Computational Modeling of Optical Response from Excitons in a Nano Optical Medium

Consider a time-harmonic electromagnetic plane wave incident on a microscopic semiconductor. Inside the medium, at any given frequency omega, more than one polariton mode can arise with the same frequency but different wavenumbers due to the presence of excitons. Besides Maxwell's boundary conditions, additional boundary conditions are required to handle the multi-mode polariton. In order to model the confinement effect of excitons in the microscopic semiconductor, Maxwell's equations and the Schrodinger equation are coupled to characterize the polarization in terms of the quantum description. In the weak confinement regime, we derive a perturbed dispersive dielectric constant by taking the exciton effect into account. We also analyze and compute the optical linear response of the exciton in both one-dimensional and two-dimensional confinements. For the one-dimensional case, the existence and uniqueness of the analytical solution are established in the resonance region. A finite difference method is developed to compute the two dimensional confinement.