# Patent

## Title
Multimode optical fibers

## Abstract

A multimode optical fiber has an equivalent modal dispersion value (DMDinner&outer) of less than 0.11 ps/m for (Δλmax×D)>0.07 ps/m as measured on a modified DMD graph. The modified DMD graph accounts for chromatic dispersion to ensure that the multimode optical fiber has a calculated effective bandwidth EBc greater than 6000 MHz-km when used with multimode transverse sources.

## Background
CROSS REFERENCE TO PRIORITY APPLICATIONS
This application is a continuation of commonly assigned U.S. application Ser. No. 12/498,439 for Multimode Optical Fibers (filed Jul. 7, 2009, and published Feb. 4, 2010, as Publication No. 2010/0028020 A1), now U.S. Pat. No. 7,995,888, which itself claims the benefit of pending French application Ser. No. 08/03873 for Fibres Optiques Multimodes (filed Jul. 8, 2008, at the French Patent Office). Each foregoing patent application, patent application publication, and patent is hereby incorporated by reference in its entirety.


FIELD OF THE INVENTION
The present invention relates to the field of optical fiber transmissions and more specifically to multimode fibers used for short-distance optical transmission systems that require large bandwidth.
BACKGROUND OF THE INVENTION
Multimode optical fibers are used for short-distance applications and local networks. The core of a multimode fiber generally has a diameter of approximately 50 microns (μm) and a numerical aperture greater than 0.2. By way of comparison, a single-mode fiber generally has a diameter of approximately 8 to 9 microns (μm) and a numerical aperture greater than 0.12. Thus, for a particular wavelength, several optical modes propagate simultaneously along the fiber, carrying the same information. The bandwidth is directly linked to the group velocity of the optical modes propagating in the multimode core of the fiber. To guarantee a high bandwidth, it is necessary for the group velocities of all the modes to be identical. In other words, the intermodal dispersion (i.e., the difference in group velocity between the slower mode and the faster mode) should be minimized for a particular wavelength. The multimode fibers have been the subject of international standardization under standard ITU-T G.651, which, in particular, defines criteria (e.g., bandwidth, numerical aperture, and core diameter) that relate to the requirements for optical fiber compatibility. The standard ITU-T G.651 is hereby incorporated by reference in its entirety.
To reduce the intermodal dispersion in a multimode fiber, it has been proposed since the 1970s to produce graded-index fibers with a parabolic core profile. Such an optical fiber has been used for many years and its characteristics have been described in particular in the publications “Multimode Theory of Graded-Core Fibers” by D. Gloge et al., Bell System Technical Journal 1973, pp. 1563-1578, and “Pulse Broadening in Graded-Index Optical Fibers” by Olshansky et al., Applied Optics, Vol. 15, No. 2, February 1976. Each of these publications is hereby incorporated by reference in its entirety.
A graded-index profile can be defined by a relationship between the index value n at a point as a function of the distance r from this point to the center of the fiber:




  n
  =
  
    
      n
      1
    
    ⁢
    
      
        1
        -
        
          2
          ⁢
          
            
              Δ
              ⁡
              
                (
                
                  r
                  a
                
                )
              
            
            α
          
        
      
    
  




wherein,

    
    
        α≧1;
        n1 is the maximum index of the multimode core;
        a is the radius of the multimode core; and
    
    






  Δ
  =
  
    
      (
      
        
          n
          1
          2
        
        -
        
          n
          0
          2
        
      
      )
    
    
      2
      ⁢
      
        n
        1
        2
      
    
  




wherein,

    
    
        n0 is the minimum index of the multimode core, generally corresponding to the index of the cladding (most often made of silica).
    
    


A multimode fiber with a graded index therefore has a core profile with a rotational symmetry such that along any radial direction the value of the index decreases continuously from the center of the fiber to its periphery. These curves are generally representative of the theoretical or target profile of the optical fiber, though fiber-manufacturing constraints may lead to a slightly different profile.
When a light signal propagates in such a core having a graded-index, the different modes experience a different propagation medium, which affects their speed of propagation differently. By adjusting the value of the parameter α, it is therefore possible to theoretically obtain a group velocity that is virtually equal for all the modes and thus a reduced intermodal dispersion for a particular wavelength. A value for the parameter α of between 1.8 and 2.2 generally allows a satisfactory limitation of the modal dispersion.
That said, an optimum value of the parameter α is valid only for a particular wavelength. Thus, a multimode fiber typically transmits a monochromatic optical signal having a particular wavelength for which the alpha (α) profile of the fiber has been optimized. U.S. Pat. No. 6,363,195, which is hereby incorporated by reference in its entirety, proposes to compensate for the modal dispersion of a multimode optical link by using a concatenation of multimode fibers in order to optimize the bandwidth for two transmission windows, one centered on 850 nanometers and the other on 1300 nanometers. This patent proposes to use a length of a first multimode fiber having a value of parameter α1 of between 0.8 and 2.1 to optimize the bandwidth at 850 nanometers and a length of a second multimode fiber having a value of parameter α2 between the first value α1 and 8 to optimize the bandwidth at 1300 nanometers.
Furthermore, the exact parameter value α is difficult to control during fiber manufacturing. In order to compensate the profile deviations from a theoretical profile having an optimum value α, U.S. Pat. No. 7,139,457 proposes a concatenation of multimode fibers. The alpha (α) profile of each fiber and the length of each fiber are optimized in order to maximize the bandwidth over a given optical link. U.S. Pat. No. 7,139,457 is hereby incorporated by reference in its entirety.
Using fiber concatenations for modal dispersion compensation leads to more complex and more costly optical systems. Moreover, the foregoing documents are not concerned with the spectral dispersion of the sources used.
In this regard, the sources used in optical transmission systems are not generally monochromatic. By way of example, the widely used vertical-cavity, surface-emitting diode lasers (VCSEL) have a wide-spectrum discrete emission. The VCSELs used in high-speed transmissions are generally longitudinally, but not transversally, single mode. Each transverse mode of the laser has its own wavelength corresponding to the various peaks of the emission spectrum (i.e., the emission spectrum has a spatial dependence).
Accordingly, a multimode fiber has an alpha profile with a value of parameter α optimized only for a given wavelength. Thus, the introduction of a polychromatic optical signal originating from a transverse multimode source in a multimode fiber causes the appearance of a modal dispersion and consequently a reduction in the bandwidth.
U.S. Patent Publication No. 2004/0184492, which is hereby incorporated by reference in its entirety, proposes to use only one single transverse mode of a VCSEL source by conditioning the emitted signal before its introduction into the multimode fiber. This signal conditioning is achieved by diffractive elements and/or by offsetting the VCSEL output from the center of the multimode fiber. However, such a conditioning of the signal at the input of the multimode fiber involves a significant degradation of the signal modulation and consequently an increase in the bit error rate (BER).
U.S. Patent Publication No. 2005/0078962, which is hereby incorporated by reference in its entirety, proposes to offset the VCSEL output from the center of the multimode fiber in order to introduce the signal into a “large bandwidth zone.” Such an offsetting, however, is difficult to control and has to be adjusted for each fiber. Moreover, it may introduce a power loss, which is detrimental to the transmission quality.
Thus, there is a need for a multimode optical fiber that has a reduced modal dispersion when used with a transverse polychromatic and multimode source without requiring conditioning or offsetting of the signal emitted by the source.
SUMMARY OF THE INVENTION
To this end, the invention proposes to use the chromatic dispersion of the multimode optical fiber to compensate for the modal dispersion induced by a polychromatic signal.
In fact, a multimode fiber typically has chromatic dispersion on the order of −100 ps/(nm·km) at a wavelength of 850 nanometers. The chromatic dispersion can vary between about −80 and −120 ps/(nm·km) in the 840-nanometer to 860-nanometer spectral range. Such chromatic dispersion will induce a modal dispersion by further delaying the optical fiber's higher order modes, which have shorter wavelengths; the higher order modes are mainly excited by the transverse modes having the greatest divergences and therefore also the shorter wavelengths. This dispersion is independent of the modal dispersion because the chromatic dispersion depends on the material whereas the modal dispersion depends on the profile of the fiber.
The invention, therefore, proposes to modify the profile of a multimode fiber by adjusting the value of parameter α to a value different from optimum in order to introduce a modal dispersion that will compensate, within the same fiber, the modal dispersion induced by the chromatic dispersion when a transverse polychromatic and multimode source is used.
The present invention relates specifically to a multimode optical fiber having a refractive index profile chosen in such a manner that a measurement of the dispersion modal delay (DMD), the DMD graph of which has been modified by adding a delay (Δttrace) to each trace:




  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  




wherein,

    
    
        rtrace is the center position of the injection of the light pulse corresponding to the trace;
        a is the core radius of the multimode fiber;
        L is the length of the multimode optical fiber;
        D is the chromatic dispersion of the multimode fiber at the wavelength of the light pulse;
        β is the coefficient of the delay; and
        Δλmax is the maximum spectral width of a source intended to be used with the fiber,

produces an equivalent modal dispersion value (DMDinner&outer), as measured at a quarter of the height of the leading edge of the first trace and at a quarter of the height of the trailing edge of the last trace, of less than 0.11 ps/m for (Δλmax×D)>0.07 ps/m.

    
    


In one exemplary embodiment, the multimode optical fiber has chromatic dispersion between −80 ps/(nm·km) and −120 ps/(nm·km) for wavelengths between 840 nanometers and 860 nanometers.
The coefficient β of the delay Δttrace which is added to each trace, is larger than or equal to 1, typically equal to 1 or 2.
In another exemplary embodiment, the multimode optical fiber has a calculated effective bandwidth (EBc) greater than 6000 MHz-km.
The present invention also proposes an optical system that includes a polychromatic optical source emitting multiple transverse modes with a maximum spectral width (Δλmax) and an optical link, which is formed from a portion (e.g., a fiber segment) of at least one multimode optical fiber according to the present invention.
According to another exemplary embodiment, the maximum spectral width of the source (Δλmax) is between 1 nanometer and 2 nanometers.
According to other exemplary embodiments, the source is a surface-emitting laser (VCSEL) or a light-emitting diode (LED).
According to another exemplary embodiment, the optical system has a distance by Gigabit Ethernet rate product greater than 3000 Gb/s·m.
The present invention also relates to a method for selecting multimode optical fibers. In this regard, multimode optical fibers, which have a graded-index profile with a given value of parameter α, are manufactured. Dispersion modal delay is measured for each multimode optical fiber from respective DMD graphs. The modal dispersion (DMDinner&outer) is measured at a quarter of the height of the leading edge of the first trace and at a quarter of the height of the trailing edge of the last trace.
The respective DMD graphs are then modified by adding a delay (Δttrace) to each trace according to the following equation:




  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  




wherein

    
    
        rtrace is the center position of the injection of the light pulse corresponding to the trace;
        a is the core radius of the multimode fiber;
        D is the chromatic dispersion of the multimode fiber at the wavelength of the light pulse;
        Δλmax is the maximum spectral width of a source intended to be used with the fiber.
    
    


Those multimode optical fibers with an equivalent modal dispersion value measured on the modified DMD graph of less than 0.11 ps/m are then selected.
The foregoing, as well as other characteristics and advantages of the invention and the manner in which the same are accomplished, are further specified within the following detailed description and its accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 graphically represents an emission spectrum of a VCSEL laser.
FIG. 2A illustrates the basic scheme of the optical spectrum for a source with three modes.
FIG. 2B graphically represents three DMD graphs for an optical fiber according to the prior art with three monochromatic sources having three different wavelengths.
FIG. 3 graphically represents a DMD graph for an optical fiber according to the prior art with a polychromatic source having three emitted wavelengths.
FIG. 4 graphically represents a DMD graph for an optical fiber according to the invention with three monochromatic sources having three different wavelengths.
FIG. 5 graphically represents a DMD graph for an optical fiber according to the invention with a polychromatic source having three emitted wavelengths.
FIG. 6 graphically represents a transformation of the profile of an optical fiber according to the invention compared with a profile having an optimized value of parameter α.
FIG. 7 schematically depicts the calculation of the delay due to the modal dispersion DMD according to the criteria of the standard FOTP-220.
FIG. 8 graphically represents a correlation between the sensitivity of the system and the effective modal bandwidth for multimode optical fibers according to the invention and for multimode optical fibers according to the prior art.
FIG. 9 graphically represents a correlation between the sensitivity of the system and the effective bandwidth of the fiber for multimode optical fibers according to the invention and for multimode optical fibers according to the prior art.



DETAILED DESCRIPTION
In this regard, the invention proposes an optimized multimode optical fiber for use with a polychromatic source, such as a VCSEL laser, having several transverse modes.
FIG. 1 shows an emission spectrum of a VCSEL laser, with a mode centered on 850 nanometers for the excitation of the fundamental mode LP01. FIG. 1 shows that each transverse mode of the laser has its own wavelength. The maximum RMS (Root Mean Square) spectral width generally authorized for high-speed transmission is 0.46 nanometers RMS for the VCSEL (as defined in the standard IEEE 802.3ae).
In this regard, when the optical signal emitted by the VCSEL is introduced into the multimode fiber, each transverse mode of the VCSEL diffracts differently. The transverse modes of the highest order diverge more rapidly (i.e., due to their phase and spatial distribution of their energy), and will therefore be coupled more specifically in the high order modes of the fiber. Those having ordinary skill in the art will appreciate that the high order modes of the VCSEL occupy the lowest wavelengths in the spectrum. This spectral and spatial distribution of the VCSEL modes results in the highest order modes of the fibers mostly carrying the lowest wavelengths in the spectrum. Therefore, the chromatic dispersion will further delay the higher order modes relative to the delay of the fundamental mode.
The chromatic dispersion will thus introduce a modal dispersion referred to as “Modal and Chromatic Dispersion Interferences” (MCDI) resulting in a limitation of the bandwidth.
The modal dispersion induced by the chromatic dispersion can be expressed according to the following equation:

Δτ=2×ΔλRMS×D×L 

wherein,

    
    
        Δτ is the modal dispersion of the light pulse;
        λRMS is a half-width of the emission spectrum of the source;
        D is the chromatic dispersion in the multimode fiber, typically −100 ps/(nm·km) at 850 nanometers; and
        L is the length of the multimode fiber considered.
    
    


To date, high-bitrate transmission Ethernet networks are in operation, with bitrates of the order of 10 GbE (10 Gb/s). To provide such bitrates over more than 300 meters and 550 meters, respectively, it is necessary to guarantee an effective bandwidth greater than or equal to 2000 MHz-km and 4700 MHz-km, respectively. The standard TIA-492AAAC-A standardizes the required performances for 50-micron, high-bitrate multimode fibers. In the case of multimode fibers, however, the bandwidth depends on the source used. The effective modal bandwidth (EMB) corresponds to the bandwidth of the source-fiber pair when the chromatic dispersion is disregarded. The effective bandwidth (EB) corresponds to the bandwidth of the fiber when both the modal dispersion and the chromatic dispersion are taken into account.
In this regard, the effective modal bandwidth (EMB) is determined by a measurement of the delay caused by the modal dispersion, known as “Dispersion Mode Delay” (DMD) graphical representation. The procedure for measuring the DMD is the subject of standardization, such as IEC 60793-1-49 and FOTP-220, each of which is hereby incorporated by reference in its entirety. To carry out this EMB measurement, care is generally taken to use a source or a fiber length such that the chromatic dispersion is actually negligible; the purpose is to characterize the modal dispersion of the fiber.
A DMD graphical representation is obtained by injecting a light pulse having a particular wavelength λ0 at the center of the fiber and measuring the pulse delay after a particular fiber length L. The introduction of the light pulse of particular wavelength λ0 is radially offset to cover the entire core of the multimode fiber. When the parameter α is set to an optimum value (αoptimum), there is virtually no shift in the light pulse delay for a particular wavelength λ0 regardless of the injection point of the pulse along the radius r of the fiber core; the intermodal dispersion is low and the effective bandwidth high.
However, this alignment on the DMD graphical representation of the light pulse delays, regardless of the radius r, is only valid for a particular wavelength λ0 for a particular value of the parameter α(i.e., αoptimum).
FIG. 2A illustrates the basic scheme of the optical spectrum for a source with three modes. FIG. 2B illustrates three diagrams of DMD graphs of a multimode fiber according to the prior art. The DMD graphs correspond to three sources having three different wavelengths as measured according to the recommendations of standards IEC 60793-1-49 and FOTP-220.
FIG. 2B clearly shows that each pulse has the same delay after a given length of fiber regardless of the radial injection point of the signal (r/a). The modal dispersion is therefore virtually zero for a given signal wavelength. However, the graph in FIG. 2B also shows that the pulses do not have the same delay depending on their wavelength. It is noted that the dependence of the delay and the effective wavelength on the signal is well known and given by the actual definition of chromatic dispersion.
When a polychromatic emission source having several transverse modes is used, a modal dispersion is introduced despite the optimization of parameter α. In this regard, FIG. 3 shows an exemplary diagram of the DMD traces of a multimode fiber according to the prior art. The source presents three transverse modes having three distinct wavelengths. (It should be understood that the source could have more than three transverse modes, but the description is limited to three for clarity of the disclosure.)
FIG. 3 clearly shows that after propagation over a distance L, the delay of the LP01 mode of the VCSEL is not the same as the delay of the VCSEL's LP11 mode or LP21 mode. The different propagation times between the VCSEL modes constituting the optical signal, even with an optimized value of parameter α for a reduced modal dispersion, occurs because the different modes do not have exactly the same propagation wavelength. Consequently, the chromatic dispersion of the fiber induces an additional difference in group velocity between the fiber modes, which does not appear in a DMD measurement, as it is dependent on the VCSEL spectrum. A modal dispersion is therefore induced in the fiber by the chromatic dispersion (MCDI) when the light signal injected at the input has several transverse modes, each having a different wavelength.
The delay induced by the chromatic dispersion between two transverse modes of fibers with respective wavelengths λ1 and λ0 is given by the following equation:

Δτ=(λ1−λ0)×D×L)

For a spectral spacing of 1 nanometer and a dispersion of −100 ps/(nm·km), delays of 0.1 ps/m are obtained (i.e., the same order of magnitude as the modal dispersion of a fiber having an EMB of 5000 MHz-km.) The modal dispersion induced in the fiber by the chromatic dispersion (MCDI) is therefore not negligible.
This modal dispersion induced by the chromatic dispersion will be added to the modal dispersion induced by the refractive index profile. It is independent of the profile of the fiber because the chromatic dispersion essentially depends on the material of the optical waveguide.
The invention thus proposes to introduce a modal dispersion into the multimode fiber to compensate for the modal dispersion induced by the chromatic dispersion. The compensation of the modal dispersion is achieved in the same fiber; therefore, there is no concatenation of fibers.
In this regard, the invention proposes to choose a value of parameter α different from the optimum value to introduce a non-zero modal dispersion into the multimode fiber for a given wavelength. In an optical link over which a polychromatic signal propagates, the modal dispersion is then substantially zero.
FIG. 4 shows three diagrams of DMD graphs of a multimode fiber according to the invention. These DMD graphs correspond to three monochromatic sources having three different wavelengths and measured according to the recommendations of standards IEC 60793-1-49 and FOTP-220.
FIG. 7 illustrates a schematic diagram of the calculation of the delay due to the modal dispersion DMD according to the criteria of the standard FOTP-220 as published in its version TIA SCFO-6.6 (Nov. 22, 2002).
A light pulse is injected at different radial positions (r1, r2, r3, r4) with respect to the center of the multimode optical fiber core. The width of the pulse ΔTref is measured at a quarter of the height, generally at the output, of the fiber of length L. The delay due to the modal dispersion DMDinner&outer is then measured between a first point in time tinner at a quarter of the height of the leading edge of the first trace r1, and a second point in time touter at a quarter of the height of the trailing edge of the last trace r4. The value of DMDinner&outer is then defined according to the following relationship:

DMDinner&outer=(touter−tinner−ΔTref)/L 

FIG. 4 clearly shows that a modal dispersion was introduced into the fiber according to the invention for a particular wavelength λ0, λ1, λ2. This modal dispersion is caused by the graded-index profile, which does not allow the same velocity of propagation for all the modes. This modal dispersion is controlled, however, to compensate for the modal dispersion induced by the chromatic dispersion MCDI in the same fiber when a polychromatic optical signal is propagated.
FIG. 5 shows a DMD graph of a multimode fiber according to the invention with a polychromatic source having three transverse modes having three distinct wavelengths. It is noted that the modal dispersion is then substantially zero; the modal dispersion induced by the chromatic dispersion has been compensated for by the modal dispersion for a given parameter α of the profile.
FIG. 6 illustrates the principle of the transformation of the DMD graph for a fiber according to the present invention. The value of parameter α of the fiber according to the present invention is chosen such that the multimode fiber has, at a given wavelength, a dispersion modal delay (DMD) that is controlled at each radial point of the fiber.
The term “delay” Δt is used to designate the time lag between (i) a light pulse after propagation over a given length L of fiber at a radial distance r from the center of the fiber and (ii) a light pulse of the same wavelength being propagated over the same length L at the center of the fiber. It should be understood, however, that this “delay” can just as well be an “advance” in that the light pulse being propagated at a radial distance r from the center of the fiber can arrive before the light pulse being propagated at the center of the fiber.
The multimode optical fiber according to the present invention has a graded-index profile with a value of parameter α optimized such that a DMD measurement gives an equivalent modal dispersion value of less than 0.11 ps/m. In this regard, the DMD measurement on a modified DMD graph comports with the standard FOTP-220 with a light pulse duration ΔTRef at a quarter of the height at the end of the fiber having length L, such that ΔTRef/L=0.11 ps/m.
The term “equivalent modal dispersion” refers to the delay, taking account of the chromatic dispersion, measured starting from a modified DMD graph and calculated according to the method defined in the standard FOTP-220 described with reference to FIG. 7.
In accordance with the foregoing, the DMD graph is modified by adding a delay Δttrace to each trace according to the equation:




  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  




wherein,

    
    
        rtrace is the center position of the injection of the light pulse corresponding to the trace measured;
        a is the core radius of the multimode fiber;
        Δλmax is the maximum spectral width of the source that can be used with the fiber;
        D is the chromatic dispersion of the multimode fiber at the emission wavelength of the source; and
        L is the length of the optical link.
    
    


From such a modified DMD graph, the equivalent modal dispersion is calculated according to the equation defined by the standard FOTP-220:

DMDinner&outer=(touter−tinner−ΔTref)/L 

The invention proposes optimizing the value of parameter α of the multimode fiber for applications in which the chromatic dispersion cannot be disregarded (e.g., when the source used is a transverse multimode source and when the fiber length is such that the chromatic dispersion induces a modal dispersion that cannot be ignored). The modification of the DMD graph for calculating an equivalent modal dispersion will be carried out only for source-fiber pairs verifying the equation, (Δλmax×D)>0.07 ps/m, (i.e., for fibers intended to be used with sources having a non-negligible spectral width).

The modification of the DMD graph to take account of the chromatic dispersion makes it possible to guarantee a calculated effective bandwidth (EBc) greater than 6000 MHz-km for multimode fibers used with transverse multimode sources.
The coefficient β (of the relationship adding a delay Δttrace to each trace of the DMD graph) can be larger than or equal to 1 (e.g., 1 or 2). The delay added to each trace must make it possible to compensate the delay of the edge modes with respect to the central modes induced by the chromatic dispersion. The dispersion modal delay imposed in the fiber by the choice of parameter α compensates for the advance induced by the chromatic dispersion for a given wavelength.
The fiber according to the present invention is optimized for use with a given polychromatic emission source having several transverse modes and for an optical link of a given length.
The maximum spectral width of the source can be between 1 nanometer and 2 nanometers. Most of the commercially available VCSELs have an RMS (Root Mean Square) spectral width, measured as a standard deviation relative to the wavelength of greatest power, between 0 and 0.46 nanometers; a value λRMS of 0.46 nanometers would lead to a maximum spectral width Δλmax on the order of 2 nanometers.
Multimode fibers are typically used for short-distance applications and local networks. The fiber lengths typically used are between a few meters and several hundred meters. In such a deployment, the modal dispersion induced by the chromatic dispersion remains limited and it is possible to compensate for it by a fiber profile with an optimized graded-index.
Testing has shown that the fiber according to the present invention has surprisingly better system performance when the chromatic dispersion is non-negligible. Tests have been carried out with a source having an RMS spectral width of 0.33 nanometer and a multimode fiber having a length of 750 meters. The effective bandwidths (EBc) calculated after modification of the DMD graph according to the present invention are effectively better correlated with the system performance than are the effective modal bandwidths (EMBc).
FIGS. 8 and 9 show tests illustrating the sensitivity of an optical system for multimode fibers according to whether the chromatic dispersion is taken into account (FIG. 9) or not (FIG. 8).
As noted, FIG. 8 shows the correlation between the power received (Prec) by an optical receiver for a binary error rate (BER) of 10−8 and the calculated effective modal bandwidth (EMBc) without modification of the DMD graph to take into account the chromatic dispersion.
FIG. 9 shows the correlation between the power received (Prec) by an optical receiver for a binary error rate (BER) of 10−8 and the calculated effective bandwidth (EBc) from the DMD graph modified to take into account the chromatic dispersion.
For calculation purposes, the sources in the simulations of FIGS. 8 and 9 are VCSELs with a maximum spectral width value Δλmax of 1.1 nanometers and a fiber length L of 750 meters. The calculation of the delay Δttrace uses a chromatic dispersion value D of −100 ps/(nm·km).
Those having ordinary skill in the art will appreciate that, typically, the BER is a function of the bandwidth of the fiber. There is a strong theoretical correlation between the two. The bandwidth is the result of the chromatic dispersion and the modal dispersion. When the source is defined, the value of the chromatic dispersion bandwidth is fixed. It is therefore expected that the binary error rate will no longer be a function only of the modal dispersion. Two fibers having the same modal dispersion but a different alpha, for example, should have the same BER.
In this regard, FIG. 8 shows that two fibers having the same EMBc value have significantly different penalties (e.g., fibers 117 and 103 versus fibers 105, 107 and 108). Similarly, fiber 101, which clearly has an EMBc value greater than the others, does not have a better system performance than fiber 110. Therefore, the selection of multimode fibers solely according to the effective modal bandwidth (EMB) criterion is not the most favorable for system applications using polychromatic sources having multiple transverse modes.
The fact of “simulating” the effect of the chromatic dispersion, knowing the coupling mechanism between a VCSEL and a multimode fiber, by artificially modifying the delay times on the DMD graph according to the formula:




  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  




makes it possible to effectively compensate for the modal dispersion induced by the chromatic dispersion in order to achieve (i) an equivalent modal dispersion value at the end of the fiber of less than 0.11 ps/m and (ii) an effective bandwidth greater than 6000 MHz-km.

Comparatively, FIG. 9 shows that fibers 103 and 117 have a narrower effective bandwidth EB than fibers 105, 107 and 108. This proves, in fact, that their respective system performances are not as good. This is not apparent from FIG. 8, however, in which fibers 103, 105, 107, 108 and 117 all have substantially equal bandwidths (i.e., the fibers would have been considered to be of the same quality.)
Similarly, in FIG. 9, fibers 101 and 110 have close bandwidth values for similar system performance. This is not the case in FIG. 8 where fiber 101 appears to be clearly better than fiber 110.
The present invention, therefore, makes it possible to select multimode optical fibers having optimum system performances. The selection of the fibers can take place in the following manner:
Multimode optical fibers are manufactured according to any known technique. Each multimode optical fiber has a graded-index profile with a given value of parameter α. A measurement of the dispersion modal delay is carried out for each fiber, starting with a DMD graph plotted for each fiber. This modal dispersion can be measured according to the recommendations of the standard FOTP-220 (i.e., the modal dispersion DMDinner&outer is measured at a quarter of the height of the leading edge of the first trace and at a quarter of the height of the trailing edge of the last trace).
Each DMD graph of each fiber is then modified by adding a delay Δttrace to each trace:




  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  




wherein,

    
    
        rtrace is the center position of the injection of the light pulse corresponding to the trace;
        a is the core radius of the multimode fiber;
        D is the chromatic dispersion of the multimode fiber at the wavelength of the light pulse; and
        Δλmax is the maximum spectral width of the source intended to be used with the fiber.
    
    


Subsequently, the multimode optical fibers having an equivalent modal dispersion value measured on the modified DMD graph of less than 0.11 ps/m are selected. The use of such fibers makes it possible to produce high-speed Ethernet transmission networks over great distances having very good performances (e.g., with a distance by Gigabit Ethernet speed product greater than 3000 Gb/s·m.)
The present invention is not limited to the foregoing exemplary embodiments. In particular, it is within the scope of the present invention to employ a fiber in combination with any type of a polychromatic source other than a VCSEL possessing several transverse modes, such as light-emitting diodes (LEDs).
This application incorporates entirely by reference the following commonly assigned patent application publication and patent applications: U.S. Patent Application No. 60/986,737 for a Microbend-Resistant Optical Fiber, filed Nov. 9, 2007, (Overton); U.S. Patent Application No. 61/041,484 for a Microbend-Resistant Optical Fiber, filed Apr. 1, 2008, (Overton); U.S. Patent Application No. 61/112,595 for a Microbend-Resistant Optical Fiber, filed Nov. 7, 2008, (Overton); International Patent Application Publication No. WO 2009/062131 A1 for a Microbend-Resistant Optical Fiber, (Overton); and U.S. patent application Ser. No. 12/267,732 for a Microbend-Resistant Optical Fiber, filed Nov. 10, 2008, (Overton).
This application further incorporates entirely by reference the following commonly assigned patents, patent application publications, and patent applications: U.S. Pat. No. 4,838,643 for a Single Mode Bend Insensitive Fiber for Use in Fiber Optic Guidance Applications (Hodges et al.); U.S. Patent Application Publication No. US2007/0127878 A1 for a Single Mode Optical Fiber (de Montmorillon et al.); U.S. Patent Application Publication No. US2007/0280615 A1 for a Single-Mode Optical Fiber (de Montmorillon et al.); U.S. Pat. No. 7,356,234 for a Chromatic Dispersion Compensating Fiber (de Montmorillon et al.); U.S. Pat. No. 7,483,613 for a Chromatic Dispersion Compensating Fiber (de Montmorillon et al.); U.S. Patent Application Publication No. US2008/0152288 A1 for an Optical Fiber (Flammer et al.); U.S. patent application Ser. No. 12/098,804 for a Transmission Optical Fiber Having Large Effective Area (Sillard et al.), filed Apr. 7, 2008; U.S. patent application Ser. No. 12/418,523 for a Dispersion-Shifted Optical Fiber (Sillard et al.), filed Apr. 3, 2009; U.S. patent application Ser. No. 12/436,423 for a Single-Mode Optical Fiber Having Reduced Bending Losses, filed May 6, 2009, (de Montmorillon et al.); U.S. patent application Ser. No. 12/436,484 for a Bend-Insensitive Single-Mode Optical Fiber, filed May 6, 2009, (de Montmorillon et al.); U.S. patent application Ser. No. 12/489,995 for a Wavelength Multiplexed Optical System with Multimode Optical Fibers, filed Jun. 23, 2009, (Lumineau et al.); U.S. Patent Application No. 61/101,337 for a Bend-Insensitive Optical Fiber, filed Sep. 30, 2008, (de Montmorillon et al.); U.S. Patent Application No. 61/112,006 for a Bend-Insensitive Single-Mode Optical Fiber, filed Nov. 6, 2008, (de Montmorillon et al.); and U.S. Patent Application No. 61/112,374 for a Bend-Insensitive Single-Mode Optical Fiber, filed Nov. 7, 2008, (de Montmorillon et al.).
This application further incorporates entirely by reference the following commonly assigned patents, patent application publications, and patent applications: U.S. Pat. No. 5,574,816 for Polypropylene-Polyethylene Copolymer Buffer Tubes for Optical Fiber Cables and Method for Making the Same; U.S. Pat. No. 5,717,805 for Stress Concentrations in an Optical Fiber Ribbon to Facilitate Separation of Ribbon Matrix Material; U.S. Pat. No. 5,761,362 for Polypropylene-Polyethylene Copolymer Buffer Tubes for Optical Fiber Cables and Method for Making the Same; U.S. Pat. No. 5,911,023 for Polyolefin Materials Suitable for Optical Fiber Cable Components; U.S. Pat. No. 5,982,968 for Stress Concentrations in an Optical Fiber Ribbon to Facilitate Separation of Ribbon Matrix Material; U.S. Pat. No. 6,035,087 for an Optical Unit for Fiber Optic Cables; U.S. Pat. No. 6,066,397 for Polypropylene Filler Rods for Optical Fiber Communications Cables; U.S. Pat. No. 6,175,677 for an Optical Fiber Multi-Ribbon and Method for Making the Same; U.S. Pat. No. 6,085,009 for Water Blocking Gels Compatible with Polyolefin Optical Fiber Cable Buffer Tubes and Cables Made Therewith; U.S. Pat. No. 6,215,931 for Flexible Thermoplastic Polyolefin Elastomers for Buffering Transmission Elements in a Telecommunications Cable; U.S. Pat. No. 6,134,363 for a Method for Accessing Optical Fibers in the Midspan Region of an Optical Fiber Cable; U.S. Pat. No. 6,381,390 for a Color-Coded Optical Fiber Ribbon and Die for Making the Same; U.S. Pat. No. 6,181,857 for a Method for Accessing Optical Fibers Contained in a Sheath; U.S. Pat. No. 6,314,224 for a Thick-Walled Cable Jacket with Non-Circular Cavity Cross Section; U.S. Pat. No. 6,334,016 for an Optical Fiber Ribbon Matrix Material Having Optimal Handling Characteristics; U.S. Pat. No. 6,321,012 for an Optical Fiber Having Water Swellable Material for Identifying Grouping of Fiber Groups; U.S. Pat. No. 6,321,014 for a Method for Manufacturing Optical Fiber Ribbon; U.S. Pat. No. 6,210,802 for Polypropylene Filler Rods for Optical Fiber Communications Cables; U.S. Pat. No. 6,493,491 for an Optical prop Cable for Aerial Installation; U.S. Pat. No. 7,346,244 for a Coated Central Strength Member for Fiber Optic Cables with Reduced Shrinkage; U.S. Pat. No. 6,658,184 for a Protective Skin for Optical Fibers; U.S. Pat. No. 6,603,908 for a Buffer Tube that Results in Easy Access to and Low Attenuation of Fibers Disposed Within Buffer Tube; U.S. Pat. No. 7,045,010 for an Applicator for High-Speed Gel Buffering of Flextube Optical Fiber Bundles; U.S. Pat. No. 6,749,446 for an Optical Fiber Cable with Cushion Members Protecting Optical Fiber Ribbon Stack; U.S. Pat. No. 6,922,515 for a Method and Apparatus to Reduce Variation of Excess Fiber Length in Buffer Tubes of Fiber Optic Cables; U.S. Pat. No. 6,618,538 for a Method and Apparatus to Reduce Variation of Excess Fiber Length in Buffer Tubes of Fiber Optic Cables; U.S. Pat. No. 7,322,122 for a Method and Apparatus for Curing a Fiber Having at Least Two Fiber Coating Curing Stages; U.S. Pat. No. 6,912,347 for an Optimized Fiber Optic Cable Suitable for Microduct Blown Installation; U.S. Pat. No. 6,941,049 for a Fiber Optic Cable Having No Rigid Strength Members and a Reduced Coefficient of Thermal Expansion; U.S. Pat. No. 7,162,128 for Use of Buffer Tube Coupling Coil to Prevent Fiber Retraction; U.S. Pat. No. 7,515,795 for a Water-Swellable Tape, Adhesive-Backed for Coupling When Used Inside a Buffer Tube (Overton et al.); International Patent Application Publication No. WO 2007/013923 A2 for a Grease-Free Buffer Optical Fiber Buffer Tube Construction Utilizing a Water-Swellable, Texturized Yarn (Overton et al.); European Patent Application Publication No. 1,921,478 A1, for a Telecommunication Optical Fiber Cable (Tatat et al.); U.S. Patent Application Publication No. US2007/0183726 A1 for an Optical Fiber Cable Suited for Blown Installation or Pushing Installation in Microducts of Small Diameter (Nothofer et al.); U.S. Patent Application Publication No. US 2008/0037942 A1 for an Optical Fiber Telecommunications Cable (Tatat); U.S. Patent Application Publication No. US2008/0145010 A1 for a Gel-Free Buffer Tube with Adhesively Coupled Optical Element (Overton et al.); U.S. Patent Application Publication No. US2008/0181564 A1 for a Fiber Optic Cable Having a Water-Swellable Element (Overton); U.S. Patent Application Publication No. US2009/0041414 A1 for a Method for Accessing Optical Fibers within a Telecommunication Cable (Lavenne et al.); U.S. Patent Application Publication No. US2009/0003781 A1 for an Optical Fiber Cable Having a Deformable Coupling Element (Parris et al.); U.S. Patent Application Publication No. US2009/0003779 A1 for an Optical Fiber Cable Having Raised Coupling Supports (Parris); U.S. Patent Application Publication No. US2009/0003785 A1 for a Coupling Composition for Optical Fiber Cables (Parris et al.); U.S. patent application Ser. No. 12/391,327 for a Buffer Tube with Hollow Channels, filed Feb. 24, 2009, (Lookadoo et al.); and U.S. patent application Ser. No. 12/466,965 for an Optical Fiber Telecommunication Cable, filed May 15, 2009.
In the specification and/or figures, typical embodiments of the invention have been disclosed. The present invention is not limited to such exemplary embodiments. The figures are schematic representations and so are not necessarily drawn to scale. Unless otherwise noted, specific terms have been used in a generic and descriptive sense and not for purposes of limitation.

## Claims

1. A multimode optical fiber, wherein the multimode optical fiber possesses a refractive index profile such that a measurement of the dispersion modal delay (DMD), the DMD graph of which has been modified by adding a positive delay (Δttrace) to each trace:




  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  



wherein
rtrace is the center position of the injection of the light pulse corresponding to the trace,
a is the core radius of the multimode optical fiber,
L is the length of the multimode optical fiber,
D is a chosen value for typical chromatic dispersion,
β is the coefficient of the delay, and
Δλmax is a chosen value for the maximum spectral width between the wavelength of the highest order mode and the wavelength of the lowest order mode such that (Δλmax×D)>0.07 ps/m,

gives a calculated effective bandwidth (EBc) of greater than 6000 MHz·km as calculated using the modified DMD graph.

2. The multimode optical fiber according to claim 1, wherein the multimode optical fiber has a calculated effective bandwidth (EBc) of greater than 9000 MHz·km as calculated using the modified DMD graph.

3. The multimode optical fiber according to claim 1, wherein the multimode optical fiber has a calculated effective bandwidth (EBc) of greater than 12,000 MHz·km as calculated using the modified DMD graph.

4. The multimode optical fiber according to claim 1, wherein D, the chosen value for typical chromatic dispersion, is between −80 ps/(nm·km) and −120 ps/(nm·km).

5. The multimode optical fiber according to claim 1, wherein D, the chosen value for typical chromatic dispersion, is the chromatic dispersion of the multimode optical fiber at the wavelength of the light pulse.

6. The multimode optical fiber according to claim 1, wherein the multimode optical fiber has chromatic dispersion between −80 ps/(nm·km) and −120 ps/(nm·km) for wavelengths between 840 nanometers and 860 nanometers.

7. The multimode optical fiber according to claim 1, wherein the coefficient of the delay (β) is equal to 1.

8. The multimode optical fiber according to claim 1, wherein the coefficient of the delay (β) is greater than 1.

9. The multimode optical fiber according to claim 1, wherein the coefficient of the delay (β) is equal to 2.

10. The multimode optical fiber according to claim 1, wherein the multimode optical fiber has a graded-index profile.

11. The multimode optical fiber according to claim 1, wherein:
the measurement of the dispersion mode delay (DMD) on the modified DMD graph comports with the standard FOTP-220 with a light pulse duration ΔTRef at a quarter of the height at the end of the multimode optical fiber having the length L; and
ΔTRef/L is about 0.11 ps/m or less.

12. An optical system, comprising:
a polychromatic optical source for emitting multiple transverse modes having a maximum spectral width; and
an optical link comprising the multimode optical fiber according to claim 1.

13. The optical system according to claim 12, wherein the polychromatic optical source has a maximum spectral width of between 1 nanometer and 2 nanometers.

14. The optical system according to claim 12, wherein:
the polychromatic optical source has a maximum spectral width and the multimode optical fiber has a chromatic dispersion such that the product of the polychromatic optical source's maximum spectral width and the multimode optical fiber's chromatic dispersion is greater than 0.07 ps/m; and
the multimode optical fiber has an equivalent modal dispersion value of less than 0.11 ps/m.

15. The optical system according to claim 12, wherein:
the polychromatic optical source defines the maximum spectral width (Δλmax) and the multimode optical fiber defines the chromatic dispersion (D) such that Δλmax×D is greater than 0.07 ps/m; and
the multimode optical fiber has an equivalent modal dispersion value of less than 0.11 ps/m.

16. The optical system according to claim 12, wherein the polychromatic optical source has a Root Mean Square spectral width of between 0 and 0.46 nanometers.

17. The optical system according to claim 12, wherein the polychromatic optical source is a surface emitting laser (VCSEL) or a light-emitting diode (LED).

18. The optical system according to claim 12, wherein the optical system has a distance by Gigabit Ethernet rate product greater than 3000 Gb/s·m.

19. A multimode optical fiber having a graded-index profile, wherein:
at wavelengths between 840 nanometers and 860 nanometers, the multimode optical fiber has chromatic dispersion between −80 ps/(nm·km) and −120 ps/(nm·km); and
the multimode optical fiber has a calculated effective bandwidth (EBc) greater than 6000 MHz·km as calculated from measurements on a DMD graph;
wherein the DMD graph is modified by adding a positive delay (Δttrace) to each trace:





  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  



wherein,
rtrace is the center position of the injection of the light pulse corresponding to the trace,
a is the core radius of the multimode optical fiber,
L is the length of the multimode optical fiber,
D is the chromatic dispersion of the multimode optical fiber at the wavelength of the light pulse,
β is the coefficient of the delay, β being greater than or equal to 1, and
Δλmax is a chosen value for the maximum spectral width between the wavelength of the highest order mode and the wavelength of the lowest order mode such that (Δλmax×D)>0.07 ps/m; and

wherein the calculated effective bandwidth (EBc) is calculated from measurements on the modified DMD graph at a quarter of the height of the leading edge of the first trace and at a quarter of the height of the trailing edge of the last trace.

20. The multimode optical fiber according to claim 19, wherein the multimode optical fiber has a calculated effective bandwidth (EBc) of greater than 8000 MHz·km as calculated using the modified DMD graph.

21. The multimode optical fiber according to claim 19, wherein the multimode optical fiber has a calculated effective bandwidth (EBc) of greater than 11,000 MHz·km as calculated using the modified DMD graph.

22. A method for characterizing a multimode optical fiber, comprising:
measuring the dispersion modal delay on a DMD graph plotted for a multimode optical fiber, wherein the modal dispersion (DMDinner&outer) is measured at a quarter of the height of the leading edge of the first trace and at a quarter of the height of the trailing edge of the last trace;
modifying the DMD graph of the multimode optical fiber by adding a positive delay (Δttrace) to each trace:





  
    Δ
    ⁢
    
      
    
    ⁢
    
      t
      trace
    
  
  =
  
    Δ
    ⁢
    
      
    
    ⁢
    
      λ
      max
    
    ×
    D
    ×
    
      
        L
        ⁡
        
          (
          
            
              r
              trace
            
            a
          
          )
        
      
      β
    
  



wherein
rtrace is the center position of the injection of the light pulse corresponding to the trace,
a is the core radius of the multimode optical fiber,
L is the length of the multimode optical fiber,
D is a chosen value for typical chromatic dispersion,
β is the coefficient of the delay, and
Δλmax, is a chosen value for the maximum spectral width between the wavelength of the highest order mode and the wavelength of the lowest order mode; and

determining calculated effective bandwidth (EBc) for the multimode optical fiber using the modified DMD graph.

23. The method for characterizing a multimode optical fiber according to claim 22, wherein (Δλmax×)>0.07 ps/m.

24. The method for characterizing a multimode optical fiber according to claim 23, wherein D, the chosen value for chromatic dispersion, is between −80 ps/(nm·km) and −120 ps/(nm·km).

25. The method for characterizing a multimode optical fiber according to claim 23, wherein D, the chosen value for chromatic dispersion, is about −100 ps/(nm·km).

26. The method for characterizing a multimode optical fiber according to claim 23, wherein Δλmax, the chosen value for maximum spectral width, is between 1 nanometer and 2 nanometers.

27. The method for characterizing a multimode optical fiber according to claim 23, wherein Δλmax, the chosen value for maximum spectral width, is about 1.1 nanometers.

28. A method for selecting multimode optical fibers, comprising:
performing the method of claim 23 for each of a plurality of multimode optical fibers; and
selecting those multimode optical fibers having a calculated effective bandwidth (EBc) greater than 6000 MHz·km.

29. A method for selecting multimode optical fibers, comprising:
performing the method of claim 23 for each of a plurality of multimode optical fibers; and
selecting those multimode optical fibers having a calculated effective bandwidth (EBc) greater than 9000 MHz·km.

30. A method for selecting multimode optical fibers, comprising:
performing the method of claim 23 for each of a plurality of multimode optical fibers; and
selecting those multimode optical fibers having a calculated effective bandwidth (EBc) greater than 12,000 MHz·km.

31. A method for selecting multimode optical fibers, comprising:
performing the method of claim 23 for each of a plurality of multimode optical fibers; and
selecting those multimode optical fibers having an equivalent modal dispersion value of less than 0.11 ps/m as measured on the modified DMD graph.

32. A method for selecting multimode optical fibers, comprising:
performing the method of claim 23 for each of a plurality of multimode optical fibers; and
selecting those multimode optical fibers having actual chromatic dispersion between −80 ps/(nm·km) and −120 ps/(nm·km) at wavelengths between 840 nanometers and 860 nanometers.