In this letter, we investigate the image field of the quasi-monochromatic random source in the two-dimensional negative-index slab. The prominent temporal-coherence gain of the image is observed in the numerical simulations even when the frequency-filtering effects are very weak. We find that the signals originating from the source will take the different time-"group" retarded time to reach the image location along the different optical paths. Based on the new physical picture, a simple phenomenological theory is constructed to obtain the image field and demonstrate that the temporal-coherence gain is from different "group" retarded time. The phenomenological theory agrees well with the FDTD simulation and the strict Green's function method. These results should have important impacts on the study of coherence mechanism and the design of novel devices.
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