  We present the discovery of a novel and intriguing global geometric structure
of the (interior) transmission eigenfunctions associated with the Helmholtz
system. It is shown in generic scenarios that there always exists a sequence of
transmission eigenfunctions with the corresponding eigenvalues going to
infinity such that those eigenfunctions are localized around the boundary of
the domain. We provide a comprehensive and rigorous justification in the case
within the radial geometry, whereas for the non-radial case, we conduct
extensive numerical experiments to quantitatively verify the localizing
behaviours. The discovery provides a new perspective on wave localization. As
significant applications, we develop a novel inverse scattering scheme that can
produce super-resolution imaging effects and propose a method of generating the
so-called pseudo surface plasmon resonant (PSPR) modes with a potential sensing
application.
