Formation of Hollow Beams Through Coherent Fiberoptical Bundles

``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.

Abstract

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 a ring.

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

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 % each.

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 other end.

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 ring.

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 delicate.

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 dot.

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.

Methodology

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 readily available.

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 Figure 1. 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 measurements.

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.

Results

Figure 7 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.

Discussion

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 focused laser.

Acknowledgments

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.

References