A multimode fiber can be used as a waveguide for lighting and transmission
of optical energy of a light source in scientific, medical, industrial
or other applications. The beam shape of the transmitted power can be
therefore very important in such applications depending on the required
beam specification (Ersoy, 2007). Beam power measurements and profiling
make it possible to directly check the fiber waveguide beam profile and
mode characteristics. It is also possible to look at the emerging light
beam from the beam shaping optics following the guiding fiber. Such monitoring
verifies that whether all the related optical/electro-optical components
are performing as expected and be able to make real-time adjustments for
the precise and optimum performance. For flow cytometry, for instance,
it is necessary to create a flat-topped beam to provide uniform illumination
of the flow cell.
Fiber splicing is a coupling technique by which the cut ends of two optical
fibers can be attached together, resulting in nearly a single piece of
long fiber optical transmission line (Senior, 1992). Because of the mentioned
importance, experimental study of the beam profile variation in a fiber
splicing joint is presented in this report. Moreover we take a brief look
at the developed theoretical formulations in beam transmission and image
information in fibers and fiber coupling.
Our expectation is that obtained results could shed some light on the
case of optimum parallel energy transfer in fibers/fiber bundles and higher
optical bandwidth could be resulted for data links in communication (Raddatz
et al.,1998). Information about image and power distribution in
a fiber or fiber splice joint can also provide information about the uniformity
of the transmitted light beam profile (Tsekrekos et al., 2007).
In this study the theory of power transfer in multimode fiber coupling
is developed and we try to formulate a transfer function for the implemented
multimode plastic optical fibers.
MATERIALS AND METHODS
This study was conducted in Institute of Water and Energy a research
center of Sharif University of Technology during period of 2006-2008.
Transmitted power distribution in a fiber splice joint has been investi-gated
in many references (Fujii et al., 1984; Cherin and Rich, 1978)
and different fiber splice connectors have been designed in order to reduce
transmitted power loss. Fiber bundles as well as single fiber line can
be used for image transmittance in optical apparatus and different types
of connectors have been designed for this objective (Ren et al.,
2001). As shown in Fig. 1, a low power incandescent
white lamp illuminates the source fiber; receiving fiber fixed on a 3D-translational
stage is aligned with the source fiber using the micrometer stage and
the emerging light from the receiving fiber is measured by a power meter.
In this study we have used 40 cm long plastic multimode optical fibers
as the source and receiving fibers with an overall diameter of 2 mm including
core, cladding plus core diameter of 980 μm and the protective sleeve.
The nominal core diameter of this fiber is about 860 μm (99%) of
the whole diameter. Index of refraction of the core for a typical plastic
fiber is n1 = 1.45 and the cladding n2 = 1.44, which
results a Numerical Aperture (NA) of about 0.17.
By monitoring output transmitted power the case of the maximum transmitted
power is obtained for the best x-and y-alignment for a given axial gap
separation, z. The variation of optical power by any misalignments in
x and y directions can be obtained using the related micrometers and power
recording (Fig. 1). It is also possible to consider
the variation of the transmitted power as a function of the axial distance,
z , in such coupling.
||Set up for transmitted power measurement
|Fig . 2:
Intersection of the receiving fiber cross section (top
circle) and emerging beam cross section (bottom circle)
Typical axial gap separation is in the range of
0.01 mm to 1 mm and offset variation range of the receiving fiber (fixed
to the translational stage) is on the order of the fiber core diameter.
The theoretical model for the intensity/power transmission can be derived
from the geometrical optics by considering the beam cross sectional intersections.
If we assume a cone of light emerging from the source fiber then the amount
of light delivered to the receiving fiber depends on the acceptance angle
of the receiving fiber or the core cross section of such fiber. Thus we
consider such light acceptance cone by the overlap of the base cone of
the emerged light from the source and the cross section circle of the
receiving fiber. The circular cross sections and the overlap intersections
are indicated in Fig. 2. Using the intersection of the
areas of receiving fiber and the base of the emerging cone light we can
determine the transmitted intensity variation.
In the case of x-y offset misalignment, the overlap area of two circles
can be expressed by the following piecewise functions:
in which R is the radius of cone base of the emerging beam, r2
is the core radius of receiving fiber and d is the distance between the
fiber beam image circle (R) and receiving fiber core centers. It must
be pointed out that the value of R is given by
where, θ is the acceptance angle of the cone light, r1 is
the core radius of the source fiber and z is the axial distance. The minimum
cross section is zero and the maximum cross section is equal to the cross
section of the receiving fiber according to Eq. 1. For
the case of similar source and receiving fibers we have r1
= r2. Similar to our recent report on double fibers (Golnabi
and Azimi, 2008) the variation of the received intensity depends on the
beam overlap cross section.
To study intensity profile and transmitted image of the source fiber
a CCD camera is used in experimental arrangement of Fig.
1, instead of the power meter just behind the source fiber.
||Arrangement for the image and intensity profile measurements
CCD cameras are used widely for image capturing and designing vision systems in different applications (Zhang et al.. 2005). As shown in Fig. 3. for image recording the focusing lens is placed in position and for intensity distribution experiments when intensity profile is required the focusing lens in front of the CCD camera is removed.
RESULTS AND DISCUSSION
Using the mentioned methods experimental results concerning optical fiber coupling
are described in this section. Results include intensity preview of the transmitted
intensity and also the image analysis. The measured intensity scans as a function
of the x-and y-variations are shown in this section. Figure 4
shows the power variation as a function of x distance. In such experiments two
fibers have a longitudinal air gap distance of about z = 0.01 mm. As shown in
Fig. 4, the output intensity starts at 0.52 nW level and decreases
to about 0.02 nW for an axial separation of about 0.9 mm. By increasing more
axial separation the output power is almost constant, which is just the output
due to background signal (stray light and detector dark noise). As can be seen
in Fig. 4, decrease as a function of x value is nearly linear
with a rate of about 0.55 nW/mm.
In Fig. 5, the output power variation as a function
of y scan is displayed. As can be shown in Fig. 5, transm-itted
power is decreasing by increasing y value. Such decrease is almost linearly
and continues until an offset y value of about 0.9 mm. From this point
the transmitted power is almost constant, which agrees with overlap cross
section given by Eq. 1 for the case of d > R+r2.
Theoretical calculation estimates that transmitted power should drop to
zero at this point, but experimental value shows a small value because
of the background signal.
||Intensity variation in receiving fiber in x-scan (z
= 0.01 mm, y = 0)
Intensity variation in receiving fiber in y-scan (z
= 0.01 mm, x = 0)
As expected because of the symmetry transmitted power for y-offset should
be the same as x-offset results. The transmitted power is changing nearly
linearly and start from 0.52 nW and drops to a value of about 0.05 nW
(Fig. 5). Results of Fig. 4 and 5
indicate that the power distribution in x-and y-directions are similar
and as theory indicates depends on the cross section overlap as obtained
by the geometrical optics analysis.
In order to check the validity of Eq. 1 in Fig.
6 expression given by Eq. 1 against d is plotted.
The general behavior of the transmission function is very close to the
overlap cross section described in theoretical discussion. In Fig.
6, d is the axial offset distance of the source and receiving fiber
that can be related to x/y variation in experimental measurements.
To see the effect of the axial serration, z, on the x-and y-scan this
separation is increased from the z = 0.1 mm (Fig. 4)
to 1mm and the transmitted power is shown as a function of x-scan in Fig.
7. Comparing the results of Fig. 4 and 7 two points can be mentioned.
||Variation of the cross section as a function of, d,
plotted by Eq. 1
||Intensity variation for x-scan for (z = 1 mm, y = 0)
Fist point is that by increasing the z value
the amount of the transmitted power is reduced in comparison with the
previous case (z = 0.01 mm). Second and perhaps the more important point
is that distribution behavior of the transmitted power is changed from
a near linear to a nonlinear response as can be shown in Fig.
7. Thus it is concluded that axial separation has influence on the
power distribution and one must consider this key point in precise analysis.
Knowing the importance of z variation, in the next study the intensity
variation as a function of the air gap variation, z, is investigated and
the result is shown in Fig. 8. It is noted that intensity
is given by dividing the power by the beam cross section. Looking at Eq.
1, it is noticed that the cross section depends on R2 value
and therefore the intensity curve shows a nonlinear behavior. As shown
in Fig. 8, transmitted power generally shows a decease
by an increase in the axial z-value. This power change is from 0.42 nW
at z value of about 0.01 mm and drops to 0.07 nW for the z = 2.6 mm and
for further z value the output is almost constant, which shows the background
noise equivalent power. By fitting data points it is noticed that output
intensity in z direction changes according to P0/(r1+ztanθ)-2in
which θ is the acceptance angle of the fiber and P0 is
the launched power.
Programs usually use a colormap for the image presentation in color format
and for example Matlab uses a colormap, which is a numerical array with
three columns to show color values.
||Intensity variation in receiving fiber in z-scan (x
= 0, y = 0)
Comparing images taken at two axial distances (z = 18
mm, z = 7.6 mm)
This array is called a colormap and
each row in the matrix represents individual color using numbers in the
range of 0 to 1. The number in each row indicates the intensity of Red,
Green and Blue making up a specific color. This method of representation
of image is called RGB format. For example for red color the number is
(1, 0, 0) and for yellow is (1, 1, 0).
For image analysis, the image of the emerging beam of the source fiber
is investigated and such an image is shown in Fig. 9
for two different axial distances. To compare the images, results of two
experiments at different z values are obtained separately and then exposed
on each other as shown in Fig. 9. The inside circle
corresponds to the image case of z = 18 mm and outer circle corresponds
to z value of 7.6 mm. Details about he the image capturing, applications
(Awcock and Thomas, 1995) and presentation methods can be found in our
recent reports (Golnabi, 2006; Golnabi and Asadpour, 2007). As can be
shown in Fig. 9, by using a camera calibration method
(He and Li, 2008) one can measure core diameter of the fiber by this technique.
Using two images of a single fiber at two distances one is able to determine
the acceptance angle of the fiber.
||Comparing two image profiles at given axial distances
In our measurements the acceptance
angle estimated to be about 0.2° for this particular fiber with a
core diameter of about 0.946 mm and white light source. The nominal core
diameter for this fiber is 0.860 mm.
In the final study the intensity profile for the transmitted image is
obtained by using the image analysis (Golnabi, 2006). We compare two image
profiles for given axial distances from fiber end. It is noted that for
both axial z values the intensity profile is like a flat-top function.
As can be shown in (Fig. 10), a uniform intensity profile
is obtained for the given plastic optical fiber illuminated by an incoherent
It shows that output intensity level for the z = 18 mm is higher than
that of z = 6.7 mm (Fig. 10). For a given transmission
power since the image cross section for z = 18 mm is smaller than for
z = 6.7 mm thus the intensity for such case is higher, which agrees with
the result of Fig. 9. The horizontal scale of Fig.
10 shows the column number related to the data image from CCD to a
buffer storage matrix, which has the same order for both functions. As
can be seen the transmission function is wider for the case of z = 6.7
mm, which corresponds to the larger image circle as shown in Fig.
9 and as a results the transmission function is wider for this image
taken at a shorter axial distance from the fiber end.
The Sharif University of Technology Research Program supported this research.
The authors like to thank the Research Council for the grant devoted to