Optical fibers having an inner core and an outer core

A multimode optical fiber includes an inner core and an outer core on the inner core having different refractive index profiles. The refractive index profile of the outer core is graded, while the refractive index profile of the inner core may be graded. The refractive index profiles have the same value at the inner core--outer core boundary.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention is directed to optical fibers for transmitting 
optical signals and, more particularly, to improved multimode optical 
fibers that possess unique refractive index profiles. Optical fibers 
according to the invention possess high bandwidth and high numerical 
aperture at multiple wavelengths while favorably accounting for material 
dispersion effects. 
2. Description of the Related Art 
There are major needs for high bandwidth, high numerical aperture optical 
fibers for applications in short and medium distance fiber optic 
communications network systems. Bandwidth is the amount of information 
that can be transmitted in a specified time interval and is among the most 
important characteristic features of an optical fiber link. The current 
ever-growing demand for high bandwidth is for voice, video, and data 
transmission in short and medium distance applications such as local area 
networks (LANs) and metropolitan area networks (MANs). In particular, 
current high data rate network forms, such as asynchronous transfer mode 
(ATM) and Ethernet, operate at several hundred megahertz (MHz) with 
bandwidths of 1000 MHZ (1 gigahertz (GHz)) and greater already planned for 
implementation. 
Step index fibers according to the prior art are characterized by a single 
core region having a uniform refractive index, surrounded by a cladding 
layer having a lower refractive index. Graded index fibers according to 
the prior art are characterized by a single core region having a 
continuously varying refractive index from a higher value at the center of 
the fiber to a lower value at the core-cladding boundary. The graded core 
region is also surrounded by a cladding layer. 
High numerical aperture multimode step index (SI) glass optical fiber can 
operate at data rates of 10-100 MHZ, but these lower rates are already 
approaching the physical bandwidth limits of the fiber. Standard single 
mode glass optical fiber can possess much higher bandwidth, as high as 
5-10 GHz, but the prohibitive costs of splicing and connecting the several 
micron diameter fiber cores work against their wide spread use in LAN and 
MAN applications where multiple connections are required. Low numerical 
aperture, difficult to connect, multimode graded index (GI) glass optical 
fiber can also provide a higher bandwidth of approximately 1 GHz, but only 
at selected operating wavelengths. A multimode graded index glass optical 
fiber exhibits different bandwidth performance at different wavelengths 
due to the effect of material dispersion. 
It is well established for optical fibers that fiber bandwidth performance 
is determined in large measure by the specific characteristics of the 
refractive index profile. In the presence of material dispersion, these 
index profile characteristics are different under different operating 
wavelengths. For example, it is desirable to operate silica based fibers 
at approximately 850, 1300, and 1550 nanometers (nm). Attempts to optimize 
bandwidth performance at multiple wavelengths have had limited success 
because of the complicated material compositions and fabrication 
conditions needed in forming graded refractive index profiles. It is well 
known that the precise control of the graded refractive index profiles 
required, for example, in presently available graded index glass optical 
fibers is a difficult and challenging task. The above problems and 
shortcomings of graded index silica based, i.e., glass, optical fibers 
apply equally to graded index polymer optical fibers. 
SUMMARY OF THE INVENTION 
An object of the invention is to provide a high numerical aperture 
multimode optical fiber exhibiting high bandwidth performance. 
Additional objects and advantages of the invention will be set forth in 
part in the description which follows, and in part will be obvious from 
the description, or may be learned by practice of the invention. The 
objects and advantages of the invention will be realized and attained by 
means of the elements and combinations particularly pointed out in the 
appended claims. 
To achieve the objects and in accordance with the purpose of the invention, 
as embodied and broadly described herein, there is provided an optical 
fiber, comprising: an inner core having a first refractive index profile; 
an outer core on the inner core having a second refractive index profile 
which is lower than the first refractive index profile, wherein the first 
and second refractive index profiles have a comon value at an inner 
core-outer core boundary; and a cladding layer on the outer core. 
Also in accordance with the present invention there is provided a method of 
making an optical fiber including an inner core having a first refractive 
index profile, an outer core on the inner core and having a second 
refractive index profile which is lower than the first refractive index 
profile, wherein the first and second refractive index profiles have a 
common value at an inner core-outer core boundary, and a cladding layer on 
the outer core, comprising: forming the inner core having the first 
refractive index profile; forming the outer core on the inner core fiber 
and having the second refractive index profile; and forming a cladding 
layer on the outer core. 
It is to be understood that both the foregoing general description and the 
following detailed description are exemplary and explanatory only and are 
not restrictive of the invention, as claimed. 
The accompanying drawings, which are incorporated in and constitute a part 
of this specification, illustrate several embodiments of the invention 
and, together with the description, serve to explain the principles of the 
invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Reference will now be made in detail to the present exemplary embodiments 
of the invention, examples of which are illustrated in the accompanying 
drawings. Wherever possible, the same reference numbers will be used 
throughout the drawings to refer to the same or like parts. 
Improved high bandwidth performance, greater than 1 GHz, at multiple 
operating wavelengths is needed in high numerical aperture multimode 
fibers that account for material dispersion effects. The present invention 
addresses this important need. 
The present invention provides improved multimode optical fibers having 
unique refractive index profiles that favorably account for material 
dispersion of the fiber. Multimode optical fibers according to the 
invention have high bandwidth performance, high numerical aperture, and 
operate at multiple wavelengths. 
Numerical aperture is an important property of an optical fiber. Higher 
numerical aperture means greater acceptance angles for input light into 
the fiber. Thus, fiber-to-fiber splices exhibit lower loss, 
fiber-to-device coupling is more efficient, and fiber bending losses are 
lower. 
Optical fibers constructed in accordance with the present invention are 
inner core-outer core multimode optical fibers generally having the 
construction of an exemplary optical fiber 100 shown in FIG. 1. As seen in 
FIG. 1, optical fiber 100 includes an inner core region 102 surrounded by 
an outer core region 104. A cladding layer 106 surrounds outer core region 
104 and is the outermost region of the optical fiber. 
In various embodiments of the invention, the refractive index profile 
across inner core region 102 either remains essentially uniform, decreases 
from the center of optical fiber 100 following a straight line 
characteristic, or decreases with a curvilinear shape characterized as an 
alpha (.alpha.)-profile, to the interface between inner core region 102 
and outer core region 104. 
The refractive index of outer core region 104 in preferred embodiments of 
the present invention follows a smooth and monotonic decrease with 
increasing fiber radius from the center of optical fiber 100. In selected 
embodiments, the refractive index profile of outer core region 104 either 
decreases with a straight line characteristic, or with a curvilinear shape 
characterized as an alpha (.alpha.)-profile, to the interface between 
outer core region 104 and cladding layer 106. 
FIG. 2 illustrates refractive index profiles of optical fibers according to 
embodiments of the present invention. More particularly, FIG. 2 is a graph 
of refractive index "n" versus optical fiber radius "r" according to 
various embodiments of the present invention. With reference to FIG. 2, 
the refractive index profile of inner core region 102 extends from the 
center of optical fiber 100 at radius r=0 to the boundary between inner 
core region 102 and outer core region 104 at radius r=a.sub.0. In certain 
embodiments, the refractive index of inner core region 102 smoothly 
decreases from a value of n.sub.0 at the center of optical fiber 100 (r=0) 
to a value of n.sub.1 at the inner core-outer core boundary (r=a.sub.0). 
This smooth decrease can have a curvilinear profile, such as curvilinear 
profile 200, or a linear profile such as a linear profile 202. In another 
embodiment, the refractive index of the inner core region is uniform, 
having a constant value of n.sub.1 across the entire inner core region. In 
FIG. 2, linear profile 204 that is a horizontal line is an example of such 
a uniform refractive index. 
The refractive index profile of outer core region 104 extends from the 
boundary between inner core region 102 and outer core region 104 at radius 
r=a.sub.0 to the boundary between outer core region 104 and cladding layer 
106 at radius r=a. In the outer core region of the profile, the refractive 
index follows a smooth and monotonic decrease from a value of n.sub.1 at 
the inner core-outer core boundary to a value of n.sub.2 at the outer 
core-cladding boundary (r=a). The general shape of the decreasing outer 
core refractive index profile is either curvilinear or linear in shape, as 
shown by profiles 206 and 208, respectively, in FIG. 2. The refractive 
index profile of cladding layer 106 is essentially uniform, as shown by 
profile 210 in FIG. 2 which is a horizontal line. As seen in FIG. 2, the 
refractive index of cladding layer 106 is equal to the lowest refractive 
index of outer core region 104. 
It is intended that optical fibers can be constructed according to 
embodiments of the present invention utilizing all permutations of the 
inner and outer core region refractive index profiles described above and 
illustrated in FIG. 2. With respect to all of the possible permutations of 
inner core region and outer core region refractive index profiles, these 
profiles are continuous at the boundary between inner core region 102 and 
outer core region 104. The refractive index profiles of FIG. 2 are 
continuous at the inner core-outer core boundary in the following 
mathematical sense. If the profiles are expressed as a function n(r), then 
Lim n(r)=n(a.sub.Q, a.sub.Q. That is, the graph in FIG. 2 exhibits no 
discontinuities (e.g., a step change in refractive index, where n(a.sub.0) 
would not exist) at the boundary between the inner and the outer core 
regions. 
Each of the uniform and curvilinear inner core and outer core refractive 
index profiles, 200, 204, and 206 essentially follow an .alpha.-profile 
characterized by the following equation (1): 
##EQU1## 
for any positive real number .alpha.. The above equation for n(r) 
describes how the refractive index n varies as a function of fiber radius 
r. In the case when equation (1) describes inner core region 102, and with 
reference to FIG. 2, n.sub.i is either n.sub.0 or n.sub.0, depending on 
whether the index of the inner core region is graded or uniform, 
respectively; n.sub.j =n.sub.1 ; and r'=a.sub.0. In the case when the 
profile of inner core region 102 has a uniform flat refractive index, 
n.sub.i =n.sub.j =n.sub.1. In the case when the profile of inner core 
region 102 has a graded refractive index, n.sub.i =n.sub.0. 
In the case where equation (1) describes outer core region 104, and with 
reference to FIG. 2, n.sub.i =n.sub.1 ; n.sub.j =n.sub.2 ; and r'=a. 
In the case for outer core region 104, when index profile 208 is linear, 
then the refractive index has the following form: 
##EQU2## 
where a.sub.0 is the radius of inner core region 102; .alpha. is the 
radius from the center of optical fiber 100 to the outer core-cladding 
boundary; n.sub.1 is the refractive index at the inner core-outer core 
boundary; and n=n.sub.2 at r=a, where n.sub.2 is the refractive index of 
cladding layer 106, as shown in FIG. 2. 
In other selected embodiments of the present invention, when the refractive 
index of outer core region 104 is extrapolated back over inner core region 
102 to the center of optical fiber 100, the resulting extrapolated value 
is higher than the refractive index of inner core region 102. For example, 
with reference to FIG. 2, when section 206 is extrapolated back to r=0, 
its extrapolated portion has a higher refractive index than section 204 
over the entire inner core region 102. Similarly, when section 208 is 
extrapolated back to r=0, its extrapolated portion has a higher refractive 
index than any of sections 200, 202, and 204, over the entire inner core 
region 102. 
In an optical fiber, light is confined by bouncing back and forth between 
the core-cladding boundaries by total internal reflection. Such 
confinement is best described by guided modes. In a multimode fiber, 
different modes can be visualized as light traveling at different angles 
with respect to the longitudinal direction. Thus, in an optical signal 
transmission system, different transmitted modes will travel different 
distances from a transmitter before they reach a receiver and, therefore, 
arrive at different times. When used as transmission signals, very short 
optical pulses, after traveling some distance in such fiber, are broadened 
by modal and material dispersion effects. Such effects are a primary cause 
for the bandwidth limitation of the transmission system and an important 
subject for analysis and understanding. 
In general, guided modes in an optical fiber are described by the following 
scalar wave equation (3): 
##EQU3## 
where .nu. is the azimuthal mode number of the mode, .beta. is the 
propagation constant of the mode, r is the radius of the fiber, k.sub.0 is 
the free space wave vector, .PHI. is the field solution, and n=n(r) is the 
refractive index of the fiber at radius r. 
Equation (3) is solved by standard approximation methods, one of which is 
the WKB method. Thus, the value of propagation constant .beta. is obtained 
from the following WKB equation (4): 
##EQU4## 
where .mu. is the radial mode number, and a.sub.1 and a.sub.2 are the 
positions where the integrand vanishes. 
In the presence of material dispersion, the group delay time t is 
determined by 
##EQU5## 
where n.sub.1 and n.sub.2 are the refractive indices at the inner 
core-outer core boundary and of cladding layer 106, respectively, as shown 
in FIG. 2; m is the mode number, and c is the speed of light. The 
bandwidth of the fiber is obtained from the transfer function which is 
derived from the group delay time t. 
The bandwidth and numerical aperture of a transmission medium define the 
performance limits and applications for which the medium is suitable. 
Along with outstanding bandwidth performance, the optical fibers of the 
present invention provide improved numerical apertures, especially as 
compared to low numerical aperture step index optical fibers and graded 
index optical fibers. Calculation of the coupling loss profile allows 
quantitative analysis of the fiber numerical aperture. 
Low fiber coupling loss for a given optical fiber geometry is a direct 
result of the fiber having a high numerical aperture, meaning a large 
acceptance angle. FIG. 3 is a graph comparing coupling loss results for 
step index and graded index profile fibers with those of an inner 
core-outer core design according to the invention, as in FIGS. 1 and 2. 
More particularly, FIG. 3 is a graph of coupling loss in decibels versus 
position within the core(s) represented as r/R, where r is a variable 
radius and R is the radius at the core-cladding boundary. For example R=a 
in FIG. 2. In FIG. 3, data plot 300 is a coupling loss of a graded index 
(GI) fiber, data plot 302 is a coupling loss of an inner core-outer core 
fiber according to the present invention, and data plot 304 is a coupling 
loss of a high numerical aperture step index (SI) fiber. 
With reference to FIG. 3, the numerical aperture of a fiber constructed 
according to the invention is larger than that of a graded index fiber 
over the entire core radius, as illustrated by data plots 302 and 300, 
respectively, with the inner core region of the optical fiber according to 
the invention possessing the higher numerical aperture. Since numerical 
aperture is a measure of the acceptance angle over which light rays 
entering the fiber will be guided, a larger numerical aperture is 
preferred. The numerical aperture of the inner core-outer core profile 302 
is much higher than that of low numerical aperture step index and graded 
index optical fibers and nearly matches that of a high numerical aperture 
step index optical fiber, such as shown in plot 304, resulting in easy 
fiber-to-fiber connections and much reduced coupling and bend loss. 
In another embodiment, one or more of inner core region 102, outer core 
region 104, or cladding layer 106 includes glass. In certain embodiments, 
one or more of inner core region 102, outer core region 104, or the 
cladding layer 106 includes at least one organic polymer. In other 
embodiments, outer core region 104 includes a composition of at least two 
organic polymers having different refractive indexes. In other selected 
embodiments, inner core region 102 is glass, and outer core region 104 
includes at least one organic polymer. 
Those skilled in the fiber optic art will be able to construct the optical 
fibers herein disclosed using well-known materials and fabrication 
techniques without additional disclosure. Skilled practitioners will, for 
example, choose appropriate glass and polymer compounds to produce desired 
indices of refraction based on such design factors as, for example, length 
of the fiber, diameter, desired rigidity, cost, material availability, and 
present manufacturing capability. These materials are readily available in 
reference texts and patents, and the following specific materials are 
exemplary only. 
A partial list of polymer compositions suitable for the cores and/or the 
cladding includes styrene acrylonitrile, fluoroalkyl methacrylate 
polymers, copolymers of methylmethacrylate and vinyl phenyl acetate 
(P(MMA-VPAc)) polyesters, acetonitrile butadiene styrene, polyolefins, 
polymethylmethacrylate, copolymers of methylmethacrylate and vinyl 
benzoate (P(MMA-VB)), copolymers of vinylidene fluoride and 
tetrafluorethylene, methyl methacrylate styrene, polystyrenes, polyesters, 
and polycarbonates. Further polymer compositions can be found in, for 
example, Plastic Optical Fibers and Application, Vol. 25, Information 
Gatekeepers, Boston Mass. 1994 ("Gatekeepers"); and L. Homak, Polymer for 
Lightwave and Integrated Optics: Technology and Applications, Marcel 
Dekker, N.Y., 1992 ("Homak"). The above materials publications are all 
incorporated herein by reference. 
Similarly, a partial list of suitable glass compositions includes those 
found in S. E. Miller and A. G. Chynoweth (eds.), Optical Fiber 
Telecommunications, Academic, N.Y., 1979 ("Miller I"); S. E. Miller and I. 
P. Karninow (eds.), Optical Fiber Telecommunications II, Academic Press, 
New York, N.Y., 1988 ("Miller II"); and Marvin J. Weber, CRC Handbook of 
Laser Science and Technology: Optical Materials Part 3, Applications, 
Coatings, and Fabrication, Vol. 5, CRC Press, 1987 ("Weber"). The above 
materials publications are all incorporated herein by reference. 
Skilled practitioners also will, for example, choose appropriate 
manufacturing processes to produce the above desired materials based on 
such design factors as, for example, length of the fiber, diameter, 
desired rigidity, cost, material availability, and present manufacturing 
capability and expertise. These processes are readily available in 
reference texts and patents, and the following specific materials are 
exemplary only. 
For graded index regions of polymer optical fibers, a partial list of 
suitable manufacturing processes includes, for example, centrifugal 
molding, photo locking, photo copolymerization, photo bleaching, 
multi-stage copolymerization, interfacial gel copolymerization, and 
polymerization initiator diffusion. Additional suitable manufacturing 
processes for polymer optical fibers, are disclosed in, for example, 
Homak; Gatekeepers; Emslie, Review ofPolymer Optical Fibers, Journal of 
Material Science, Vol. 23 (1988); M. J. Bowden and S. R. Thunrer, Polymers 
for High Technology, American Chemical Society, Washington, 1987; U.S. 
Pat. No. 5,235,660; U.S. Pat. No. 5,555,525; and U.S. Pat. No. 5,593,621. 
The above manufacturing process publications are all incorporated herein 
by reference. 
Similarly, for graded index regions of glass fibers, a partial list of 
suitable manufacturing processes includes, for example, standard melt 
drawing from a glass preform, inside and outside vapor deposition, 
extrusion, and sol-gel process. Additional suitable manufacturing 
processes for polymer optical fibers, are disclosed in, for example, 
Miller I, Miller II, Weber, U.S. Pat. No. 3,711,262, U.S. Pat. No. 
4,062,665, and U.S. Pat. No. 5,522,003. The above manufacturing process 
publications are all incorporated herein by reference. 
Thus, broadly, the present invention is also directed to a method for 
manufacturing an optical fiber comprising steps of forming an inner core 
with a first refractive index profile and forming an outer core 
surrounding the inner core and having a second refractive index profile. 
The method also includes a step of forming a cladding layer to surround 
the outer core. The first refractive index profile is established to be 
uniform across the inner core or to decrease from the center of the 
optical fiber with either a linear or curvilinear characteristic. The 
second refractive index profile is established to decrease from the inner 
core-outer core boundary with either a linear or curvilinear 
characteristic. Further, the first and second refractive index profiles 
are established such that they have a common value at the inner core-outer 
core boundary. 
The invention will be fturther clarified by the following examples, which 
are intended to be purely exemplary of the invention, especially the 
specific wavelengths used. This invention is not limited to the specific 
wavelengths below, but instead may encompass the x-ray, ultraviolet, 
visible, near infrared, mid-infrared, and far infrared wavelength regions. 
EXAMPLE 1 
A general procedure for optical fibers enables calculation of group delay 
time as a function of mode number, taking explicitly into account material 
dispersion of the fiber in the limit of zero spectral source width and no 
mode coupling. The starting point is the WKB approximation relating the 
mode number m to the propagation constant .beta.. In the presence of 
material dispersion, the group delay time t is determined by Equation (5) 
above. 
The inner core-outer core refractive index profile consists of two regions, 
flat uniform inner-core region 204 and linear outer core region 208, as 
shown in FIG. 2, in the form of equation (6): 
##EQU6## 
where a.sub.0 is the inner-core radius and is given by a.sub.0 =a(0.5+q). 
Here q is a parameter dictating the inner core-outer core radius ratio. 
For example, q of zero indicates that the inner core occupies 50% of the 
overall core radius. In the limit when the inner core dimension a.sub.0 is 
zero, the value of q=-0.5. The entire core region then consists solely of 
the outer core having a linear refractive index, and the core index 
profile is triangular in shape. In the opposite limit when q=0.5, the 
exemplary inner core-outer core index profile assumes the shape of a 
standard step index profile. 
In the following numerical simulations, the inner core material is 13.5% 
molar GeO.sub.2 and 86.5% molar SiO.sub.2, and the outer core material is 
0.1% molar GeO.sub.2, 5.4% molar B.sub.2 O.sub.3, and 94.5% molar 
SiO.sub.2. There is a refractive index difference of 0.0206 at 850 nm 
between the core center and cladding. The refractive indices for the core 
center and cladding are 1.4737 and 1.4531, respectively, at 850 nm. 
FIG. 4 shows the group delay time t as a function of mode number m for q=0 
at .lambda.=850 nm. It is noted that although the group delay has 
significant spreading, the majority of modes are concentrated in a narrow 
region, indicating that the bandwidth should be reasonably high for the 
fiber. This observation is validated by the additional calculations in 
Examples 2 and 3. 
EXAMPLE 2 
The impulse response function, h(t).varies..vertline.dm/dt.vertline., is 
determined from the group delay time as a function of mode number. FIG. 5 
shows the impulse response function generated from FIG. 4 of Example 1 
assuming equal modal power distribution among all guided modes. The 
discontinuity at about 1.16 ns in this particular example results from the 
non-monotonic behavior of the curve in FIG. 4. This impulse response in 
the time domain can be used, via a Fourier transform, to obtain the 
transfer function in the frequency domain. 
EXAMPLE 3 
The transfer function is calculated in the frequency domain from the 
preceding impulse response function to obtain the bandwidth performance. 
FIG. 6 shows the transfer function generated from the data of FIGS. 4 and 
5 of Examples 1 and 2. The 3 dB bandwidth at 850 nm, from the transfer 
function in FIG. 6, is determined to be 1.81 GHz for a 100 meter length of 
optical fiber. Similar calculations at 1300 nm produce a bandwidth of 3.46 
GHz for a 100 meter length of optical fiber. There is a refractive index 
difference of 0.0209 at 1300 nm between the core center and cladding. The 
refractive indices for the core center and cladding are 1.4684 and 1.4475, 
respectively, at 1300 nm. 
EXAMPLE 4 
Bandwidth calculations were carried out following the procedures of 
Examples 1-3 for different values of q for the GeO.sub.2 doped silica 
fiber of Example 1. FIG. 7 shows the results at both wavelengths of 850 
and 1300 nm in data plots 700 and 702, respectively. It is recognized that 
for GeO.sub.2 doped silica when q=0.02, the bandwidth is optimized at both 
wavelengths, with bandwidths of 4.74 GHz for a 100 meter fiber length at a 
wavelength of 850 nm, and 3.35 GHz for a 100 meter fiber length at a 
wavelength of 1300 nm. 
EXAMPLE 5 
Bandwidth calculations were carried out following the procedures of 
Examples 1-3 for different values of q for a P.sub.2 O.sub.5 doped silica 
fiber having an inner core-outer core index profile the same as that of 
Example 1 (i.e., a flat uniform inner-core and a linearly decreasing outer 
core). The inner core region is composed of 10.5% molar P.sub.2 O.sub.5 
and 89.5% molar SiO.sub.2 and the outer core region is composed of 13.5% 
molar B.sub.2 O.sub.3 and 86.5% molar SiO.sub.2. The refractive index 
difference between the core center and cladding is 0.0086 at 850 nm. The 
refractive indices for the core center and cladding are 1.4593 and 1.4507, 
respectively, at 850 nm. The refractive index difference between the core 
center and cladding is 0.0089 at 1300 nm. The refractive indices for the 
core center and cladding are 1.4537 and 1.4448, respectively, at 1300 nm. 
FIG. 8 shows the bandwidth as a function of q at both wavelengths of 850 
and 1300 nm for such a fiber system in data plots 800 and 802 
respectively. It is noted that when q=0.02, the bandwidth is optimized at 
both wavelengths, 7.86 GHz for a 100 meter fiber length at a wavelength of 
850 nm, and 8.14 GHz for a 100 meter fiber length at a wavelength of 1300 
nm. 
EXAMPLE 6 
Bandwidth calculations were carried out following the procedures of 
Examples 1-3 for an exemplary polymer optical fiber constructed in 
accordance with the present invention, at a wavelength of 650 nm which is 
centered at a major optical transmission window of a 
polymethylmethacrylate (PMMA) polymer. In this case, the refractive index 
of the inner core region of the fiber is flat and uniform, having a 
refractive index n.sub.1 =1.51, and the inner core region is composed of 
PMMA that is molecularly doped with benzyl benzoate (approximately 20% by 
weight) in order to raise the refractive index value above that of the 
host polymer PMMA. The cladding layer is composed essentially of PMMA 
having a refractive index of approximately 1.49. The refractive index of 
the outer core of the exemplary fiber has the linear form of Equation (2). 
For this example, q=0, meaning that the inner core radial thickness 
a.sub.0 is equal to the radial thickness (a-a.sub.0) of the outer core. 
The bandwidth is determined by standard WKB analysis of the group delay 
time as in Examples 1-3 above, and is found to be 1.0 GHz for a 100 meter 
polymer fiber length. 
EXAMPLE 7 
Bandwidth calculations were carried out following the procedures of 
Examples 1-3 for another exemplary polymer optical fiber constructed in 
accordance with the present invention at a wavelength of 650 nm, a major 
optical transmission wavelength of PMMA polymer. As in Example 6, the 
refractive index of the inner core region of the fiber is flat and 
uniform, having a refractive index n.sub.1 =1.51, and this inner core 
region is composed of PMMA that is molecularly doped with benzyl benzoate 
(approximately 20% by weight) in order to raise the refractive index value 
above that of the host PMMA. The cladding layer is composed essentially of 
PMMA having a refractive index of approximately 1.49. In contrast to 
Example 6, however, the refractive index of the outer core of the 
exemplary fiber follows the curvilinear form of Equation (1) with a=2. As 
in the Example 6, q=0, and the inner core occupies half of the overall 
core radius. The bandwidth is determined by standard analysis of the group 
delay time dispersion spectrum as in Examples 1-3 above and is found to be 
2.0 GHz for a 100 meter polymer fiber length. The increase in bandwidth as 
compared to Example 6 reveals that, for a given inner core profile of the 
same dimension and polymer material composition, it is important to 
optimize the functional form of the refractive index profile of the outer 
core in order to achieve the maximum bandwidth performance. While an 
example varying q for a polymer fiber to optimize bandwidth at multiple 
wavelengths has not been shown, the above techniques and calculations in 
Example 5 shown for inner core-outer core glass optical fibers are equally 
applicable to inner core-outer core polymer optical fibers. 
It will be apparent to those skilled in the art that various modifications 
and variations can be made in the multimode optical fiber of the present 
invention and its method of manufacture without departing from the scope 
or spirit of the invention. As an example, the fiber may carry light of 
different wavelengths than those specifically named above. While shown 
having a circular cross-section in FIG. 1, the optical fiber may have any 
one of a number of geometrical cross-sections, including square, 
rectangular, or hexagonal. Further the q values may be adjusted to 
optimize transmission at more wavelengths than in the two wavelength case 
illustrated in Examples 4 and 5. While Examples 1-7 concern either 
all-glass or all-polymer fibers, the present invention specifically 
contemplates and encompasses fibers which contain both glass and polymer 
materials. Finally, though the specification refers to optical fibers 
throughout, optical fibers are merely one class of optical waveguides, 
which are also contemplated and encompassed by this invention. 
Other embodiments of the invention will be apparent to those skilled in the 
art from consideration of the specification and practice of the invention 
disclosed herein. It is intended that the specification and examples be 
considered as exemplary only, with a true scope and spirit of the 
invention being indicated by the following claims.