Research

Beautiful sunset

The colors in this beautiful sunset over the University of Toledo campus partially capture my passion for optics.
If you like this sort of thing check out optics picture of the day.

I find light to be one of the most fascinating things in the world. The way it propagates through matter, the way it bounces from and passes through various materials, the way it interferes with itself and other light to create unusual color patterns. From the wonderfully symmetric equations that model its motion to the bizarre consequences of its constant speed to the beautiful pictures that we perceive when it hits our eyes, light is truly an endlessly interesting topic. I'm currently working on a masters thesis in theoretical optics (details below). My research interests are in anything that requires creativity and problem solving skills. This usually means theoretical projects, but also includes design projects, and can include designing and executing experiments to validate theoretical predictions. I prefer to avoid projects that are simply large data collection operations followed by numerical model generation. My three most significant projects are listed below in some detail. They are not all directly related to optics, but they all required creativity, and I quite enjoyed them.

Wilberforce Pendulum

Wilberforce data and model

Plotted data points are measured periods and curves are plots of our theory. Straight lines show the zero coupling limit. RMS departure of data from theory is about one-eighth the plotting symbol size.

The wilberforce pendulum is an example of a coupled oscillator system. As part of a lab course during my undergraduate work, my lab partner Tom Wilhem, my professor, David Van Baak, and I derived the theoretical normal modes of such a pendulum in various configurations, and took data to support the theory. Although the Wilberforce pendulum was thoroughly understood before our investigations, it had been investigated primarily in the special configuration where energy could be exchanged completely between its two modes of oscillation. Our contribution was to derive the normal modes for any arbitrary tuning.

We had hoped that the paper would be published in the American Journal of physics, but that never happened. In any case, I'm happy to present the full paper pdf and full paper doc

You can also view the slides I used for a presentation of this work in January 2014 in odp format

Light Pipe Design

lightpipe prototype

An example CAD drawing of a light pipe that I designed at Sound Off Signal.

During the summer of 2008, the Calvin College enterprise center landed me an internship at Sound Off Signal, a local company that manufactures police lights. I worked on several project there, but my main task was to modify an existing product that lit a firetruck's cargo area. I was to replace the many LED design with a single LED design which would be cheaper to manufacture. The project did not require deriving any new theory, but it did appeal to my creative nature. Based on a well-established phenomenon known as total internal reflection, I was able to design a plastic light pipe to distribute light from a single source and illuminate the cargo area more evenly than the existing product. This research furthered my interest in optics and internal reflection in particular.

MS Thesis

Finite beam reflectivities

Reflectivities for beams of different widths. The plane wave exhibits a discontinuous jump in reflectivity at the critical angle, but the finite beams do not.

My MS thesis work is purely theoretical and it investigates the amplified total internal reflection phenomenon. I calculate the reflection coefficients for a totally internally reflected beam and show that it can be intense than an incident beam if the reflecting medium is a gain medium. The complete thesis, titled, "Amplified Total Internal Reflection at the Surface of Gain Medium," is available as a pdf, and the abstract is also available in plain text. Finally, the slides I used during my thesis defence are available (Note: I exported them from a prezi, so they don't look as slick as they did when I presented, but information freedom is important to me).