Solitons in Exciton-Polariton System: Reduced Modelling, Analysis, and Numerical Studies

<p>In this dissertation, we study the behavior of exciton-polariton quasiparticles in semiconductor microcavities, under the sourceless and lossless conditions.</p><p>First, we simplify the original model by removing the photon dispersion term, thus effectively turn the PDEs system to an ODEs system, </p><p>and investigate the behavior of the resulting system, including the equilibrium points and the wave functions of the excitons and the photons. </p><p>Second, we add the dispersion term for the excitons to the original model and prove that the band of the discontinuous solitons now become dark solitons. </p><p>Third, we employ the Strang-splitting method to our sytem of PDEs and prove the first-order and second-order error bounds in the $H^1$ norm and the $L_2$ norm, respectively. </p><p>Using this numerical result, we analyze the stability of the steady state bright soliton solution. This solution revolves around the $x$-axis as time progresses </p><p>and the perturbed soliton also rotates around the $x$-axis and tracks closely in terms of amplitude but lags behind the exact one. Our numerical result shows orbital </p><p>stability but no $L_2$ stability.</p>

Dissertation