Comments on "On the computation of the complete spectral Green's dyadic for layered bianisotropic structures" [with reply]

Abstract

In the above paper, 1 the authors have shown how to compute their complete spectral Green's dyadic (CSGD) for multilayered bianisotropic planar structures. Their method consists of the following steps.Step 1) Transform normally directed current components into equivalent sheets of transverse currents.Step 2) Compute the transverse spectral Green's dyadics and the transverse fields attributed to transverse currents.Step 3) Calculate the normal field components from the transverse fields. While the authors have elaborated somewhat in steps 1 and 2, they have somehow treated step 3 in a rather ad-hoc manner by simply stating that, "the complete spectral (electric) Green's dyadic can finally be obtained after algebraically calculating the normal component of the (electric) field from (its) transverse components." Specifically, they refer the readers to [1] ([24] in the above paper) for an example of the explicit expressions for normally directed fields. As is well known, the dyadic Green's function in its default definition represents the response due to point source of arbitrary orientation. Still, in view of the rationale behind [2] (not the 1971 edition in [8] of the above paper), as well as [3]-[5], it will be incomplete if one had not mentioned explicitly the source point/plane singularities for the Green's function expansions in the space/spectral domain. These singularities cannot be deduced merely from the algebraic relations between normal E z ; H z and transverse Et; Ht.In order to present the truly complete spectral Green's dyadic, let us consider, for example, the expression of G E J defined and expanded as E zf kt; z = dz 0 GE J kt; z; z 0 Jzs kt; z 0 kt =kxx + kyŷ(1)The indexes f and s in the subscripts correspond respectively to the field and source layers (not interfaces as in the equivalent boundary method). Gdenotes the Green's dyadic element in the above paper, which, as asserted by the authors, can be obtained from the algebraic relations between normal and transverse fields. For complete representation in the spectral domain, one must specify as well the source plane term G E J , which can be determined to be G E J = 0 zzs j!1s z 0 z 0 fs :Manuscript (z 0 z 0 ) is the Dirac delta function, 1s = zzszzs 0 zzszzs, and the (absolute) constitutive dyadics are = 0 r ; = 0 r ; = (1=c) r ; = (1=c) r . Note that we have included the Kronecker delta symbol fs to demand the unambiguous specification of the source layer, especially for normal sources located on the interface between two different media. Apparently, this term contains some form similar to that of (8) in the above paper, but has not been associated by them to the final source plane singularity of the CSGD. Perhaps such association is slightly more noticeable in [6, eq. (40)] ([21] in the above paper) or from the source-incorporated normal field expressions in [6, eqs. (27), (28)], rather than from the source-free expressions of [1] referred by the authors. Indeed, by conforming to the coordinate system in Fig. 1 in the above paper, we have th...