MXPA00004058A - Multimode fiber link dispersion compensator - Google Patents

Abstract

Disclosed is a dispersion compensated multimode waveguide fiber link. The dispersion of essentially any wavelength can be compensated by adding a compensating waveguide fiber to the link, the compensating waveguide having a profile shape and a&lgr;p wavelength which counters dispersion caused by the original waveguide fiber of the link. Analytical expressions relating the compensator waveguide profile and&lgr;p to the original link and compensated profile and&lgr;p are provided for the embodiment which includes&agr;profiles.

Description

DISPERSION COMPENSATOR FOR MULTIMODAL FIBER LINK BACKGROUND OF THE INVENTION The invention relates to a compensated waveguide link for dispersion which includes a compensating multimode optical waveguide fiber which is optically coupled to the link to increase the bandwidth at one or more preselected wavelengths. The multimode optical waveguide fiber has long been preferred for use in shorter link length systems, such as local area networks, in which the link length is typically less than 5 km and the speed of Data transmission is in the order of hundreds of Mbits / sec. The large diameter of the center of the multimode waveguides, typically 50 μm, 62.5 μm, 100 μm, or larger allows for a low splice loss and low connection losses. In addition, multimode waveguides provide operation in two wavelength windows, centered around 850 nm and 1300 nm, and have sufficient bandwidth at both wavelengths to meet the area network data rate requirements local. Because the waveguide attenuation in the 1300 nm operation window is smaller, the method of manufacturing multimode waveguides can be adjusted to provide a greater bandwidth in the larger wavelength window. This setting provides a larger wavelength window that can carry higher data rates over longer distances, compared to the lower wavelength window. In this form full use is made of the lowest attenuation at 1300 nm. Thus, for example, multimode fibers having a bandwidth of 160 MHz-km at 850 nm and 500 MHz-km at 1300 nm (fiber 160/500) have been specified for many local networks or for other applications of longitude short. Applications in which bandwidth is optimized in smaller work windows are required in certain systems. In these cases, the wavelength of the maximum bandwidth is moved to a shorter wavelength such as 780 nm or 850 nm. However, because the laser sources in the smaller window have become more powerful, narrower in line width, and relatively free of parasites, the need for a greater bandwidth in the wavelength region has arisen. centered at 850 nm. In addition, for certain local area network applications, the demand for higher bit rates continues. In this way a practical need for greater bandwidths in the 850 nm window has arisen while sufficient bandwidth in the 1300 nm window is maintained at the same time. Because many networks have been installed using the two window bandwidth values of 160 MHz-km and 500 MHz-km in the respective 850 nm and 1300 nm windows, an investigation has been initiated to discover an economically feasible way to adjust or compensate the two window bandwidths in the multimode waveguide fiber links installed.

DEFINITIONS - Refractive index profile is an indication of the value of the refractive index of a material along a line that has a first and a last point. In the case of an optical waveguide fiber, a refractive index value is defined at each point along the radius of the waveguide. - A general expression for an index profile is, n2 (r) = n-? 2 [1-2? F (r / a)], in which n (r) is the refractive index at point r in the waveguide radius, nor is the refractive index in the center line of the waveguide,? = (n-i2 - n22) / 2n12, where n2 is a reference refractive index usually taken as the minimum value of the coating layer index and f (r / a) is a function of r divided by radius from the center a. - A profile a is a refractive index profile in which f (r / a) = (r / a) a. - Bandwidth is a standard measure of the scattering property of a waveguide over a range of frequencies. In particular, the bandwidth of a waveguide is the range of frequencies through which the energy penalty due to dispersion is less than 3 dB where the launch energy is used as the basis of comparison. The bandwidth can be expressed in standardized frequency units, MHz-km, which is the bandwidth of a waveguide length of 1 km. When the bandwidth units are simply expressed as MHz, the bandwidth value represents the total length of the measured waveguide. For example, a waveguide that is 2 km long, having a standardized bandwidth of 500 MHz-km, has an end-to-end bandwidth of (500 MHz-km) / 2 km = 250 MHz.

BRIEF DESCRIPTION OF THE INVENTION There is a need for a technically substantiated, low cost way to compensate for the bandwidth in one of the two operating wavelength windows. In addition, this need exists in certain applications to compensate for a wavelength window without having to unduly sacrifice the bandwidth in the other wavelength window. It is contemplated that a refractive index profile n (r) may be found which has a local maximum close to a window of selected wavelength to be compensated and a local maximum in another window of selected working wavelength. The present invention meets the need for a multimode link bandwidth compensator. A first aspect of the invention is a compensated multimode link for dispersion comprising a first multimode fiber length, which has an index profile that provides the respective preselected bandwidths in a first and second wavelength window. The multimode waveguide has a central region and a surrounding coating layer. The central region has a circular cross section of radius a, the radius measured from the center line of the waveguide. In a short notation, the multimode waveguide is said to have the bandwidth BWi, at the wavelength? -i and a bandwidth BW2 at the wavelength? 2. Although the profile n ^ r) can take many forms, the profile in general produces a curve of bandwidth vs. wavelength which has a local maximum in wavelength? p ?. A respective target bandwidth in each of the two working windows is achieved by a combination of the location of? P? in relation to? i and? 2, and the maximum bandwidth that is located in the wavelength? p ?. In order to achieve the respective target bandwidths in each of the two windows, the profile is designed such that the maximum or peak bandwidth is present at a wavelength? P1 which lies between the lengths of central wave of the two operation windows? -iy? 2. The answer bandwidth vs. The wavelength of the waveguide can be calculated from the geometry and the index profile of the waveguide. Mathematical relationships are quite complex even when mode coupling and mode mixing are not considered. Even using numerical methods and a computer, some considerations of simplification usually have to be made. In this way the term "mathematically derivable" is used herein to indicate a particular set of waveguide fiber properties, specifically the refractive index profile and the geometry of the coating layer and the center can be used; - to estimate the delay in relative mode, - to predict? p or - to estimate the bandwidth in? p. The correspondence between the calculated waveguide parameters and the experimental compensation parameters, given below, demonstrates the validity of the considerations used in this application. The compensated link is completed by optically joining a second multimode waveguide fiber to the first fiber. The second multimode waveguide has an index profile n2 (r) which compensates for the relative modal delays that occur in the first waveguide. A compensation method uses a compensating waveguide which has a maximum bandwidth at a wavelength? P2. An example of a profile as such is a profile. When placing? P2 outside the wavelength range defined by? < \ y? 2 one of the bandwidths, that of the larger wavelength window or that of the smaller wavelength window can be compensated for by the second fiber. In the case in which the profile errors in the first waveguide are errors, the compensating waveguide can not correct in general the group delay of the modes in both? -i and? 2, so that the increase in one bandwidth is done at the expense of the other. This is because the change in a produces a change in? P and thus shifts the curve vs. bandwidth. wavelength towards a longer or shorter wavelength. When the profile errors that reduce the bandwidth are of a more random nature or not, it is possible to compensate both the bandwidth of the greater wavelength window and the bandwidth of the smaller wavelength window with a single compensating waveguide. In this way, it is generally appropriate to stipulate that at least one bandwidth can be compensated. An alternative assertion is that the compensating waveguide can operate to equalize the group delay by more than one wavelength. Notice that the compensated bandwidths BWcompí and BWCOmP2 are expressed in MHz. In this way, the end-to-end bandwidth of the waveguide fiber is compared before and after compensation. The compensation should be sufficient to improve the end-to-end bandwidth in MHz although the link has been made larger by the compensating waveguide. In a preferred embodiment of the compensated multimode link, any of the first or second multimode waveguide has a profile, defined above, in which a rests in the range of about 0 to 8. This choice of index profile allows it to be equal group delays so at a selected wavelength and is flexible enough to provide acceptable bandwidth to work in both the 1300 nm window and the 850 nm window. The calculation of compensation waveguide parameters is also made easier by choosing the profiles a. In a more preferred embodiment, both of the first and second multimode wavelengths comprising the link have respective profiles. For this choice of refractive index profile, the working relationships between the compensated link parameters, the first waveguide and the second waveguide take a particularly simple form. A first waveguide fiber having an a = a-t, in the interval 0.8 <; to? < 2.1, can be compensated by a second waveguide fiber having an a = 2 in the interval a-i < a2 < 8. This choice serves to increase the bandwidth at a lower wavelength operating point such as 850 nm. Using the same ai for the first fiber, the bandwidth at a higher wavelength operating point, such as 1300 nm, can be increased by using a second waveguide, that is, compensation, having an a2 in the interval 0.8 < 2 < ai. Defining ai as a characteristic of the first waveguide, cc2 as a characteristic of the second waveguide or compensating waveguide, and aComp as a characteristic of the compensated link, then, to increase the bandwidth of the smaller wavelength, a? comp = (ai + ca2) / (1 + c), where c = L2 / L, where Li is the length of the first waveguide, L2 is the length of the second waveguide, and c is a number in the range of 0 to 1. Similarly, if the bandwidth of the largest wavelength is compensated, ahcomp = (ai + ca2) / (1 + c). In a second aspect of the invention, the refractive index profile of the first length, Li, takes the form n -? (R) = ncn2 [1-2? F? (R / a?)] In which ncn is the refractive index in the center line and ai is the radius of the center. The relative index? -i is known as the minimum value of the refractive index of the coating layer nc ?. The second multimode length has a refractive index profile of the same shape n22 (r) = nC | 22 [1-2? -? F (r / a2)] The combination of the first and second fiber can be chosen to compensate the bandwidth in any of a greater or lesser wavelength of operation. In a preferred embodiment, either f -? (R / a -?) Or f2 (r / a2) has the form (r / a) a, ie a profile a. In a more preferred embodiment, both the first and the second waveguides have respective profiles. The limits and relationships of the respective a, a-i for the first fiber, a2 for the second fiber and comp for the combination of the two fibers is as indicated above. The most advantageous operating windows for the multimode waveguide fiber are centered at 850 nm and 1300 nm. At these wavelengths, and in a range +/- 30 nm around these wavelengths, the characteristics of attenuation vs. wavelengths show a local minimum. In a particular embodiment of the invention, a link having? P? in the range of about 1150 nm to 1250 nm, it is compensated at the 850 nm operating point by optically bonding a compensating waveguide having? p2 in the range of about 450 nm to 650 nm. Additional features of this modality are given in a later example. To maintain the purpose of the compensated link, that is, to increase the data rate, the preferred embodiments of the invention are those in which the length of the compensation waveguide or second waveguide is minimal. Thus, a preferred embodiment of the invention is one in which the a of the compensation fiber is larger compared to that of the first fiber. The larger one provides equal compensation using shorter compensation lengths compared to a minor offset waveguide. The fractional length c, c = L2 / L ?, which is in the range of 0 to 1, has a preferred range of 0.01 to 0.50. In cases where a is in the range of about 2.5 to 3, the preferred range of c is reduced to about 0.01 to 0.25.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a chart of the relative index? vs. radio for profiles to alternatives. Figure 2 is a chart of compensated bandwidth vs. fractional length of the compensating waveguide at 850 nm. Four compensating waveguides are shown. Figure 3 is a letter of a vs? P for an example of multimode waveguide fiber. Figure 4 is an illustrative chart of the bandwidth at 850 nm vs. the fractional amount of the compensating fiber added to a bond.

DETAILED DESCRIPTION OF THE INVENTION The multimode waveguide fiber of high bandwidth can be manufactured by adding glass-forming metal oxides that alter the refractive index to a siliceous-based glass When a glass is called a siliceous base, the weight percent of SiO2 typically it is not less than 70% by weight. The bandwidth is made to be a maximum when the travel time of each mode in the waveguide is as close as possible to the travel time in the waveguide in any other way. In the ideal case, the index profile is configured to provide equal optical paths for all modes. Deviations from the ideal profile shape, ie profile errors, result in relative delays between the modes. These relative delays scatter or scatter a light signal, which consists of many modes. The present invention is directed to a multimode fiber link in which signal dispersion, due to profile errors arising either from manufacturing imperfections or from optimization at an incorrect wavelength, of a first portion of the link be compensated for the remaining portion of the link. A primary feature of the invention is that it has been found that the compensation profiles provide an adequate profile error correction while at the same time keeping the length of the compensation waveguide as short as possible. Adding length to a link adds attenuation and, because no waveguide is perfect, the added length also introduces some group delay differences so due to its own profile errors. Advantageously, the possible profile control in the current waveguide manufacturing processes is such that the gain in bandwidth provided by the compensating fiber improves the overall performance of the link despite the profile attenuation and error present in the compensating waveguide. The examples of refractive index profiles are illustrated in Figure 1, which is a chart of the relative refractive index?, Vs. the waveguide radius. Profile 2 is a step index which can be approximated by a profile in which it is very large. For most fabricated step index profiles, a greater than approximately 8 provides an accurate description of the variation of the index with the radius. Profile 4 of Figure 1 is a parabola described by a profile having a = 2. The profile 6 is triangular having a = 1 and the profile 8 is an example of a profile having a < 1. Figure 1 serves to show the flexibility of the profiles a. The most complex profiles can be described in terms of the profile by dividing the center region into radial segments and assigning a particular to each segment. Because the refractive index of the glass changes with the wavelength, a multimode waveguide can have a refractive index that equals mode delay through a narrow band of wavelengths. The bandwidth reaches a maximum value at a wavelength within this narrow band. The bandwidth decreases in wavelengths above and below the wavelength of maximum bandwidth. Two curves of bandwidth vs. wavelengths are shown in Figure 4. The bandwidth curve 10 has a sharper peak than that of the bandwidth curve 12, due to the refractive index which provides that the bandwidth curve 10 has fewer errors which results in non-equal delays. Note that although the bandwidth curve 12 contains more profile errors, as shown, because of the decreased maximum bandwidth, the bandwidths of curves 10 and 12 in the 850 nm and 1300 nm operation windows They are almost the same. When designing a profile for dual window operation, a bandwidth curve with sharp peaks vs. wavelength may not be as effective as one that is flatter but almost more constant over an extended wavelength range . Figure 4 also shows how the bandwidth at 1300 nm can be altered in relation to the bandwidth at 850 nm. The mode groups of a signal at 1300 nm have a different range of optical paths compared to the mode groups of a signal at 850 nm. By adjusting the amount of contaminant that alters the refractive index in the waveguide along the waveguide radius, a better mode delay compensation could be provided for any of the modes at the longer wavelength or modes at the shortest wavelength. In effect, the maximum bandwidth of the bandwidth versus wavelength curve can be moved to higher or lower wavelength values. For example, the wavelength of the maximum bandwidth? P can be matched to either 1300 nm or 850 nm and thus move the maximum bandwidth to one or the other of these wavelengths of operation. Choosing a value of? P which is between 1300 nm and 850 nm decreases the bandwidth by one wavelength while at the same time increasing the bandwidth in the other window. Optically joining multimode waveguide fibers having values of p that are separated will cause group delays different from the signal in the different waveguides so that a measurement of the bandwidth vs. wavelength of a set as such of united waveguides will yield a? p which is between the separated p? The present invention uses the ability to place? P at a preselected wavelength in a given multimode waveguide to adjust the? P of an installed link and thus change the bandwidth of the link to an operating wavelength. particular. A multimode fiber length, the compensation fiber, having a? P separated from the? P of the installed link is optically linked to the link to provide a balanced link having an? P altered and an altered bandwidth characteristic vs. length. cool. Because the length of the compensating wave guide fiber is added to the existing link, it is important that the compensating waveguide be as short as possible. The present invention fulfills this requirement by making the compensator? P either rather larger, that is to say above 1300 nm, or quite smaller, that is to say below 850 nm. This choice of? P provides the compensation at the point of operation of greater or lesser wavelength while at the same time maintaining the length of the compensation fiber less than or equal to the original length of the link. As will be seen in the following examples, effective compensation is possible using compensating fiber lengths in the range of 1% to 50% of the original link length. This is precisely the characteristic that makes the compensating fiber a practical tool for adjusting the bandwidth of the link. The? P of a compensating waveguide can be adjusted by adjusting the a of a profile compensator a. An illustrative letter of a vs? P is shown as curve 14 in figure 3. Notice that an a of about 2.25 provides a? P of about 500 nm and an a of about 1.97 provides a? P of about 1200 nm.

EXAMPLE 1 Compensating waveguide that has a of 2.21 Four multi-mode waveguide fibers were each optically joined to a compensating waveguide fiber having an a of 2.21 at the same time. The bandwidths in MHz, measured using an overfilled launch condition (NA and the size of the source spot greater than that of the fiber) for compensation lengths of 2%, 10%, 27% and 50% of the first length are shown in table 1.

TABLE 1 a = 2.21 AB AB AB AB AB 850/1300 850/1300 850/1300 850/1300 850/1300 MHz MHz MHz MHz MHz c = 0 c = 2% c = 10% c = 27% c = 50% Fiber # 1 92/328 106/333 111/435 121/459 134/291 Fiber # 2 95/525 113/742 119/755 126/552 139/305 Fiber # 3 106/841 127/920 133/943 152/451 177/247 Fiber # 4 99/579 110/478 116/782 125/447 143/277 The four fibers under test were each approximately 1.73 km in length. The same compensating fiber was used in each of the four test links. The effects of the compensating wave guide fiber are given over the bandwidth at both 850 nm and 1300 nm. The bandwidth at 850 nm increases as the fractional length, c, of the compensating fiber increases from 2% to 50%, where c is defined as the ratio of compensator length to original fiber length. The measured bandwidth of the bandwidth in MHz is the end-to-end bandwidth in each case and thus includes the increase in link length due to the addition of the compensating waveguide. In the fractional compensator lengths of up to about 27%, the bandwidth at 1300 nm is also increased by the addition of the compensator. Probably this increase is due to a mode separation or mode mixing action of the compensator which shifts the displacement from? p towards shorter wavelengths.

The benefit due to the compensating waveguide is achieved by waveguides having low bandwidth at 1300 nm, fiber # 1, high bandwidth at 1300 nm, fiber # 3 and bandwidth at a moderate 1300 nm, fibers # 2 and # 4. A chart of the data at 850 nm from Table 1, normalized to a length of 1 km, is shown in Figure 2. The symbols show the actual data points and the lines are adjusted using a linear model in which the characteristic of the system, aCOmp is written in terms of the a of the original link, ai, and of the a of the compensating waveguide, a2, that is + c). This equation can be solved for the fractional length c as, c = (a? -aCOmp) / (comp-a2). This equation offers a good approximation of c for a-values in the range of about 0.5 to 6. A more exact relationship which includes the intermodal correlation coefficients is found in M. Eve's work, cited below. The data also show good correlation with a multiple path time dispersion model established in Opt. Quant. Electr., 10, 41-51, 1978, "Multipath time dispersion theory of an optical network", M. Eve. In this model the compensated bandwidth in GHz is expressed in terms of the original bandwidth in GHz, the pulse width rms in the original link, yes, the pulse width rms in the original link plus the compensator, s2, as, BW8mp = BW? (1 / { 1- (ms2 / s?).}.). The models adjust the data points close enough so that the models are useful for predicting the properties of the compensating waveguide as well as the performance of the system compensated. Notice that the expression for W8mp predicts very high compensated bandwidths for choices of m for which the term ms2 / s-? It is close to one. In this way there is an optimal choice of m for any determined multimode link.

COMPARATIVE EXAMPLE Compensating waveguide that has a = 3 The four multimode waveguide fibers of the example are compensated with a different fiber that has a higher one, particularly an a in the range of 2.5 to 3.0. Table 2 shows the Bandwidth measurements in the four compensator lengths.

TABLE 2 a = 3 AB AB AB AB 850/1300 850/1300 850/1300 850/1300 850/1300 MHz MHz MHz MHz MHz c = 0 c = 0.65% c = 9.4% c = 27% c = 50% Fiber # 1 92/328 104/319 127/354 147/117 76/46 Fiber # 2 95/525 110/527 129/347 139/112 75/45 Fiber # 3 106/841 125/820 153/314 132/98 61/42 Fiber # 4 99/579 111/538 131/303 137/101 67/43 In the case of the compensating fiber with the highest Compensation benefits are presented with compensator lengths much shorter. The compensator a_ = 3 begins to dominate the performance of the link to a percent length in the range of about 12% to 25%, which establishes a practical upper limit on fiber length compensatory. This is seen in Table 3 in which the link bandwidth performance was measured at points between 9.4% and 27%.

TABLE 3 a = 3 AB AB AB AB AB 850/130 850/1300 850/1300 850/1300 850/1300 850/130 MHz MHz M MHHzz 0 0MMHHzz M MHHzz M MHHzz c = 12% c = 14% cc == 1166 %% cc == 1199 %% cc == 2211 %% cc == 2244 %% Fiber # 1 134/342 145/315 1 14455 // 223355 1 15511 // 119955 1 15511 // 117733 1 15500 // 114488 Fiber # 2 145/418 152/297 1 15533 // 222255 1 16644 // 119911 1 16622 // 116644 1 16666 // 114411 Fiber # 3 179/300 193/254 1 19966 // 119966 2 20077 // 117700 2 20099 // 114466 2 20066 // 112255 Fiber # 4 148/312 159/288 1 16666 // 221111 1 16644 // 117766 1 16699 // 117766 1 17711 // 113377 The compensation in the operation window at 850 nm is observed to go through a maximum for the compensation fiber lengths between 16% and 25% of the first fiber. Table 4 shows the relative influence of the different guides Compensator wave have about? p. Table 4 gives the length of compensating waveguide, which has a particular a, sufficient for move? p from the link from about 1200 nm to 1150 nm.

TABLE 4 % of compensator compensator length 0.53 3.0 2.0 2.25 3.6 2.13 6.0 2.07 The benefit derived from the compensator with the higher one is evident. Although the particular embodiments of the invention have been described and discussed, the invention is nevertheless limited only by the following claims.

Claims (14)

NOVELTY OF THE INVENTION CLAIMS

1. - A balanced multimode waveguide fiber link for dispersion comprising: a first multimode waveguide length having a long dimension Li, a centerline along the long dimension, a refractive index profile n- (r) which extends through a central region of the center of circular cross-section and radius ai, the center of the circular region resting on the center line; a coating layer, having a minimum thickness ti, surrounding and coming into contact with the central region having a minimum refractive index nc ?, in which at least a portion of the profile n - (r) is greater than nc1; the profile n? (r) providing a first bandwidth, BWi, at the wavelength? -i, a maximum bandwidth BWp1, at the wavelength? p-? and a second bandwidth BW2, at the wavelength? 2? being BW-, BW2 and BWpi mathematically derivable from n -? (r), nc ?, ai and t-t, in which ?? £? p1 < ?2; a second multimode waveguide length, optically bonded to the first multimode waveguide length having a long dimension L2, a centerline along the long dimension, refractive index profile n2 (r) extending on a central region of the center of circular cross-section and radius a2, resting the center of the circular region on the center line; a coating layer, having a minimum thickness t2 surrounding and contacting the central region having a minimum refractive index nc2, in which at least a portion of the profile n2 (r) is greater than nc2; providing the profile n2 (r) a third bandwidth, BW3, at the wavelength? -i, a maximum bandwidth BWp2, at the wavelength? p2, and a fourth bandwidth BW4, at the length of wave? 2, being BW3, BW4 and BWp2 mathematically derivable from nc2, a2 and t2, in which? p2 < ? -? or? p2 > ?2; forming the combination of the first and second multimode waveguide a multimode waveguide link of length Li + L2, and having a bandwidth BWcompied in MHz in? -i, a bandwidth BWcompied in MHz in? -i, in which at least one of BW8mpi or BWcomp2 is greater than BW1 or BW2, in MHz, respectively.

2. The compensated multimode link for dispersion according to claim 1, in which n? (R) is a profile a having a = cc? and 0 < a-i < 8.

The multimode link compensated for dispersion according to claim 1, wherein n2 (r) is a profile a having a = a2 and 0 < a2 < 8.

The compensated multimode link for dispersion according to claim 1, in which n -? (R) and n2 (r) are profiles a having a = a-i, and 0.8 << to? < 2.1 and having a = a2 and a-i < 2 < 8, respectively, the link being characterized by an a = a8mp and 0.8 < a8rnp < a2 and L2 = c, in which 0 < c < 1, and c = (a acomp ^ acomp- 2).

5. The compensated multimode link for dispersion according to claim 1, wherein n -? (R) and n2 (r) are profiles a having a = a-i, and 0.8 < ai < 2.1 and having a = a2 and 0.8 < a2 < a ?, respectively, the link being characterized by a compensation = occomp and 0.8 < acomp < 2 and L2 = cL-i, in which 0 < c < 1, and c = (a? -acomP) (occomP-a2).

6. The compensated multimode link for dispersion of any of claims 4 or 5 in which 0.01 < c < 0.50.

7. A balanced multimode waveguide fiber link for dispersion comprising: a first multimode waveguide length having a long dimension Li, a centerline along the long dimension, a refractive index of the central line ncn, a relative index? -i, a refractive index profile n-? 2 (r) = ncn [1-2? f? (r / a?], which extends through a central region of the center of circular cross section and radio ai, resting the center of the circular region on the center line; a coating layer, having a minimum thickness ti, surrounding and coming into contact with the central region having a minimum refractive index nc ?, in which at least a portion of the profile n - (r) is greater what nc ?, and nc? is the benchmark for the relative index? i; providing the profile n ^ r) a first bandwidth BW-i, at the wavelength? i, a maximum bandwidth BWp1, at the wavelength? p ?, and a second bandwidth BW2, at the Wavelength? 2, being BW-i, BW2 and BWP? mathematically derivable from n -? (r), nc ?, a -i, and t1 t in which? - \ < ? p? < ?2; a second multimode waveguide length, optically joined to the first multimode waveguide length, having a long dimension L2, a centerline along the long dimension, a refractive index on the centerline of nc? 2, a relative refractive index? 2, a refractive index profile n22 (r) = n22 [1 -2? 2f (r / a2)], which extends through the central region of the center of circular cross section and radio a2, resting the center of the circular region on the center line; a coating layer, having a minimum thickness t2, surrounding and coming into contact with the central region having a minimum refractive index nc2, in which at least a portion of the profile n2 (r) is greater than nc2; the profile n2 (r) providing a third bandwidth BW3, at the wavelength? -i, a maximum bandwidth BWP2, at the wavelength? p2, and a fourth bandwidth BW4, at the length of wave? 2, being BW3 BW4 and BWp2 mathematically derivable from n2 (r), nc2, a2 and t2, in which,? p2 < ? i or? 2 < ? p2; forming the combination of the first and second multimode waveguides a multimode waveguide link of length Li + L2, and having a bandwidth BWcomp ?, in MHz in? i, and having a bandwidth BW8m 2. in MHz in? 2, in which at least one of BWcompí or BW8mp2 is greater than BW1 or BW2, respectively.

8. The compensated multimode link for dispersion according to claim 7, wherein f -? (R / a -?) = (R / a?) 1 and 0 < ai < 8

9. - The compensated multimode link for dispersion according to claim 7, wherein f2 (r / a2) = (r / a2) 2 and 0 < a2 < 8. The compensated multimode link for dispersion according to claim 7, wherein f? (R / a1) = (r / a2) a1 and f2 (r / a2) = (r / a2) a2, taking 1.8 < a-i < _2.1, _y a-i < 2.1, and a-i < a2 < 8, respectively, the link being characterized by an a = a8mp and 1.8 < aCOmp < a2 and L2 = CLL in which 0 < c < 1, and c = (to acomp) (acomp-a2) - 11.- The compensated multimode link for dispersion according to claim 7, in which f? (R / a -?) = (R / a2) 1 and f2 (r / a2) = (r / a2) a2, taking 0.8 < a-i < 2.1 and a-i < a2 < 8, respectively, the link being characterized by an a = aCOmp and 0.8 < aCOmp < 2 and L2 = cL ^ in which 0 < c < 1, and c = (ai - aComp) (xcomp-a2). 12. The offset multimode link for dispersion of any of claims 10 or 11 in which 0.01 < c < 0.50. 13.- The compensated multimode link for dispersion according to claim 7, in which? -? is in the range of about 850 +/- 30nm and? 2 is in the range of about 1300 +/- 30nm. 14. The compensated multimode link for dispersion according to claim 11, wherein? P? it is in the range of about 1150 nm to 1250 nm and? p2 is in the range of about 450 nm to 650 nm.