Spatio-Temporal Theory of Optical Kerr Nonlinear Instability - Nesrallah, Michael J. (Université d'Ottawa / University of Ottawa, 2016)
This work derives a nonlinear optical spatio-temporal instability. It is a perturbative analysis that begins from Maxwell’s equations and its constituent relations to derive a vectorial nonlinear wave equation. In fact, it is a new theoretical method that has been developed that builds on previous aspects of nonlinear optics in a more general way. The perturbation in the wave equation derived is coupled with its complex conjugate which has been taken for granted so far. Once decoupled it gives rise to a second-order equation and thus a true instability regime because the wavevector can become complex. The solution obtained for the perturbation that co-propagates with the driving laser is a generalization to modulation and filamentation instability, extending beyond the nonlinear Schrodinger and nonlinear transverse diffusion equations[1][2]. As a result of this new mechanism, new phenomena can be explored. For example, the Kerr Nonlinear Instability can lead to exponential growth, and hence amplification. This can occur even at wavelengths that are typically hard to operate at, such as into far infrared wave- lengths. This provides a mechanism for obtaining amplification in the far infrared from a small seed pulse without the need for population inversion. The analysis provides the basic framework that can be extended to many different avenues. This will be the subject of future work, as outlined in the conclusion of this thesis.
Keywords: Nonlinear Optics; Kerr Nonlinearity; Light-Matter Interaction; Modulation Instability; Filamentation Instability; Kerr Amplification; Perturbation; Instability Analysis; Maxwell's Equations; Spatio-Temporal