Finite-difference time-domain simulations of exciton-polariton resonances in quantum-dot arrays

The optical properties of nanosize quantum-dot (QD) arrays are found to vary significantly around the exciton resonance frequency of the QDs. In order to simulate the interactions between electromagnetic waves and QD arrays, a general auxiliary-differential-equation, finite-difference time-domain approach is introduced and utilized in this article. Using this numerical method, the exciton-polariton resonances of single-layer and double-layer GaAs QD arrays are studied. The optical properties of a single-layer QD array are found to be characterized by the Mie resonance of its constituent QDs, while a double-layer QD array is characterized by the quasi-dipole formed by two QDs positioned in each of the two layers.