Theory of Maxwell's fish eye with mutually interacting sources and drains

Maxwell's fish eye is predicted to image with a resolution not limited by the wavelength of light. However, interactions between sources and drains may ruin the subwavelength imaging capabilities of this and similar absolute optical instruments. Nevertheless, as we show in this paper, at resonance frequencies of the device, an array of drains may resolve a single source, or alternatively, a single drain may scan an array of sources, no matter how narrowly spaced they are. It seems that near-field information can be obtained from far-field distances.