Recent observations show a population of active galaxies with milliarcseconds offsets between optical and radio emission. Such offsets can be an indication of extreme phenomena associated with supermassive black holes including relativistic jets, binary supermassive black holes, or even recoiling supermassive black holes. However, the multi-wavelength structure of active galaxies at a few milliarcseconds cannot be fathomed with direct observations. We propose using strong gravitational lensing to elucidate the multi-wavelength structure of sources. When sources are located close to the caustic of lensing galaxy, even small offset in the position of the sources results in a drastic difference in the position and magnification of mirage images. We show that the angular offset in the position of the sources can be amplified more than 50 times in the observed position of mirage images. We find that at least 8% of the observed gravitationally lensed quasars will be in the caustic configuration. The synergy between SKA and Euclid will provide an ideal set of observations for thousands of gravitationally lensed sources in the caustic configuration, which will allow us to elucidate the multi-wavelength structure for a large ensemble of sources, and study the physical origin of radio emissions, their connection to supermassive black holes, and their cosmic evolution.
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