Effective resonance representation of propagators in complex ducts-a multiresolution and homogenization approach

We use the multiresolution homogenization theory to study the effective resonances representation of transient electromagnetic propagation in complex random multilayer ducts. The theory permits explicit choice of the smoothing (homogenization) scale, and can be applied to a wide range of micro-scale properties. The analytical study is based on a Wroskian equivalence result, which establishes the relation between the "true" Wronskian W and that of the homogenized problem W^(eff). Since the roots of W in the complex ω plane constitute the duct resonance, the Wronskian equivalence theorem is used as a basic apparatus for the effective resonance study. With this, the time-domain spectral properties of the multiresolution homogenization formulation are studied analytically and demonstrated numerically. Effective representations of reflection from complex random multilayer ducts are considered.