Some reflections on double negative materials

We study the energy conservation property and loss condition of a left-handed material (LHM). First we argue by energy conservation that an LHM has to be a backward-wave material (BWM). Then we derive the equivalence of the loss and the Sommerfeld far-field radiation conditions for BWM. Next, we solve the realistic Sommerfeld problem of a point source over an LHM half space and an LHM slab. With this solution, we elucidate the physics of the interaction of a point source with an LHM half space and an LHM slab. We interpret our observation with surface plasmon resonance at the interfaces as well as the resonance tunneling phenomenon. This analysis lends physical insight into the interaction of a point source field with an LHM showing that super-resolution beyond the diffraction limit is possible with a very low loss LHM slab.