Abstract: 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 reso-

nance 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.

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