Note on the positiveness of magnetic energy stored in the Wire-SRR metamaterial

Abstract

Recently, a new energy density formula for electromagnetic waves in the metamaterial consisting of arrays of conducting wires and split-ring-resonators (SRR) has been derived [Phys. Rev. E 80, 046601 (2009), arXiv:0909.1043]. According to that formula, the positiveness is obvious for the electric part of the energy density but not clear for the magnetic part. In this paper, I show that the magnetic energy density is also positively definite.