Method for characterizing performance of a multimode fiber optical link and corresponding methods for fabricating a multimode optical fiber link showing improved performance and for improving performance of a multimode optical fiber link

Abstract

Disclosed is a method of characterizing a multimode optical fiber link including a light source and two or more multimode fibers. The method includes a step of characterizing each of said multimode fibers using a measurement of the Dispersion Modal Delay (DMD) for each of said multimode fibers, and delivering, for each of said multimode fibers, at least three fiber characteristic curves as a function of a radial offset value r; a step of characterizing the light source by at least three source characteristic curves showing at least three parameters of the source as a function of a fiber radius r and obtained by a technique similar to the DMD measurement; and a step of computing an Effective Bandwidth (EB) of the link, comprising calculating a transfer function using both each of said source characteristic curves and each of said at least three fiber characteristic curves for each of said multimode fibers.

Claims

1. A method of characterizing a multimode optical fiber link comprising a light source and at least two multimode fibers, the method comprises: a step of characterizing said light source by at least three source characteristic curves obtained by: exciting a nominal multimode fiber with said light source being directly modulated with a digital electrical signal at a nominal bit rate; scanning with a single mode fiber an output signal of said nominal multimode fiber, at different radial offset values r, from an axis of said nominal fiber where r=0 to a radial offset value r=a, where a is the core radius of said nominal fiber, analyzing with a spectrum analyzer an output optical spectrum of said single mode fiber for each radial offset value r, said source characteristic curves each showing a source parameter as a function of said radial offset value r; a step of characterizing each of said multimode fibers using a measurement of the Dispersion Modal Delay (DMD), wherein an output trace of light pulses launched into said multimode fiber at different radial offset values r is detected by using a single mode fiber and wherein said measurement of said DMD is used to calculate, for each of said multimode fibers, at least three fiber characteristic curves as a function of said radial offset value r; and a step of computing an Effective Bandwidth (EB) of said link, comprising calculating a transfer function using both each of said source characteristic curves and each of said at least three fiber characteristic curves for each of said multimode fibers.

2. The method according to claim 1, wherein said source characteristic curves comprise: a curve showing a received coupled power P.sub.source(r) of said source as a function of said radial offset value r, 0<r<a; a curve showing a center wavelength λ.sub.0(r) of said source as a function of said radial offset value r, 0≦r≦a; a curve showing a root mean square spectral width Δλ(r) of said source as a function of said radial offset value r, 0≦r≦a.

3. The method according to claim 1, wherein said at least three fiber characteristic curves calculated for each of said multimode fibers comprise: a curve showing a Radial Offset Bandwidth ROB(r) of said multimode fiber as a function of said radial offset value r, 0≦r≦a.sub.i; a curve showing a Radial Offset Delay ROD(r) of said multimode fiber as a function of said radial offset value r, U≦r≦a.sub.i; a curve showing a Radial Coupling Power P.sub.DND(r) of said multimode fiber as a function of said radial offset value r, 0≦r≦a.sub.i, where a.sub.i is the core radius of multimode fiber of index i.

4. The method according to claim 3, wherein said step of characterizing said light source and said step of characterizing each of said multimode fibers use the same single mode fiber.

5. The method according to claim 1, wherein said step of computing Effective Bandwidth (EB) of said link derives said Effective Bandwidth from a transfer function {tilde over (H)}(ƒ), where: $\tilde{H}\left(f\right)=\underset{r=0}{\overset{r=a}{.Math.}}.Math..Math.P_{\mathrm{source}}\left(r\right).Math.{\tilde{P}}_{\mathrm{DMD}}\left(r\right).Math.\mathrm{OMBc}\left(r\right).Math.e^{-i.Math..Math.2.Math.\pi \left(\widetilde{\mathrm{\Delta \tau }}.Math.\left(r\right)+{\widetilde{\mathrm{\Delta \tau }}}_{\mathrm{DMD}}\left(r\right)\right).Math.f}.Math.e^{-\left(\frac{1}{{{\tilde{\sigma }}_{\mathrm{ch}}\left(r\right)}^2}+\frac{1}{{{\tilde{\sigma }}_{\mathrm{DMD}}\left(r\right)}^2}\right).Math.f^2}$ with: ${\tilde{P}}_{\mathrm{DMD}}\left(r\right)=\frac{1}{N}.Math.\underset{i=1}{\overset{N}{.Math.}}.Math..Math.P_{\mathrm{DMD},i}\left(r\right)$ $.Math.\left(r\right)=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\mathrm{CD}}_i.Math.\left({\lambda }_c\left(r\right)-{\lambda }_{\mathrm{DMD}}\right)$ ${\mathrm{DMD}}_{}.Math.\left(r\right)=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\mathrm{ROD}}_i\left(r\right)$ ${\tilde{\sigma }}_{\mathrm{ch}}\left(r\right)=\frac{0.187}{\mathrm{\Delta \lambda }\left(r\right).Math.\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\mathrm{CD}}_i.Math.\sqrt{0.3.Math.{\log }_e.Math.10}}$ $\frac{1}{{{\tilde{\sigma }}_{\mathrm{DMD}}\left(r\right)}^2}=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.{\left(\frac{L_i.Math.\sqrt{0.3.Math.{\log }_e.Math.10}}{{\mathrm{ROB}}_i\left(r\right)}\right)}^2$ where i is the index of the multimode fiber in said optical link made of N multimode fiber sections, i=1 corresponding to the multimode fiber section closest to said light source, N being an integer greater than or equal to two, L.sub.i is the length in said link of the multimode fiber of index i, CD.sub.i is the chromatic dispersion of the multimode fiber of index i expressed in ps/nm-km, λ.sub.DMD is the wavelength of said measurement of the Dispersion Modal Delay, and OMBc(r) is the OMBc (for “Overfilled Modal Bandwidth calculated”) weight function.

6. The method according to claim 5, wherein said Effective Bandwidth of said optical link is a −3 dB bandwidth of said {tilde over (H)}(ƒ) transfer function.

7. The method according to claim 5, wherein said chromatic dispersion CD.sub.i for multimode fiber of index i in {tilde over (Δ)}.sub.τ(r) is replaced by a function of the wavelength CD.sub.i(λ), such that: $.Math.\left(r\right)=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\int }_{{\lambda }_{\mathrm{DMD}}}^{{\lambda }_c\left(r\right)}.Math.{\mathrm{CD}}_i\left(\lambda \right).Math.d.Math..Math.\lambda$

8. The method according to claim 5, wherein said chromatic dispersion CD.sub.i is assumed to be the same for all multimode fibers in said optical link.

9. The method according to claim 5, wherein modal dispersion is assumed to be the same for all multimode fibers in said optical link.

10. A method of fabricating multimode optical fiber links comprising a light source and at least two multimode optical fibers, the method comprising: selecting a set of multimode optical fibers and a set of light sources; computing an Effective Bandwidth (EB) of all possible optical links made up of one of said light sources and of two or more multimode fibers in said sets in compliance with the method; of claim 1; and selecting only those multimode optical fiber links for which the effective bandwidth EB>3000 MHz-km.

11. A method of improving the performance of a multimode optical fiber link comprising a light source and at least two multimode fibers, wherein said method comprises: computing the Effective Bandwidth of said multimode optical fiber link in compliance with the method of claim 1; for at least one of said multimode fibers, repeating the steps of: modifying a length of said multimode fiber; assessing said Effective Bandwidth of said link with said modified length in compliance with the method; of claim 1; and for said at least one of said multimode fibers, selecting the length which corresponds to the greatest Effective Bandwidth for said link.

12. A method of fabricating multimode optical fiber links comprising a light source and at least two multimode optical fibers, the method comprising: selecting a set of multimode optical fibers; selecting a set of light sources having different wavelengths in a window of wavelengths sensibly comprised between 850 nm and 950 nm; for a concatenation of multimode optical fibers in said set, computing an Effective Bandwidth (EB) of an optical link made of said concatenation of fibers and one of said light sources in said set, in compliance with the method of claim 1, and for each light source in said set; repeating said computing step for several concatenation of multimode optical fibers in said set; selecting only the concatenation of multimode optical fibers forming multimode optical fiber links for which the effective bandwidth EB>3000 MHz-km over the whole window of wavelengths sensibly comprised between 850 nm and 950 nm.

Description

4. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] 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:

[0097] FIG. 1 shows a synoptic diagram of the method of characterizing a multimode optical fiber link according to the invention;

[0098] FIG. 2 shows an example of an optical communication system including an optical multimode fiber link;

[0099] FIG. 3 illustrates the DMD measurement technique;

[0100] FIG. 4a shows an example of DMD plot resulting from a DMD measurement for a multimode fiber characterized according to an embodiment of the invention;

[0101] FIG. 4b illustrates the ROD curve derived from the DMD plot of FIG. 4a;

[0102] FIG. 4c illustrates the ROB curve derived from the DMD plot of FIG. 4a;

[0103] FIG. 4d illustrates the P.sub.DMD curve derived from the DMD plot of FIG. 4a;

[0104] FIG. 5 illustrates the source characterization technique according to embodiments of the invention;

[0105] FIG. 6a shows the optical spectrum of a source characterized with the technique of FIG. 5 in an exemplary embodiment of the invention;

[0106] FIG. 6b depicts the center wavelength λ.sub.c(r) as a function of the radial offset value of a source characterized with the technique of FIG. 5 in an exemplary embodiment of the invention;

[0107] FIG. 6c illustrates the root mean square spectral width Δλ(r) as a function of the radial offset value of a source characterized with the technique of FIG. 5 in an exemplary embodiment of the invention;

[0108] FIG. 6d illustrates the output power P(r) as a function of the radial offset value of a source characterized with the technique of FIG. 5 in an exemplary embodiment of the invention;

[0109] FIG. 7a shows the center wavelength λ.sub.c(r) as a function of the radial offset value of five transceivers Tx1 to Tx5 in an exemplary embodiment of the invention;

[0110] FIG. 7b illustrates the root mean square spectral width & of transceivers Tx1 to Tx5, as a function of the radial offset value r, in the exemplary embodiment of FIG. 7a;

[0111] FIG. 7c illustrates the output power P source of transceivers Tx1 to Tx5 as a function of the radial offset value r in the exemplary embodiments of FIGS. 7a and 7b;

[0112] FIG. 7d illustrates the difference between the center wavelength and the median wavelength of transceivers Tx1 to Tx5 as a function of the radial offset value r in the exemplary embodiments of FIGS. 7a to 7c;

[0113] FIGS. 8a to 8c illustrate the three fiber characteristic curves derived according to an embodiment of the invention for ten multimode fibers called Fiber 1 to Fiber 10;

[0114] FIG. 9 illustrates the Effective bandwidth improvement, achieved through concatenation of fibers, for optical links made of transceivers Tx1 to Tx5 of FIGS. 7a to 7d and fibers Fiber 1 to Fiber 10 of FIGS. 8a to 8c.

[0115] The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

5. DETAILED DESCRIPTION

[0116] The general principle of the invention relies on separate source and fiber characterizations, allowing isolating the relevant metrics that characterize both the source and the different spans of fibers, and a new method for assessing the Effective Bandwidth, starting from these new metrics.

[0117] FIG. 1 illustrates by a synoptic diagram the method of characterizing a multimode optical fiber link according to the invention. Such an optical link comprises a source, as well as two or more multimode optical fiber spans. Such a method relies on a characterization 170.sub.i of each multimode fiber of index i in the link using a DMD measurement technique. According to an embodiment of the invention, characterization 170.sub.i of fiber i yields three fiber characteristic curves derived from the DMD plot.

[0118] Such a method also relies on a separate characterization 171 of the source, using a technique similar to the DMD measurement technique, which allows obtaining three source characteristic curves.

[0119] Both the fiber characteristic curves delivered by step 170.sub.i and the source characteristic curves delivered by step 171 feed a computing step 172 for computing a transfer function H(f). In a step 173, the Effective Bandwidth of the multimode optical fiber link is then derived from the transfer function H(f).

[0120] All these steps will be described in more details below in relation to the other figures.

[0121] FIG. 2 shows an example of an optical communication system including a multimode fiber, objet of the present effective bandwidth computing method. A multi Gigabits Ethernet optical communication system successively comprises a driver 8 of a transmitter 1, a VCSEL source 9 of a transmitter 1, a launch cord 2, a connector 3, a multimode fiber link 4, a connector 3, a launch cord 2, a PIN diode 6 of a receiver 5, an amplifier 7 of a receiver 5. A digital signal at 10 Gbps or 25 Gbps or more is generated by the driver 8, which directly modulates the VCSEL source 9.

[0122] According to embodiments of the invention, multimode fiber link 4 is made from a concatenation of several multimode fiber spans 4.sub.i (though not illustrated in FIG. 1).

[0123] Each multimode fiber 4.sub.i is characterized, according to embodiments of the invention, based on the DMD measurements, as described in the standard TIA FOTP-220 or IEC 60793-1-49 (TIA-455-220-A, “Differential Mode Delay Measurement of Multimode Fiber in the Time Domain” (January 2003)).

[0124] FIG. 3 illustrates the DMD measurement technique. An ultrafast laser pulse is launched into a multimode fiber MMF using a single mode fiber SMF. The SMF is scanned radially, and for each radial offset position, the shape of the transmitted pulse is recorded using a high bandwidth optical receiver 30 and a sampling oscilloscope.

[0125] More precisely, an optical reference pulse s.sub.ref(t) at 850 nm is emitted by a source and launched into the core 10 of a single-mode launch fiber SMF, with a core diameter of 5 μm. From the end of the SMF, it is stepped across the core 20 of a multimode fiber MMF under test. Such a MMF has typically a core diameter of 50 μm. For each lateral offset across the core (0 to 24 microns), the propagation delay of the resultant output pulse is recorded. Each output pulse contains only those modes excited at a given input radial position. The output waveforms for each of the radial offsets are plotted along the vertical axis and are displaced by 1-micron increments, as shown on the right part of FIG. 3, also called a DMD plot. The relative pulse delay for each waveform is plotted along the horizontal axis in units of picoseconds per meter (ps/m). The DMD is determined by first measuring the difference pulse in delay using the leading edge of the fastest pulse and the trailing edge of the slowest pulse. From this difference we subtract the temporal width of the launch pulse, which yields the modal dispersion of the fiber.

[0126] According to an embodiment of the invention, three curves that characterize the multimode fiber 4.sub.i of core radius a are calculated from the DMD plot: [0127] a curve showing a Radial Offset Bandwidth ROB.sub.i(r) of the multimode fiber 4.sub.i as a function of the radial offset value r, 0≦r≦a; [0128] a curve showing a Radial Offset Delay ROD.sub.i(r) of the multimode fiber 4.sub.i as a function of the radial offset value r, 0≦r≦a; [0129] a curve showing a Radial Coupling Power P.sub.DMD.sub.i(r) of the multimode fiber 4.sub.i as a function of the radial offset value r, 0≦r≦a, which may be expressed as a relative power.

[0130] The Radial Offset Bandwidth is described in several prior art documents, among which patent document EP2207022. As described in this patent document, the radial offset bandwidth ROB(r) is defined as the −3 dB bandwidth of a transfer function

[00008]$H^r\left(f\right)=\frac{S_s\left(f,r\right)}{S_e\left(f\right)},$

where:

[0131] S.sub.e(ƒ) is the Fourier transform of the time profile of the inlet pulse s.sub.e(t), launched in the DMD measurement,

[0132] S.sub.s(ƒ, r) is the Fourier transform of the time profile of the outlet pulse s.sub.s (t, r) for a radial offset r, at the output of the multimode fiber under test,

[0133] and f indicates frequency.

[0134] An interesting characteristic of the ROB is its high sensitivity to localized defects in refractive index. Hence, if the ROB decreases too quickly on increasing the radial offset r, then it is likely that the fiber presents an irregular index profile.

[0135] ROB is normalized to the fiber length in the DMD measurement and is generally expressed in MHz.Math.km, or GHz.Math.km.

[0136] As regards the ROD, it corresponds to the mean temporal position of the fiber output response for a given delay.

[0137] The ROD curve for the fiber somehow corresponds to the λ.sub.c curve for the source, while the ROB curve for the fiber somehow corresponds to the Δλ curve for the source.

[0138] ROD is normalized to the fiber length used in the DMD measurements to be expressed typically in ps/m. Note that the absolute value of the ROD is not relevant, only the relative value between offset launches matters.

[0139] FIG. 4a illustrates a DMD plot obtained by characterizing a multimode fiber through a DMD measurement technique. FIGS. 4b to 4d show respectively the ROD curve, the ROB curve and the P.sub.DMD curve as a function of the radial offset value derived from the DMD plot according to an embodiment of the invention.

[0140] FIG. 5 illustrates the source characterization technique according to embodiments of the invention. This characterization is similar to that of the DMD measurement technique.

[0141] A nominal multimode graded-index fiber, with a core 31 showing a diameter of 50 μm, is first excited with the source to be characterized. The source is excited with a typical digital electrical signal, than can be obtained with a pattern generator used with a pseudo random bit sequence, at a typical bit rate. Such a digital electrical signal is illustrated on FIG. 5, which shows the power of the signal, expressed in mW, as a function of time, expressed in ns. As may be observed, the pattern of such a digital signal illustrates the possible multimode nature of the source. The nominal multimode graded-index fiber has sensibly the same core diameter and numerical aperture as the multimode fibers used in the link. Actually, it must be noted that the multimode fibers in the link preferably have sensibly the same core diameter (±10%) and the same numerical aperture (±10%). However, some of them may be for example OM3 fibers, and some others OM4 fibers. A single mode fiber 32 scans the output of the nominal fiber, in a manner similar to that used in the standard DMD measurements, thus preferably from 0 to 25 μm, with a 1-micron step. A larger step, e.g. 2 μm supported by interpolation can also be done. An optical spectrum analyzer 30 placed at the output of the single mode fiber 32 records the output optical spectrum for each position of the SMF.

[0142] Without lack of generality, the single mode fiber 32 used for the source characterization, also called probe fiber, may be the same as the single mode fiber 10 used for the fiber characterization.

[0143] Although not illustrated on FIG. 5, such a technique allows collecting a series of optical spectra, which have to be post-processed, so as to generate three source characteristic curves, namely: [0144] a curve showing the received coupled power P.sub.source(r) of the source as a function of the radial offset value r of the SMF 32, 0≦r≦a. Such a power may be expressed as a relative power; [0145] a curve showing a center wavelength λ.sub.c(r) of the source as a function of the radial offset value r of the SMF 32, 0≦r≦a; [0146] a curve showing a root mean square spectral width Δλ(r) of the source as a function of the radial offset value r of the SMF 32, 0≦r≦a,
where a is the core radius of the multimode nominal fiber 31.

[0147] In an exemplary embodiment of the invention, the inventors have simulated the coupling between a transversally multimode (and longitudinally single mode) laser into a 50 μm graded-index multimode fiber. As shown in FIG. 6a, such a source exhibits seven mode groups, named MG1 to MG7. As can be read on FIG. 6a, the center wavelength λ.sub.c is 850.0 nm. The position of the source with respect to the nominal multimode fiber 31 is arbitrarily chosen.

[0148] FIGS. 6b to 6d illustrate the three curves that characterize the source-fiber coupling, according to the technique of FIG. 5: more precisely, FIG. 6d illustrates the output power P.sub.source(r) of the source as a function of the radial offset value; FIG. 6b illustrates the center wavelength λ.sub.c(r) of the source as a function of the radial offset value; FIG. 6c depicts the root mean square spectral width Δλ(r) of the source as a function of the radial offset value. It is interesting to note that the RMS spectral width Δλ(r) also significantly varies along the fiber core 31.

[0149] Once a DMD measurement has been carried out for characterizing each multimode fiber under test, and once the source has been characterized using the technique of FIG. 5, the method of the invention proposes to compute the Effective Bandwidth of the multimode optical fiber link, made of the source and several spans of multimode fibers.

[0150] Using the three fiber-characteristic curves of FIGS. 4b to 4d for each multimode fiber 4.sub.i along with the three source-characteristic curves of FIGS. 6b to 6d, the method according to an embodiment of the invention proposes to compute the Effective Bandwidth (hereafter called EB) as the bandwidth at −3 dB of the transfer function H(ƒ), such that:

[00009]$10.Math.{\log }_{10}.Math..Math.\frac{H\left(\mathrm{EB}\right)}{H\left(0\right)}.Math.=-3.$

[0151] Assuming Gaussian and independent radial transfer functions or modal

[00010]$\left(P_{\mathrm{DMD}}\left(r\right).Math.e^{-\left(\frac{1}{{{\sigma }_{\mathrm{DMD}}\left(r\right)}^2}\right).Math.f^2}\right)$

and chromatic

[00011]$\left(P_{\mathrm{source}}\left(r\right).Math.e^{-\left(\frac{1}{{{\sigma }_{\mathrm{ch}}\left(r\right)}^2}\right).Math.f^2}\right)$

dispersions, and taking into account the delays between these radial transfer functions respectively induced by chromatic (Δτ(r)) and modal (Δτ.sub.DMD(r)) dispersions, the total transfer function resulting from the coupling between a source and a fiber can be expressed with these metrics as follows:

[00012]$H\left(f\right)=\underset{r=0}{\overset{r=a}{.Math.}}.Math..Math.P_{\mathrm{source}}\left(r\right).Math.P_{\mathrm{DMD}}\left(r\right).Math.\mathrm{OMBc}\left(r\right).Math.e^{-i.Math..Math.2.Math.\pi \left(\mathrm{\Delta \tau }\left(r\right)+{\mathrm{\Delta \tau }}_{\mathrm{DMD}}\left(r\right)\right).Math.f}.Math.e^{-\left(\frac{1}{{{\sigma }_{\mathrm{ch}}\left(r\right)}^2}+\frac{1}{{{\sigma }_{\mathrm{DMD}}\left(r\right)}^2}\right).Math.f^2}$

where:

[0152] Δτ(r)=L.Math.CD.Math.(λ.sub.c(r)−λ.sub.DMD) is the delay induced by the chromatic dispersion (CD) expressed in ps/nm/km, with L the multimode fiber length in said link (e.g. 500 m),

[0153] λ.sub.DMD is the wavelength of the DMD measurements that is also the operating wavelength of the link,

Δτ.sub.DMD(r)=L.Math.ROD(r),

[00013]${\sigma }_{\mathrm{ch}}\left(r\right)=\frac{0.187}{\mathrm{\Delta \lambda }\left(r\right).Math.L.Math.\mathrm{CD}.Math.\sqrt{0.3.Math.{\log }_e.Math.10}}$

is linked to the chromatic dispersion CD bandwidth, and

[00014]${\sigma }_{\mathrm{DMD}}\left(r\right)=\frac{\mathrm{ROB}\left(r\right)}{L.Math.\sqrt{0.3.Math.{\log }_e.Math.10}}$

[0154] The OMBc (for “Overfilled Modal Bandwidth calculated”) are the weight functions corresponding to over-filled launch.

[0155] More information on OMBc weight functions can be found in “Calculated Modal Bandwidths of an OM4 Fiber and the Theoretical Challenges” by Abhijit Sengupta, International Wire & Cable Symposium, Proceedings of the 58.sup.th IWCS/IICIT, pp. 24-29. As disclosed in this document, overfilled modal bandwidth calculated (OMBc) of a multimode fiber can be predicted from the weighted linear combination of differential modal delay data. Actually, coupled power in each mode is calculated from the overlap integral of a Gaussian mode field of a single mode probe fiber (SMPF) and the specific mode of the MMF for each radial offset position. The coupling efficiency at each radial offset is calculated as the total coupled power summed over all modes normalized to unit incident power. The overfilled launch source is expressed as a linear combination of SMPF modes fields at the radial offset positions of the DMD scan. Per the definition of OFL, the weights for different offset positions are optimized so that the total energy in each mode of the MMF is equal. These theoretical DMD weighting values are tabulated to obtain the OMBc for the DMD data measured from 0-30 microns (i.e. complete DMD data). These weights are then adjusted to provide optimal values for the case where the DMD data does not exist at radii higher than 25 microns.

[0156] However, embodiments of the invention deal with a link made of a concatenation of at least two long enough fibers. In that case, the transfer function H(ƒ) is replaced with {tilde over (H)}(ƒ), which is calculated as follows:

[00015]$\tilde{H}\left(f\right)=\underset{r=0}{\overset{r=a}{.Math.}}.Math..Math.P_{\mathrm{source}}\left(r\right).Math.{\tilde{P}}_{\mathrm{DMD}}\left(r\right).Math.\mathrm{OMBc}\left(r\right).Math.e^{-i.Math..Math.2.Math.\pi \left(\widetilde{\mathrm{\Delta \tau }}.Math.\left(r\right)+{\widetilde{\mathrm{\Delta \tau }}}_{\mathrm{DMD}}\left(r\right)\right).Math.f}.Math.e^{-\left(\frac{1}{{{\tilde{\sigma }}_{\mathrm{ch}}\left(r\right)}^2}+\frac{1}{{{\tilde{\sigma }}_{\mathrm{DMD}}\left(r\right)}^2}\right).Math.f^2}$

with:

[00016]${\tilde{P}}_{\mathrm{DMD}}\left(r\right)=\frac{1}{N}.Math.\underset{i=1}{\overset{N}{.Math.}}.Math..Math.P_{\mathrm{DMD},i}\left(r\right)$$.Math.\left(r\right)=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\mathrm{CD}}_i.Math.\left({\lambda }_c\left(r\right)-{\lambda }_{\mathrm{DMD}}\right)$${\mathrm{DMD}}_{}.Math.\left(r\right)=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\mathrm{ROD}}_i\left(r\right)$${\tilde{\sigma }}_{\mathrm{ch}}\left(r\right)=\frac{0.187}{\mathrm{\Delta \lambda }\left(r\right).Math.\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\mathrm{CD}}_i.Math.\sqrt{0.3.Math.{\log }_e.Math.10}}$$\frac{1}{{{\tilde{\sigma }}_{\mathrm{DMD}}\left(r\right)}^2}=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.{\left(\frac{L_i.Math.\sqrt{0.3.Math.{\log }_e.Math.10}}{{\mathrm{ROB}}_i\left(r\right)}\right)}^2$

[0157] where i is the index of the fiber in the concatenated link made of N fiber sections: i=1 is the first fiber section, i.e. the closest to the source.

[0158] Hence, assuming we have a collection of source and fiber pieces for which the corresponding and above-mentioned metrics are known, embodiments of the invention allow calculating the effective bandwidth according to the above formula of all possible links to find the best link, i.e. the link that deliver the largest effective bandwidth.

[0159] It should be noted that {tilde over (P)}.sub.DMD(r) is expected to be more or less the same for all fibers when they are of the same type. In embodiments of the invention, it is assumed that the connection between two fibers does not mix the mode. Therefore we can use the P.sub.DMD,i(r) of any of the fibers. In the above formula, we propose to use the average.

[0160] In practice, there are also connectors between fibers to form the optical link. Ideally, the connectors do not mix or filter the mode groups. In other words, placing a connector at the fiber output during the fiber metric assessment is not expected to change the metric of the fiber.

[0161] Note that Δτ(r) in the formula can be refined as follows:

[00017]$\mathrm{\Delta \tau }\left(r\right)=L.Math.{\int }_{{\lambda }_{\mathrm{DMD}}}^{{\lambda }_c\left(r\right)}.Math.\mathrm{CD}\left(\lambda \right).Math.d.Math..Math.\lambda$$.Math.\left(r\right)=\underset{i=1}{\overset{N}{.Math.}}.Math..Math.L_i.Math.{\int }_{{\lambda }_{\mathrm{DMD}}}^{{\lambda }_c\left(r\right)}.Math.{\mathrm{CD}}_i\left(\lambda \right).Math.d.Math..Math.\lambda$

in case we know how Chromatic Dispersion varies with the wavelength.

[0162] One can also assume that the chromatic dispersion is substantially equal for all fiber pieces, or that the modal dispersion is the same. These assumptions simplify the formula of concatenations.

[0163] One can also imagine assessing the effect of a fiber shortening on the fiber performances, or define the specification of the fiber metric of one or several spans to add, in order to improve the performance of the whole link at one or several wavelengths.

[0164] FIGS. 7a to 7d illustrate the source characteristic curves derived according to an embodiment of the invention for five transceivers called Tx1 to Tx5 operating at 10 Gbps.

[0165] More precisely, FIG. 7a illustrates the center wavelength λ.sub.c of the transceiver, expressed in nm, as a function of the radial offset value r expressed in μm for transceivers Tx1 to Tx5; FIG. 7b illustrates the root mean square spectral width Δλ of the transceiver, expressed in nm, as a function of the radial offset value r expressed in μm for transceivers Tx1 to Tx5; FIG. 7c illustrates the output power P.sub.source of the transceiver, expressed in μW, as a function of the radial offset value r expressed in μm for transceivers Tx1 to Tx5; FIG. 7d illustrates the difference between the center wavelength and the median wavelength of the transceiver, expressed in nm, as a function of the radial offset value r expressed in μm for transceivers Tx1 to Tx5.

[0166] FIGS. 8a to 8c illustrate the three fiber characteristic curves derived according to an embodiment of the invention for ten multimode fibers called Fiber 1 to Fiber 10.

[0167] More precisely, FIG. 8a illustrates, for each of the ten fibers, the Radial Offset Delay ROD(r) expressed in ps/m as a function of the radial offset value r; FIG. 8b illustrates, for each of the ten fibers, the Radial Offset Bandwidth ROB(r) expressed in ps/m as a function of the radial offset value r; FIG. 8c illustrates, for each of the ten fibers, the Radial Coupling Power P.sub.DMD(r) as a function of the radial offset value r.

[0168] The inventors have computed the Effective bandwidth of all possible optical links made of one the sources Tx1 to Tx5 and of a concatenation of two fibers of same length, chosen among the ten fibers Fiber 1 to Fiber 10.

[0169] FIG. 9 illustrates the Effective bandwidth improvement, achieved through concatenation of fibers. More precisely, for each possible optical link symbolized with a square form, FIG. 9 illustrates: [0170] on the Y axis, the difference between the Effective Bandwidth obtained for the concatenation of fibers and the maximum Effective Bandwidth of the two fibers making the optical link (EB of concatenation-Max (EB of each fiber span), expressed in MHz-km; [0171] on the X axis, the Effective Bandwidth obtained for the concatenation of fibers (EB of concatenation, expressed in MHz-km).

[0172] For a given optical link, when the difference between the EB of the concatenation and the maximum EB of the two fibers making the link is positive, it means that the concatenation of fibers improves the total bandwidth: in other words, the modal and chromatic dispersion of one fiber compensate for one or the other of the second fiber.

[0173] On FIG. 9, the circled square form referenced as 90 corresponds to the optical link, which Effective Bandwidth was best improved thanks to concatenation of fibers, as compared to an optical link comprising a single span of fiber. This best improvement occurs for transceiver Tx1 coupled with a span of multimode fiber Fiber 4 (showing an Effective Bandwidth EB=5300 MHz-km) and a span of multimode fiber Fiber 10 (showing an Effective Bandwidth EB=5270 MHz-km): actually, the Effective Bandwidth of the optical link thus built shows an Effective Bandwidth EB=6300 MHz-km. The Effective Bandwidth of the optical link thus shows an increase of around 1000 MHz-km, thanks to the concatenation of fibers.

[0174] The method according to embodiments of the invention allow isolating and extracting the relevant information for characterizing both a source and multimode fibers, into a single set of curves for the source and into a single set of curves for each fiber. A standardized use of such a method would hence considerably simplify sorting method and/or link engineering, and make easier the collaboration between source and fiber manufacturers.