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We study resonance for the Helmholz equation with a finite frequency in aplasmonic material of negative dielectric constant in two and three dimensions.We show that the quasi-static approximation is valid for diametrically smallinclusions. In fact, we quantitatively prove that if the diameter of ainclusion is small compared to the loss parameter, then resonance occursexactly at eigenvalues of the Neumann-Poincar\'e operator associated with theinclusion.

Plasmon resonance with finite frequencies: a validation of the quasi-static approximation for diametrically small inclusions