Asymptotic of resonances of a micro-cavity with impedance boundary condition

This work is aimed at understanding the amplification and confinement of electromagnetic fields in open sub-wavelength metallic cavities. We present a theoretical study of the electromagnetic diffraction by a real conducting planar interface which contains a sub-wavelength rectangular cavity. We derive a rigorous asymptotic expansion of the resonances associated to the Helmholtz operator when the width of the cavity shrinks to zero.