Laguerre-Gaussian Modes: Final Summary

My freshman Monroe project essentially consisted of two main parts: imaging Laguerre-Gaussian laser modes and their superpositions for Louisiana State University’s machine learning research and testing the coupling of these modes and superpositions into a single-mode optical fiber.

For LSU, I took images of |l1, p1> + |l2, p2>, where l = ±1, 0, and p = 0, 1, plus the original six, pure modes. The percentage of multiplexing was changed in increments of 10, for 9 percentages, though only 5 were imaged because of symmetry. I encountered some difficulties with recording crisp images of the superpositions. However, after some adjustments, Professor Novikova and I deemed the images satisfactory. We sent them to LSU and have yet to hear back. We know, though, that our collaborators did receive them, so hopefully they will send some feedback soon. If I hear any news, I will post an update.

For the fiber optic coupling part of my project, I investigated the double and single vortices as well as the superpositions of l=±1, 0, while p was fixed at 0. Before even starting the data collection, I experienced the notorious difficulties of aligning a laser for maximum coupling efficiency. Once I analyzed the results, not only did I encounter high percent errors between expected and measured efficiencies, but I also realized that we lacked a clear standard to describe the success of the coupling. Mainly, we know, at least, that it is possible to filter out individual modes and their superpositions. We also know that the coupling efficiency decreases when only one mode is transmitted through the fiber. However, we need to develop a method of determining to what extent we have separated the mode and how well we have maintained its purity.

More important than any results I found were all the questions and obstacles that arose throughout my research process. We realized that, despite not yielding many conclusive results, my research exposed and unpacked important problems in the lab. If not for my project, these hindrances may have gone unnoticed for a while longer, negatively affecting others’ research. For one, we determined that we do not truly know how to generate crips LG modes and superpositions on the SLM. Others have accomplished this feat. [1] However, their procedures are not easily replicated, and the question of generating superpositions in addition to the pure modes remains fuzzy. Therefore, creating a reliable method to produce these images has become a real concern in our lab. Developing such a procedure would require extensive research into other labs’ methods as well as our own testing.

An important takeaway from my time in the lab was that, when doing original research, no standard of “common,” agreed upon knowledge exists. Recent findings are not set in stone, so researchers must work and think for themselves. They must converse with others in the field, collaborate, problem-solve, and think unconventionally. This sense of unknown can feel frustratingly like groping in the dark sometimes, but it is also exciting. In reality, original research means the project is completely unique. Who knows what unexpected findings will emerge!

Indeed, research takes patience and persistence. Often, as soon as researchers solve one problem, we get excited to push onward, so we barely have time to appreciate the solutions we have created. But, when I reflect on my project, I am thrilled with the skills I have learned and the knowledge I have gained. I have barely scratched the surface, but these past three weeks have only made me want to continue my involvement in the lab.

Both the people I met in the lab and the subject of the research itself contributed to this decision. My colleages’ passion for physics, willingness to explain concepts to me, and obvious competence inspired me. They all seemed like such experts, without ever asserting that they have all the answers. They respected each other, debated, and never gave up. I aspire to this work ethic. Furthermore, when I wrote the initial proposal for this project, I predicted that I would complete my three weeks with my interest in optics confirmed. I was right. I have grown to love light and its fascinating properties even more. It amazes me that something as seemingly insubstantial as an electromagnetic wave can shape humans’ reality and perception of the world. I definitely want to learn more about light. This fall, I will continue to research with Professor Novikova in the fall semester. I can tell that this project is only the beginning of something exciting. I cannot wait to see how it all unfolds.

[1] Ando, Taro; Ohtake, Yoshiyuki; Matsumoto, Naoya; Inoue, Takashi; & Fukuchi, Norihiro. (2008). Mode Purities of Laguerre-Gaussian Beams Generated via Complex Amplitude Modulation Using Phase-Only Spatial Light Modulators. Optics Letters, 34-36. (Jan 1, 2009). Vol. 34, no. 1. Doi: 101918.

Ando, Taro; Ohtake, Yoshiyuki; Matsumoto, Naoya; Inoue, Takashi; Fukuchi, Norihiro; & Hara, Tsutomu. Generation of High Quality Higher-Order Laguerre-Gaussian Beams Using Liquid-Crystal-on-Silicon Spatial Light Modulators. (2008). Journal of the Optical Society of America A. (July 2008). Vol. 25, no. 7. Doi: 93896