From scattering theorem to Lorentz reciprocity
In Sees. 2.1.2 and 3.4.2 it was shown how Lorentz reciprocity in physical space led, via Kerns’ formulation and its generaliztion to include eigenmodes within anisotropic media, to a scattering theorem in plane-stratified systems (‘reciprocity in k-space’). In this chapter we consider the reverse derivation. Our starting point is the scattering theorem (2.112) for the plane-stratified medium (which for concreteness is taken to be a magnetoplasma), and from it we shall derive the Lorentz-reciprocity theorem, (4.89) and (4.91), relating currents and fields in a given medium and their mirror images, with respect to a magnetic meridian plane, in a conjugate medium. Since the plane-stratified magneto-plasma is self-conjugate, as we have seen in Chap. 2, all fields and currents, given and conjugate, are located in the same medium.
KeywordsAnisotropic Medium Angular Spectrum Elementary Layer Current Element Multilayer Medium
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