Light–matter interaction in cold atomic ensembles is one of the central topics in modern quantum and atomic optics with important applications in various quantum technologies. The collective response of dense atomic gases under light excitation depends crucially on the spatial distribution of atoms and the geometry of the ensemble. We analyze near-resonant light transmission in two-dimensional dense ultracold atomic ensembles with short-range positional correlations. Based on coupled-dipole simulations, we show that the collective effects, manifested as notable shifts of transmission resonance frequency and considerable modification of optical depths, are influenced strongly by positional correlations. Mean-field theories such as the Lorentz–Lorenz relation are not capable of describing such collective effects. We also investigate the statistical distribution of eigenstates and provide a connection between the transmission spectra and eigenstate distribution by utilizing the population weighted detuning and decay rate of all eigenstates. We further demonstrate the intricate interplay between dipole–dipole interactions and positional correlations by increasing the number densities of atoms.
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