Energy spectrum of electromagnetic normal modes in dissipative media: modes between two metal half spaces

The energy spectrum of the electromagnetic normal modes plays a central role in the theory of the van der Waals and Casimir interaction. In dissipative media it appears as if there are distinct normal modes with complex valued energies. The summation of the zero-point energies of these modes render a complex valued result. Using the contour integration, resulting from the use of the generalized argument principle, gives a real valued and different result. We resolve this contradiction and show that the spectrum of true normal modes form a continuum with real frequencies. We illustrate the problem in connection with the van der Waals interaction between two metal half spaces.