Formation of Hollow Beams Through Coherent Fiberoptical Bundles
Dhruv Bansal / The Wheatley School
Laser Teaching Center
Stony Brook University
``Hollow beams'' are laser beams that look like rings in
cross-section. These beams are often used to trap or cool atoms.
Traditionally, they are formed by using complex Axicon lenses.
This paper explores the possibility of using laser light shined
into a coherent fiberoptic bundle on angle as an alternative to
using an Axicon lens.
Normal laser beams have a typical Gaussian intensity profile.
Physicists can trap atoms or molecules with these beams using
differences in potential energy as barriers for the particles.
A problem with using normal laser beams for atom trapping is
that, because of their normal Gaussian nature, there are a large
number of photons in the middle of the beam. These photons can
interact with the atoms being trapped -- this is usually best
Using a ring shaped hollow beam, physicists could still
trap atoms using potential energy barriers but they have the
advantage of the beam being hollow -- meaning that there are no
photons in the middle to interact untowardly with the atoms.
These hollow beams are formed using special Axicon lenses which
are rather expensive and complex.
The method researched in this paper for generating hollow beams
could be an improvement. Fiberoptic bundles are collections of
individual fiberoptic cables. They transmit light, unchanged,
from one end to the other.
The ``ring effect'' was discovered by a researcher at the Laser
Teaching Center. It is essentially unheard of in research
circles. When light from a laser diode is shined into a bundle
parallel to the bundle's axis, the resultant image is a large
dot. This is as expected. If, however, the laser is aimed so
that it enters the bundle with some angle, the resultant image is
In the course of this research, it was firmly established
that the incident angle of the laser source affects the diameter
of the ring. Furthermore, through the use of a photodetector, it
was shown that the Gaussian profile of the ring has two peaks,
meaning that it actually has a minimum intensity in the middle.
The ring that emerges from the bundle can easily be focused into
a beam of parallel rays that is in the shape of a hollow cylinder
-- a traditional hollow beam. This is a very desirable result.
Compared to complex lenses, fiberoptic bundles would be a more
flexible and less expensive method of producing hollow beams.
Introduction and Review of Pertinent Literature
Fiberoptic cables are solid tubes of one type of glass surrounded
with a thin sheath of a different type of glass. These cables
employ total internal reflection to transfer light from one end
to the other. Light bounces repeatedly off the interface between
the two different types of glass. The core of each cable is
typically about 50 mm and the sheath is between 2 and 3 mm.
There is some inevitable loss due to absorption by the glass. By
a process known as scattering, some light is also lost at the end
of the cable when light bounces back off the interface between
the glass core and the exit medium. Both absorption and
scattering reduce the amount of transmitted light by about 4 to 5
Collections of fiberoptic cables are referred to as fiberoptic
bundles or light guides. These are macroscopic devices often
containing thousands of individual fiberoptic cables bound
together. This binding is brought about by gluing the individual
cables to one another using simple epoxy. The opaque epoxy does
not transmit light. The insignificant sheath around each cable
does not transmit light either. The result is that, between the
sheath, the epoxy, scattering, and absorption, only about 60 - 65
% of incident light exits at the end of a 1 ft cable (another 4
to 5 % is lost per additional foot of length).
Bundles come in two types -- coherent and incoherent. Incoherent
bundles are less expensive and are used when the incident light
is uniform (i.e. bright white light, etc.). The orientation of
the incident light is not preserved through the transmission.
This is because the individual cables making up the bundle are
poorly aligned, twisting and turning throughout the length of the
bundle. Coherent bundles are more precisely constructed and,
resultantly, more expensive. Incident light is precisely
transmitted through the length of the cable. One can even read
text placed at one end of the bundle from the aperture on the
An interesting effect occurs when bundles are improperly
constructed. The ends of each cable should be cut exactly
perpendicular to the axis of the bundle. Sometimes, this is not
the case. Each cable may extend a tiny and irregular amount past
the end of the bundle. This protrusion of cable acts, as any
irregular piece of glass might act, as a small prism, heavily
distorting the transmitted light. The result of this unwanted
defect is sometimes a noticeable ring. Similarly, in this
project, incident light which entered on an angle emerged as a
In various experiments that involve the cooling or the trapping
of atoms or molecules, laser beams have been employed to hold
these atoms in place. Because of differences in potential energy,
the atoms tend to stay in the middle of the laser beam. Thus,
the trapping is complete using conventional beams.
The drawback is that, at the center of these beams where the
atoms are trapped, the beam is at its most intense. Photons,
sometimes very energetic, can interact with the atoms being
trapped, thus creating unwanted effects. The photons at the
center of the beam interfere with the experiment.
Hollow laser beams conveniently bypass this problem. They still
employ potential energy differences to trap atoms at their
center, but lack any photons in their center to adversely
interact with the trapped atoms [Ovchinnikov].
These hollow beams have been traditionally formed using
sophisticated lenses, such as the conical Axicon lens, to convert
normal laser beams into hollow beams. This process works very
well, but the complex lenses used are expensive and rather
This paper proposes another method. A student researcher in the
Laser Teaching Center at Stony Brook University accidentally
discovered that light from a simple diode laser, when shined at
an angle into the aperture of a coherent fiberoptic bundle,
emerged as a well-defined ring. When shone in parallel to the
axis of the bundle, the light emerged as a rather large but solid
This was the main cause for this research. Why did tilting the
diode laser with respect to the bundle's axis cause a ring to
appear? Was the incident angle related to the diameter of the
emerging ring? Recognizing that the emerging ring can easily be
focused with a simple lens into a hollow beam, would the ring be
a feasible substitute for a traditional hollow beam?
The answers to some of these questions are obvious. From even
casual observation it is manifest that the diameter of the ring
(and indeed, its intensity) are related to the angle of
incidence. Increasing the angle increases the diameter. It is
also clear that there will be a dip in the intensity in the
middle of each ring as there is no visible light there. This is
because the intensity of the ring, as measured along its
diameter, is essentially the intensity of two perfectly Gaussian
distributions -- one for each half of the ring. For the first
half of the ring, the intensity is low, then sharply rises to
peak at the centroid of the ring, and then fades away again,
precisely mirroring its rise. This same, almost definitively
Gaussian profile is repeated on the other half of the ring.
In-between, there is almost no light. This was a strong
indication that the intensity profile for larger angles of
incidence was probably double-Gaussian.
For smaller angles, it was not so clear. Was the seemingly solid
dot that appears when the angle of incidence is zero (parallel to
the bundle's axis) truly solid? Was it, too, ring-like but to a
small degree? Or was it perfectly Gaussian, and, as the angle of
incidence increased, did it somehow become double-Gaussian?
These hypotheses could be tested by scanning along the diameter
of the ring and recording the measured intensity.
Correlating the resultant data with the detector position and the
angle of incidence would allow one to determine both the
relationship between the angle of incidence and the diameter of
the ring and the intensity profile of the ring.
The central experiment in this project involved changing the
angle of incidence of diode laser light on the aperture of a
fiberoptic bundle while at the same time being able to measure
the intensity profile across the diameter of the emergent ring.
There were a number of ways this could be done. Either the laser
diode or the bundle could be tilted. The only drawback is that
the experiment is concerned with the precise angle of incidence.
If the laser is set up pointing at the aperture of the bundle,
then rotated, the location where the laser hits the aperture
would move. Even if the laser is rotated about its tip, the
point of impact would still move. There would not be a change in
angle, but a displacement along with a change in angle.
A parabolic mirror could also be used. If the aperture is placed
at the focal point of the mirror, then any laser light shined
parallel to the major axis of the mirror would hit the focal
point -- would hit the aperture. By raising or lowering the
laser diode, the angle of incidence at the focal point would
change. Unfortunately, however, parabolic mirrors of a good
enough quality to preserve the incident angle and the initial
intensity of the light are prohibitively expensive and not
Finally, a track could be used. This is what ended up working.
The bundle was mounted on a tabletop. A small hole was made
(on the same vertical level as the bundle's aperture) which
could slide along a track perpendicular to the bundle's axis.
Between the aperture, the center of the hole's track, and the
hole itself, there formed a simple right triangle, which,
through simple trigonometry, would reveal the angle of incidence.
The laser's position and orientation wouldn't matter in this
setup. The laser light would have to pass through the minute
hole in order to reach the aperture. If the laser could be
aligned so that its light passed through the hole and hit the
aperture, then the angle of incidence would be assured. Moving
the hole would require moving the laser and realigning it each
time, but this way, there would be no displacement -- only a
change in the angle of incidence.
The final result is shown in
The photodetector is simply
mounted on another track at the same vertical level as the
bundle's exit aperture to sweep across the ring's diameter and
take intensity measurements. The photodetector's output is run
into a multimeter capable of keeping a running average of
Thus the experiments began. The slit was moved a distance on the
track (which corresponds, of course, to a certain angle of
incidence), the laser was aligned, all the lights were shut off,
and the photodetector was moved along its track. It was moved to
a point and allowed to measure for 30 seconds while the
multimeter took a running average. The measured intensity was
recorded and the photodetector was moved again. In this manner,
it was possible to create position vs. intensity diagrams for a
number of different incident angles.
The collected data is depicted on a few simple scatterplots.
Figure 2 shows the intensity
profile when the angle of incidence is 0. The most interesting
detail here is that the profile appears to be double-Gaussian. There
is a clear and distinct dip in the middle of the profile at
approximately 63 cm. On either side, one can see the two Gaussian
peaks. As the angle of incidence increases, in Figures 3 through 6,
these two peaks grow farther and farther apart.
is a summary of the data. This is a
graph of entrance angle v. centroid diameter. The centroid
diameter is the distance between the two peaks on the intensity
profile. Visually, centroid diameter is the distance between
the two brightest points on the ring. From the graph, it is
obvious that, were the first data point (theta = 0) not
included, the graph would have a very strong linear correlation.
This is an indication that, indeed, entrance angle is directly
proportional to the resultant ring diameter. The graph follows
the path of a straight line very closely. The only reason it
deviates is that there is a certain minimum size for the bundle's
output. When the entrance angle is 0, the diameter cannot be 0.
The emergent beam from the bundle's exit aperture is not very
tightly focused and thus spreads very rapidly. As the
photodetector was placed about 46 cm away from the aperture, the
beam spread to quite a distance by the time it encountered the
plane of the detector.
There were three goals in this project. Did the entrance angle
have a relationship to the exit diameter? This was easily
verified and proved by matching various entrance angles with
various exit diameters in Figure 7.
The second goal was to assess the possibility of using this
method to create hollow beams rather than using the traditional
Axicon lens method. In this too, the project was successful.
Complex lenses produce a very tight and very specific kind of
hollow beam. It is possible to vary the diameter and intensity
of the bundle's hollow beam by simply changing the entrance angle
of the laser diode. This would allow for a lot of flexibility in
intensity and size.
Useful hollow beams, of course, would be much smaller than the
ones produced in this project. Making these beams smaller,
however, would be no problem -- one would merely have to
construct a bundle with a smaller diameter (this bundle was 1.27
cm in diameter). This would make the emergent beam smaller. A
simple thin lens would focus the spreading exit beam into a
During the summer of 2000, I was involved in a research program
at Stony Brook University which allowed me to do optics research
in Stony Brook's Laser Teaching Center. I worked under the
guidance of Dr. John Noe and Professor Harold Metcalf. Karl Fey,
a fellow student researcher in the laboratory, discovered that
laser light shined into a coherent fiberoptic bundle on angle
will emerge as a well-defined ring. This was the impetus for all
of my research.
I would like to thank both Dr. Noe and Professor Metcalf for
their tireless patience and infinite enthusiasm. I would also
like to thank all my colleagues at the lab for making research
fun. Most of all, however, I'd like to thank my Science Research
advisor Mr. Paul Paino for helping me to write this paper.
Yu. B. Ovchinnikov et al. (September 1st, 1998),
``Gravito-optical atom trap based on a conical hollow beam,''
Europhysics Letters, Vol. 43 (5), pgs. 510-515