A novel expanded beam coupling arrangement for use in association with single mode fibers is disclosed. An appropriate length of multimode fiber is fused to the endface of an input single mode fiber, where the length of the multimode fiber is chosen to provide the desired lensing conditions of the input beam. The multimode fiber is thus used as a lens, but provides many advantages over prior art optical connectors which use conventional quarter-pitch GRIN lenses epoxied to the fiber endfaces. In particular, the misalignment associated with the epoxied arrangement is reduced since the multimode fiber-lens connector of the present invention may be chosen to comprise the same outer diameter as the single mode fiber. Additionally, the use of a section of optical fiber as a lens allows for a fused connection to be used instead of an epoxied connection, which results in a more stable and rugged interface between the fiber and the lens.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a coupler for use in association with 
single mode fibers and, more particularly, to such a coupler which 
comprises an appropriate length of multimode fiber connected to the end of 
the single mode fiber wherein the section of multimode fiber performs as a 
lens. 
2. Description of the Prior Art 
A common problem in the design of single mode optical components is the 
need to provide efficient and stable optical coupling. Typically, this 
coupling is between two single mode optical fibers located at different 
ports on a given device. A standard method of coupling two single mode 
fibers requires the expansion of the input beam passing through an input 
single mode fiber using a lens, often a graded-index (GRIN) lens. The 
expanded beam then passes through the optical component(s) after which a 
second lens focuses the beam onto the core of the output single mode 
fiber. One such arrangements disclosed in U.S. Pat. No. 4,193,663 issued 
to C. Timmermann on Mar. 18, 1980. In this arrangement, a lens is adhered 
to the end of the fiber, where the lens is made of a material having a 
melting point which is low in relation to the melting point of the fiber, 
resulting in a light guide having an essentially semispherical lens at the 
end. In one embodiment, the lens is made of epoxy in order to facilitate 
the adhesion to the fiber. The use of a GRIN lens as a coupling mechanism 
between two fibers is disclosed in U.S. Pat. No. 4,268,112 issued to K. P. 
Peterson on May 19, 1981. Several different embodiments are disclosed 
which are based on the optical transmission characteristics of a Luneberg 
lens. In particular, a spherical "bead" of graded-index material is used, 
where the bead is formed around a wire, for example, tungsten, in order to 
leave a precision hole through the center of the bead. Input and output 
fibers are then inserted at opposite ends of this hole, where the ends of 
the fibers are positioned at the focal points of the spherical bead. Both 
of these arrangements require that the axes of the lenses intersect the 
center of the fiber core and that the lenses themselves be situated in the 
plane of the fiber junction. An alternative prior art arrangement which 
substantially mitigates these difficulties is disclosed in U.S. Pat. No. 
4,327,963 issued to G. D. Khoe et al on May 4, 1982. In this arrangement a 
convex spherical graded index lens is used which is rotationally symmetric 
about any axis through its center. Therefore, alignment between the fiber 
and the lens is somewhat simplified, yet the center of the lens must still 
be aligned with the core of the fiber. 
A problem remaining with these and other prior art coupling designs is the 
sensitivity to misalignment at the fiber/lens interface. This misalignment 
creates both the need for precise micropositioning during fabrication and 
the need to maintain a stable fiber/lens bond while the device is in use. 
SUMMARY OF THE INVENTION 
The problem remaining in the prior art has been solved in accordance with 
the present invention which relates to a coupler for use in association 
with single mode fibers and, more particularly, to a coupler which 
comprises an appropriate length of multimode fiber connected to the end of 
a single mode fiber, wherein the section of multimode fiber performs as a 
lens. 
It is an aspect of the present invention to provide a coupling arrangement 
which is smaller, less expensive, and more rugged than prior art 
arrangements while providing the same advantages associated with prior art 
expanded beam coupling arrangements. 
Another aspect of the present invention is to overcome the above-described 
misalignment problem by utilizing an arrangement wherein the single mode 
transmission fiber and multimode fiber-lens comprise essentially the same 
outer diameter and are connected using a fusion technique. Therefore, when 
the fibers are joined, the surface tension during the fusion process will 
automatically align the fibers. 
Yet another aspect of the present invention is to provide a stable, rugged 
interface between the communcation fiber and the lens. Since the multimode 
fiber-lens may be directly fused to the single mode transmission fiber, 
the bond between them is significantly stronger and more stable than that 
of prior art arrangements which required that a conventional lens be 
epoxied to the end of the single mode fiber. 
A further aspect of the present invention is to provide a coupler which is 
relatively smaller in dimension than prior art couplers for use in 
association with large arrays of single mode fibers arranged in close 
proximity to each other, for example, as a ribbon connector. Additionally, 
the discussed advantage of reduced misalignment sensitivity is most useful 
in the fiber array situation.

DETAILED DESCRIPTION 
As stated above, the present invention provides an optical coupler which 
utilizes a section of multimode fiber as a lens which can be directly 
fused onto the end of the transmission fiber. In practicing the present 
invention, any type of multimode fiber may be utilized, two examples being 
a step-index multimode fiber and a graded-index multimode fiber. As is 
well-known in the art, "step-index" refers to a fiber which comprises a 
core region having a refractive index n.sub.o and a cladding region having 
a refractive index n.sub.1, where n.sub.o &gt;n.sub.1 and a definite "step" 
exists between the indices of these two regions. A graded-index fiber, on 
the other hand, is defined as a fiber with an index of refraction that is 
a function of the various glasses used to form the concentric layers of 
core and cladding in the fiber, thus providing a more gradual change in 
refractive index than the step-index fiber. One particular form of 
graded-index fiber, which may be used in association with the present 
invention, can be defined as a square law medium, where the radial 
dependence of the refractive index in a square law medium can be 
represented by 
EQU n(r)=n.sub.o [1-g.sup.2 r.sup.2 ].sup.1/2 (1) 
where n.sub.o is defined as the refractive index on the optical axis and g 
is the focusing parameter given by 
EQU g=.sqroot.2.DELTA./a (2) 
where .DELTA. is the relative index difference between n.sub.o and the 
fiber cladding and a is the core radius. FIG. 1 illustrates a Gaussian 
beam 10 exiting a single mode fiber 12 and passing through a square law 
medium 14. The waist position and beam size associated with Gaussian beam 
10 may be found from equations well-known in the art and fully described 
in the article "Coupling Characteristics between Single-Mode Fibers and 
Square Law Medium" by R. Kishimoto et al appearing in IEEE Tran. Microwave 
Theory Tech., Vol. MTT-30, No. 6, June 1982 at pp. 882-93. In order to 
achieve the maximum expansion at Z=0 of input beam 10 as it passes through 
square law medium 14 (which is desirable in many cases to provide maximum 
coupling efficiency), square law medium 14 should comprise a length L 
equal to .pi./2 g, where g is the focusing parameter defined in equation 
(2). This is commonly referred to in the art as a quarter-pitch square law 
device. It is to be understood that this discussion of a square law 
embodiment is exemplary only, and for the purposes of explanation, not 
limitation, since a fiber-lens formed in accordance with the present 
invention may utilize any gradient which is capable of achieving focusing. 
In general, the present invention relates to using any type of multimode 
fiber of an appropriate length as a lens which can be directly fused to 
the end of single mode fiber 12 to provide efficient and stable optical 
coupling of the single mode fiber to other fibers or optical components in 
the system. 
In order to provide the advantages of "single fiber" uniformity with a 
minimum of misalignment between the communication fiber and the 
fiber-lens, it is desirable, although not necessary, to utilize a 
multimode fiber-lens which comprises the same outer diameter as the single 
mode communication fiber. The surface tension of the molten glass tends to 
self-align the multimode fiberlens to the single mode fiber, thus 
facilitating the alignment. 
It is to be understood that a coupler formed in accordance with the present 
invention may utilize any method of connecting the multimode fiber-lens to 
the single mode transmission fiber. For example, a UV curing cement may be 
used to secure the fiber-lens to the endface of the single mode fiber. 
Alternatively, the fiber-lens may be epoxied to the endface of the single 
mode transmission fiber. However, an advantage of the present invention is 
that the coupling lens is formed from a section of optical fiber, thus 
allowing the lens to be directly fused to the endface of the single mode 
fiber. As stated above, the utilization of a fusion joining process 
provides a coupling arrangement which is more rugged and less susceptible 
to subsequent misalignment problems. FIGS. 2-4 illustrate the steps 
involved in an exemplary fusion process used in the formation of a 
coupling arrangement of the present invention which utilizes a section of 
graded-index multimode fiber to form the fiber-lens. The first step in the 
formation process is to fuse the endface of single mode fiber 12 to the 
endface of a graded-index multimode fiber 16. This is accomplished, as 
shown in FIG. 2, by placing the ends of fibers 12 and 16 in a heat source 
18, for example, an electric arc, which will rsult in forming a low loss 
fusion region between single mode fiber 12 and graded-index multimode 
fiber 16. As stated above, the maximum expansion of an input beam will 
occur if graded-index multimode fiber-lens 16 comprises a quarter pitch 
length. Therefore, the next step in the process of forming an exemplary 
coupler of the present invention is to reduce multimode fiber 16 to the 
above-defined quarter pitch length. The reduction in the length of 
multimode fiber 16 may simply be accomplished by scribing and breaking 
fiber 16 at the desired location. However, this method is difficult to 
control and may not provide reproducible results. In an alternative 
method, fused fibers 12 and 16 may be placed in a housing to provide 
additional structural support and subsequently polished to the desired 
length. As shown in FIG. 3, a capillary tube 20 may be used as such a 
housing, where fused fibers 12 and 16 are waxed or epoxied in place. FIG. 
4 illustrates a fiber-lens coupler 22 which have been polished to achieve 
the desired quarter pitch length. It is to be noted that subsequent to the 
final polishing, housing 20 may be removed, where such removal may be 
necessary when the size of the coupler is required to be as small as 
possible. The above-described ribbon connector arrangement is one example. 
Alternatively, housing 20 may be left intact to provide a degree of 
additional stability and ruggedness. As will be discussed in greater 
detail hereinafter, there exist many instances when the fiber-lens of the 
present invention should comprise a length greater than the quarter pitch 
length. In that case, the arrangement is made to the appropriate longer 
length. Alternatively, a fiber-lens of less than quarter pitch length may 
be required, most notably when an epoxy or other material is used to join 
the single mode fiber to the fiber-lens since the presence of this 
additional material adds to the effective overall length of the fiber-lens 
coupler. 
An alternative coupling arrangement of the present invention, as stated 
above, utilizes an appropriate length L.sub.s of a step-index multimode 
fiber fused to an endface of the single mode transmission fiber. FIG. 5 
illustrates a fiber-lens of the present invention formed using a section 
of step-index multimode fiber 16.sub.s. Similar to the above-described 
arrangement, the length L.sub.s of step-index multimode fiber-lens 
16.sub.s is chosen to provide a beam width capable of achieving sufficient 
optical coupling. As is known in the art, the radius of the core of a 
step-index fiber influences the beam width, where a relatively large core 
region is desirable for the purposes of the present invention. In the 
formation of a step-index fiber-lens, the multimode fiber-lens is first 
fused to the endface of the single mode transmission fiber, as shown in 
FIG. 2. The fiber-lens is then polished or cleaved to the appropriate 
length L.sub.s, where the end portion of fiber-lens 16.sub.s is placed in 
a heat source to obtain a rounded profile, as shown in FIG. 5. The rounded 
endface of fiber-lens 16.sub.s will function to collimate the beam passing 
through rather than allowing the beam to continue to expand indefinitely. 
It is to be noted that a fiber-lens formed from a section of graded-index 
multimode fiber, as previously discussed, may also comprise a rounded 
endface, where this structure may be useful in situations requiring 
extreme focusing of a wide angle beam. 
As briefly mentioned above, the quarter pitch fiber-lens, useful when two 
single mode fibers are to be butt-coupled or maintained in relatively 
close proximity, may not provide sufficient coupling between fibers which 
are significantly displaced. It is often necessary to separate input and 
output fibers by a considerable distance, which for fiber-lenses may only 
be the range of a few millimeters. In this case, a quarter-pitch 
graded-index fiber-lens would not be desirable since the collimation of 
the beam exiting the fiber-lens is not perfect, i.e., the beam width will 
continue to expand, resulting in poorer coupling to the output fiber. For 
large separations, optimum coupling occurs when using fiber-lenses which 
are longer than quarter pitch length. FIG. 6 illustrates such a 
arrangement, where each fiberlens 16 comprises a length L' greater than 
the determined quarter pitch length. 
Referring to FIG. 6, a guided input light beam I passes through single mode 
input fiber 12.sub.I and enters coupler 22.sub.I which comprises a 
multimode fiber-lens 16.sub.I fused to the end of input single mode fiber 
12.sub.I by the process described above. As previously discussed, 
fiberlens 16.sub.I may be formed from a section of graded-index multimode 
fiber and comprise a length L' which is greater than the quarter pitch 
length L. (Alternatively, a stepindex fiber may be utilized which exhibits 
partial beam convergence). Therefore, the output beam I' from coupler 
22.sub.I converges to a waist W', as shown in FIG. 6. Convergent beam I' 
subsequently passes a distance X through optical component 30, which may 
in fact comprise a number of optical components. The detailed structure of 
optical component(s) 30 is not pertinent to the practice of the present 
invention. After passing through optical component(s) 30, the light beam, 
now referred to as divergent output beam O', enters output coupler 
22.sub.O, as shown in FIG. 6. Output coupler 22.sub.O comprises the same 
length L' as input coupler 22.sub.I (for a symmetric arrangement, but in 
general may comprise any desired length) and is configured to perform the 
inverse operation of input coupler 22.sub.I. Here, divergent beam O' 
passes through multimode fiber-lens 16.sub.O where it is refocussed and 
coupled to output single mode fiber 12.sub.O. As shown in FIG. 6, fiber 
12.sub.O is fused to the end of multimode fiberlens 16.sub.O in the same 
manner described above in association with FIGS. 2-4. 
To further explain the relationship between fiber-lens length and coupling 
efficiency, FIG. 7 illustrates coupling loss (in dB) as a function of 
axial displacement for two exemplary coupling arrangements utilizing 
fiber-lenses formed in accordance with the present invention. The first 
arrangement utilizes a pair of quarter pitch length (251 .mu.m) 
graded-index fiber-lenses (in particular, AT&T 62.5/125 .mu.m fiber), 
where the loss associated with this arrangement is illustrated by curve A. 
The second arrangement utilizes a pair of graded-index fiber-lenses, each 
fiber-lens comprising a length (300 .mu.m) greater than the quarter pitch 
length. As expected, the quarter pitch length fiber-lens arrangement 
experiences minimum loss, 0 db, when the fibers are butt-coupled (i.e., 
axial displcement equals zero). Curve B indicates that this exemplary 
extended length fiber-lens arrangement will exhibit a 0 dB coupling loss 
when the input and output fibers are separated by approximately 250 .mu.m. 
As seen by reference to FIG. 7, a 2 dB loss is experienced by the quarter 
pitch length fiber-lens arrangement when the fibers are displaced by 500 
.mu.m, where the extended length fiber-lens arrangement may be displaced 
by an additional 200 .mu.m, to a distance of approximately 700 .mu.m, 
before a 2 dB coupling loss is observed. It is to be noted that if the 
extended-length fiber-lens is used in a butt-coupled arrangement, it will 
exhibit a loss of approximately 0.5 dB, which is greater than 0.0 dB 
quarter-pitch length fiber-lens arrangement. 
Fiber-lens formed in accordance with the present invention may also be 
evaluated for lateral misalignment tolerances. The results of these 
measurements are given in FIG. 8. Also shown in FIG. 8 are calculations of 
lateral misalingment tolerances for unlensed fibers, using the equations 
referred to above in association with the Kishimoto article. Referring to 
FIG. 8, a 5 .mu.m lateral displacement between conventional unlensed 
single mode fibers results in a reduction in coupling efficiency from 100% 
for zero displacement to approximately 30%. This is a serious reduction, 
since a 5 .mu.m tolerance is often used in the industry as the maximum 
allowable tolerance. Using an exemplary graded-index multimode fiber-lens 
arrangement of the present invention provides a coupling efficiency of 
approximately 80%, well within industry specifications for this 5 .mu.m 
tolerance. In fact, as seen by reference to FIG. 8, a lateral displacement 
of 10 .mu.m between the single mode fibers will not completely disrupt 
transmission when the exemplary fiber-lens arrangement of the present 
invention is used, since a coupling efficiency of over 40% exists for this 
misalignment. However, when no lensing arrangement is used, transmission 
is essentially lost between two fibers which are displaced by 10 .mu.m. It 
is to be noted that with selective choice of multimode fiber parameters, 
both the axial and longitudinal misalignment tolerances can be increased 
considerably. 
In addition to using the fused fiber-lens of the present invention in the 
above-described one-to-one coupling arrangement, the present invention is 
applicable to situations using fiber array coupling arrangements. Fiber 
arrays are often arranged in what is referred to as a "ribbon" 
configuration, i.e., a 1.times.N array. Connecting two ribons together is 
an extremely difficult task which, by the nature of the proximity of the 
fibers to each other, demands almost perfect alignment. Utilizing the 
fused fiber-lens coupling arrangement of the present invention is seen to 
overcome this alignment problem since, as described above, the use of a 
fusion region between the single mode transmission fiber and the multimode 
fiber-lens overcomes the alignment problems associated with prior art 
coupling arrangements.