Multimode optical fiber and methods of manufacturing thereof

Abstract

The present invention generally relates to the field of fiber optics, and more particularly, to apparatuses, systems, and methods directed towards improving effective modal bandwidth within a fiber optic communication environment. In an embodiment, a multimode optical fiber in accordance with the present invention comprises a core and cladding material system where the refractive indices of the core and cladding are selected to modify the shape of the profile dispersion parameter, y, as a function of wavelength in such a way that the alpha parameter (-parameter), which defines the refractive index profile, produces negative relative group delays over a broad range of wavelengths. The new shape of the profile dispersion parameter departs from traditional fibers where the profile dispersion parameter monotonically decreases around the selected wavelength that maximizes the effective modal bandwidth (EMB).

Claims

1. A multimode optical fiber (MMF) for operating within a spectral window, said MMF comprising: a cladding; and a core, said core having a radius a and a refractive index profile, said core comprising at least one dopant, a concentration of said at least one dopant varying between a center of said core and a, wherein said spectral window is defined by an overlapping range of wavelengths (1) at which said MMF has an effective modal bandwidth (EMB) equal to or above a predefined minimum with one of a peak EMB or a minimum EMB occurring at wavelength .sub.p which is less than a maximum wavelength of said spectral window and (2) at which a differential mode delay (DMD) plot of said MMF exhibits a shift to the left of its higher order modes relative to its lower order modes, wherein said DMD plot is measured by launching a plurality of optical pulses into one end of said core at various radial distances r and observing an arrival of said optical pulses at another end of said core at said various radial distances r to determine a velocity of any one of said plurality of optical pulses launched into said core at some radial distance r relative to any other of said plurality of optical pulses launched into said core at some other radial distance r, and wherein said shift to the left is characterized by some of said plurality of optical pulses having a faster velocity relative to at least one other optical pulse having a slower velocity, said at least one other optical pulse having a slower velocity being launched into said core at a lower radial distance r than any of said some of said plurality of optical pulses having a faster velocity wherein said refractive index profile is characterized by a predefined value , wherein said core includes _opt profile comprised of values _opt() defined by a function of wavelength , wherein for a given said _opt() value minimizes a group delay of said MMF when said is set equal to _opt(), said _opt profile having one of a concave shape with a maximum _opt value or a convex shape with a minimum _opt value, and wherein is less than or equal to said one of said maximum _opt value or said minimum _opt value.

2. The MMF of claim 1, wherein said at least one other optical pulse having a slower velocity is launched into said core at a radial distance of 5 microns.

3. The MMF of claim 1, wherein said predefined minimum is 4700 MHz.Math.km.

4. The MMF of claim 1, wherein said spectral window is at least 50 nm.

5. The MMF of claim 1, wherein said spectral window is at least 100 nm.

6. The MMF of claim 1, wherein said spectral window is at least 200 nm.

7. The MMF of claim 1, wherein said .sub.opt profile has one of said concave shape with said maximum .sub.opt value=.sub.opt(.sub.p) or said convex shape with said minimum .sub.opt value=.sub.opt(.sub.p).

8. The MMF of claim 1, wherein said core includes a dispersion parameter profile defined by a function of wavelength , said dispersion parameter profile having one of a concave shape with a maximum or a convex shape with a minimum.

9. The MMF of claim 8, wherein said dispersion parameter profile has one of said concave shape with said maximum at occurring at .sub.p or said convex shape with said minimum occurring at .sub.p.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates DMD radial waveform plots for two fibers with equal radial mode group delays but opposite slope signs.

(2) FIG. 2 illustrates an example of the improvements of BER when using L-MMF.

(3) FIG. 3 illustrates graphs of a profile dispersion parameter and .sub.opt for an exemplary MMF with .sub.p=850 nm.

(4) FIG. 4 illustrates an EMB modeled as a function of the wavelength for typical MMF construction with .sub.p=850 nm.

(5) FIG. 5 illustrates the measured EMB as a function of the wavelength for typical MMFs with several values of .sub.p ranging from 800 nm to 960 nm.

(6) FIG. 6A illustrates an alpha-profile MMF doped with Ge.

(7) FIG. 6B illustrates the modal bandwidth (EMB) as a function of the wavelength for the MMF of FIG. 6A.

(8) FIG. 7 illustrates a cross sectional perspective view of a core and cladding according to an embodiment of the present invention.

(9) FIG. 8 illustrates a shape of a refractive index profile of a core and cladding according to an embodiment of the present invention.

(10) FIG. 9A illustrates an alpha-optimum distribution and an alpha-profile value for an MMF according to an embodiment of the present invention.

(11) FIG. 9B illustrates the EMB as a function of the wavelength for the fiber of FIG. 9A.

(12) FIG. 10A illustrates an alpha-optimum distribution and an alpha-profile value for an MMF according to an embodiment of the present invention.

(13) FIG. 10B illustrates the EMB as a function of the wavelength for the fiber of FIG. 10A.

(14) FIG. 11 illustrates a flow chart representative of a method according to an embodiment of the present invention.

(15) FIG. 12 illustrates .sub.opt values for three exemplary dopant concentrations.

(16) FIG. 13 illustrates an .sub.opt profile for a fiber according to an embodiment of the present invention.

(17) FIG. 14 illustrates maximum relative group delays for the fiber of FIG. 13.

(18) FIGS. 15-17 illustrate DMD plots for the fiber of FIG. 13.

(19) FIG. 18 illustrates an EMB summary for the fiber of FIG. 13.

(20) FIG. 19 illustrates an .sub.opt profile for a fiber according to another embodiment of the present invention.

(21) FIG. 20 illustrates maximum relative group delays for the fiber of FIG. 19.

(22) FIGS. 21-23 illustrate DMD plots for the fiber of FIG. 19.

(23) FIG. 24 illustrates an EMB summary for the fiber of FIG. 19.

(24) FIG. 25 illustrates a flow chart representative of a method according to another embodiment of the present invention.

(25) FIG. 26 illustrates a dopant concentration profile for a fiber according to an embodiment of the present invention.

(26) FIGS. 27-29 illustrate DMD plots for the fiber of FIG. 26.

(27) FIG. 30 illustrates an EMB summary for the fiber of FIG. 26.

(28) FIG. 31 illustrates an exemplary CWDM system according to an embodiment of the present invention.

(29) FIG. 32 illustrates operational wavelength channels for the CWDM system of FIG. 31.

(30) FIG. 33 illustrates attenuation for the CWDM system of FIG. 31.

(31) FIG. 34 illustrates chromatic dispersion for the CWDM system of FIG. 31.

DETAILED DESCRIPTION

(32) A cross-sectional view of an exemplary multimode optical fiber (MMF) in accordance with the present invention is shown in FIG. 7. This fiber includes a core region having a center and a radius a, and a cladding region surrounding the core. Both the core and the cladding are comprised of optically conductive materials such that the refractive index at the center of the core (n.sub.1) is greater than the refractive index of the cladding (n.sub.2), and the distribution of the refractive indices throughout the optical fiber is generally referred to as the fiber's refractive index profile.

(33) In an embodiment, the MMF of the present invention includes a dispersion parameter profile having a concave or a convex shape with minimum/maximum value at or near to the wavelength which has the peak EMB or .sub.p. Such an MMF can have a refractive index profile that includes a generally parabolic shape as shown in FIG. 8. This refractive index profile can be attained by including, in the core, one or more dopants in respective concentrations, and it can be defined by equation (1) where the -value is selected pursuant the fiber's .sub.opt profile. An -value selected pursuant to the present invention may be referred to as .sub.d through this specification.

(34) Instances of exemplary characteristics of an MMF provided in accordance with some embodiments of the present invention are shown in FIGS. 9A-10B. FIGS. 9A and 9B illustrate exemplary characteristics of an MMF that uses dopants such as, for example, Boron (B) to decrease the refractive index of the core and/or cladding and Fluorine (F) to decrease the refractive index of the cladding. Certain combination of concentrations of these dopants in the core and cladding can produce concave like functions for the alpha optimum profile as shown by the solid line in FIG. 9A. By designing the fiber to have a refractive index profile with a power exponent of .sub.d<.sub.opt, it is possible to maintain negative relative group delays over a broad spectral region while maintaining a high modal bandwidth as illustrated in FIG. 9B.

(35) FIGS. 10A and 10B illustrate exemplary characteristics of another MMF that is doped with, for example, phosphorous (P) to increase the refractive index of the cladding. Small amounts of phosphorous, or other dopants, in the core in combination with dopant(s) such as fluorine in the cladding can produce convex like functions for the alpha optimum profile as shown in FIG. 10A. By designing the fiber to have a refractive index profile with a power exponent of .sub.d<.sub.opt, it is possible to maintain negative relative group delays in a broad spectral region while maintaining a high modal bandwidth as illustrate in FIG. 10B.

(36) FIG. 11 illustrates a flow chart outlining the process for determining .sub.d and developing an MMF profile according to an embodiment of the present invention. This embodiment can be used in a design and/or manufacturing process for an MMF with one or more dopants, where the concentration profile of each dopant is based on the same .sub.d value. It is to be understood that the same .sub.d value does not require the same dopant concentration value. In step 100, the initial parameters are selected for the MMF. These parameters can include, but are not limited to, numerical aperture, index contrast , core and cladding dimensions, peak EMB, maximum coupling loss, chromatic dispersion parameters (e.g., chromatic dispersion coefficient D, zero dispersion wavelength .sub.z), manufacturing tolerances, and/or desired spectral windows for a minimum value of the effective modal bandwidth EMB.sub.0. Once the initial parameters are provided, one or more dopants together with their respective concentrations are selected in step 105. The selection in step 105 may be based on some pre-existing criteria, such as, for example, a library of dopants compatible for the fabrication of SiO.sub.2 fiber core and cladding. A very brief example of such a library is provided in Table III. The range of combinations among these and other dopants is very extensive, and can be computed numerically from the Sellmeier coefficients.

(37) TABLE-US-00003 TABLE III Sellmeier Sellmeier Doping element coefficients coefficients Sample & concentration a.sub.i b.sub.i 1 Cl (~0.06 wt %) 0.50716 0.04014 0.59707 0.11359 0.69879 8.81674 2 Cl (0.3 wt %) 0.88671 0.07954 0.21675 0.1244 0.69401 8.83315 3 F (0.9 wt %) 0.87219 0.07417 Cl (0.13 wt %) 0.21238 0.1298 0.94959 10.22611 4 P (12.5 wt %) 0.51512 0.02636 Cl (~0.03 wt %) 0.62804 0.11614 1.0743 10.6931 5 B2O3 (13.3 mol %) 0.690618 0.0619 0.401996 0.123662 0.898817 9.09896 6 P205 (9.1 mol %) 0.69579 0.061568 0.452497 0.119921 0.712513 8.656641

(38) Alternatively, the selection in step 105 may be random. Upon the selection of the dopant(s) and respective concentration(s), an initial verification step 110 is performed where the basic characteristics such as, but not limited to, numerical aperture, , D, and .sub.z are computed. The initial verification can allow for a relatively early determination of whether the selected material(s) will result in an MMF that falls within some desired guidelines. This can be especially useful in determining whether the MMF will satisfy certain standards characteristics such as those defined by the OM3 and OM4 standards. This determination can be made in step 115 where if it is determined that the MMF will not satisfy some predetermined criteria, a new selection of a dopant(s) and concentration(s) must be made in step 105. While this verification and comparison process embodied in the two steps 110 and 115 is performed immediately after the dopant selection step of 105, this is not a requirement. Instead it may be performed during any time following step 105. However, for practical purposes, early determination of a non-compatible selection in step 105 may provide time, computing, and/or cost savings.

(39) If at step 115 it is determined that the selected material(s) and respective concentration(s) are satisfactory, in step 120 the profile of the dispersion parameter y() and the optimum -value .sub.opt() are calculated using equations (3) and (4), and in step 125 the concavity of the dispersion parameter y() around the peak EMB .sub.p is evaluated. Note that the term concavity as used herein refers to both a concave and a convex shape. If the profile of the dispersion parameter is not concave or convex around the peak EMB, steps 105-125 are repeated with a new dopant(s) and/or concentration(s). If, on the other hand, the profile of the dispersion parameter does exhibit desired concavity around the peak EMB value, the method proceeds to step 130 where an .sub.d value is chosen based on the optimum -value at peak EMB .sub.opt(.sub.p) and the manufacturing tolerances. In an embodiment, .sub.d follows the following equation:
.sub.d=.sub.opt(.sub.p)+b.Math.abs(T.sub.)/2(6)
where T.sub. manufacturing tolerance for the -parameter which depends on manufacturer (e.g., 0.01) and parameter b is utilized to increase the broadband windows for high EMB, relax the conditions for relative negative mode group delay tilt, to include the small dependence of alpha with wavelength, or to adjust for the different process used by fiber manufacturers. In order to produce an MMF which exhibits the L-MMF condition, the sign of b must be negative.

(40) In some cases, for example multicomponent fiber, it may not be possible to find relatively simple analytical expressions such as equations (6). In those cases, use of a full numerical model to find the optimum .sub.d value for each component may be required.

(41) After determining the .sub.d value, the relative mode group delays t.sub.g() are derived in step 135 by using equation (2) and substituting .sub.d in place of ; the differential mode delay (DMD) profiles are computed in step 140 from the earlier-derived mode group delays t.sub.g(); and the effective modal bandwidth EMB() is computed in step 145 from the earlier computed DMD profiles. Thereafter, a final verification of performance compliance is made in step 150 where the values obtained in steps 135-145 are evaluated. In one example, the evaluation in step 150 can be limited to the evaluation of the EMB() to verify that it is in compliance with the minimum required value EMB.sub.0 for the spectral window originally defined in step 100. In other examples, the values derived in steps 135 and 140 can also be evaluated. For instance, the maximum values for the relative mode group delays are checked to fall within some predetermined range group (e.g., a range specified by the OM3 or OM4 standard). Furthermore, the sign (e.g., positive versus negative) of the relative mode group delay values can also be evaluated to confirm the presence of an L-MMF condition for at least some of the operating wavelengths. In another instance, the DMD plots can be evaluated for visual confirmation of fiber's transmission characteristics (e.g., the presence of a left shift of the majority of peak pulse at increasing radial offsets at various wavelengths). Moreover, the plots can be used to measure the DMD value at various operating wavelengths which in it of itself can be a prerequisite to meeting some preexisting standard. Note that the recitation of verification processes is not meant to be limiting and/or exhaustive. If the verification process returns a favorable result, the MMF parameters are saved in step 155 for later use such as, for example, the manufacture of the MMF. If, on the other hand, the verification step 150 fails, steps 105-145 are repeated for new dopant(s) and/or concentration(s).

(42) As an example, the method described in FIG. 11 may be used to produce a broadband MMF that uses B.sub.2O.sub.3 and small amounts of GeO.sub.2. The addition of B.sub.2O.sub.3 dopant to the fiber's core has the effect of reducing the refractive index and therefore reducing the , increasing phase velocity and group velocity relative to pure Si, and varying the shape of the dispersion parameter y() and .sub.opt.

(43) In order to maintain 1% at an operating wavelength of about 850 nm to reduce coupling losses when mated with legacy fibers, modeling results indicate that Fluorine doping in the cladding and/or combined doping of GeO.sub.2B.sub.2O.sub.3 in the core may be desired. The effect of B.sub.2O.sub.3 on .sub.opt is shown in FIG. 12 where the wavelength-dependent .sub.opt profiles are modeled for three dopant concentrations. The (a) .sub.opt profile is based on a concentration of 13.3 mol % of B.sub.2O.sub.3; the (b) .sub.opt profile is based on a concentration of 4.1 mol % of GeO.sub.2 and 7.7 mol % of B.sub.2O.sub.3; and the (c) .sub.opt profile is based on a concentration of 0.1 mol % of GeO.sub.2 and 5.5 mol % of B.sub.2O.sub.3.

(44) To produce a broadband MMF with high modal bandwidth and negative group delays the required concentration of dopants should be precisely controlled. This may allow the negative group delay condition to be maintained for at least 200 nm for EMB>4.7 GHz.Math.km, and over 300 nm for OM3 fibers.

(45) In an embodiment, the fibers that satisfy the requirements for high EMB and negative group delays can have a core with GeO.sub.2 dopant concentration between 3 to 6 mol % and B.sub.2O.sub.3 dopant concentration between 4 and 9 mol %. For such fiber the cladding includes a less than 4 wt % dopant concentration of B.sub.2O.sub.3 and/or F. For example of the .sub.opt value of an MMF co-doped with 4.1 mol % Ge and 7.7 mol % B.sub.2O.sub.3 in the core, and 3 wt % F in the cladding is shown in FIG. 13 as the parabolically shaped solid line. The ideal designed alpha (.sub.d) for the profile shape is 2.1147 and is equivalent to the value at the vertex of the parabolic plot. For this example, it is assumed that tolerances of 0.005 in the .sub.d value (with respect to the ideal .sub.d value) are permissible in order to remain within the desired EMB limits.

(46) Given the potential .sub.d values shown in FIG. 13, it is possible to derive the maximum values for the relative mode group delays using equation (2). These results are provided in FIG. 14 where the maximum relative group delays are plotted as a function of wavelength for the three separate target .sub.d values (.sub.d=2.1197 for triangle markers; .sub.d=2.1147 for dot markers; and .sub.d=2.1097 for square markers). The dotted horizontal lines represent the range limits of maximum delays for EMB>4.7 GHz.Math.km. Based on these results it is possible to tell that all three instances remain within the maximum delay limits over a relatively broad range of wavelengths. Furthermore, it is possible to tell that for MMFs having .sub.d=2.1147 or 2.1097, the maximum relative mode group delays within the region of interest have a negative value. This provides an indication of an L-MMF condition occurring throughout the range of interest for the respective fibers. On the other hand, for an MMF having .sub.d=2.1197, at least some maximum relative group delays will have a positive value. While this may not be desirable in some cases, in other cases the positive values may form a part of an overall analysis of the performance resulting from a fiber with a certain .sub.d value. In other words the existence of positive .sub.d values does not necessarily take the resulting fiber or the process by which that fiber was made outside the scope of the present invention. This, as further described later in the specification, is because at higher wavelengths, MCDC may not be of such high concern. As such, a fiber which meets the L-MMF condition over only a part of its operational wavelength window may still be desirable. The results provided in FIG. 14 highlight the potential need for selecting an appropriate .sub.d value so as to remain within appropriate operational limits considering potential manufacturing tolerances.

(47) Given the maximum relative group delays, it is then possible to determine a series of DMD plots for a respective fiber. FIGS. 15-17 show the DMD plots computed for the maximum relative group delays of the fiber with .sub.d=2.1147. The DMD pulses in these plots were computed using TIA's procedure described in the FOTP-220 standard, which is incorporated herein by reference in its entirety. These plots simulate the measured DMD pulses at each wavelength as indicated at the top of each figure. Having a DMD plot for a given wavelength, it is then possible to compute the EMB for that respective wavelength. For the examples of FIGS. 15-17 the respective EMB values are provided at the top of each DMD plot, and a summary of the EMB values as a function of wavelength is provided in FIG. 18.

(48) As another example, the method described in FIG. 11 may also be used to produce a broadband MMF that uses P.sub.2O.sub.5 as the core dopant and F as the cladding dopant. The addition of P.sub.2O.sub.5 dopant to the fiber's core has the effect of increasing the refractive index and therefore increasing the , i.e., the difference in core-cladding refractive index, reducing phase velocity and group velocity relative to pure Si, and varying the shape of the dispersion parameter y() and .sub.opt. In order to maintain 1% at an operating wavelength of about 850 nm to reduce coupling losses when mated with legacy fibers, modeling results indicate that Fluorine doping in the cladding and/or combined doping of GeO.sub.2P.sub.2O.sub.5 in the core may be preferred. This may allow the negative group delay condition to be maintained for at least 200 nm for EMB>4.7 GHz.Math.km, and over 300 nm for OM3 fibers.

(49) In an embodiment, the fibers that satisfy the requirements for high EMB and negative group delays can have a core with P.sub.2O.sub.5 dopant concentration between 6 to 10 mol %. FIG. 19 illustrates an .sub.opt profile for a fiber having a 9.1 mol % concentration of P.sub.2O.sub.5 and 90.9 mol % concentration of SiO.sub.2. Based on this profile, an .sub.d is selected to be 2.01205 (illustrated in FIG. 19 via a dashed line). The selected .sub.d provides a basis for deriving the maximum values for the relative mode group delays using equation (2). The maximum relative group delays as a function of wavelength for the target .sub.d are shown in FIG. 20, with the horizontal dotted lines representing represent the range limits of maximum delays for EMB>4.7 GHz.Math.km.

(50) From the derived group delays, it is then possible to determine a series of DMD plots for a respective fiber. FIGS. 21-23 show the DMD plots computed for the maximum relative group delays shown in FIG. 20. The DMD pulses in these plots were computed using TIA's procedure described in the FOTP-220 standard. These plots simulate the measured DMD pulses at each wavelength as indicated at the top of each figure. Having a DMD plot for a given wavelength, it is then possible to compute the EMB for that respective wavelength. For the examples of FIGS. 21-23 the respective EMB values are provided at the top of each DMD plot, and a summary of the EMB values as a function of wavelength is provided in FIG. 24.

(51) Another method for designing an MMF according to an embodiment of the present invention is outlined in the flow chart of FIG. 25. This embodiment can be especially applicable in design and/or manufacturing processes of MMFs with two or more dopants where the -value of at least one dopant concentration profile is different from the -value of at least one other dopant concentration profile. An exemplary representation of a fiber having dopant concentration profiles differing with respect to their power exponent is illustrated in FIG. 26. However, this method can still be used to design fibers using only a single primary dopant also.

(52) In step 200, the initial parameters are selected for the MMF. These parameters can include, but are not limited to, numerical aperture, index contrast , core and cladding dimensions, peak EMB, maximum coupling loss, chromatic dispersion parameters (e.g., chromatic dispersion coefficient D, zero dispersion wavelength .sub.z), manufacturing tolerances, and/or desired spectral windows for a minimum value of the effective modal bandwidth EMB.sub.0. Once the initial parameters are provided, the dopants together with respective concentrations are selected in step 205. The selection in step 205 may be based on some pre-existing criteria, such as, for example, a library of dopants compatible for the fabrication of SiO.sub.2 fiber core and cladding. Alternatively, the selection in step 205 may be random.

(53) Upon the selection of the dopants and respective concentrations, an initial verification step 210 is performed where the basic characteristics such as, but not limited to, numerical aperture and are computed for the selected materials and concentrations. The initial verification can allow for a relatively early determination of whether the selected material will result in an MMF that falls within some desired guidelines. This can be especially useful in determining whether the MMF will satisfy certain standards characteristics such as those defined by the OM3 and OM4 standards. This determination can be made in step 215 where if it is determined that the MMF will not satisfy some predetermined criteria, a new selection of a dopants and concentration profiles must be made in step 205. While this verification and comparison process embodied by the two steps 210 and 215 is performed immediately after the dopants selection step of 205, this is not a requirement. Instead it may be performed during any time following step 205. However, for practical purposes, early determination of a non-compatible selection in step 205 may provide time, computing, and/or cost savings.

(54) If at step 215 it is determined that the selected materials and concentrations are satisfactory, in step 220 the spectral characteristics of the fiber with the selected materials are modeled using the Sellmeier coefficients given by:

(55) $\begin{array}{cc}{n}^2\left(\right)=1+\underset{i=1}{\overset{3}{.Math.}}\frac{a_i{}^2}{{}^2-b_i^2}& \left(7\right)\end{array}$
Because the concentrations of the dopants vary along the radial position of the fiber's core, modeling of the spectral characteristics is achieved by taking this radial variance into consideration. Consequently, equation (7) becomes a function of and r, and also takes into consideration that more than one dopant may be used.

(56) After determining the spectral characteristics for the MMF, the relative mode group delays t.sub.g() are derived in step 225 by using numerical models, such as for example WentzelKramer-Brillouin or Finite Time Domain Difference; the differential mode delay (DMD) profiles are computed in step 230 from the earlier-derived mode group delays t.sub.g(); and the effective modal bandwidth EMB() is computed in step 235 from the earlier computed DMD profiles.

(57) Thereafter, a final verification of performance compliance is made in step 240 where the values obtained in steps 225, 230 and/or 235 are evaluated. In one example, the evaluation in step 240 can be limited to the evaluation of the EMB() to verify that it is in compliance with the minimum required value EMB.sub.0 for the spectral window originally defined in step 200. In other examples, the values derived in steps 230 can also be evaluated. For instance, the DMD plots can be evaluated for visual confirmation of fiber's transmission characteristics (e.g., the presence of a left shift of the majority of peak pulse at increasing radial offsets at various wavelengths). Moreover, the plots can be used to measure the DMD value at various operating wavelengths which in it of itself can be a prerequisite to meeting some preexisting standard. Note that the recitation of verification processes is not meant to be limiting and/or exhaustive. If the verification process returns a favorable result, the MMF parameters are saved in step 245 for later use such as, for example, the manufacture of the MMF. If, on the other hand, the verification step 240 fails, steps 205-240 are repeated for a new dopant and/or concentration.

(58) As an example, the method described in FIG. 25 may be used to produce a broadband MMF that uses Ge and F as its dopants. FIG. 26 illustrates exemplary concentration profiles for the Ge and F dopants, with Ge mol % concentration being represented via the solid line and F mol % concentration being represented via the dotted line. Both of these concentrations can be represented with the following equations as a function of radial offset r from the center of the core:

(59) $\begin{array}{cc}\mathrm{For}\mathrm{Ge}\text{:}{X}_{\mathrm{Ge}}\left(r\right)=X_{\mathrm{Ge}}^{\mathrm{Max}}\left(1-{\left(\frac{r}{a}\right)}^{{}_d^{\mathrm{Ge}}}\right)& \left(8\right)\\ \mathrm{For}F\text{:}{X}_F\left(r\right)=X_F^{\mathrm{Max}}\left({\left(\frac{r}{a}\right)}^{{}_d^F}\right)& \left(9\right)\end{array}$
where .sub.d.sup.Ge and .sub.d.sup.F are parameters which determine the shape of the respective dopant concentration profile and X.sub.Ge.sup.Max and X.sub.F.sup.Max are parameters that define the maximum concentrations of respective dopants at some radial offset position. The values for these parameters can be selected based on some pre-existing criteria, such as, for example, generally known dopant concentrations and concentration profile shapes, or at random. In the example of FIG. 26, the .sub.d values are selected to be .sub.d.sup.Ge=1.9963 and .sub.d.sup.F=2.0093.

(60) Taking equations (8) and (9) into consideration it is then possible to generate the spectral characteristics of the fiber as a function of radial offset r and wavelength . Expanding on equation (7), the resultant refractive index profile is computed using:

(61) $\begin{array}{cc}{n}^2\left(r,\right)=1+\underset{i=1}{\overset{3}{.Math.}}\frac{\left(a_i+X_{\mathrm{Ge}}\left(r\right){\mathrm{da}}_i^{\mathrm{Ge}}+X_F\left(r\right){\mathrm{da}}_i^F\right){}^2}{{}^2-\left(b_i+X_{\mathrm{Ge}}\left(r\right){\mathrm{db}}_i^{\mathrm{Ge}}+X_F\left(r\right){\mathrm{db}}_i^F\right)}& \left(10\right)\end{array}$
where X.sub.Ge and X.sub.F are the mole fractions, and da.sub.i the db.sub.i the material specific variation terms. Given the result-set of equation (10), it is possible to derive the maximum values for the relative mode group delays, and then using those values to determine a series of DMD plots for the respective fiber as shown in FIGS. 27-29. The DMD pulses in these plots were computed using TIA's procedure described in the FOTP-220 standard. These plots simulate the measured DMD pulses at each wavelength as indicated at the top of each figure (825 nm to 1175 nm). Having a DMD plot for a given wavelength, it is then possible to compute the EMB for that respective wavelength. For the examples of FIGS. 27-29 the respective EMB values are provided at the top of each DMD plot, and a summary of the EMB values as a function of wavelength is provided in FIG. 30. In these figures it is observed that the negative DMD tilt (e.g., the L-MMF) and the EMB4.7 GHz.Math.km conditions can be maintained from 850 nm to 950 nm.

(62) These results indicate that using the MMF of the currently described embodiment can be especially advantageous in the shorter wavelengths region of about 850 nm to about 950 nm. At longer wavelengths (e.g., >975 nm) the attenuation and chromatic dispersion can be significantly lower accounting for a least 2 dB reduction in transmission penalties compared with the penalties at 850 nm. Therefore, at those longer wavelengths MCDC may not be required. By modifying the exponents in the dopant concentration functions shown in equations (8) and (9), the peak EMB wavelength or .sub.p can be shifted either to the left or to the right. For example by using .sub.d.sup.Ge=1.9963 and .sub.d.sup.F=2.0163, .sub.p becomes 900 nm.

(63) Concepts disclosed herein can be applied to designing optical fibers for use with laser transceivers emitting multiple transverse modes (e.g., VCSEL transceivers). This fiber can be used in channels requiring the transmission and receiving of multiple signals over a broad range of wavelengths.

(64) Concepts embodied by the present invention may be applicable in unidirectional and/or bidirectional CWDM (coarse wavelength-division multiplexing). It has been recognized that performance of CWDM systems depend not only on modal bandwidth, but also on the total bandwidth resulting from the modal and chromatic dispersion interaction.

(65) In order to equalize the reach or performance of the transmitter wavelength in a CWDM channel as illustrated in FIG. 31, MCDC (modal-chromatic dispersion compensation) should preferably be applied to the shorter wavelength of the utilized spectra in such a way that the penalties due to dispersion and attenuation are balanced. For example, FIG. 32 shows the case where n=8 wavelengths separated by s=40 nm. This configuration may allow 100 Gbps or 128 Gbps bidirectional transmission per fiber by multiplexing different wavelength VCSELs with serial rates of 25 Gbps or 28 Gbps. It may also enable 200 Gbps bidirectional transmission per fiber using VCSEL transceivers with serial rates of 50 Gbps. Transceivers operating with the first 4 shorter wavelengths (i.e., 850 nm to 970 nm) are subject of significantly more attenuation (as shown in FIG. 33) and chromatic dispersion (as shown in FIG. 34) than transmitters operating with the longer wavelengths. Therefore, the impact of MCDI (modal-chromatic dispersion interaction) described herein can be more significant for the shorter wavelengths than the longer wavelengths.

(66) Additionally, design techniques described herein may be combined with any known fiber manufacturing techniques to the extent necessary. For example, those of ordinary skill will be familiar with the general concept of manufacturing optical fibers where in a first stage a preform is produced and in a second stage a fiber is drawn from that preform. Those familiar with the relevant art will also be familiar with the techniques used to introduce/add one or more dopants during the manufacturing stages. This step typically occurs during the preform formation stage where a controlled introduction of dopants results in a preform having some desired dopant concentration profile. In some embodiments, it is at this stage that the selected dopants can be controlled in accordance with the design parameters of the present invention. Furthermore, in some embodiments, the reference to a broad spectral region may be understood to refer to a region that is at least 50 nm, at least 100 nm, at least 150 nm, at least 200 nm, at least 250 nm, and/or at least 300 nm. However, this should not be interpreted as limiting the meaning of the term broad spectral region, as in some embodiments this term may also have a customary meaning as would be understood by those of ordinary skill in the relevant art.

(67) Note that while this invention has been described in terms of several embodiments, these embodiments are non-limiting (regardless of whether they have been labeled as exemplary or not), and there are alterations, permutations, and equivalents, which fall within the scope of this invention. Additionally, the described embodiments should not be interpreted as mutually exclusive, and should instead be understood as potentially combinable if such combinations are permissive. It should also be noted that there are many alternative ways of implementing the methods and apparatuses of the present invention. For example, while extensive references have been made to VCSEL systems throughout the specification, the present invention may be implemented with other, non-VCSEL optical sources. It is therefore intended that claims that may follow be interpreted as including all such alterations, permutations, and equivalents as fall within the true spirit and scope of the present invention.

(68) Furthermore, the subject matter described herein, such as for example the methods for designing and/or manufacturing an MMF in accordance with the present invention, can be implemented at least partially in software in combination with hardware and/or firmware. For example, the subject matter described herein can be implemented in software executed by a processor. In one exemplary implementation, the subject matter described herein can be implemented using a non-transitory computer readable medium having stored thereon computer executable instructions that when executed by the processor of a computer control the computer to perform steps of a method or process. Exemplary computer readable media suitable for implementing the subject matter described herein include non-transitory computer-readable media, such as disk memory devices, chip memory devices, programmable logic devices, and application specific integrated circuits. In addition, a computer readable medium that implements the subject matter described herein may be located on a single device or computing platform or may be distributed across multiple devices or computing platforms. Devices embodying the subject matter described herein may be manufactured by any means, such as by semiconductor fabrication or discreet component assembly although other types of manufacturer are also acceptable, and can be manufactured of any material, e.g., CMOS.

REFERENCES

(69) The following references are incorporated herein in their entirety: Jack Jewell, Extended Wavelength Receivers for forward compatibility, Presented in T11 PI6, June 2013 ftp://ftp.t10.org/t11/document. 13/13-214 v0.pdf; Buck, Fundaments of Optical Fibers, Willey, April 204, ISBN: 978-0-471-22191-3; TIA-455-220-A, DMD Measurement of Multimode Fiber in the Time Domain, January 2003; IEC 60793-1-49, Measurement methods and test proceduresDifferential Mode Delay; Gholami A., Molin, D., Sillard, P., Physical Modeling of 10 GbE Optical Communication Systems, IEEE OSA JLT, 29(1), 2011, pp. 115-123; J. Castro, R. Pimpinella, B. Kose, and B. Lane, Investigation of the Interaction of Modal and Chromatic Dispersion in VCSEL-MMF Channels, IEEE OSA JLT, 30(15), pp. 2532-2541; R. Pimpinella, J. Castro, B/ Kose, and B. Lane, Dispersion Compensated Multimode Fiber, Proceeding of the 60th IWCS 2011; J. Castro, R. Pimpinella, B. Kose, and B. Lane, Mode Partition Noise and Modal-Chromatic Dispersion Interaction Effects on Random Jitter, IEEE OSA JLT, 31(15), pp. 2629-2638; Marcuse, Principles of Optical Fiber Measurements, Academic Press, NY, 1981; Solomon Musikant, Optical Materials, CRC Press, May 22, 1985; H. M. Presby and l. P. Kaminow, Binary silica optical fibers: refractive index and profile dispersion measurements, Applied Optics, Vol. 15, Issue 12, pp. 3029-3036 (1976); C. R. Hammond, Silica Based Binary Glass Systems: wavelength dispersive properties and composition in optical fibers, Optical and Quantum Electronics, vol, 10, pp. 163-170, 1977; O. V. Butov, et al. Refractive index dispersion of doped silica for fiber optics,, Optics Communication, vol 213, pp. 301-308, 2002.