outer cladding (n.sub.cl) such that: n1>n0(n1610.sup.3). Adding such an inner depressed core in the center part of the optical core as shown in FIG. 2 allows readjusting the inter-mode effective index difference n.sub.eff and improving the capacity of transmission of spatially-multiplexed optical signals, as compared to prior art FMFs. Therefore, in this exemplary embodiment, the core's trapezoid profile is in some way truncated to its center with a region of depressed refractive index to improve the mode coupling of the FMF. Such a trench has for instance an outer radius R0 between 0.8 m and R10.8 m.

(29) As used herein, the term inner depressed core is used to designate a radial portion of the optical fibre having a refractive index lower than the refractive index of the optical core's center part.

(30) Hereafter each section or part of the optical fibre profile is again defined using surface integrals. The term surface should not be understood geometrically but rather should be understood as the area under the profile curve having two dimensions (expressed here in micrometers).

(31) According to the invention, the inner depressed core is defined by a surface integral A.sub.0 as follow:
A.sub.0=2.sub.0.sup.R0(n1n(r))dr

(32) Considering now the surface integral A.sub.trap as the surface integral of trenchless core's refractive-index profile, defined by the following equation:
A.sub.trap=2(n1.Math.R1+.sub.R1.sup.R2n(r)dr)

(33) According this particular embodiment of the invention, the center part of the optical core is defined by the following surface integral A.sub.core:
A.sub.core=2.sub.0.sup.R2n(r).Math.dr=A.sub.trapA.sub.0

(34) The surface integrals A.sub.0 and A.sub.trap are chosen to have a ratio A.sub.0/A.sub.trap lower than or equal to 0.01. With such a ratio, the trade-off between DMA and n.sub.eff min is even more improved.

(35) It should be noted that a ratio chosen with A.sub.0 equal to zero reverts to exhibit the index profile of the first embodiment. It should also be noted that the properties discussed above in relation with FIG. 1 (R1/R2, R2, n1, n2, S) apply again here for this second exemplary embodiment.

(36) The inventors of the present invention further discovered that the slope and the ratio A.sub.0/A.sub.trap have an effect on the inter-mode effective refractive index difference n.sub.eff, and they developed the following inequality to guaranty a guiding of at least five LP modes with a low mode coupling, while keeping DMA low (i.e. DMA0.050 dB/km):

(37) $S{J\left(\frac{A_0}{A_{\mathrm{trap}}}\right)}^2+K\left(\frac{A_0}{A_{\mathrm{trap}}}\right)+L$
with J=65010.sup.3 m.sup.1, K=7810.sup.3 m.sup.1 and L=4.010.sup.3 m.sup.1 to get n.sub.eff min0.910.sup.3 (referred to as Criterion 1); or
with J=190010.sup.3 m.sup.1, K=20910.sup.3 m.sup.1 and L=7.610.sup.3 m.sup.1 to get n.sub.eff min1.310.sup.3 (referred to as Criterion 2); or
with J=5800.10.sup.3 m.sup.1, K=58010.sup.3 m.sup.1 and L=1710.sup.3 m.sup.1 to get n.sub.eff min1.510.sup.3 (referred to as Criterion 3).

(38) Dopants may be used in the silica matrix, such as, for example, Bore Dioxide and/or Fluorine, to decrease the refractive index with respect to the refractive index (n.sub.co) of the core's center part so as to obtain the inner depressed core with the desired index difference n0. This portion of the core is said down-doped with respect to the core's center part.

(39) Alternatively, the concentration of refractive index increasing dopants, such as, for example Germanium oxide and/or Phosphorus oxide, is less in the inner depressed core having an index difference n0 than in the core center part having an index difference n1 from R0 to R1.

(40) FIG. 3 illustrates a graphic showing the impact of the transition slope S of the trapezoid index profile on the n.sub.eff min of the FMF. This graphic exhibits the relationship between the slope S of the trapezoid index profile (y-axis) as a function of the surface integral ratio A.sub.0/A.sub.trap (x-axis) (x=0 representing the first exemplary embodiment and x>0 representing the second exemplary embodiment). The curves 10, 20 and 30 represent the curves obtained by numerical simulation with fiber parameters that give, respectively, the following minimal inter-mode effective index differences: n.sub.eff min0.910.sup.3 (continuous line), n.sub.eff min1.310.sup.3 (broken line) and n.sub.eff min1.510.sup.3 (dotted line). The black dots, black circles and black stars on the graphic are examples from Table 1 discussed below meeting respectively the following conditions: n.sub.eff min0.910.sup.3, n.sub.eff min1.310.sup.3 and n.sub.eff min1.510.sup.3.

(41) Table 1 gives the parameters of index profiles of twelve examples of FMFs according to the exemplary embodiments of FIGS. 1 (Ex.1) and 2 (Ex.2 to Ex.12) according to the invention. The profile parameters were established at a wavelength of 633 nm.

(42) TABLE-US-00001 TABLE 1 R0 R1 R2 R3 n0 n1 n2 Acore S Examples (m) (m) (m) (m) (103) (103) (13) (103 m) A0/Atrap (103/m) r nd Ex. 1 5.54 8.54 19.75 13.5 0 190 0.000 4.5 0.65 1.4573 Ex. 2 1.05 4.93 9.30 19.75 14.7 16.7 0.2 234 0.017 3.9 0.53 1.4573 Ex. 3 1.55 5.51 9.30 19.75 14.2 16.2 0.2 250 0.023 5.9 0.70 1.4573 Ex. 4 4.55 5.46 10.30 19.75 14.2 16.2 0.2 237 0.071 3.4 0.53 1.4573 Ex. 5 1.55 4.93 9.30 19.75 14.7 16.7 0.2 232 0.025 3.9 0.53 1.4573 Ex. 6 3.55 5.19 9.80 19.75 14.7 16.7 0.2 236 0.056 3.7 0.53 1.4573 Ex. 7 3.55 5.46 10.30 19.75 14.2 16.2 0.2 241 0.055 3.4 0.53 1.4573 Ex. 8 2.05 6.51 9.30 19.75 14.7 16.7 0.2 256 0.030 6.1 0.70 1.4573 Ex. 9 3.05 6.86 9.80 19.75 14.2 16.2 0.2 258 0.044 5.6 0.70 1.4573 Ex. 10 1.40 6.99 9.57 19.75 10.7 15.7 0.2 249 0.053 6.1 0.73 1.4573 Ex. 11 3.57 5.94 10.62 19.75 12.7 15.7 0.2 241 0.081 3.4 0.56 1.4573 Ex. 12 3.55 5.45 10.30 19.75 14.2 16.2 0.2 241 0.055 3.4 0.53 1.4411

(43) It should be noted that only the 1.sup.st example (Ex.1) illustrates the example of FIG. 1 (i.e. the depressless weakly-coupled FMF), whereas the eleven other examples (Ex.2 to Ex.12) illustrates the example of FIG. 2 (i.e. the inner-depressed core weakly-coupled FMF). The 12.sup.th example (Ex.12) illustrates a trapezoidal profile identical to that of the 7.sup.th example (Ex.7) but with a refractive index n.sub.d of 1.4411 and an index-refractive difference n1 close to that of Silica. The results obtained with these profile parameters are set later in Table 2.

(44) As discussed above in relation with background of the invention, DMA impacts mode-dependence losses with highest optical losses for the higher order modes. One origin of the high DMA can be due to the coupling of the highest order modes with cladding or leaky-modes when the effective indexes of the higher order modes are too close to the refractive index of the cladding. But when effective index difference between the higher order mode and the cladding modes is sufficiently high (preferably larger than 0.810.sup.3), the inventors attribute the origin of the unexpected extra losses occurring for the highest order modes to small angle light scattering (SALS) contributions. For each LP mode guided in the FMF at a wavelength of 1550 nm, more than 70% of losses are due to the Rayleigh scattering. The remaining losses cover, on the one hand, losses induced by absorption mechanisms (together losses by OH-peak, Infrared and Ultraviolet losses) and, on the other hand, losses induced by SALS. DMA is considered as being the difference in term of losses (comprising Rayleigh losses, losses by absorption and SALS losses) between the LP mode having the highest losses and the LP mode having the lowest losses.

(45) One of the purposes of the invention is to reduce as greatest as possible the SALS component of the DMA in order to enhance the capacity of transmission of spatially-multiplexed optical signals on FMFs.

(46) A parameter to evaluate the SALS component of the loss of each mode guided in the FMF has been established as follow (expressed in dB/km):

(47) $C_{\mathrm{el}}\left(\mathrm{mode}i\right)=8\left(\frac{A_{\mathrm{core}}}{}\right){10}^3{C}_0\left(\mathrm{mode}i\right)$$\mathrm{with}$$C_0\left(\mathrm{mode}i\right)=\frac{{\left({n\left(r\right)}^2-{n\left(r+\mathrm{dr}\right)}^2\right)}^2}{{n\left(r+\mathrm{dr}\right)}^4}{E_i\left(r,\right)}^2\mathrm{rdrd}$
r being the radial distance from the center of the optical and the azimuthal component in polar coordinates and E.sub.i(r, ) the mode field amplitude distribution at radius r and angle of mode i

(48) Designing such a trapezoid refractive-index profile with unexpected extra losses such as C.sub.el (mode i)0.05 dB/km or even more such C.sub.el(mode i)0.015 dB/km allows to meet the specific needs for both reduced loss and weak-coupled FMFs (as shown in Table 2 below).

(49) Moreover, in order to limit intra-mode non-linearity (and thus keep good optical guiding properties within the FMF), refractive index profile of the FMF is designed so that effective area A.sub.eff of each guided mode is larger than 80 m.sup.2.

(50) Table 2 gives the characteristics n.sub.eff min, DMA and, for each LP mode guided by the fiber, the unexpected extra loss coefficient C.sub.el, the total loss TL resulting from absorption and diffusion loss mechanisms, the maximum bend loss BL (for a radius of 10 mm) and the effective area A.sub.eff, with the index profiles of the twelve examples of FMFs of Table 1.

(51) As used herein, the effective area of an optical fiber is the area of the optical fiber in which light is propagated and is determined at the specified mode, at a wavelength of 1550 nm, unless otherwise specified. The effective area A.sub.eff.sub.v of mode LP.sub.v is defined as follows:

(52) If 0:

(53) $A_{{\mathrm{eff}}_v}=\frac{4}{3}\frac{{\left({}_0^{}{.Math.{}_v.Math.}^2\mathrm{rdr}\right)}^2}{{}_0^{}{.Math.{}_v.Math.}^4\mathrm{rdr}}$
where .sub.v is the mode field amplitude distribution of the mode LP.sub.v at the radius r, i.e. at the polar distance r in the polar coordinates of a point in a system of axes transverse to and centered relative to the fiber; and

(54) if =0:

(55) 0$A_{{\mathrm{eff}}_{0v}}=2\frac{{\left({}_0^{}{.Math.{}_{0v}.Math.}^2\mathrm{rdr}\right)}^2}{{}_0^{}{.Math.{}_{0v}.Math.}^4\mathrm{rdr}}$

(56) Table 2 also provides assessment of the bending losses per turn of 10 mm bending radius for each LP modes. The bending loss data illustrated in Table 2 are collected according to measurements complying with the requirements of the IEC 60793-1-47 (ed.2.0), which is herein incorporated by reference. To properly characterize macrobending losses of the LP.sub.01 mode, a two-meter portion of SMF can be spliced on the injection side of FMF under test to filter out the high order modes. For the high order modes, it is necessary to use mode converters at the input and the output of the FMF to correctly evaluate power in the desired modes. While characterization of FMFs is not standardized yet, loss of LP.sub.01 mode can be measured according to IEC 60793-1-40 (ed1.0) standard (method A), which is herein incorporated by reference. However, in order to properly characterize the losses of the fundamental mode, a two-meter portion of SMF can be spliced on the injection side of FMF under test to filter out the high order modes. For the high order modes, it is necessary to use mode converters at the input and the output of the FMF to correctly evaluate power in the desired modes.

(57) TABLE-US-00002 TABLE 2 n.sub.eff min DMA n.sub.eff A.sub.eff C.sub.el TL BL Examples (10.sup.3) (dB/km) LP modes (10.sup.3) (m) (dB/km) (dB/km) (dB/turn) Ex. 1 1.0 0.015 LP01 11.2 101 0.000 0.229 <0.001 LP11 8.4 97 0.001 0.228 <0.001 LP21 5.0 110 0.001 0.226 <0.001 LP02 4.0 105 0.001 0.226 <0.001 LP31 1.0 133 0.002 0.214 <50 Ex. 2 1.2 0.010 LP01 14.0 97 0.002 0.245 <0.001 LP11 11.1 91 0.003 0.245 <0.001 LP21 7.4 103 0.004 0.243 <0.001 LP02 6.2 101 0.006 0.243 <0.001 LP31 3.1 118 0.006 0.239 <0.001 LP12 1.8 136 0.005 0.235 <10 Ex. 3 1.3 0.002 LP01 13.9 128 0.002 0.242 <0.001 LP11 11.7 111 0.003 0.244 <0.001 LP21 8.7 119 0.005 0.245 <0.001 LP02 7.4 109 0.007 0.243 <0.001 LP31 5.1 125 0.008 0.245 <0.001 LP12 3.4 119 0.009 0.244 <0.01 LP41 1.1 137 0.010 0.242 <1 Ex. 4 1.3 0.012 LP01 12.7 136 0.003 0.237 <0.001 LP11 10.6 114 0.005 0.241 <0.001 LP21 7.8 121 0.006 0.241 <0.001 LP02 6.5 99 0.004 0.235 <0.001 LP31 4.3 132 0.007 0.238 <0.001 LP12 2.3 139 0.005 0.229 <10 Ex. 5 1.4 0.011 LP01 13.8 100 0.003 0.244 <0.001 LP11 11.1 91 0.003 0.245 <0.001 LP21 7.4 103 0.004 0.243 <0.001 LP02 6.0 102 0.006 0.241 <0.001 LP31 3.1 118 0.006 0.238 <0.001 LP12 1.7 139 0.005 0.234 <10 Ex. 6 1.6 0.014 LP01 13.3 123 0.003 0.241 <0.001 LP11 11.1 101 0.005 0.245 <0.001 LP21 7.9 110 0.006 0.244 <0.001 LP02 6.3 93 0.004 0.237 <0.001 LP31 4.0 123 0.006 0.240 <0.001 LP12 2.0 142 0.006 0.231 <10 Ex. 7 1.6 0.012 LP01 13.0 135 0.003 0.239 <0.001 LP11 11.0 109 0.004 0.243 <0.001 LP21 8.1 119 0.005 0.242 <0.001 LP02 6.5 100 0.004 0.235 <0.001 LP31 4.5 131 0.006 0.239 <0.001 LP12 2.5 145 0.006 0.231 <1 Ex. 8 1.5 0.004 LP01 14.2 132 0.003 0.244 <0.001 LP11 12.1 110 0.004 0.247 <0.001 LP21 9.2 118 0.006 0.248 <0.001 LP02 7.7 107 0.008 0.244 <0.001 LP31 5.6 123 0.008 0.248 <0.001 LP12 3.6 118 0.010 0.247 <0.001 LP41 1.5 134 0.011 0.246 <1 Ex. 9 1.6 0.006 LP01 13.6 156 0.003 0.241 <0.001 LP11 11.9 122 0.004 0.244 <0.001 LP21 9.2 128 0.005 0.245 <0.001 LP02 7.6 107 0.007 0.239 <0.001 LP31 6.0 133 0.007 0.245 <0.001 LP12 3.9 128 0.010 0.242 <0.001 LP41 2.2 142 0.010 0.244 <0.1 Ex. 10 1.6 0.003 LP01 13.4 149 0.006 0.243 <0.001 LP11 11.5 121 0.004 0.242 <0.001 LP21 8.8 129 0.005 0.242 <0.001 LP02 7.2 126 0.015 0.244 <0.001 LP31 5.5 133 0.007 0.243 <0.001 LP12 3.8 123 0.011 0.245 <0.01 LP41 1.8 142 0.010 0.242 <10 Ex. 11 1.3 0.074 LP01 12.4 163 0.006 0.238 <0.001 LP11 10.8 120 0.006 0.242 <0.001 LP21 8.2 127 0.006 0.241 <0.001 LP02 6.2 103 0.005 0.229 <0.001 LP31 4.9 138 0.006 0.238 <0.001 LP12 2.6 154 0.008 0.229 <10 LP41 1.2 156 0.007 0.233 <10 Ex. 12 1.6 0.005 LP01 13.0 135 0.003 0.168 <0.001 LP11 11.0 109 0.004 0.168 <0.001 LP21 8.1 119 0.005 0.169 <0.001 LP02 6.5 100 0.004 0.170 <0.001 LP31 4.5 131 0.006 0.171 <0.001 LP12 2.5 145 0.006 0.173 <1

(58) As is demonstrated here, thanks to profile parameters chosen according to our invention (gathered in Table 1), each FMF tested is able to guide at least five LP modes, with n.sub.eff min0.910.sup.3, C.sub.el0.015 dB/km and DMA0.02 dB/km.

(59) All examples in Tables 1 and 2 fulfill the structural requirements of: the surface integral A.sub.core is between 18010.sup.3 and 27010.sup.3 m; the radius R2 is between 6.8 and 11.5 m; the refractive-index difference n1 is between 1310.sup.3 and 1810.sup.3; the transition slope S is between 1.710.sup.3 and 1210.sup.3 m.sup.1.

(60) In a further preferred embodiment, the value of radius R3 of the intermediate portion of the cladding is such that R31.8R2.

(61) According to a particular feature, the refractive index of the outer cladding (n.sub.Cl) is chosen to be close to the refractive index of silica. In another exemplary embodiment, refractive index of the outer cladding (n.sub.Cl) can be chosen between 1.437 and 1.458, or, alternatively, the refractive index of the optical core is chosen to be close to the index of silica to reduce the total losses of the FMF. So that, cladding refractive index (n.sub.Cl) can be down-doped up to 2010.sup.3 with respect to Silica refractive index in order to provide ultra-low loss FMFs by reducing their Rayleigh contribution (thanks to a low-Ge or pure Silica core structure).

(62) We now refer to Table 3 that gives the parameters of index profiles of six comparative examples (Comp.Ex.1 to Comp.Ex.6) of optical fibers out of the scope of the present invention, i.e. which do not satisfy the criteria of the present invention.

(63) TABLE-US-00003 TABLE 3 R1 R2 R3 n0 n1 n2 A.sub.core S Examples (m) (m) (m) (10.sup.3) (10.sup.3) (10.sup.3) (10.sup.3 m) A.sub.0/A.sub.trap (10.sup.3/m) r Comp. Ex. 1 5.06 11.50 19.75 15.7 0.2 263 0.000 2.5 0.44 Comp. Ex. 2 7.29 8.28 19.75 16.7 0.2 262 0.000 17.0 0.88 Comp. Ex. 3 8.28 8.28 19.75 15.7 0.2 263 0.000 1.00 Comp. Ex. 4 8.01 8.01 19.75 14.7 16.7 0.2 260 0.041 1.00 Comp. Ex. 5 2.51 11.64 19.75 11.5 13.5 0.2 190 0.020 1.5 0.22 Comp. Ex. 6 5.73 10.82 19.75 10.7 15.7 0.2 228 0.131 3.1 0.53

(64) As for Table 2, Table 4 gives the characteristics n.sub.eff min, DMA and, for each LP mode guided by the fiber, the unexpected extra loss coefficient C.sub.el, the total loss TL resulting from absorption and diffusion loss mechanisms, the maximum bend loss BL (for a radius of 10 mm) and the effective area .sub.eff, with the index profiles of the six examples of optical fibers of above Table 3.

(65) TABLE-US-00004 TABLE 4 n.sub.eff .sub.min DMA n.sub.eff A.sub.eff C.sub.el TL BL Examples (10.sup.3) (dB/km) LP modes (10.sup.3) (m) (dB/km) (dB/km) (dB/turn) Comp. 0.8 0.008 LP01 13.4 112 0.001 0.240 <0.001 Ex. 1 LP11 11.0 112 0.002 0.239 <0.001 LP21 7.9 129 0.004 0.238 <0.001 LP02 7.2 123 0.004 0.239 <0.001 LP31 4.5 146 0.005 0.233 <0.001 LP12 3.4 153 0.004 0.232 <0.1 Comp. 1.0 0.015 LP01 14.5 120 0.003 0.246 <0.001 Ex. 2 LP11 12.2 111 0.007 0.250 <0.001 LP21 9.2 116 0.012 0.254 <0.001 LP02 8.2 100 0.013 0.256 <0.001 LP31 5.6 119 0.017 0.259 <0.001 LP12 3.7 107 0.019 0.259 <0.01 LP41 1.5 126 0.023 0.262 <10 Comp. 1.0 0.069 LP01 14.6 125 0.009 0.253 <0.001 Ex. 3 LP11 12.4 115 0.023 0.266 <0.001 LP21 9.5 120 0.040 0.283 <0.001 LP02 8.6 103 0.045 0.288 <0.001 LP31 6.0 123 0.059 0.302 <0.001 LP12 4.2 109 0.066 0.309 <0.01 LP41 2.0 129 0.080 0.321 <10 Comp. 1.7 0.076 LP01 14.2 149 0.015 0.256 <0.001 Ex. 4 LP11 12.3 117 0.028 0.271 <0.001 LP21 9.6 121 0.046 0.289 <0.001 LP02 7.9 101 0.054 0.289 <0.001 LP31 6.1 123 0.068 0.310 <0.001 LP12 3.9 115 0.080 0.317 <0.001 LP41 2.2 129 0.092 0.331 <0.01 Comp. 0.4 0.013 LP01 10.3 86 0.002 0.228 <0.001 Ex. 5 LP11 7.1 99 0.002 0.223 <0.001 LP21 3.6 137 0.002 0.215 <0.01 LP02 3.3 171 0.002 0.216 <1 Comp. 0.5 0.022 LP01 11.9 174 0.012 0.244 <0.001 Ex. 6 LP11 10.5 119 0.010 0.246 <0.001 LP21 8.0 127 0.008 0.243 <0.001 LP02 5.2 113 0.008 0.223 <0.001 LP31 4.8 139 0.007 0.238 <0.001 LP12 2.2 175 0.012 0.228 <50 LP41 1.1 160 0.006 0.231 <10

(66) Comp.Ex.1 is an example of optical fiber having a trapezoid shape core profile (A.sub.0/A.sub.trap=0) characterized by a slop S that does not satisfy the Criterion 1. As a consequence, n.sub.eff min in between LP21 and LP02 modes is too small.

(67) Comp.Ex.2 is an example of optical fiber having a trapezoid shape core profile with depressed center characterized by a slope S that is too large. As a consequence, the core-cladding transition is too sharp for the highest order modes and unexpected extra loss coefficient C.sub.el of LP12 and LP41 is not desirable (C.sub.el>0.015 dB/km).

(68) Comp.Ex.3 is an example of optical fiber having a step index profile. The unexpected extra loss coefficient C.sub.el for the modes LP21, LP02, LP31, LP12 & LP41 is not desirable since upper than 0.02 dB/km. Consequently, DMA is too high (DMA>0.05 dB/km) to meet the fiber communication capacity demands.

(69) Comp.Ex.4 is an example of optical fiber having a step index profile with depressed center part allowing to get an improved and sufficiently high minimal inter-mode effective index difference compared to Com. Ex.3 (n.sub.eff min>1.510.sup.3) but too much high unexpected extra losses (C.sub.el>0.02 dB/km). Consequently, DMA is too high (DMA>0.05 dB/km) to meet the fiber communication capacity demands.

(70) Comp.Ex.5 is an example of optical fiber having a trapezoid core shape profile with depressed center characterized by a slope S that is too small and does not satisfy the Criterion 1. As a consequence, only four LP modes are guided and n.sub.eff min in between LP21 and LP02 modes is too small.

(71) Comp.Ex.6 is an example of optical fiber having a trapezoid core shape profile with depressed center characterized by a slop Se that does not satisfy the Criterion 1 and a ratio A.sub.0/A.sub.trap upper than 0.1. As a consequence, n.sub.eff min in between LP02 and LP31 modes is too small.