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Dallenbach layer is composed of an absorbing magnetic-dielectric layerattached to a perfect electric conductor (PEC) sheet. Under linearity and timeinvariance (LTI) assumptions Rozanov has established analytically a sum-ruletrade-off between the absorption efficacy over a predefined bandwidth and thethickness of the layer, that is the so-called Rozanov bound. In recent yearsseveral proposals have been introduced to bypass this bound by using non-LTIabsorbers. However, in practice, their implementation may be challenging. Here,we expose additional hidden assumptions in Rozanov's derivation, and thus weintroduce several new sum rules for LTI layer absorbers that are not covered bythe original Rozanov's criterion, and give rise to more relaxed constraints onthe absorption limit. We then, demonstrate practical LTI designs of absorbingthin layers that provide absorption beyond the Rozanov's bound. These designsare based on the replacement of the original PEC boundary by various types ofpenetrable impedance sheet.

Sum Rule Bounds Beyond Rozanov Criterion in Linear and Time-Invariant Thin Absorbers