  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.
