Disclosed is a mode field modifier which can be used in a fiber-to-fiber connector or a source-to-fiber connector. In a downtaper-type mode field modifier embodiment, the modifier comprises a modifier core of refractive index n.sub.1 surrounded by first and second cladding layers having refractive indices n.sub.2 and n.sub.3, respectively. In an uptaper-type mode field modifier embodiment, the modifier comprises a modifier core of refractive index n.sub.1 surrounded by a cladding layer having a refractive index n.sub.2. The refractive indices are such that n.sub.1 >n.sub.2 >n.sub.3. In both embodiments, there is a nonadiabatic taper intermediate the ends of the mode field modifier, whereby a substantial amount of mode coupling occurs therein.

CROSS-REFERENCE TO RELATED APPLICATION 
This application is related to U.S. Pat. No. 4,763,976 (issued on Aug. 16, 
1988) (Nolan et al.) filed on May 21, 1987. 
BACKGROUND OF THE INVENTION 
This invention relates to optical fiber connectors, and, more particularly, 
to connectors which are capable of connecting an optical fiber to a source 
or to another optical fiber with very low loss and with little sensitivity 
to lateral misalignment. 
Although the present invention finds utility in the coupling of light from 
a source to an optical fiber, the present discussion concerning connector 
alignment problems will be limited to fiber-to-fiber connectors. The butt 
connection between the ends of two optical fibers will result in an 
insertion loss that is caused by various fiber misalignment parameters, 
examples of which are: (a) lateral misalignment between the axes of the 
two fibers, (b) longitudinal separation between the endfaces of the two 
fibers, and (c) angular misalignment between the axes of the two fibers. 
Since the butted fiber arrangement, wherein the two fiber endfaces are 
adjacent one another, is particularly sensitive to lateral displacement, 
this type of connector is difficult to use in field applications. 
Beam expanders employing lenses or tapered fibers have been employed in 
in-line connectors for single-mode fibers which are extremely sensitive to 
lateral misalignment due to the small core diameters thereof. Although 
such beam expanders exhibit a reduced sensitivity to lateral displacement, 
they are more sensitive to angular misalignment. The art of aligning two 
connector halves is sufficiently advanced that such increased sensitivity 
to angular misalignment can be tolerated. Expanded beam connectors are 
therefore receiving a considerable amount of attention. However, the cost 
of lens-type expanded beam connectors is so high that they have not 
achieved widespread use. 
The basic principal of tapered expanded beam connectors of the downtaper 
type is described in the publication K. P. Jedrzejewski et al. 
"Tapered-Beam Expander for Single-Mode Optical-Fiber Gap Devices", 
Electronics Letters, 16th January 1986, vol. 22, No. 2, pp. 105-106. That 
publication teaches a connector of the type wherein a single-mode fiber 
having a core refractive index n.sub.1 and a cladding refractive index 
n.sub.2 is threaded through a capillary tube of glass having a refractive 
index n.sub.3 which is slightly lower than n.sub.2. The capillary tube is 
uniformly heated to collapse it about the fiber. The central region of the 
combined fiber and capillary tube is then tapered to a minimum neck 
diameter of 40 .mu.m, which is appropriate for fiber handling and 
cleaving. A taper ratio of 4:1 is said to be adequate for minimizing 
insertion loss. The field is initially guided by, and substantially 
confined to, the core of the single-mode fiber. As the energy propagates 
through the taper toward the small diameter end thereof, the field spreads 
out and is eventually no longer guided by the core but is effectively 
guided by the waveguide consisting of the cladding and the capillary tube. 
The Jedrzejewski et al. publication teaches that the taper should be 
adiabatic since such a taper will suffer negligible loss through mode 
coupling, and equations are set forth therein defining the condition for a 
taper to remain adiabatic. The requirement that the taper be adiabatic has 
been heretofore widely accepted because it has been thought that all of 
the power coupled to modes other than the fundamental mode will be lost, 
thereby resulting in an unacceptable connector loss. In an adiabatically 
tapered structure such as that disclosed by Jedrzejewski et al., wherein 
the total coupler length of both connector halves is 2 cm (about the 
minimum adiabatic length), a maximum beam expansion of approximately four 
times can be achieved. The required length for such adiabatic connectors 
increases roughly quadratically with increased beam expansion. 
It has also been thought that tapered beam expanders of the up taper type 
should be adiabatically tapered. Such uptapered beam expanders are 
described in the publications: N. Amitay et al., "Optical Fiber Tapers - A 
Novel Approach to Self-Aligned Beam Expansion and Single-Mode Hardware", 
Journal of Lightwave Technology, vol. LT-5, No. 1, January 1987, pp. 
70-76; D. Marcuse, "Mode Conversion in Optical Fibers with Monotonically 
Increasing Core Radius", Journal of Lightwave Technology, vol. LT-5, No. 
1, January 1987, pp. 125-133; and H. M. Presby et al., "Optical Fiber 
Tapers at 1.3 .mu.m for Self-Aligned Beam Expansion and Single-Mode 
Hardware", Journal of Lightwave Technology, vol. LT-5, No. 8, August 1987, 
pp. 1123-1128. The Amitay et al. and the Marcuse publications state that 
conversion of the fundamental mode to higher-order modes or radiation by 
the taper, which at the enlarged end can support multimode propagation, 
must be negligible if a very low excess coupling loss is to be maintained. 
The Presby et al. publication states that losses exceeding 1 dB are 
incurred for tapers having lengths up to 1 cm and that for longer lengths, 
i.e., more gradual tapers, the loss decreases. Presby et al. also state 
that a relatively gradual and smooth transition from fiber to taper takes 
place over a length of about 6 cm and that no significant amount of mode 
conversion takes place in the taper. Such adiabatic taper lengths would 
result in inordinately long connectors. 
The efficient coupling of light from a source to an optical fiber is also 
an important requirement in optical transmission systems. The design of a 
local area network or subscriber loop is critically dependent on the 
available optical power. As light propagates through the system, loss 
occurs, and eventually the optical power level becomes too low to be 
reliably detected. By increasing the efficiency of coupling light from a 
source such as a laser diode or LED into a single-mode fiber, system 
performance would be significantly enhanced. Various advantages could 
result from such an improvement. For example, low cost LED's might be 
substituted for high cost laser diodes. 
Various methods are currently used to couple light from a source into a 
fiber, including butt-coupling, spherical and aspheric lenses, 
gradient-index lenses, and adiabatically tapered fibers. These methods can 
alter the alignment requirements for the fiber, but they cannot offer 
significant improvements in coupling efficiency because of modal-volume 
conservation. 
SUMMARY OF THE INVENTION 
It is therefore an object of the present invention to provide a tapered 
beam expander the length of which is shorter than that of conventional 
tapered fiber beam expanders. Another object is to provide a tapered beam 
expander that is capable of providing relatively large beam expansion in 
relatively short distance. A further object is to provide an optical 
signal connector having an increased coupling efficiency. 
Briefly, the present invention relates to a mode field modifier for 
coupling a transmission optical fiber to a source of light such as another 
mode field modifier or light generating means such as a laser or LED. Two 
such mode field modifiers can be connected end-to-end with their axes in 
substantial alignment to effect a low loss connection between fibers 
connected thereto. The present mode field modifier is also useful for 
connecting an optical fiber to a light source or detector. The modifier 
comprises a modifier core having a refractive index n.sub.1 surrounded by 
cladding means having a refractive index that is less than n.sub.1. 
Intermediate the ends of the mode field modifier is a tapered region which 
is characterized in that it has a nonadiabatic taper, whereby a 
significant amount of mode coupling occurs therein. The mode field 
modifier preferably comprises an adiabatic region of sufficient length 
that the relative phases of the modes at the junction between the 
adiabatic and tapered regions have that relationship which is necessary to 
substantially couple the maximum possible amount of the energy from the 
source to the transmission optical fiber. The length of the adiabatic 
region depends upon such factors as the length and taper angle of the 
tapered region, and the refractive indices of the core and cladding means. 
In one embodiment the small diameter end is located adjacent the source, 
the portion of the modifier at the small diameter end constituting the 
adiabatic region. In addition, the cladding means comprises a first 
cladding layer of refractive index n.sub.2 surrounding the modifier core 
and a second cladding layer of refractive index n.sub.3 on the surface of 
the first cladding layer, n.sub.2 being greater than n.sub.3. The 
diameters of at least the core and first cladding layer at the large 
diameter end are greater than the corresponding diameters at the small 
diameter end, whereby the mode field of an optical signal propagating in 
one end of the modifier is modified as it propagates through the tapered 
region. The diameters of the core and first cladding layer at the small 
diameter end are sufficiently small that the field of a signal propagating 
in the large diameter end of the modifier toward the small diameter end 
thereof spreads and is effectively guided by the waveguide consisting of 
the first and second claddings. 
In another embodiment the large diameter end is located adjacent the 
source, and the portion of the modifier at the large diameter end 
constitutes the adiabatic region. 
For a given beam expansion, the axial length of a non-adiabatically tapered 
region of the present coupler can be much shorter than an adiabatically 
tapered region of a conventional mode field modifier. Because of the large 
beam expansion that can be achieved, the present connector is especially 
useful for connecting light sources to single-mode optical fibers having 
small core diameters.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 1 shows an in-line fiber-to-fiber connector of the downtaper mode 
field diameter modification type. Two connector halves or mode field 
modifiers 12 and 14 are secured together in axial alignment by sleeve 16. 
Transmission optical fibers 17 and 19, which are to be connected to one 
another, are fused to or are mechanically connected to the short fibers or 
"pigtails" 18 and 20 which extend from the large diameter ends of mode 
field modifiers 12 and 14, respectively. When an optical signal is to be 
coupled from fiber 17 to fiber 19, modifier 12 is referred to as the input 
modifier. An optical signal propagating in fibers 17 and 18 is coupled to 
the core of input mode field modifier 12. As this signal propagates toward 
the small diameter end of modifier 12, the mode field diameter expands, 
the expanded beam coupling into the small diameter end of mode field 
modifier 14. Because of the large size of the beam at the small diameter 
ends, the expanded beam connector is much less sensitive to lateral 
misalignment. As the signal propagates through output mode field modifier 
14, the mode field contracts as the energy traverses the up-taper of that 
modifier. 
The simplest embodiment of the fiber-to-fiber connector of the present 
invention is shown in greater detail in FIGS. 2 and 3, and the refractive 
index profile of the large diameter end thereof is shown in FIG. 4. Mode 
field modifier 40 comprises a core 42 of refractive index n.sub.1 
surrounded by concentric cladding layers 44 and 46 having refractive 
indices n.sub.2 and n.sub.3, respectively, wherein n.sub.1 &gt;n.sub.2 
&gt;n.sub.3. Core 42 and cladding 44 constitute an optical fiber pigtail 48 
which extends from endface 50 of second cladding layer 46. Mode field 
modifier 60 is similarly formed of core 56, first cladding layer 58 and 
second cladding layer 62, core 56 and cladding layer 58 constituting a 
fiber pigtail 54 which extends from endface 52. The refractive indices of 
core 56 and cladding layers 58 and 62 are preferably n.sub.1, n.sub.2 and 
n.sub.3, respectively. Each of the mode field modifiers 40 and 60 is 
illustrated as comprising a large diameter region W and a small diameter 
region A joined by a tapered region N. The two regions A are adiabatic 
regions wherein substantially no mode coupling occurs. In the embodiment 
shown in FIG. 2, the diameters of regions A are either substantially 
constant, or they may contain an insignificant amount of taper depending 
upon the fabrication technique. For either of these variations of the 
illustrated embodiment, the amount of taper, if any, is insufficient to 
provide more than an insignificant amount of beam expansion. In an 
alternative embodiment, the amount of adiabatic taper in region A would be 
sufficient to provide some measurable amount of beam expansion that is 
additive with the beam expansion that is caused by nonadiabatic region N. 
The endface of one of the regions A is positioned adjacent the 
corresponding endface of the other region A to form interface 64. The 
axial lengths of regions W are not critical, and the lengths of these 
regions may, insofar as device operation is concerned, be zero. As a 
practical matter, it may be easier to construct mode field modifiers 
having regions W of finite length. The combined length of both regions A, 
which is equal to L.sub.a, is critical, as will be hereinafter described. 
Although the lengths of adiabatic regions A of devices 40 and 60 are 
preferably 1/2 L.sub.a, those lengths could be unequal, provided they 
total L.sub.a. 
It is known that the diameters of at least the cores and first cladding 
layers must change intermediate endfaces 50 and 52 and interface 64 for 
devices 40 and 60 to function as mode field modifiers. As stated above, 
regions N were heretofore adiabatically tapered since it was thought that 
otherwise, all of the power coupled to modes other than the fundamental 
mode would be lost. As indicated in the aforementioned Jedrzejewski et al. 
publication, the maximum adiabatic taper for a tapered single-mode fiber 
is given by 
##EQU1## 
where a is the radius of the core at a given point along the taper and the 
beat length z.sub.b is given by 
EQU z.sub.b =2.pi./(.beta..sub.1 -.beta..sub.2) (2) 
where .beta..sub.1 is the propagation constant of the fundamental mode 
(designated the HE.sub.11 or LP.sub.01 mode) and .beta..sub.2 is the 
propagation constant of the first higher order mode which can couple to 
the fundamental mode (usually the HE.sub.12 or LP.sub.02 mode). The term z 
is the distance along the axis of the connector. 
In accordance with the present invention a low loss connector is formed 
with nonadiabatically tapered regions N, i.e. they have taper angles 
defined by the relationship 
##EQU2## 
whereby a substantial amount of mode coupling occurs therein. As a result 
of the modification of the present invention, length L.sub.n of the 
tapered region is much shorter than that of an adiabatic taper capable of 
providing the same beam expansion. If the length of a connector 
constructed in accordance with the present invention is about the same as 
that of an adiabatic device, the beam expansion achieved by the connector 
of the present invention can be much larger than that of the adiabatic 
connector. 
The above-described connector can be fabricated by the technique described 
in the aforementioned Jedrzejewski et al. publication. A length of 
single-mode fiber is selected to provide the desired pigtail lengths. 
After the coating is stripped from a central portion of the fiber, it is 
threaded through a glass capillary tube, and the stripped portion of the 
fiber is centered in the tube. The tube has a lower softening point 
temperature and a lower refractive index than the fiber cladding. The tube 
is collapsed onto the fiber by heating the tube to its softening point. 
The method and apparatus described in U.S. Pat. No. 4,799,949 issued 
1/24/89 (which is incorporated herein by reference) may be employed to 
stretch the central portion of the collapsed tube, thereby forming tapered 
regions N and small diameter regions A, the length of which is greater 
than L.sub.a. The resultant double-tapered device is cleaved to separate 
it into two halves, and the length of each region A is adjusted to the 
desired value in the manner described hereinbelow. 
It has been found that low insertion loss can be achieved in a 
nonadiabatically tapered connector by optimizing the following variables: 
(a) refractive index profile, (b) taper profile, and (c) length L.sub.a, 
which is the combined lengths of the adiabatic regions A of mode field 
modifiers 40 and 60. The shapes of tapered region N and adiabatic region A 
are to some extent determined by the fabrication process. With adequate 
process control of the shapes, they could be used as additional design 
parameters. 
The refractive index profile and taper ratio are determined by the desired 
amount of beam expansion, the loss tolerances which are acceptable, and 
practical fabrication requirements such as the ability to minimize glass 
expansion mismatches and the ability to control the index profile and 
taper geometry. When the mode field modifier is formed by conventional 
techniques, whereby diameter D.sub.1 is proportional to the outside 
diameter (OD) of region W, and diameter D.sub.2 is proportional to the OD 
of region A, the taper ratio is equal to the ratio of the OD of region W 
to the OD of region A. The taper profile (the length, shape and taper 
ratio thereof) and the index profile control the amount of inter-mode 
coupling and the cutoffs of higher order modes. Length L.sub.a sets the 
phase difference between the power-carrying modes, which is a critical 
parameter for fiber-to-fiber connectors that ensures that most of the 
power is coupled back into the fundamental mode in the up-taper of the 
output mode field modifier. 
Computer modeling has shown that a single-mode fiber-to-fiber connector can 
be designed such that the fundamental mode of the input fiber is converted 
to 2, 3 or 4 modes which propagate in adiabatic region A. Designs 
resulting in the propagation of more than four modes in region A are also 
possible. An appropriate length L.sub.a can be calculated which will 
result in the proper phasing of the modes to obtain maximum conversion to 
the fundamental mode in the output mode modifier. The principle of the 
present invention is also applicable to connectors for few-moded 
transmission fibers such as two-mode fibers. To connect two n-moded 
fibers, a similar analysis can be performed to determine the shape and 
length of the tapered region to generate at least (n+1) power-carrying 
modes in region A and to determine the proper length L.sub.a for achieving 
maximum combination of the down-converted modes in the output mode field 
modifier. 
The ability of the connector packaging to control angular offset between 
the two mode field modifiers limits the maximum amount of beam expansion 
that can be employed, since the sensitivity of the connector to angular 
offset increases with increased beam expansion. By "packaging" is meant 
that support/alignment mechanism (schematically represented by sleeve 16 
of FIG. 1) a function of which is to control the axial and lateral 
alignment of the mode field modifiers. Because this nonadiabatic design 
allows for significantly shortened connectors, the overall maximum length 
(between endfaces 50 and 52) will be primarily determined by packaging 
considerations necessary to provide adequate angular alignment rather than 
by a need to provide an adequate beam expansion. 
When designing a connector, the type of fibers to be connected must be 
taken into consideration. The number of modes propagating at the small 
diameter end of the taper and the phase relationship of those modes can be 
theoretically determined for any given taper. Knowing the mode 
distribution of the energy in the input fiber and the mode conversion and 
propagation characteristics of the tapered regions, the total length 
L.sub.a of the two adiabatic regions A is then determined in order to 
ensure low loss at the wavelengths of interest. Standard coupled local 
mode theory can be used. Since this theory is well known, it is only 
briefly outlined here. 
In coupled mode theory, the solution to the scalar wave equation, 
.PSI.(x,y,z), where positive z is the direction of optical propagation, 
can be expanded in terms of the local modes of the waveguide, 
.PSI.(x,y;z), where z is now a parameter which allows the normal modes to 
vary as the waveguide is tapered. This expansion can be written as: 
##EQU3## 
where the c.sub.j are the expansion coefficients and the B.sub.j are the 
propagation constants. The coupled local mode equations are then 
##EQU4## 
where the coupling matrix is 
##EQU5## 
and the normalization is 
##EQU6## 
The local modes at any point in the connector may be obtained using finite 
element analysis, which is another standard technique in the field, or, in 
the case of step-index profiles, the equations for the local modes may be 
written down exactly. Using these solutions, along with initial conditions 
appropriate to the desired input to the device, equation (5), the 
above-written coupled mode equation, can be numerically integrated for a 
variety of lengths until the correct length for maximum transmission is 
found. 
The following theoretical example is presented to illustrate the design of 
a non-adiabatically tapered connector, reference being made to FIG. 2. A 
commercially available single-mode optical fiber, hereinafter referred to 
as a type SM single-mode fiber, was selected for use in the fabrication of 
the connector. The resultant connector will therefore be well suited for 
connecting two similar single-mode fibers. An operating wavelength of 1300 
nm is assumed. The selected fiber has a GeO.sub.2 -doped SiO.sub.2 core 
(n.sub.1 =1.451278 at 1300 nm) and a SiO.sub.2 cladding (n.sub.2 
=1.446918); .DELTA..sub.12 of the fiber is 0.3%. The symbol .DELTA..sub.2 
is the relative index difference, e.g. .DELTA..sub.12 =(n.sub.1.sup.2 
-n.sub.2.sup.2)/2n.sub.1.sup.2. The core r.sub.1 is 4.0 .mu.m and the 
cladding radius r.sub.2 is 62.5 .mu.m. The diameter D.sub.1 is therefore 
125 .mu.m. 
It is assumed that the length of sections W is set by processing 
conditions, or perhaps, by mechanical mounting conditions in the connector 
package, and that length is used in specifying the maximum overall length 
of the connector. 
It is necessary to specify a clad-overclad delta, .DELTA..sub.23. A low 
value of .DELTA..sub.23 gives a mode expansion which is a weaker function 
of taper ratio near the peak expansion (and therefore mode expansion is 
less sensitive to process variations). However, the process of stretching 
and forming the connector becomes more difficult for very low values of 
.DELTA..sub.23 because the overclad softening point is very close to the 
clad softening point, and fiber distortions occur in the taper region. In 
addition, the fibers become more susceptible to bending loss with low 
values of .DELTA..sub.23. It has been found that, for the types of glasses 
described herein, the process works best with values of .DELTA..sub.23 
between 0.1% and 0.3%, and for the purpose of this example, .DELTA..sub.23 
will be chosen to be 0.15%. To provide such a delta value with respect to 
silica, a borosilicate tube can be employed as the outer cladding. 
Given this value of .DELTA..sub.23, one can calculate the overclad radius 
needed for the desired beam expansion and the corresponding taper ratio. 
It is known that the beam expansion reaches a local maximum near a taper 
ratio of approximately 4:1, depending on the index profile, and a taper 
ratio near this maximum expansion point is selected for this example. In 
the case of the step index profile of the present example, this 
calculation can be done exactly (see, for example, M. J. Adams, An 
Introduction to Optical Waveguides, Wiley, NY, 1981). For the present 
example, wherein r.sub.2 is 62.5 .mu.m, a taper ratio of 5:1 will be 
specified. This value of taper ratio is not chosen for optimized 
expansion, but rather, for simplicity of the results, since with these 
values of r.sub.2 and taper ratio, only two modes propagate in the 
adiabatic regions A, and the results are more simple than those obtained 
for a larger number of modes. Due to the predetermined taper ratio, 
D.sub.2 is 25 .mu.m. 
Finally, a length and shape for the nonadiabatic taper region must be set. 
As will be discussed below, the length of the adiabatic region L.sub.a 
needed for optimum performance is determined by the different propagation 
constants of the modes in the adiabatic region. Because of this, and 
because the length L.sub.a will also change depending on the shape and 
length of the nonadiabatic taper, an iterative design procedure is needed. 
As a starting point, an estimate for L.sub.a can be obtained by 
determining the beat length of the two lowest modes in the adiabatic 
regions A. The beating of these modes will dominate the behavior of the 
transmission into the output fundamental mode, and so L.sub.a can be 
initially estimated to be approximately this length. A maximum acceptable 
connector length (L.sub.a =2L.sub.n) is set by packaging considerations. 
The shape will be set by fabrication methods. For the purposes of this 
example, a value of L.sub.n= 800 .mu.m will be chosen because such a short 
taper shows pronounced nonadiabatic effects. A simple cosine shape for the 
nonadiabatic taper will be chosen: 
##EQU7## 
where R is the taper ratio (R=D.sub.1 /D.sub.2 =5.0) and z is the distance 
along the axis from the start of the nonadiabatic taper. The adiabatic 
region is assumed to be of constant radius. 
Using the above parameters, the coupled mode equation (5) are numerically 
integrated along the connector for various lengths L.sub.a until a length 
is found for which the transmission through the device and into the 
fundamental mode of the output fiber is optimized for the wavelength of 
interest (1300 nm). Following this method, the graph of FIG. 5 was 
obtained. As shown in this figure, the output of this connector, as 
measured by the power of the fundamental mode propagating in output fiber 
54, varies dramatically with changes in the length L.sub.a of the 
adiabatic region. The sinusoidal variation has a period of 930 .mu.m, 
which is the beat length of the two modes which propagate in the adiabatic 
region. The model reveals that about 30% of the power has been transferred 
out of the fundamental mode at the beginning of the adiabatic region. The 
small loss at the maximum transmission point is the result of power lost 
to a higher mode which is cut off in the down taper of the input mode 
field modifier. 
For the case modeled here, there is a length L.sub.a =380 .mu.m for which 
the transmission is over 96%. The length tolerance needed to maintain a 
transmission of over 90% is on the order of 0.1 mm, which should not be 
difficult to fabricate. It should be noted that the curve of FIG. 5 would 
repeat itself as L.sub.a is increased, so that it would exhibit additional 
maxima at values of L.sub.a of about 1310 .mu.m, about 2240 .mu.m, etc. 
A device with a larger value of .DELTA..sub.23 and/or a larger value of 
r.sub.2 can have more than just two propagating modes in the adiabatic 
region. In such cases the same design procedure can be followed, but the 
transmission curve will have a more complex structure which is 
characteristic of that number of modes beating against one another. 
For the index profile modeled above, the maximum beam expansion occurs for 
a taper ratio of 3.319. FIG. 6 shows the transmission into the fundamental 
mode of the output fiber for this device. The behavior is somewhat more 
complex than in the previous example, because there are three modes 
propagating in the adiabatic region A. Again there is an adiabatic length, 
L.sub.a =4480 .mu.m, for which very high transmission (greater than 99%) 
is possible. 
In order to experimentally demonstrate these effects, a device was 
fabricated using a length of single-mode fiber wherein the core diameter 
r.sub.1 was 4.0 .mu.m, the cladding diameter r.sub.2 was 150 .mu.m, the 
core index n.sub.1 was 1.461, and .DELTA..sub.12 was 0.3%. The second 
cladding layer was a borosilicate tube having a 2.8 mm outside diameter, a 
350 .mu.m inside diameter, and a refractive index such that .DELTA..sub.23 
was 0.15%. The tube was collapsed, and a double-tapered device was formed, 
the final taper ratio being 5.5 (which is larger than for optimal beam 
expansion). The actual taper shape was complex, but it can be fairly well 
approximated using the aforementioned cosine shape with a nonadiabatic 
taper length Ln=3.1 mm. 
The resultant double-tapered device was tested by measuring the throughput 
thereof into the fundamental mode of the output fiber as a function of 
wavelength. The length of the adiabatic region was approximately 16 mm. 
Light from a monochromator was launched into 2 km of the above-described 
type SM single-mode fiber. The output of this fiber was input into the 
pigtail of the nonadiabatic device, and the output of the device was input 
into another 2 km length of type SM single-mode fiber. These long lengths 
of launch and collect fibers were used to ensure that only light from the 
fundamental mode of the device was excited in the input to the device and 
measured at the output of the device. 
The calculated transmission function of the tested device at 1300 nm is 
plotted as a function of length L.sub.a in FIG. 7. Four modes propagate in 
the adiabatic regions A. Similar calculations were performed for a variety 
of wavelengths, and the wavelength dependence of the transmission as a 
function of length L.sub.a was determined. The best fit to the 
experimental data was for a length L.sub.a =15.60 mm, which is within the 
error of the approximate determination of this length mentioned above. In 
FIG. 8 the transmission is plotted as a function of wavelength for the 
actual device (solid line) and the calculation (circles). Greater than 90% 
transmission was obtained at 1200 nm in the measured device. The 
reasonably good agreement between experiment and theory for wavelengths 
above 1200 nm indicates that the device indeed shows the expected 
nonadiabatic effects. Below 1200 nm the type SM single-mode fibers are 
multi-moded; therefore., the launch and collect conditions are more 
complex than the model assumptions, and deviations in this region are to 
be expected. 
A nonadiabatically tapered connector designed in accordance with the 
present invention can achieve a beam expansion of four times with a 
"minimum required connector length" (L.sub.a +2L.sub.n) less than 4 mm. 
Only small increases in length are needed for greater amounts of beam 
expansion when a nonadiabatic taper is utilized. A connector having 
adiabatic tapers would require a total length of 2 cm, which is roughly 
the minimum adiabatic length, to achieve a four times beam expansion, and 
the required length of that type of connector increases roughly 
quadratically with increased beam expansion. 
A nonadiabatically tapered mode field modifier can also increase the 
coupling efficiency of a source-to-fiber connector. As shown in FIG. 9, 
light from a source such as LED 70 is coupled to into nonadiabatic 
connector 72 having fiber pigtail 74 to which transmission fiber 76 is 
connected. Housing 78 contains a cavity for positioning source 70 in 
proper alignment with the small diameter endface 86 of modifier 72. Mode 
field modifier 72 comprises a core 80 of refractive index n.sub.1 
surrounded by concentric cladding layers 82 and 84 having refractive 
indices n.sub.2 and n.sub.3, respectively the relationships of which are 
similar to the refractive indices described in conjunction with FIG. 2. 
The refractive index profile of connector 72 is similar to that 
illustrated in FIG. 4. Core 80 and cladding 82 constitute fiber pigtail 
74, which extends from endface 86 of modifier 72. Modifier 72 comprises 
tapered region N' of length L.sub.n ' and adiabatic region A' of length 
L.sub.a '. Light from source 70 impinges upon endface 86 and excites all 
of the propagating local modes. For a prior art adiabatically tapered 
connector, only power in the fundamental mode of the connector will couple 
into the fundamental mode of a single-mode fiber. Because the present 
nonadiabatically-tapered connector employs inter-modal power transfer, the 
power from several modes can be coupled into a single output mode. Thus, 
it is possible to choose a nonadiabatic design which couples most of the 
power from all the modes propagating in region A' into the fundamental 
mode that propagates in the single-mode fiber 74. The power coupling 
enhancement depends on the source and the number of coupled modes. 
The objective of this design is to maximize the power launched into the 
output single-mode or few-mode fiber. Ultimately, the design of a 
source-fiber connector might involve a trade-off between this and other 
requirements such as sensitivity to offset tolerances, but these factors 
are not taken into consideration in the present example. The first step in 
designing a source-fiber connector is to specify the source and output 
single-mode fiber parameters. The output field pattern of the source is 
required for modeling purposes. Additionally, packaging and process 
requirements will provide limits on the overall length of the device and 
on the clad overclad delta, .DELTA..sub.23. 
Ideally, the output field distribution of a source would be exactly matched 
to the mode field of the fundamental mode of the single-mode fiber. In 
practice, of course, this is not the case, and the fields may be very 
different, depending on the source. As in the case of the fiber-to-fiber 
connector, it has been found that a source-to-fiber connector can be 
designed so that power launched into higher order modes of the connector, 
which always occurs because of the imperfect matching of the fields, can 
be coupled into the fundamental mode at the output, thereby resulting in 
increased output power. The amount of improvement compared to an adiabatic 
connector with the same expansion depends on the field distribution and 
coherence properties of the source. A highly coherent source with a field 
distribution closely matching the fundamental propagating mode field 
distribution of the connector would not be improved significantly, while a 
source with a very different field could be coupled much more efficiently 
into the output fiber. 
To illustrate the potential improvement of a nonadiabatic connector as 
compared to an adiabatic one, consider the example where the input to the 
connector is a plane wave; such an input might be approximately provided 
by a laser with a large output beam diameter or by a significant 
source-connector separation. The fiber parameters n.sub.1, r.sub.1, and 
.DELTA..sub.12 are taken to be the same as in the previous fiber-to-fiber 
example wherein the type SM single-mode fiber was employed. It is also 
assumed that the clad-overclad delta, .DELTA..sub.23 is 0.15% and the 
wavelength is 1300 nm. Radius r.sub.2 is again taken to be 62.5 .mu.m, and 
a 5:1 final taper ratio is chosen. 
The lengths L.sub.a and L.sub.n are determined in a different manner than 
in the fiber-to-fiber case. The objective is to couple all the light from 
the higher-order modes propagating at the coupler input into the 
fundamental mode at the output. Because the inter-modal coupling becomes 
stronger for sharper tapers, there is a maximum length L.sub.n ' beyond 
which the coupling is not sufficiently strong to transfer all of the 
power. This maximum length must be determined by numerical integration of 
the coupled mode equations for a variety of taper lengths (and lengths 
L.sub.a '). Shorter taper lengths will also give complete coupling for 
certain lengths L.sub.a ', but, as the length L.sub.n ' is made shorter, 
the appropriate length L.sub.a ' for complete coupling varies more and 
more rapidly with slight variations in L.sub.n '. The choice must then be 
made in light of process tolerance considerations and packaging 
requirements. For this particular choice of connector parameters, a length 
L.sub.n =800 .mu.m gives maximum coupling. 
The theory for determining the length L.sub.a ' of adiabatic region A' is 
essentially the same as in the fiber-to-fiber connector, with one 
significant change. Whereas the initial conditions for the fiber-to-fiber 
connector are determined by the modal power distribution in the input 
transmission fiber 17 (FIG. 1), the initial conditions for the present 
embodiment are determined by the overlap of the source light field with 
the normal modes of the connector at the input endface 86. If 
.PSI..sub.source is the field of the light source, then the initial values 
of the expansion parameters are given by 
##EQU8## 
Using these conditions, the coupled local mode equation (5) can be 
integrated in the same manner as discussed above to obtain the optimum 
length L.sub.a '. 
The output of the connector, as measured by power into the fundamental mode 
of the output fiber, is once again a sinusoidal function of the length 
L.sub.a ', as is shown FIG. 10. In this figure, a transmission of 1.0 
would signify that all of the power launched into both input modes has 
been coupled into the fundamental mode at the output. The actual maximum 
transmission is about 0.96, which represents a 76% increase in power over 
the adiabatic case. Having a larger number of modes propagating at the 
input of the connector allows even larger gains. 
As is true with many optical fiber devices, the theory for predicting the 
behavior of such devices is well-defined, but the actual devices do not 
perform exactly as predicted. A certain amount of empirical tuning of any 
given device should be undertaken after the theoretical design is 
determined. For example, the length of the adiabatic region of either of 
the above-described embodiments could be made slightly longer than the 
calculated length. Small thicknesses can be removed by grinding and 
polishing, and the device can be tested by propagating light therethrough. 
When it appears that the device is operating at one of the maximum 
transmission peaks of the curve of either FIG. 5 or FIG. 10, for example, 
no further processing need be done. Since the percent transmission of 
adjacent maxima are substantially identical, it is immaterial which of the 
maxima is chosen for the length L.sub.n or L.sub.n '. 
The following modifications can be made to the present mode field modifier 
to give greater beam expansion or stronger mode coupling. In one 
modification the mode field modifier has a more complex refractive index 
profile such as that illustrated in FIG. 11. The publication W. J. Stewart 
et al., "Design Limitation on Tapers and Couplers in Single-Mode Fibers", 
Proc. IOPOC, 1985, pages 559-562 (FIGS. 4 and 5) teaches that such index 
structures have larger nonadiabatic effects than the structures discussed 
above in connection with FIG. 4. That is, the maximum adiabatic taper 
angle is smaller in the W-type index profiles of the type represented by 
FIG. 11. In the applications discussed herein, especially in the 
application of the source-fiber connector, strong mode coupling is 
desired. There may be practical (fabrication) limits as to how large a 
taper angle can be made, and so an index structure showing stronger 
nonadiabatic effects for a given taper might be desirable. 
FIG. 11 also illustrates the fact that the refractive index profile need 
not be of the step type. Either by design or as a result of the 
manufacturing process, part or all of the profile can be rounded as 
illustrated by curve 90. 
Another modification, which is illustrated in FIG. 12, is disclosed in the 
aforementioned Nolan et al. U.S. Pat. No. 4,763,976, which is incorporated 
herein by reference. In this embodiment, elements similar to those of FIG. 
2, are represented by primed reference numerals. Fiber pigtail 48' extends 
from endface 50' of mode field modifier 40'. The refractive index of 
region 91 is preferably the same as that of fiber cladding 44' and is 
greater than that of region 46'. Cladding 44' and layer 91 therefore 
constitute the first cladding layer and region 46' constitutes the second 
cladding layer. To fabricate the device of FIG. 12, fiber 48' is inserted 
into an aperture 92 in a tube comprising concentric regions 91 and 46'. 
The tube is symmetrically heated to collapse it uniformly about fiber 48' 
The combination of the fiber and the tube is then tapered as described 
above in conjunction with FIG. 2, and the small diameter end is cleaved to 
form mode field modifier 40'. As taught in Pat. No. 4,763,976, the beam 
expansion is increased since the diameter of the first cladding layer of 
the mode field modifier is effectively larger than the cladding diameter 
of the transmission line fiber connected to the mode field modifier. 
Instead of having a fiber pigtail extending from the endface thereof, the 
mode field modifier can be provided with an axial hole into which the end 
of a transmission line fiber can be inserted. A method of forming the 
fiber positioning hole is illustrated in FIGS. 13 and 14 in which the 
advantageous feature of FIG. 9 is also incorporated. In this embodiment, 
which is disclosed in U.S. Pat. No. 4,763,976, mode field modifier 99 
comprises a core 93 and a second cladding layer 94 having optical 
characteristics similar to core 42 and second cladding 46 of FIG. 2, for 
example. The first cladding layer comprises concentric layers 95 and 96, 
the refractive index of layer 96 being equal to or less than that of layer 
95. The compositions of layers 95 and 96 differ, the glass of layer 95 
being more soluble in a given solvent than that of layer 96. Cladding 97 
must be resistant to being dissolved in the given solvent. When end 97 of 
modifier 99 is immersed in the given solvent, layer 95 is more readily 
etched so that hole 98 of FIG. 14 is formed. 
It is known that "gap" devices such as polarizers, Faraday isolators, and 
beamsplitters can be put into the gap between two beam expanding devices. 
For larger beam expansions, a larger gap can be tolerated for a given loss 
budget because the beam is better collimated. Such a gap device could be 
placed between the two adiabatic regions A of FIG. 2. Small gaps between 
mode field modifiers in a fiber-to-fiber connector can be essentially 
ignored. However, the calculation of the length of the adiabatic region 
must take into consideration the length of larger gaps. 
FIG. 15 shows an in-line fiber-to-fiber connector of the uptaper mode field 
diameter modification type. Two connector halves or mode field modifiers 
112 and 114 are secured together in axial alignment by sleeve 116. 
Transmission optical fibers 117 and 119, which are to be connected to one 
another, are fused to or are mechanically connected to the pigtails which 
extend from the mode field modifiers. An optical signal propagating in 
fiber 117 is coupled to the core of input mode field modifier 112. As this 
signal propagates toward the large diameter end of modifier 112, the mode 
field diameter expands, the expanded beam coupling into the large diameter 
end of mode field modifier 114. As the signal propagates through output 
mode field modifier 114, the mode field contracts as the energy traverses 
the down-taper of that modifier. 
The uptaper fiber-to-fiber connector of the present invention is shown in 
greater detail in FIG. 16, and its refractive index profile is shown in 
FIG. 17. Mode field modifier 112 comprises a core 120 of refractive index 
n.sub.1 surrounded by cladding layer 121 having refractive index n.sub.2, 
wherein n.sub.1 &gt;n.sub.2. The small diameter end of core 120 and cladding 
121 constitute an optical fiber pigtail which is available for connection 
to transmission fiber 117. Mode field modifier 114 is similarly formed of 
core 125, and cladding layer 126, the small diameter end of which 
constitutes a fiber pigtail which is available for connection to 
transmission fiber 119. The refractive indices of core 125 and cladding 
126 are preferably n.sub.1 and n.sub.2, respectively. Each of the mode 
field modifiers 112 and 114 is illustrated as comprising a large diameter 
region A' and a small diameter region S joined by a tapered region N'. The 
two regions A' are adiabatic regions wherein substantially no mode 
coupling occurs. In the embodiment shown in FIG. 16, the diameters of 
regions A' are either substantially constant, or they may contain an 
insignificant amount of taper depending upon the fabrication technique. 
For either of these variations of the illustrated embodiment, the amount 
of taper, if any, is insufficient to provide more than an insignificant 
amount of beam expansion. In an alternative embodiment, the amount of 
adiabatic taper in region A' would be sufficient to provide some 
measurable amount of beam expansion that is additive with the beam 
expansion that is caused by nonadiabatic region N'. The endface of one of 
the regions A' is positioned adjacent the corresponding endface of the 
other region A' to form interface 129. The axial lengths of regions S are 
not critical, but the lengths of these regions should be sufficiently long 
to make connection thereto. As described above in connection with 
downtaper connectors, the combined length L.sub.a ' of both regions A' is 
critical. Although the lengths of adiabatic regions A' of devices 112 and 
114 are preferably 1/2L.sub.a ', those lengths could be unequal. 
In accordance with the present invention the connector of FIG. 16 is formed 
with nonadiabatically tapered regions N', i.e. they have taper angles 
defined by the relationship expressed by equation (3), whereby a 
substantial amount of mode coupling occurs therein. Therefore, length 
L.sub.n ' of the tapered region is much shorter than that of an adiabatic 
taper capable of providing the same beam expansion. 
Low insertion loss can be achieved in a nonadiabatically uptapered 
connector in a manner similar to that described above in connection with 
nonadiabatically downtapered connectors. The length L.sub.n ' can be 
computed after the values of n.sub.1, n.sub.2, D1' , D.sub.2 ' and the 
length L.sub.n ' and shape of region N' are known. 
The design of a nonadiabatically uptapered fiber-to-fiber connector is 
illustrated by the following theoretical example. The connector is to be 
used to connect two of the aforementioned type SM single-mode fibers 
wherein core radius is 4.0 .mu.m, n.sub.1 is 1.451278 and .mu.is 0.3%. The 
operating wavelength is again 1300 nm. The nonadiabatic taper region N' is 
to have a cosine shape and have a length of 500 .mu.m. The final draw 
ratio D.sub.2 '/D1 to be 0.15. 
The length of the adiabatic region L.sub.a ' needed for optimum performance 
is determined in accordance with the above-described procedure. Using the 
above parameters, the coupled mode equation (5) are numerically integrated 
along the connector for various lengths L.sub.a ' until a length is found 
for which the transmission through the device and into the fundamental 
mode of the output fiber is optimized for operation at 1300 nm. This 
results in the graph of FIG. 18 wherein the output of the connector, as 
measured by the power of the fundamental mode propagating in output fiber 
119, varies dramatically with changes in the length L.sub.a ' of the 
adiabatic regions. For the case modeled here, there is a length L.sub.a 
'=10.83 mm for which the transmission is about 97%. 
Each of the devices 112 and 114 of FIG. 16 can be fabricated by forming a 
preform of diameter D.sub.1 '. The core/cladding diameter ratio is the 
same as that required for the single-mode pigtail of regions S. An end of 
the preform is heated and drawn to form a fiber of diameter D.sub.2 ' (125 
.mu.m). The preform can be severed at a point along its axis such that 
length of the large diameter region is slightly greater than L.sub.a '. 
Small thicknesses can be removed by grinding and polishing, and the device 
can be tested by propagating light therethrough until it is apparent that 
the device is operating at one of the maximum transmission peaks of the 
curve of FIG. 18. 
A source-to-fiber uptaper connector is shown in FIG. 19 wherein light from 
source 140 is coupled to into the large diameter end of a nonadiabatic 
connector 142 having fiber pigtail 144 to which transmission fiber 146 is 
connected. Housing 148 contains a cavity for positioning source 140 in 
proper alignment with the adjacent endface 150 of modifier 142. Mode field 
modifier 142 is similar in construction to modifier 114 of FIG. 16. Light 
from source 140 impinges upon endface 150 and excites all of the 
propagating local modes. Because the nonadiabatically-tapered connector 
employs inter-modal power transfer, the power from several modes can be 
coupled into a single output mode. It is therefore possible to design a 
nonadiabatic uptaper device which couples most of the power from all the 
modes propagating in the large diameter adiabatic region into the 
fundamental mode that propagates in the single-mode pigtail 144. The 
amount of inter-mode power coupling in this device can be enhanced through 
the use of index profile modifications such as the W-profile illustrated 
in FIG. 11.