Title: Numerical Simulation of Fermionic Wave Functions in Potential Wells: Bound State Transitions induced by Multi-Photon Excitation from Laser Sources operating within the Non-Perturbative Regime
Energy state transitions leading to linear and nonlinear optical effects have had a major impact on many ﬁelds in optics since their discovery. We developed a numerical simulation to investigate how Time-Dependent Schrodinger Equations (TDSE) of electrons traveling within atomic and molecular potential wells, propagated with Finite Difference Methods, and excited with different types of laser sources, can show photonic output and the possibility of output which is nonlinear with respect to the excitation from the source.
In particular, here we are interested in resonance conditions of these systems. The parame- ters of a laser source, as well as the source type, have a substantial impact on the wave equations of the particles within a system. With the right conditions, and knowledge of the systems current energy state, we can effectively choose what energy state to move the system to. We can likewise reduce the energy state by choosing conditions matching transitions to lower states, reducing the energy state of the system and stimulating photonic output.
In this thesis we will show the effects of laser source conditions both in and out of resonance, in several different atomic systems with potential wells, and resulting photonic output from state transitions for each combination of parameters. The source will be strong enough to have a substantial impact on the system, thus leaving the perturbative range of intensity, yet not so strong as to completely overpower the system’s coulomb potential, staying out of reach of the strong ﬁeld range of intensity where system potential wells are next to irrelevant.
Professor Charles DiMarzio, Advisor
Professor Hossein Mosallaei, Committee Member
Professor Carey Rappaport, Committee Member