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.

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Laguerre-Gaussian Modes: Post #3

During my last week in the lab, I finished the fiber optic coupling part of my project. The data I collected led to more questions than answers, but that’s science. There’s a special excitement and beauty in knowing that the quest for knowledge will never truly end. This project has sparked my curiosity, and there’s so much more to learn now. Here are my activities and findings from my last days in Small Hall this July:

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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.

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POST #3: Theory Behind the Initial Solution

So far I have discussed most of the practical knowledge that a crystallographer needs, but I have not mentioned much of the theory. Crystallography requires the careful analysis of thousands of reflections by a computer, but at one point, it was all done by hand. The math behind the initial solutions is very tedious, but in short, it relies on Fourier transforms. Fourier transforms are used to break complicated oscillations into only sines and cosines. A Fourier transform lets us look at the repeating patterns of reflections (similar to a harmonic function) and determine what the unit cell looks like, as well as the arrangement of its contents.

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