Abstract
Microcavity polaritons are hybrid light-material states of a bosonic nature.In the last decades, an enormous interest has been paid to their Bose-Einstein condensation phase.We develop, in this work the theoretical and numerical tools to understand and interpret the spatial and temporal dynamics of the formation of condensates of polaritons.We propose a numerical approach for the comprehensive resolution of the generalized Gross-Pitaevskii model in two-dimensions in Cartesian coordinates.We sought to understand the aspects of the condensation threshold under different spatial and temporal configurations of non-resonant optical excitation.In particular, we propose a new approach to define the threshold.Finally, for a condensation under a focal exciation in a ZnO microcavity, we were able to access, and understand, some of the experimentally observed properties.