  Transmission eigenfunctions are certain interior resonant modes that are of
central importance to the wave scattering theory. In this paper, we present the
discovery of novel global rigidity properties of the transmission
eigenfunctions associated with the Maxwell system. It is shown that the
transmission eigenfunctions carry the geometrical and topological information
of the underlying domain. We present both analytical and numerical results of
these intriguing rigidity properties. As an interesting application, we propose
an illusion scheme of artificially generating a mirage image of any given
optical object.
