Laguerre-Gaussian Modes: Post #2

Early this week, I completed the data collection for all the requested LG modes and their superpositions. I sent the images and matrices to LSU for our collaborators to inspect. We will hear back from them soon about their findings.

In the meantime, I started a new, but related, part of the project. I have been separating specific LG modes into a single-mode optical fiber. (This task connects more closely to my initial proposal). Optical fibers are extremely narrow glass tubes, which transmit light through total internal reflection. They have a wide range of applications, from telecommunications and broadcasting to medical imaging and data storage. A single-mode fiber (as opposed to a multi-mode one) has a smaller diameter, so, ideally, it allows only one constituent mode of the incoming light to pass through. (Fragments of other modes, however, inevitably enter anyway). The light in single-mode fibers also experiences fewer reflections and less attenuation, or decrease in intensity. Therefore, the light travels farther, while better maintaining the fidelity of the signal. By contrast, multi-mode fibers, with their wide cores, allow a few modes of light to enter. Thus, they are better at transmitting larger amounts of data over short distances.

My task now is to determine how well I can use a single-mode fiber to separate out the l=1 and l=2 LG modes from a laser beam. Using skills I learned in the beginning of last week, I started by aligning the laser beam into the desired fiber. Again, it took patience, as I rotated the mirror knobs, trying to match the incoming and outgoing voltages. I heartily agreed when Professor Novikova said that fiber coupling could serve as a meditation exercise!

Once satisfied with the alignment, I placed a phase mask in the beam path. This mask is equivalent to the software hologram we put on the SLM when imaging the modes, just in physical form. It consists of a flat, glass diamond, divided into four quadrants. Three quadrants contain “vortices.” The vortices can be adjusted to on and off positions by moving the phase mask, so that the light hits the fourth, empty, quadrant. The “single vortex” creates the l=1 mode, the standard circle with a dark center. The other two “double vortices” create different sizes of the l=2 mode, or a circle with a dark center and an additional ring.

First, I wanted to separate out the l=1 mode. So, I placed the single vortex on the beam. I measured the power of the incoming and outgoing light before and after the vortex was in place. I observed a sharp drop in power when the vortex was on. This decrease indicated that most of the modes, except the desired l=1 mode, were filtered out. I then slowly slid the vortex off the beam, using a camera to track the position of the mode until it disappeared. I measured the outgoing power for every five micrometers of moving the vortex. As expected, the power increased as the other modes entered the fiber. I also photographed the beam as the vortex moved across it, so that we can analyze the way the beam size relates to the position of the mode.

Yesterday, I began to repeat this procedure with one of the double vortices. The next step will be to figure out how to determine that fragments of extra modes are completely filtered out so that only the desired, pure mode remains. I will explain these results in the next post.

This week, I have come to a clearer understanding of the broader significance of my work, and I wanted to share it before I close. I have now begun to realize the connections between the various ideas I have investigated so far, from machine learning to coupling fibers. First of all, I learned that we use LG modes for a special reason. These modes exist independently from one another in space because of their orthogonality. In other words, they form a complete orthogonal basis set. This way, each mode can carry a unique set of information, which can be filtered out from the rest. The process is analogous to tuning a radio, except that it relies on mode rather than frequency, on light rather than sound. Importantly, we can use machine learning to train computers to identify different LG modes. Then, the computers can filter the laser output automatically.  Furthermore, we may also be able to teach machines to recognize superpositions of the modes. If successful, we could use multimode fibers to transmit more data without having to physically disentangle the modes upon receipt. Our collaborators at LSU are currently investigating this possibility, using the data I have provided.