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Transmission eigenfunctions are certain interior resonant modes that are ofcentral importance to the wave scattering theory. In this paper, we present thediscovery of novel global rigidity properties of the transmissioneigenfunctions associated with the Maxwell system. It is shown that thetransmission eigenfunctions carry the geometrical and topological informationof the underlying domain. We present both analytical and numerical results ofthese intriguing rigidity properties. As an interesting application, we proposean illusion scheme of artificially generating a mirage image of any givenoptical object.

Geometrical and topological properties of transmission resonance and artificial mirage