Second Harmonic Generation

My research project is modeling Second Harmonic Generation. It is a process by which photons from a laser beam are mixed in a nonlinear medium and the output photon has double the energy and frequency and half the wavelength. I will model the conversion efficiency, and the different types of phase matching. Second Harmonic Generation relates to certain topics in our course such as chapter 9 of Griffiths on absorption and dispersion of EM waves and topics from chapter 11 on radiation. Applications of frequency mixing are found in the use of radio waves in extending the tunable range of shorter wavelengths.

Induction generators: efficiency and applications

My work will focus on AC induction generators: exploring current designs and how to make them more efficient.  This offers a great deal of potential for modeling as there are many variables involved: rotor and stator size, slip, and materials to name a few.  This is a field that is currently quite popular due to the ongoing energy crisis, and the applications are ubiquitous.  To the extent that my work will explore specific applications of induction generators, I will be examining their use in harnessing wind power: specifically the unique restrictions that turbines and other types of casings impose.

Research questions will concern the effects of many different variables on overall efficiency, including magnet type, wire material, slip, and rotor/stator rotation frequencies.

Light Scattering

Project Proposal

When light travels through a medium that is not a vacuum the electric field of the electromagnetic wave induces oscillating electric dipoles in the atoms and molecules that compose the medium.  These induced dipoles affect the propagation of the waves and can also scatter the light in various directions.  For particles that are smaller than one-tenth the wavelength of the incident light Rayleigh scattering is observed.  For these small particles the scattering can be predicted by the Rayleigh theory.  By manipulating variables in the Rayleigh theory such as particle size and density, scattering angle, and wavelength, I want to numerically predict and model different scattering intensities using Mathematica.  In addition I want to approach the particle size limit for Rayleigh theory to observe what happens to the modeled scattering and compare that to Rayleigh-Debye modeled scattering, which can be used to predict the scattering of particles larger than the Rayleigh limit.