  We analyze the reflection and transmission coefficients calculated from
transfer matrix simulations on finite lenghts of electromagnetic metamaterials,
to determine the effective permittivity and permeability. We perform this
analysis on structures composed of periodic arrangements of wires, split ring
resonators (SRRs) and both wires and SRRs. We find the recovered
frequency-dependent permittivity and permeability are entirely consistent with
analytic expressions predicted by effective medium arguments. Of particular
relevance are that a wire medium exhibits a frequency region in which the real
part of permittivity is negative, and SRRs produce a frequency region in which
the real part of permeability is negative. In the combination structure, at
frequencies where both the recovered real part of permittivity and permeability
are simultaneously negative, the real part of the index-of-refraction is found
also to be unambigously negative.
