Multimode Optical Fiber with High Bandwidth, and Corresponding Multimode Optical System

Abstract

The invention concerns a multimode optical fiber, with an ct-profile graded-index core with an a-value between 1.96 and 2.05 and a N value defined as N=(R.sub.1/λ).sup.2(n.sub.1.sup.2−n.sub.0.sup.2) between 7 and 52, where R.sub.1 is the multimode core radius, n.sub.1 is the maximum index of the multimode core and n.sub.0 is the minimum index at the outer edge of the graded index core. According to the invention, a depressed region directly surrounds the graded/index core and satisfies the criteria: −2.20<Dn.sub.2<0, where Dn.sub.2 is the index difference of depressed region with external cladding, and 220 Ln(N)−1100<V.sub.2<220Ln(N)−865, where V.sub.2 is the volume of the depressed region. Such a multimode fiber shows an increased OFL-bandwidth above 10000 Hz.Math.km at an operating wavelength between 950 nm and 1310 nm.

Claims

1. A multimode optical fiber, comprising a central core surrounded by an outer optical cladding, said central core having (i) an outer radius R.sub.1, (ii) a maximum refractive index n.sub.1, (iii) a minimum refractive index n.sub.0, and (iv) a graded-index profile n(r) that is a function of the radial distance r from the center of said central core, said central core's graded-index profile n(r) is defined by the following equation: $n\left(r\right)=n_1.Math.\sqrt{1-2.Math.{\Delta \left(\frac{r}{R_1}\right)}^{\alpha }}$ where: $\Delta =\frac{\left(n_1^2-n_0^2\right)}{2.Math.n_1^2}$ and α is between 1.96 and 2.05, with α a non-dimensional parameter that is indicative of the shape of the index profile, with n.sub.0 and n.sub.1 at an operating wavelength λ, said central core has an N value between 7 and 52, where N is defined by the following equation: $N={\left(\frac{R_1}{\lambda }\right)}^2.Math.\left(n_1^2-n_0^2\right)$ with λ the operating wavelength such that λ≧950 nm, wherein said optical cladding comprises a trench, a region of depressed refractive index n.sub.2, surrounding said central core, said trench having an inner radius R.sub.1, an outer radius R.sub.2, with R.sub.2>R.sub.1, a refractive index difference Dn.sub.2=(n.sub.2−n.sub.Cl)×1000 with respect to said optical cladding having at its outer edge a refractive index n.sub.Cl, with n.sub.2 and n.sub.Cl at the operating wavelength λ, and a volume V.sub.2=π(R.sub.2.sup.2−R.sub.1.sup.2)×Dn.sub.2, where Dn.sub.2 is expressed in 10.sup.−3 and V.sub.trench is expressed in 10.sup.−3 μm.sup.2, and wherein said trench satisfies the criteria:
−2.20<Dn.sub.2<0.0
and
220×Ln(N)−1100<V.sub.2<220×Ln(N)−865.

2. The multimode optical fiber according to claim 1, wherein said central core has a numerical aperture NA=√{square root over ((n.sub.1.sup.2−n.sub.0.sup.2))} between 0.185 and 0.215 at 633 nm.

3. The multimode optical fiber according to claim 1, wherein said core outer radius R.sub.1 is between 15 and 40 μm.

4. The multimode optical fiber according to claim 1, wherein said operating wavelength λ is between 950 nm and 1310 nm.

5. The multimode optical fiber according to claim 4, wherein said operating wavelength λ is around 1060 nm.

6. The multimode optical fiber according to claim 1, wherein, for at least one operating wavelength between 950 nm and 1310 nm, said multimode optical fiber has an overfilled launch bandwidth (OFL-BW) greater than 10000 MHz.Math.km.

7. A multimode optical system comprising at least a portion of a multimode optical fiber according to claim 1.

8. The multimode optical fiber according to claim 1, wherein said central core has an N value between 7 and 13.

9. The multimode optical fiber according to claim 1, wherein said central core has an N value between 13 and 26.

10. The multimode optical fiber according to claim 1, wherein said central core has an N value between 26 and 52.

11. The multimode optical fiber according to claim 1, wherein said core outer radius R.sub.1 is between 15 and 27 μm.

12. The multimode optical fiber according to claim 1, wherein said core outer radius R.sub.1 is between 23 and 40 μm.

13. The multimode optical fiber according to claim 1, wherein said core outer radius R.sub.1 is between 23 and 27 μm.

14. The multimode optical fiber according to claim 1, wherein, at an operating wavelength of 1060 nm, said multimode optical fiber has an overfilled launch bandwidth (OFL-BW) greater than 10000 MHz.Math.km

15. A multimode optical fiber, comprising a central core surrounded by an outer optical cladding, said central core having (i) an outer radius R.sub.1 between 23 and 27 μm, (ii) a maximum refractive index n.sub.1, (iii) a minimum refractive index n.sub.0, and (iv) a graded-index profile n(r) that is a function of the radial distance r from the center of said central core, said central core's graded-index profile n(r) is defined by the following equation: $n\left(r\right)=n_1.Math.\sqrt{1-2.Math.{\Delta \left(\frac{r}{R_1}\right)}^{\alpha }}$ where: $\Delta =\frac{\left(n_1^2-n_0^2\right)}{2.Math.n_1^2}$ and α is between 1.96 and 2.05, with a a non-dimensional parameter that is indicative of the shape of the index profile, said central core has an N value between 13 and 26, where N is defined by the following equation: $N={\left(\frac{R_1}{\lambda }\right)}^2.Math.\left(n_1^2-n_0^2\right)$ with λ the operating wavelength between 950 nm and 1310 nm, wherein said optical cladding comprises a trench, a region of depressed refractive index n.sub.2, surrounding said central core, said trench having an inner radius R.sub.1, an outer radius R.sub.2, with R.sub.2>R.sub.1, a refractive index difference Dn.sub.2=(n.sub.2−n.sub.Cl)×1000 with respect to said optical cladding having at its outer edge a refractive index n.sub.Cl, with n.sub.2 and n.sub.Cl at the operating wavelength λ, and a volume V.sub.2=π(R.sub.2.sup.2−R.sub.1.sup.2)×Dn.sub.2, where Dn.sub.2 is expressed in 10.sup.−3 and V.sub.trench is expressed in 10.sup.−3 μm.sup.2, wherein said trench satisfies the criteria:
−2.20<Dn.sub.2<0.0
and
220×Ln(N)−1100<V.sub.2<220×Ln(N)−865, and wherein, for at least one operating wavelength between 950 nm and 1310 nm, said multimode optical fiber has an overfilled launch bandwidth (OFL-BW) greater than 10000 MHz.Math.km.

16. The multimode optical fiber according to claim 15, wherein said central core has a numerical aperture NA=√{square root over ((n.sub.1.sup.2−n.sub.0.sup.2))} between 0.185 and 0.215 at 633 nm.

17. The multimode optical fiber according to claim 15, wherein, at an operating wavelength of 1060 nm, said multimode optical fiber has an overfilled launch bandwidth (OFL-BW) greater than 10000 MHz.Math.km.

Description

4. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The invention can be better understood with reference to the following description and drawings, given by way of example and not limiting the scope of protection, and in which:

[0051] FIG. 1 shows a refractive index profile for an example of an optical fiber according to an embodiment of the invention;

[0052] FIG. 2 shows the range of the volume of the trench V.sub.trench for an optical fiber according to embodiments of the invention, as a function of N, to get an OFL-BW over 10000 MHz.Math.km;

[0053] FIG. 3 illustrates the median value of the time delay per mode group for several MMF, one of which complies with the requirements of the invention, while the others don't.

[0054] The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

5. DETAILED DESCRIPTION

[0055] Throughout this document, the terms operating wavelength designate the wavelength delivered by the light source of the VCSEL used (VCSELs with light transmitted at 25 Gb/s or higher at one or more wavelength(s) between 950 and 1310 nm).

[0056] Moreover, it is recalled that the Overfilled Launch Bandwidth OFL-BW is the originally standardized fiber bandwidth measurement method where the source launches light uniformly into all modes of the multimode fiber. By launching in all the mode groups uniformly, this measurement is sensitive to the core/cladding interface of the fiber and allows differentiating optimized core/cladding interface from non-optimized ones.

[0057] The multimode fiber according to an embodiment of the invention comprises a central core surrounded by an outer optical cladding. The central core has (i) an outer radius R.sub.1, (ii) a maximum refractive index n.sub.1, (iii) a minimum refractive index n.sub.0, and (iv) a graded-index profile n(r) that is a function of the radial distance r from the center of said central core. The minimum refractive index n.sub.0 of the central core also generally corresponds to the index of the cladding (most frequently in silica).

[0058] The core and the cladding form the glass portion of the optical fiber. In some embodiments, the cladding is coated with one or more coatings, for example with an acrylate polymer.

[0059] FIG. 1 shows a refractive index profile shape of a multimode fiber according to an embodiment of the invention, expressed as the refractive index difference Dn as a function of the radius. As may be observed, the center core of outer radius R.sub.1 shows a graded-index profile n(r) is defined by the following equation:

[00006]$n\left(r\right)=n_1.Math.\sqrt{1-2.Math.{\Delta \left(\frac{r}{R_1}\right)}^{\alpha .Math.}}$

where

[00007]$\Delta =\frac{\left(n_1^2-n_0^2\right)}{2.Math.n_1^2}$

and α is between 1.96 and 2.05.

[0060] The core is surrounded by an optical cladding, which comprises an inner layer of depressed refractive index directly surrounding the core. Such a trench is of inner radius R.sub.1 and outer radius R.sub.2, and shows a refractive index difference Dn.sub.2.

[0061] Embodiments of the invention allow designing MMFs operating at longer wavelength than 850 nm, preferentially between 950 and 1310 nm, and preferentially around 1060 nm. In order to optimize the bandwidth of the MMF, the volume V.sub.trench (also called V.sub.2 in the present document) and the refractive index difference Dn.sub.2 of the trench located at the corecladding interface are designed according to a criterion N=

[00008]${\left(\frac{R_1}{\lambda }\right)}^2.Math.\left(n_1^2-n_0^2\right)$

proportional to the number of modes guided by the MMF at the operating wavelength λ.

[0062] The volume of the trench V.sub.trench may be expressed as V.sub.2=π(R.sub.2.sup.2−R.sub.1.sup.2)×Dn.sub.2 (in 10.sup.−3 μm.sup.2), with Dn.sub.2=(n.sub.2−n.sub.Cl)×1000 (in 10.sup.−3) and n.sub.2 the minimum refractive index of the trench at the operating wavelength.

[0063] For alpha between 1.96 and 2.05, R.sub.1 between 15 and 40 μm, NA=√{square root over ((n.sub.1.sup.2−n.sub.0.sup.2))} between 0.185 and 0.215 at 633 nm and λ≧950 nm, [0064] Dn.sub.2 must satisfy: −2.2<Dn.sub.2<0.0 and [0065] V.sub.trench must satisfy: 220×Ln(N)−1100<V.sub.trench<220×Ln(N)−865 to have fibers with OFL-BW>10000 MHz.Math.km.

[0066] Table 1 below discloses some examples (Ex. 1 to Ex. 17) of multimode optical fibers according to embodiments of the invention, showing a profile shape according to FIG. 1.

TABLE-US-00001 TABLE 1 operating wavelength NA R1 R2 Dn2 Vtrench OFL-BW Exemple (μm) Alpha (@633 nm) (μm) (μm) (10 − 3) (10.sup.−3 μm.sup.2) n1 nref N (MHz .Math. km) Ex. 1 1060 2.02 0.193 23 25.35 −0.84 −300 1.4623 1.4499 17 19489 Ex. 2 1060 2.02 0.185 23 25.50 −1.03 −391 1.4613 1.4499 16 16251 Ex. 3 1060 2.02 0.205 23 25.00 −1.00 −295 1.4638 1.4499 19 10249 Ex. 4 1060 2.02 0.193 25 27.40 −0.71 −281 1.4623 1.4499 20 18150 Ex. 5 1060 2.02 0.185 25 27.11 −0.98 −339 1.4613 1.4499 18 18423 Ex. 6 950 2.04 0.193 25 26.92 −0.71 −223 1.4637 1.4513 25 18495 Ex. 7 1310 1.98 0.193 25 28.38 −0.88 −500 1.4594 1.4471 13 12991 Ex. 8 1060 2.02 0.205 27 29.50 −0.76 −337 1.4638 1.4499 26 10993 Ex. 9 1060 2.02 0.193 27 28.64 −0.74 −211 1.4623 1.4499 23 17388 Ex. 10 1060 2.02 0.185 27 29.11 −0.85 −316 1.4613 1.4499 21 18389 Ex. 11 1060 2.02 0.2 32 34.50 −0.53 −275 1.4632 1.4499 35 11847 Ex. 12 1060 2.02 0.185 32 33.09 −0.86 −193 1.4613 1.4499 30 19929 Ex. 13 1060 2.02 0.185 35 35.66 −1.08 −158 1.4613 1.4499 36 17697 Ex. 14 1060 2.02 0.2 38 40.32 −0.19 −107 1.4632 1.4499 50 12374 Ex. 15 1060 2.02 0.185 38 40.49 −0.15 −93 1.4613 1.4499 42 22264 Ex. 16 1060 2.02 0.215 15 17.96 −1.42 −435 1.4652 1.4499 9 11568 Ex. 17 1060 2.02 0.185 15 19.00 −1.42 −606 1.4613 1.4499 7 12723

[0067] Examples Ex.1, Ex.2 and Ex.3 of Table 1 describe three MMFs optimized to have a maximum bandwidth around an operating wavelength λ=1060 nm with core radius of R.sub.1=23 μm and a numerical aperture NA varying from 0.185 (example Ex. 2) to 0.205 (example Ex. 3). Criterion N, which is proportional to the number of modes supported by the MMF, is varying from 16 (example Ex. 2) to 19 (example Ex. 3). The trench index difference (Dn.sub.2) and the trench volume V.sub.trench have been chosen to limit the effect of the cladding (i.e. to limit the increase of the group velocity of the last mode groups) to get an OFL-BW larger than 10000 MHz.Math.km. The overfilled launch bandwidth OFL-BW thus reaches 19489 MHz.Math.km for the MMF of example Ex. 1, 16251 MHz.Math.km for example Ex. 2 and 10249 MHz.Math.km for example Ex. 3.

[0068] Examples Ex.4 to Ex.17 of Table 1 disclose other examples of multimode fibers according to embodiments of the invention with core radii R.sub.1 ranging from 15 to 38 μm, numerical aperture NA ranging from 0.185 to 0.215 and operating wavelength λ ranging from 950 nm (example Ex. 6) to 1310 nm (example Ex. 7). It may be noticed that the smaller the criterion N is, the more sensitive to variations of N the trench volume at the core/cladding interface is.

[0069] When the core radius R.sub.1 is strongly reduced to 15 μm (see examples Ex. 16 and Ex. 17), the number of modes supported by the fiber is reduced, especially when the operating wavelength is shifted to 950 nm and higher. In such conditions, the criterion N is below 10 and the impact of core/cladding geometry on the total bandwidth is increased. Ex.16 & Ex.17 depict some MMFs with core radii equal to 15 μm, with V.sub.trench=−435×10.sup.−3 μm.sup.2 and V.sub.trench==606×10.sup.−3 μm.sup.2 respectively but exhibiting an OFL-BW larger than 10000 MHz.Math.km. Actually the multimode optical fiber of example Ex. 16 shows an overfilled launch bandwidth OFL-BW=11568 MHz.Math.km, and the multimode optical fiber of example Ex. 17 shows an overfilled launch bandwidth OFL-BW=12723 MHz.Math.km.

[0070] Table 2 below presents some comparative examples, which, on the contrary to the examples in Table 1 above, are all out of the scope of the present invention.

TABLE-US-00002 TABLE 2 operating wavelength NA R1 R2 Dn2 Vtrench OFL-BW Exemple (μm) Alpha (@633 nm) (μm) (μm) (10 − 3) (10.sup.−3 μm.sup.2) n1 nref N (MHz .Math. km) Ex. 1c 1060 2.02 0.205 23 23.75 −0.98 −108 1.4638 1.4499 19 7863 Ex. 2c 1060 2.02 0.205 23 24.00 −2.94 −434 1.4638 1.4499 19 2325 Ex. 3c 1060 2.02 0.205 23 24.75 −2.94 −772 1.4638 1.4499 19 1786 Ex. 4c 1060 2.02 0.205 25 26.90 −1.47 −455 1.4638 1.4499 23 5416 Ex. 5c 1060 2.02 0.215 32 33.30 −1.47 −392 1.4652 1.4499 41 5187 Ex. 6c 1060 2.02 0.215 32 32.80 0.49 80 1.4652 1.4499 41 6548 Ex. 7c 1060 2.02 0.212 15 18.90 −1.96 −814 1.4648 1.4499 9 3227 Ex. 8c 1060 2.02 0.212 15 16.50 −2.45 −364 1.4648 1.4499 9 3511 Ex. 9c 1060 2.02 0.185 15 19.50 −1.47 −717 1.4613 1.4499 7 7692

[0071] FIG. 2 represents the range of the volume of the trench V.sub.trench for an optical fiber according to embodiments of the invention, expressed in 10.sup.−3 μm.sup.2, as a function of criterion N, to get an OFL-BW over 10000 MHz.Math.km. The dashed lines show the lower and upper limits of the volume of the trench V.sub.trench as a function of N, for multimode optical fibers with alpha between 1.96 and 2.05, core radius R.sub.1 between 15 and 40 μm and numerical aperture NA between 0.185 and 0.215, whatever the operating wavelength λ≧950 nm.

[0072] Moreover, the examples Ex. 1 to Ex. 17 of multimode optical fibers listed in Table 1 have been added in the form of black dots on FIG. 2. As may be observed, all the corresponding black dots are comprised between the lower and upper limits of V.sub.trench, as all the examples of Table 1 fulfill the criterion: 220×Ln(N)−1100<V.sub.trench<220×Ln(N)−865.

[0073] Comparative examples Ex. 1c to Ex. 9c of Table 2 have also been plotted on FIG. 2, as triangles. Most triangles fall out of the range of allowable volumes V.sub.trench, except for comparative examples Ex. 2c and Ex. 8c. However, multimode optical fibers of comparative examples Ex. 2c and Ex. 8c are also out of the scope of embodiments of the invention, as they exhibit a refractive index difference of the trench Dn.sub.2<−2.2×10.sup.−3.

[0074] As may be observed in Table 2, comparative examples Ex.1c, Ex.2c and Ex.3c exhibit the same numerical aperture NA=0.205, the same alpha α=2.02 and the same core radius R.sub.1=23 μm (and thus the same value of criterion N=19) as example Ex.3 of Table 1. However, the three multimode optical fibers of examples Ex.1c, Ex.2c and Ex.3c all have lower bandwidth performances than example Ex. 3.

[0075] It is recalled that low order mode groups travel near the center of the core, while higher order mode groups travel closer to the core-cladding interface. In order to reduce the modal dispersion DMD, and thus increase the bandwidth of the optical fiber, the difference in time delays of the mode groups travelling through the fiber must be as small as possible. Carefully designing the volume of the trench, according to embodiments of the invention, allows modifying the time delays of the mode groups near the core-cladding interface.

[0076] Trench dimensions of example Ex. 3 (i.e. trench volume and trench index) have been chosen to minimize the effect of the core/cladding interface. As may be observed on FIG. 3, which shows the median value of the time delay (expressed in ps/m) per mode group (expressed in mode group number) for example Ex. 3 of Table 1 and comparative examples Ex. 1c, Ex. 2c and Ex. 3c of Table 2, only the last mode group of example Ex. 3 has time delay strongly reduced compared to the other mode groups.

[0077] Comparative example Ex.1c has a smaller trench volume (V.sub.trench=108) than Ex.3 (V.sub.trench=295) (in absolute value). Time delays of the three last (i.e. high order) mode groups (i.e. mode groups n°11, n°12 and n°13) are strongly reduced compared to the lowest order mode groups.

[0078] As a consequence of the small trench volume V.sub.trench of comparative example Ex. 1c, and hence of the strongly reduced time delays of the three last mode groups, the OFL-BW of the multimode optical fiber of comparative example Ex. 1c is below 10000 MHz.Math.km.

[0079] Comparative example Ex.2c has a trench volume (V.sub.trench=−434 (in 10.sup.−3 μm.sup.2)) sufficient to compensate for the core/cladding interface. But the trench index is too low (Dn.sub.2=−2.94) and does not fulfill the criterion set out in embodiments of the invention (−2.2<Dn.sub.2<0.0). Although the time delay difference of the latest mode group (mode group n°13) is strongly reduced, compared to comparative examples Ex.3 and Ex.1c, the last four mode groups (i.e. mode groups n°10, n°11, n°12 and n°13) are all disturbed by the trench. Hence, although the difference in time delays between mode groups is not so high, the great number of mode groups influenced by the trench has a negative impact on the bandwidth, so that the overfilled launch bandwidth OFL-BW is reduced to ˜2300 MHz.Math.km.

[0080] In comparative example Ex.3c, both trench volume and trench depth are too large. Actually, as may be read in Table 2, V.sub.trench=−772 (in 10.sup.−3 μm.sup.2)) and Dn.sub.2=−2.94 (in 10.sup.−3). As a consequence, the last four mode groups (i.e. mode groups n°10, n°11, n°12 and n°13) are too much disturbed by the trench and the OFL-BW is further reduced to ˜1700 MHz.Math.km.

[0081] Comparative examples Ex.4c, Ex.5c and Ex.6c depict some MMFs with core radii equal to 25 μm (Ex. 4c) and 32 μm (Ex. 5c and Ex.6c). As regards comparative examples Ex.4c and Ex.5c, the trench volume is too large according to criterion N: the corresponding triangles plotted on FIG. 2 are below the lower limit set out for V.sub.trench. As regards comparative example Ex. 6c, the trench volume is too small according to criterion N: the corresponding triangle plotted on FIG. 2 is above the upper limit set out for V.sub.trench.

[0082] Comparative examples Ex.7c, Ex.8c & Ex.9c depict some MMFs with core radii equal to 15 μm too. As regards comparative examples Ex.7c and Ex.9c, the trench volume is too large according to criterion N: the corresponding triangles plotted on FIG. 2 are below the lower limit set out for V.sub.trench. As regards comparative example Ex. 8c, although the trench volume satisfies the criterion 220×Ln(N)−1100<V.sub.trench<220×Ln(N)−865, the refractive index difference Dn2 of the trench is too low (Dn.sub.2=−2.45 (in 10.sup.−3))

[0083] The criteria set out in embodiments of the invention allow increasing the OFL-bandwidth of a multimode fiber to above 10000 MHz.Math.km at an operating wavelength between 950 nm and 1310 nm. The relationship 220×Ln(N)−1100<V.sub.trench<220×Ln(N)−865 linking the minimum and maximum acceptable values for the volume of the trench V.sub.trench with the parameter N allows to easily design the optimum trench volume, and define the optimum core/cladding geometry, whatever the core size and the operating wavelength.