Abstract:
Multicore optical fibers that include between two and ten multimode cores surrounded by a cladding matrix and symmetrically arranged about a fiber axis are disclosed, with no core running along the fiber axis. The cores include a trench to stabilize delays of the higher order modes, which tend to propagate faster than do the central modes due to the amount of power at the core-clad interface. The trench also suppresses crosstalk and power leakage. The core configuration promotes efficient optical alignment and optical coupling with other multicore optical fibers or light sources, such as VSCEL and silicon-photonics light sources.

Description:
This application claims the benefit of priority under 35 U.S.C. §119 of U.S. Provisional Application Ser. No. 61/912,704 filed on Dec. 6, 2013, the content of which is relied upon and incorporated herein by reference in its entirety. 
    
    
     FIELD 
     The present disclosure relates to multicore optical fibers, and in particular relates to multicore optical fibers having multimode cores. 
     BACKGROUND 
     Optical fibers are used in a variety of telecommunications applications, including high-capacity data transmission for networks, data centers and server clusters. Conventional high-capacity optical-fiber links typically include cables (e.g., ribbon cables) that include conventional single-core multimode optical fibers, with each fiber carrying a single data channel. Unfortunately, such cables are limited in their connection density and tend to be bulky. 
     Multicore optical fibers (“multicore fibers”) have been developed in part to provide higher data capacity. A multicore fiber has multiple cores embedded in a single cladding, and these cores tend to be single-mode cores with diameters less than 10 microns. Multicore fibers thus promise higher density connections as well as greater data capacity than do conventional fibers. However, multicore fibers tend to be difficult to use in high-capacity data transmission applications since the cores are fixed in place and each core needs to be aligned with high accuracy to a corresponding optical transmitter or optical receiver. 
     SUMMARY 
     An aspect of the disclosure is a multicore optical fiber (“multicore fiber”). The multicore fiber has a cladding matrix that defines a fiber axis. The cladding matrix has a diameter DM in the range 120 μm≦DM≦220 μm. The multicore fiber also has a plurality of N multimode cores wherein 2≦N≦10. Each core is surrounded by the cladding matrix and has a central core axis that runs generally parallel to the fiber axis. None of the cores run along the fiber axis. The multimode cores are symmetrically arranged about the fiber axis with their central core axes at a radial distance RC. The multimode cores have a core pitch CP (center-to-center spacing) in the range 30 μm≦CP≦60 μm, with each multimode core having a core diameter d CO  in the range 20 μm≦d CO ≦40 μm. Each multimode core includes an inner core having a radius r CI  in the range 6 μm≦r CI ≦18 μm, a core α in the range 1.9≦α≦2.2 and a maximum core Δ of Δ 0  in the range 0.6%≦Δ 0 ≦1.9%. The inner core is surrounded by a trench having a relative refractive index Δ T  in the range −0.7%≦Δ T ≦−0.1% and a width δr T  in the range 1 μm≦δr T ≦6 μm. The trench is separated from the inner core by an inner cladding having a width δr ICL  in the range 0.5 μm≦δr ICL ≦2 μm. In an example, the inner cladding width δr ICL  is an optimum width δr ICL-OPT  that is related to the inner core radius r CI  and the relative refractive index of the trench Δ T  by the formula δr ICL-OPT =0.053 r CI −0.586 Δ T . In an example, the inner cladding width δr ICL  is within 10% of the optimum width, i.e., is in the range defined by (0.9)·δr ICL-OPT ≦δr ICL (1.1)·δr ICL-OPT . 
     Another aspect of the disclosure is a multicore fiber. The multicore fiber has a plurality of N multimode cores for 4≦N≦8 arranged symmetrically about a fiber axis and surrounded by a uniform silica cladding matrix having a diameter DM in the range 120 μm≦DM≦220 μm. Each core has a central axis located at a radius RC from the fiber axis and has a core diameter d CO  in the range 20 μm≦d CO =40 μm. Each multimode core includes an inner core having a radius r CI  in the range 6 μm≦r CI ≦18 μm, a core α in the range 1.9≦α≦2.2 and a maximum core Δ of Δ 0  in the range 0.6%≦Δ 0 ≦1.9%. The cores define a core pitch CP in the range 30 μm≦CP≦60 μm. Each core also includes an inner core, an inner cladding surrounding the inner core and a trench surrounding the inner cladding. None of the cores run along the fiber axis. 
     Another aspect of the disclosure is a multicore optical fiber that consists of: a plurality of N multimode cores for 4≦N≦8 arranged symmetrically about a fiber axis and surrounded by a uniform silica cladding matrix having a diameter DM in the range 120 μm≦DM≦220 μm, with each core having a central axis located at a radius RC from the fiber axis and having a core diameter d CO  in the range 20 μm≦d CO ≦40 μm. Each multimode core includes an inner core having a radius r CI  in the range 6 μm≦r CI ≦18 μm a core α in the range 1.9≦α≦2.2 and a maximum core Δ of Δ 0  in the range 0.6%≦Δ 0 ≦1.9%, the cores defining a pitch CP in the range 30 μm≦CP≦60 μm; and wherein each core consists of an inner core, an inner cladding surrounding the inner core and a trench surrounding the inner cladding. 
     The configuration of the individual cores and the arrangement of the cores within the cladding matrix serve to improve (as compared to single-mode cores) the optical coupling and alignment of the multicore optical fiber with either another multicore optical fiber or devices such as VCSELs and silicon-photonic emitters and receivers. The size of the multimode cores is larger than that of single-mode cores but is not as large as the typical multimode-core diameter of 50 μm. Thus, multimode cores with an inner core having a diameter in the range of 12 μm to 36 μm are expected to have a light-coupling efficiency of 15× to 30× greater than that of single-mode cores while also keeping the overall size of the multicore fiber relatively compact. Furthermore, the core pitch can be selected to generally match that of silicon-photonic devices and VCSEL light sources. The absence of a central core that runs down the fiber axis serves to maintain the symmetry of the multicore fiber so that all the cores have the same light-carrying properties and characteristics while the chance of cross-talk or other interference between the cores is also reduced. In addition, it is believed that skew, which is the difference in signal propagation time between fiber channels in synchronous parallel data transmission, will be minimized with this symmetric core configuration 
     Additional features and advantages are set forth in the Detailed Description that follows, and in part will be readily apparent to those skilled in the art from the description or recognized by practicing the embodiments as described in the written description and claims hereof, as well as the appended drawings. It is to be understood that both the foregoing general description and the following Detailed Description are merely exemplary and are intended to provide an overview or framework to understand the nature and character of the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings are included to provide a further understanding and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s) and together with the Detailed Description serve to explain principles and operation of the various embodiments. As such, the disclosure will become more fully understood from the following Detailed Description, taken in conjunction with the accompanying Figures, in which: 
         FIG. 1  is an isometric view of a section of an example multicore fiber according to the disclosure; 
         FIGS. 2A and 2B  are front-on views of example multicore fibers according to the disclosure; 
         FIG. 3  is a close-up front-end view of an example core used in the multicore fiber disclosed herein; 
         FIG. 4  is a plot of the core Δ(%) versus core radius r (no units) showing relative refractive indices of the inner core, the inner cladding and the trench surrounding the inner cladding; 
         FIG. 5  is similar to  FIG. 2A  and shows an example multicore fiber having six cores; 
         FIG. 6  is similar to  FIG. 5  and shows an example multicore fiber having eight cores. 
         FIG. 7  is a plot of the inner cladding width δr ICL  (μm) versus the core radius r CI  (μm) for the nineteen different example cores described below; and 
         FIG. 8  is an end-on microscope image of an example multicore fiber that has six cores as shown in  FIG. 5  and as set forth as Example 2.1, below. 
     
    
    
     DETAILED DESCRIPTION 
     Reference is now made in detail to various embodiments of the disclosure, examples of which are illustrated in the accompanying drawings. Whenever possible, the same or like reference numbers and symbols are used throughout the drawings to refer to the same or like parts. The drawings are not necessarily to scale, and one skilled in the art will recognize where the drawings have been simplified to illustrate the key aspects of the disclosure. 
     The claims as set forth below are incorporated into and constitute a part of this Detailed Description. 
     The entire disclosure of any publication or patent document mentioned herein is incorporated by reference. 
     Cartesian coordinates are shown in some of the Figures for the sake of reference and are not intended to be limiting as to direction or orientation. 
     The term “relative refractive index,” as used herein in connection with the multimode fibers and fiber cores discussed below, is defined as:
 
Δ( r )=[ n ( r ) 2   −n   REF   2 )]/2 n ( r ) 2 ,
 
where n(r) is the refractive index at radius r, unless otherwise specified. The relative refractive index is defined at the operating wavelength λ p , which is the wavelength where the multimode core of the optical fiber is designed to work optimally, e.g., where the differential mode delay is minimized. In one aspect, the reference index n REF  is silica glass. In another aspect, n REF  is the maximum refractive index of the cladding matrix (introduced and discussed below). The refractive index n 0  is the maximum index of the index profile. In most cases, n 0 =n(0). As used herein, the relative refractive index is represented by Δ and its values are given in units of “%,” unless otherwise specified. In cases where the refractive index of a region is less than the reference index n REF , the relative refractive index is negative and is referred to below as a trench. The minimum relative refractive index is calculated at the point at which the relative index is most negative, unless otherwise specified. In cases where the refractive index of a region is greater than the reference index n REF , the relative refractive index is positive and the region can be said to be raised or to have a positive index.
 
     The alpha parameter α as used herein relates to the relative refractive index A, which is in units of “%,” where r is the radius (radial coordinate) of the fiber, and which is defined by: 
                 Δ   ⁡     (   r   )       =       Δ   0     ⁡     [     1   -       (       r   -     r   m           r   0     -     r   m         )     α       ]         ,         
where r m  is the point at which Δ(r) is the maximum Δ 0 , r 0  is the point at which Δ(r)% is zero and r is in the range r i ≦r≦r f , where Δ(r) is defined above, r, is the initial point of the α-profile, r f  is the final point of the α-profile and a is an exponent that is a real number. For a step index profile, α&gt;10, and for a gradient-index profile, α&lt;5. It is noted here that different forms for the core radius r 0  and maximum relative refractive index Δ 0  can be used without affecting the fundamental definition of Δ. For a practical fiber, even when the target profile is an alpha profile, some level of deviation from the ideal situation can occur. Therefore, the alpha parameter α for a practical fiber is obtained from a best fit of the measured index profile. An alpha parameter in the range 2.05≦α≦2.15 provides a minimum for the differential mode delay (DMD) at 850 nm and an alpha parameter in the range 1.95≦α≦2.05 provides a minimum for the DMD at 1300 nm.
 
     The modal bandwidth (or overfill bandwidth) of an optical fiber is denoted BW and is defined herein as using overfilled launch conditions at 850 nm according to IEC 60793-1-41 (TIA-FOTP-204), “Measurement Methods and Test Procedures: Bandwidth.” The minimum calculated effective modal bandwidths BW can be obtained from measured DMD spectra as specified by IEC 60793-1-49 (TIA/EIA-455-220), “Measurement Methods and Test Procedures: Differential Mode Delay.” The units of bandwidth for an optical fiber can be expressed in MHz·km, GHz·km, etc., and a bandwidth expressed in these kinds of units is also referred to in the art as the bandwidth-distance product. The modal bandwidth is defined in part by modal dispersion. At the system level, the overall bandwidth can be limited by chromatic dispersion, which limits the system performance at a high bit rate. 
     The limits on any ranges cited herein are considered to be inclusive and thus to lie within the range, unless otherwise specified. 
     The numerical aperture or NA means the numerical aperture as measured using the method set forth in IEC-60793-1-43 (TIA SP3-2839-URV2 FOTP-177), “Measurement Methods and Test Procedures: Numerical Aperture.” 
       FIG. 1  is an isometric view of a section of a multicore fiber  10 , and  FIGS. 2A and 2B  are front-on views of example multicore fibers according to the disclosure. The multicore fiber  10  includes a central fiber axis AF, a cladding matrix  20  with an outer surface  22  and a radius RM, and a plurality of multimode cores (“cores”)  30  (individually denoted  30   a,    30   b,  etc.) that run the length of the multicore fiber generally parallel to the central axis. Each core has a central axis AC, a radius r CO  and a diameter d CO =2·r CO . Only one core  30  is shown as running the length of multicore fiber  10  in  FIG. 1  for ease of illustration. There is no central core  30 , i.e., there is no core that runs down the central fiber axis AF. In an example, cladding matrix  20  is uniform, i.e., it is made of a single material, such as pure (undoped) silica. The multicore fiber  10  has an operating wavelength λ p . 
       FIG. 2A  shows an example multicore fiber  10  having an outer coating  50  that contacts and surrounds outer surface  22  of cladding matrix  20 . In an example, coating  50  has a Young&#39;s modulus of less than 1.0 MPa, preferably of less than 0.9 MPa and in preferred embodiments of not more than 0.8 MPa. In another example illustrated in  FIG. 2B , multicore fiber  10  includes coating  50  as a primary coating and a secondary coating  52  that contacts and surrounds the primary coating. In an example, secondary coating  52  has a Young&#39;s modulus of greater than 1,200 MPa and in other embodiments of greater than 1,400 MPa. 
     As used herein, the Young&#39;s modulus, elongation to break, and tensile strength of a cured polymeric material of a primary coating is measured using a tensile testing instrument (e.g., a Sintech MTS Tensile Tester or an INSTRON Universal Material Test System) on a sample of a material shaped as a film between about 0.003″ (76 microns) and 0.004″ (102 microns) in thickness and about 1.3 cm in width, with a gauge length of 5.1 cm and a test speed of 2.5 cm/min. Additional description of suitable primary and secondary coatings  50  and  52  can be found in PCT Publication WO2005/010589. 
     The cores  30  are arranged symmetrically about central fiber axis AF with core axes AC located at a radius RC&lt;RM and have a center-to-center spacing CP. The cores  30  have an alpha parameter α and a relative refractive index Δ (“core Δ”) as described in greater detail below. The cores  30 , in combination with the surrounding cladding matrix  20 , define a core numerical aperture NA C . 
       FIG. 3  is a close-up front-end view of an example core  30 . The core  30  includes an inner core  32 , an inner cladding  33  that surrounds the inner core and a trench  34  that surrounds the inner cladding.  FIG. 4  is a plot of the core Δ versus core radius r showing inner core  32 , inner cladding  33  and trench  34  surrounding the inner cladding. The trench  34  has a relative refractive index Δ=Δ T , while cladding matrix  20  has a relative refractive index Δ=Δ CM . The trench  34  has a width δr T  and an outer radius r T . The inner cladding  33  has a relative refractive index Δ of Δ ICL , which is shown by way of example as being equal to Δ CM  of cladding matrix  20 . The inner cladding  33  has an outer radius r CL  and a width Δr ICL . 
     In examples, the depth of trench  34 , which is measured by the trench Δ of Δ T , satisfies Δ T &lt;−0.1%, or is in the range −0.7%≦Δ T ≦−0.1% or is in the range −0.5%≦Δ T ≦−0.2%. Also in examples, the width δr T  of trench  34  satisfies δr T ≧1 μm, or is in the range 1 μm≦δr T ≦6 μm or is in the range 2 μm≦δr T ≦5 μm. 
     As noted above, cores  30  are multimode, and trench  34  serves to equalize the delays of the higher order modes, which travel near the outer radius of the core and tend to propagate faster than the modes traveling in the center region of the multimode core due to the Goos-Hänchen effect. The trench also suppresses power leakage, which decreases macrobend losses compared to multimode cores that only have an inner core. In examples, the width δr ICL  of inner cladding  33  is in the range 0.5 μm≦δr ICL ≦2.0 μm, or 0.6 μm≦δr ICL ≦1.5 μm or 0.8 μm≦δr ICL ≦1.2 μm. The optimum inner cladding width δr ICL-OPT  is related to the inner core radius r CI  and the relative refractive index Δ T  of the trench  34  by the formula δr ICL-OPT =0.053 r CI −0.586 Δ T . In examples, multimode core  30  has a high overfilled modal bandwidth when |δr ICL −δr ICL-OPT |≦0.3 μm, or |δr ICL −δr ICL-OPT |≦0.2 μm, or |δr ICL −δr ICL-OPT |≦0.1 μm. Also in an example, the width δr ICL  is within 10% of the optimum width, i.e., is in the range defined by (0.9)·δr ICL-OPT ≦δr ICL ≦(1.1)·δr ICL-OPT . 
     The trench  34  also suppresses crosstalk and skew between cores  30 . In some embodiments, the crosstalk between adjacent cores  30  is less than −30 dB, or less than −35 dB or less than −40 dB. In some example embodiments, the skew between any two cores  30  of multicore fiber  10  is less than 5 ps/m, or less than 2 ps/m, or less than 1ps/m or less than 0.5 ps/m. 
     In an example embodiment, the number N of cores  30  can be 2≦N≦10, and in a further example embodiment is 4≦N≦8, and in a further example embodiment N=6. 
     Also in an example embodiment, the core diameter d CO  is in the range 20 μm≦d CO ≦40 μm and the core α is in the range 1.9≦α≦2.2. Further in an example embodiment, the core α is in the range 2.05≦α≦2.15 for λ p =850 nm or λ p  in the range from 800 nm≦λ p ≦900 nm; or the core α is in the range 2.0≦α≦2.1 for λ p =980 nm, λ p =1,060 nm, or λ p  in the range from 930 nm≦λ p ≦1110 nm; or the core α is in the range 1.95≦α≦2.05 for λ p =1,300 nm or λ p  in the range from 1250 nm≦λ p ≦1350 nm; or the core α is in the range 1.9≦α≦2.0 for λ p  in the range from 1520 nm≦λ p ≦1620 nm. 
     Further in example embodiments, the maximum core Δ, denoted Δ 0 , is in the range 0.6%≦Δ 0 ≦1.9%, or between 0.8%≦Δ 0 ≦1.3% or 0.9%≦Δ 0 ≦1.2% to enable respective numerical apertures NA C  in the ranges 0.16≦NA C ≦0.26, or 0.18≦NA C ≦0.24 or 0.185≦NA C ≦0.215. 
     Further in an example embodiment, multicore fiber  10  has a ratio between the inner core radius and inner cladding radius of p=r CI /r CL =0.94, which is the same as that of Corning® ClearCurve® multimode fiber. In other embodiments, ρ is between 0.9 and 0.95, or between 0.91 and 0.94, or between 0.92 and 0.94. Also in an example embodiment, diameter DM=2·RM of cladding matrix  20  satisfies the condition DM≦220 μm, and further in an example is in the range 120 μm≦DM≦220 μm. In some embodiments, 150 μm≦DM≦220 μm, 160 μm≦DM≦200 μm or 170 μm≦DM≦180 μm. In other embodiments, diameter DM is in the range 120 μm≦DM≦150 μm, or 120 μm≦DM≦140 μm or 120 μm≦DM≦130 μm. Further in examples, the center-to-center core pitch CP is in the range 30 μm≦CP≦60 μm, or 30 μm≦CP≦45 μm or 45 μm≦CP≦60 μm. 
     Example Multicore Preforms and Fibers 
     The multicore fiber  10  is formed by drawing a multicore preform using standard optical-fiber fabrication techniques known in the art. A multicore preform can be made by using different methods, for example, glass drilling, or stacking methods. In the following examples, the glass drilling method was used to form a multicore preform. In this method, a silica glass cylinder substrate is drilled with holes with the dimensions and locations according to a multicore fiber design. Then core canes with a designed index profile and with a diameter slightly smaller than the hole diameter are inserted into the holes to form a multicore preform. The core canes can be made by conventional preform manufacturing methods such as OVD, MCVD or PCVD. 
     The design parameters for nine example multicore fibers  10  are set forth below in Tables 1, 2 and 3. In the Tables, “PF” stands for “preform” and “MCF” stands for “multicore fiber.” In the design examples, it is assumed that the geometry of the fiber scales with the ratio of the fiber diameter over the preform diameter. The diameter of cladding matrix  20  is denoted DM while DH stands for “hole diameter” and corresponds to the core diameter d CO , which is equal to 2·r T , i.e., the outer diameter of trench  34 . Thus, by way of example, a hole diameter DH=40 μm accommodates a core  30  with a diameter d CO =30 μm (r CO =15 μm), an inner cladding width δr ICL =1.2 μm, and a trench width δr T =3.8 μm. 
     The separation distance between the centers of cores  30  that lie along a line passing through central fiber axis AF is denoted DC=2·RC. The core radial distance measured from central fiber axis AF is thus RC. The core pitch CP is the center-to-center core spacing. The core spacing CS represents the edge-to-edge separation of adjacent cores  30  as measured along a line connecting the cores&#39; respective central axes AC. The parameter W represents the spacing between the outer radii of the cores  30  and the outer edge (surface  22 ) of cladding matrix  20 . The various design parameters are included for both the initial preform and the drawn multicore fiber  10 . Note that  FIGS. 2A and 2B  can represent preform PF if the outer coating(s) is/are removed, and the reference symbol PF is included in parenthesis in  FIGS. 2A and 2B  to illustrate this point. 
     Four-Core Multicore Fiber Examples 
     Table 1 below sets forth the main design parameters for three example four-core multicore fibers  10  (Examples 1.1 through 1.3) and the corresponding preforms. For these four-core examples, the core pitch CP=(2) 0.5  RC. In the Tables below, “PAR” stands for “Parameter.” 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 THREE EXAMPLE FOUR-CORE MULTICORE FIBERS 
               
             
          
           
               
                   
                 EXAMPLE 1.2 
                   
               
             
          
           
               
                   
                 EXAMPLE 1.1 
                   
                 MCF 
                 EXAMPLE 1.3 
               
             
          
           
               
                 PAR 
                 PF (mm) 
                 MCF (μm) 
                 PF (mm) 
                 (μm) 
                 PF (mm) 
                 MCF (μm) 
               
               
                   
               
             
          
           
               
                 DM 
                 60.0 
                 160.0 
                 48.0 
                 180.0 
                 48.0 
                 160.0 
               
               
                 DH 
                 15.0 
                 40.0 
                 10.0 
                 37.5 
                 10.0 
                 33.3 
               
               
                 W 
                 7.5 
                 20.0 
                 6.7 
                 25.0 
                 5.1 
                 17.0 
               
               
                 DC 
                 30.0 
                 80.0 
                 24.7 
                 92.5 
                 27.8 
                 92.7 
               
               
                 RC 
                 15.0 
                 40.0 
                 12.3 
                 46.3 
                 13.9 
                 46.3 
               
               
                 CP 
                 21.2 
                 56.6 
                 17.4 
                 65.4 
                 19.7 
                 65.5 
               
               
                 CS 
                 8.6 
                 22.8 
                 9.4 
                 35.1 
                 11.8 
                 39.4 
               
               
                   
               
             
          
         
       
     
     In Example 1.2, for each core  30 , inner core  32  has a diameter d CI =30 μm, inner cladding has a width δr ICL =1.0 μm, and trench  34  has a width δr T =2.75 μm, so that each core has an outer diameter d CO =37.5 μm. 
     Six-Core Multicore Fiber Examples 
       FIG. 5  is similar to  FIG. 2  and shows an example embodiment of a six-core multicore fiber  10  having cores  30   a  through  30   f  symmetrically arranged about fiber axis AF at radius RC. Table 2 sets forth the main design parameters for three example six-core multicore fibers  10  (Examples 2.1 through 2.3) and the corresponding preforms. For these six-core examples, the core pitch CP=RC. 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 THREE EXAMPLE SIX-CORE MULTICORE FIBERS 
               
             
          
           
               
                   
                 EXAMPLE 2.2 
                   
               
             
          
           
               
                   
                 EXAMPLE 2.1 
                   
                 MCF 
                 EXAMPLE 2.3 
               
             
          
           
               
                 PAR 
                 PF (mm) 
                 MCF (μm) 
                 PF (mm) 
                 (μm) 
                 PF (mm) 
                 MCF (μm) 
               
               
                   
               
             
          
           
               
                 DM 
                 48.0 
                 125.0 
                 60.0 
                 155.0 
                 55.0 
                 190.0 
               
               
                 DH 
                 10.0 
                 26.0 
                 10.0 
                 25.8 
                 10.0 
                 34.5 
               
               
                 W 
                 5.8 
                 15.0 
                 11.6 
                 30.0 
                 7.5 
                 26.0 
               
               
                 DC 
                 26.5 
                 69.0 
                 26.8 
                 69.2 
                 29.9 
                 103.5 
               
               
                 RC 
                 13.2 
                 34.5 
                 13.4 
                 34.6 
                 15.0 
                 51.7 
               
               
                 CP 
                 13.2 
                 34.5 
                 13.4 
                 34.6 
                 15.0 
                 51.7 
               
               
                 CS 
                 5.8 
                 15.1 
                 6.0 
                 15.6 
                 8.5 
                 29.4 
               
               
                   
               
             
          
         
       
     
     The multicore fiber  10  of Example 2.1 has a diameter DM=125 μm, which is the same as that of a conventional multimode fiber. The holes have a diameter DH=26 μm, which is designed to accommodate respective cores  30 , each having an inner core  32  of diameter d CI =18 μm, an inner cladding  33  of width δr ICL =1.2 μm and a trench width δr T =2.8 μm. 
     Likewise, multicore fiber  10  of Example 2.3 has a core pitch CP=51.7 μm, and the cladding diameter DM=190 μm is designed to accommodate the larger pitch and the larger core size as compared to Examples 2.1 and 2.2. The holes have a diameter DH=d CO =34.5 μm, which is designed to accommodate respective cores  30 , each having an inner core  32  of diameter d CI =26 μm, an inner cladding  33  of width δr ICL =1.25 μm and a trench width δr T =3 μm. 
     Eight-Core Multicore Fiber Examples 
       FIG. 6  is similar to  FIG. 5  and shows an example embodiment of an eight-core multicore fiber  10  having cores  30   a  through  30   h  symmetrically arranged about fiber axis AF at radius RC. Table 3 sets forth the main design parameters for three example eight-core multicore fibers  10  (Examples 3.1 through 3.3) and the corresponding preforms. For these eight-core examples, the core pitch CP=(2) 0.5  RC/2. 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 THREE EXAMPLE EIGHT-CORE MULTICORE FIBERS 
               
             
          
           
               
                   
                 EXAMPLE 3.2 
                   
               
             
          
           
               
                   
                 EXAMPLE 3.1 
                   
                 MCF 
                 EXAMPLE 3.3 
               
             
          
           
               
                 PAR 
                 PF (mm) 
                 MCF (μm) 
                 PF (mm) 
                 (μm) 
                 PF (mm) 
                 MCF (μm) 
               
               
                   
               
             
          
           
               
                 DM 
                 60.0 
                 200.0 
                 60.0 
                 180.0 
                 60.0 
                 200.0 
               
               
                 DH 
                 10.0 
                 33.3 
                 10.0 
                 30.0 
                 10.0 
                 33.3 
               
               
                 W 
                 6.0 
                 20.0 
                 6.7 
                 20.0 
                 7.5 
                 25 
               
               
                 DC 
                 38.0 
                 126.7 
                 36.7 
                 110.0 
                 35.0 
                 116.7 
               
               
                 RC 
                 19.0 
                 63.3 
                 18.3 
                 55.0 
                 17.5 
                 58.3 
               
               
                 CP 
                 13.4 
                 44.8 
                 13.0 
                 38.9 
                 12.4 
                 41.2 
               
               
                 CS 
                 9.8 
                 32.8 
                 8.8 
                 26.4 
                 7.5 
                 25.0 
               
               
                   
               
             
          
         
       
     
     The multicore fiber  10  of Example 3.2 has a diameter DM=180 μm and hole diameters DH=d CO =30 μm designed to accommodate respective cores  30 , each having an inner core  32  of diameter d CI =20 μm, an inner cladding  33  of width δr ICL =1.0 μm and a trench width δr T =4 μm. 
     Example Multimode Cores 
     Tables 4 through 8 below set forth example design parameters for example multimode cores  30  for use in forming example multicore fibers  10 . Table 4 sets forth example design parameters suitable for an operating wavelength λ p =850 nm, Table 5 sets forth example design parameters suitable for an operating wavelength λ p =980 nm, Table 6 sets forth example design parameters suitable for an operating wavelength λ p =1060 nm, Table 7 sets forth example design parameters suitable for an operating wavelength λ p =1300 nm and Table 8 sets forth example design parameters suitable for an operating wavelength λ p =1550. 
     In Tables 4 through 8 below, the inner core radius r CI , the trench inner radius r CL , the inner cladding width δr ICL , the trench outer radius r T  and the trench width δr T  are measured in microns (μm). The parameter MG is the number of mode groups supported by the core  30  based on a pure (i.e., undoped) silica cladding matrix  20  having a relative refractive index Δ CM =0. The parameter Δτ is the differential mode group delay in ps/m between the mode groups with the maximum and minimum group velocities. The parameter BW is the calculated modal bandwidth in units of GHz·km, calculated according to the procedure outlined in T. A. Lenahan, “Calculation of Modes in an Optical Fiber Using the Finite Element Method and EISPACK,” Bell Sys. Tech. J., vol. 62, pp. 2663-2695 (1983). 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Example multimode cores for λ p  = 850 nm 
               
             
          
           
               
                   
                 EXAMPLE 
                 EXAMPLE 
                 EXAMPLE 
                 EXAMPLE 
               
               
                 PAR 
                 4.1 
                 4.2 
                 4.3 
                 4.4 
               
               
                   
               
             
          
           
               
                 Δ 0  (%) 
                 0.98 
                 0.95 
                 0.98 
                 1.00 
               
               
                 r CI  (μm) 
                 15.02 
                 13.06 
                 11.04 
                 8.18 
               
               
                 α 
                 2.121 
                 2.120 
                 2.121 
                 2.123 
               
               
                 Δ CL  (%) 
                 0 
                 0 
                 0 
                 0 
               
               
                 r CL  (μm) 
                 15.99 
                 13.99 
                 11.87 
                 8.89 
               
               
                 δr ICL  (μm) 
                 0.97 
                 0.94 
                 0.83 
                 0.71 
               
               
                 Δ T  (%) 
                 −0.38 
                 −0.40 
                 −0.43 
                 −0.50 
               
               
                 r T  (μm) 
                 20 
                 17.5 
                 15 
                 12 
               
               
                 δr T  (μm) 
                 4.01 
                 3.51 
                 3.13 
                 3.11 
               
               
                 r CI /r CL   
                 0.94 
                 0.93 
                 0.93 
                 0.92 
               
               
                 MG 
                 10 
                 8 
                 7 
                 5 
               
               
                 Δτ (ps/m) 
                 0.009 
                 0.014 
                 0.006 
                 0.007 
               
               
                 BW (GHz-km) 
                 31.9 
                 34.9 
                 36.4 
                 34.8 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Example multimode cores for λ p  = 980 nm 
               
             
          
           
               
                   
                   
                   
                 EXAM- 
                 EXAM- 
                 EXAM- 
               
               
                   
                 EXAMPLE 
                 EXAMPLE 
                 PLE 
                 PLE 
                 PLE 
               
               
                 PAR 
                 5.1 
                 5.2 
                 5.3 
                 5.4 
                 5.5 
               
               
                   
               
             
          
           
               
                 Δ 0  (%) 
                 1.01 
                 1.01 
                 1.10 
                 1.00 
                 1.00 
               
               
                 r CI  (μm) 
                 14.57 
                 12.74 
                 11.15 
                 9.81 
                 7.80 
               
               
                 α 
                 2.083 
                 2.083 
                 2.085 
                 2.084 
                 2.084 
               
               
                 Δ CL  (%) 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 r CL  (μm) 
                 15.57 
                 13.68 
                 12.01 
                 10.54 
                 8.50 
               
               
                 δr ICL  (μm) 
                 1.00 
                 0.94 
                 0.86 
                 0.73 
                 0.70 
               
               
                 Δ T  (%) 
                 −0.40 
                 −0.45 
                 −0.50 
                 −0.40 
                 −0.50 
               
               
                 r T  (μm) 
                 19 
                 16.67 
                 15 
                 13 
                 11 
               
               
                 δr T  (μm) 
                 3.43 
                 2.99 
                 2.99 
                 2.46 
                 2.50 
               
               
                 r CI /r CL   
                 0.94 
                 0.93 
                 0.93 
                 0.93 
                 0.92 
               
               
                 MG 
                 8 
                 7 
                 6 
                 5 
                 4 
               
               
                 Δτ (ps/m) 
                 0.009 
                 0.007 
                 0.006 
                 0.008 
                 0.008 
               
               
                 BW  
                 33.7 
                 36.7 
                 37.8 
                 33.8 
                 53.9 
               
               
                 (MHz-km) 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Example multimode cores for λ p  = 1060 nm 
               
             
          
           
               
                   
                 EXAMPLE 
                 EXAMPLE 
                 EXAMPLE 
                 EXAMPLE 
               
               
                 PAR 
                 6.1 
                 6.2 
                 6.3 
                 6.4 
               
               
                   
               
             
          
           
               
                 Δ 0  (%) 
                 0.99 
                 1.05 
                 0.95 
                 1.00 
               
               
                 r CI  (μm) 
                 15.07 
                 12.71 
                 9.80 
                 8.28 
               
               
                 α 
                 2.066 
                 2.066 
                 2.066 
                 2.064 
               
               
                 Δ CL  (%) 
                 0 
                 0 
                 0 
                 0 
               
               
                 r CL  (μm) 
                 16.10 
                 13.56 
                 10.67 
                 9.02 
               
               
                 δr ICL  (μm) 
                 1.03 
                 0.85 
                 0.87 
                 0.74 
               
               
                 Δ T  (%) 
                 −0.38 
                 −0.38 
                 −0.48 
                 −0.50 
               
               
                 r T  (μm) 
                 20 
                 17 
                 14 
                 12 
               
               
                 δr T  (μm) 
                 3.90 
                 3.44 
                 3.33 
                 2.98 
               
               
                 r CI /r CL   
                 0.94 
                 0.94 
                 0.92 
                 0.92 
               
               
                 MG 
                 8 
                 7 
                 4 
                 4 
               
               
                 Δτ (ps/m) 
                 0.009 
                 0.013 
                 0.007 
                 0.024 
               
               
                 BW  
                 30.5 
                 40.7 
                 54.1 
                 43.5 
               
               
                 (MHz-km) 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Example multimode cores for λ p  = 1300 nm 
               
             
          
           
               
                 PAR 
                 EXAMPLE 7.1 
                 EXAMPLE 7.2 
                 EXAMPLE 7.3 
               
               
                   
               
             
          
           
               
                 Δ 0  (%) 
                 1.01 
                 0.96 
                 0.96 
               
               
                 r CI  (μm) 
                 14.56 
                 12.06 
                 9.20 
               
               
                 α 
                 2.027 
                 2.026 
                 2.024 
               
               
                 Δ CL  (%) 
                 0 
                 0 
                 0 
               
               
                 r CL  (μm) 
                 15.61 
                 12.98 
                 9.97 
               
               
                 δr ICL  (μm) 
                 1.05 
                 0.92 
                 0.77 
               
               
                 Δ T  (%) 
                 −0.40 
                 −0.40 
                 −0.45 
               
               
                 r T  (μm) 
                 19 
                 16 
                 13 
               
               
                 δr T  (μm) 
                 3.39 
                 3.02 
                 3.03 
               
               
                 r CI /r CL   
                 0.93 
                 0.93 
                 0.92 
               
               
                 MG 
                 6 
                 4 
                 3 
               
               
                 Δτ (ps/m) 
                 0.006 
                 0.005 
                 0.003 
               
               
                 BW (MHz-km) 
                 47.3 
                 115.5 
                 68.1 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 Example multimode cores for λ p  = 1550 nm 
               
             
          
           
               
                 Parameter 
                 EXAMPLE 8.1 
                 EXAMPLE 8.2 
                 EXAMPLE 8.3 
               
               
                   
               
             
          
           
               
                 Δ 0  (%) 
                 0.98 
                 0.96 
                 0.96 
               
               
                 r CI  (μm) 
                 15.51 
                 12.17 
                 9.20 
               
               
                 α 
                 1.995 
                 1.993 
                 1.992 
               
               
                 Δ CL  (%) 
                 0 
                 0 
                 0 
               
               
                 r CL  (μm) 
                 16.55 
                 13.16 
                 9.92 
               
               
                 δr ICL  (μm) 
                 1.05 
                 0.99 
                 0.72 
               
               
                 Δ T  (%) 
                 −0.38 
                 −0.42 
                 −0.45 
               
               
                 r T  (μm) 
                 20 
                 16.5 
                 13 
               
               
                 δr T  (μm) 
                 3.45 
                 3.34 
                 3.08 
               
               
                 r CI /r CL   
                 0.94 
                 0.92 
                 0.93 
               
               
                 MG 
                 5 
                 3 
                 2 
               
               
                 Δτ (ps/m) 
                 0.015 
                 0.022 
                 0.004 
               
               
                 BW (MHz-km) 
                 32.7 
                 40.2 
                 77.6 
               
               
                   
               
             
          
         
       
     
       FIG. 7  is a plot of the inner cladding width δr ICL  (μm) versus the inner core radius r CI  (μm) based on measurement data for the example cores as set forth above. The plot of  FIG. 7  shows the dependence between the width δr ICL  of inner cladding  33  and the radius r CI  of the inner core  32  for the nineteen examples set forth in Tables 4 through 8. This linear dependence was unexpected and illustrates that core preforms with approximately the same ratio ρ=r CI /r CL  between the inner core and inner clad ratio ρ can be drawn into arbitrarily sized canes to make a multicore fiber  10  according to the disclosure. Tables 4 through 8 illustrate that exemplary ρ values can be between 0.9 and 0.95, or between 0.91 and 0.94, or between 0.92 and 0.94. 
     The optimum value of ρ and hence the width δr ICL  of the inner cladding  33  also have a secondary dependence on the relative refractive index Δ T  of the trench. Analysis of the parameters in Tables 5 through 8 yields the relation δr ICL-OPT =0.053 r CI −0.586 Δ T . The multimode core  30  will have a high modal overfilled bandwidth if |δr ICL −δr ICL-OPT |≦0.3 μm, or |δr ICL −δr ICL-OPT |≦0.2 μm, or |δr ICL −δr ICL-OPT |≦0.1 μm. 
       FIG. 8  is an end-on microscope image of an example multicore fiber that has six cores as shown in  FIG. 5  and as set above as Example 2.1. There are six cores  30  having an inner core  32  with an average diameter of d CO =17.9 μm surrounded by an inner cladding  33  of width δr ICL =1.2 μm and a trench  34  with width δr T =3 μm. The average core pitch CP and average core axis radius RC were measured to be 34.56 μm and 34.54 μm, respectively. The outer diameter DM of the example multicore fiber  10  of  FIG. 8  is 127.8 μm. The inner core has a maximum relative refractive index Δ 0  of 0.99%, the inner cladding has an average relative refractive index of Δ CL =0.0%, and the trench has a relative refractive index of Δ T =−0.45%. 
     The attenuation of the six cores 30 of the example multicore fiber  10  of  FIG. 8  was measured at 1310 nm using Optical Time Domain Reflectometry (OTDR), and the results are set forth in Table 6. The average attenuation at 1310 nm is 0.62 dB/km and is less than 0.7 dB/km for each core  30 . The overfilled bandwidths of several of the cores  30  were measured at 850 nm and 1300 nm using a multimode launch fiber with a core diameter of 30 μm. The overfilled bandwidths at 850 nm ranged from 2700 MHz-km to 4350 MHz-km, with an average value of 3340 MHz-km. The overfilled bandwidths at 1300 nm ranged from 707 MHz-km to 844 MHz-km, with an average value of 774 MHz-km. 
     
       
         
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Measured OTDR Attenuation 
               
             
          
           
               
                   
                 CORE NUMBER 
               
             
          
           
               
                   
                 Core 1 
                 Core 2 
                 Core 3 
                 Core 4 
                 Core 5 
                 Core 6 
               
               
                   
                   
               
             
          
           
               
                 Attenuation @ 
                 0.63 
                 0.60 
                 0.64 
                 0.65 
                 0.53 
                 0.67 
               
               
                 1310 nm 
               
               
                 (dB/km) 
               
               
                   
               
             
          
         
       
     
     It will be apparent to those skilled in the art that various modifications to the preferred embodiments of the disclosure as described herein can be made without departing from the spirit or scope of the disclosure as defined in the appended claims. Thus, the disclosure covers the modifications and variations provided they come within the scope of the appended claims and the equivalents thereto.