Moussa Kounta | Searcharxiv

arXiv2019

Homotopy analysis method applied to second-order frequency mixing in nonlinear optical dielectric media

The classical problem of three-wave mixing in a nonlinear optical medium is investigated using the homotopy analysis method (HAM). We show that the power series basis builds a generic polynomial expression that can be used to study three-wave mixing for arbitrary input parameters. The phase-mismatched and perfectly phase matched cases are investigated. Parameters that result in generalized sum- and difference-frequency generation are studied using HAM with a power series basis and compared to an explicit finite-difference approximation. The convergence region is extended by increasing the auxiliary parameter.

physics.optics↗

arXiv2017

The second hyperpolarizability of systems described by the space-fractional Schrodinger equation

The static second hyperpolarizability is derived from the space-fractional Schrödinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter $α$ decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Although the maximum response is damped, we show that the one-dimensional quantum harmonic oscillator is no longer a linear system for $α\neq 1$, where the second hyperpolarizability becomes negative before ultimately damping to zero at the lower fractional limit of $α\rightarrow 1/2$.

quant-ph↗