Document Type



Lasers produce a strong focused ray of light that is useful in many industries, including medicine and technology. For example, they can be used for guiding surgical instruments or playing compact discs. In this thesis I characterize the dynamics of a fundamental laser model. A mathematical goal is to determine the number of photons in the laser cavity as time evolves. Different choices of parameter values produce qualitatively different behaviors of the system. I perform a bifurcation analysis in order to capture the different physical situations, identifying equilibrium solutions and their stability properties. I sketch representative solutions using the bifurcation points as a guide. Some parameter regimes produce a stable equilibrium solution, meaning that the laser action persists given any nearby initial conditions. In other situations the same equilibrium solution is unstable, while a zero solution is stable, meaning the number of photons tends to zero. A model consisting of a system of differential equations is also presented and analyzed. Both models predict the behavior of the laser.



Thesis Comittee

Laura K. Gross (Thesis Director)

Thomas Kling

Edward Deveney

Uma Shama

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Original document was submitted as an Honors Program requirement. Copyright is held by the author.

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