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In this paper, we generalize Huygens' principle (HP), extinction theorem(ET), and Franz-Harrington formulation (FHF). In our previous works, thetraditional HP, ET, and FHF in homogeneous isotropic environment aregeneralized to inhomogeneous anisotropic lossy environment; the traditional FHFof homogeneous isotropic material system is generalized to inhomogeneousanisotropic lossy material system and then to piecewise inhomogeneousanisotropic lossy material system; the traditional HP, ET, and FHF of simplyconnected material system are generalized to multiply connected system and thento non-connected system; the traditional FHF of external scattering field andinternal total field are generalized to internal scattering field and internalincident field. In previous work, it is proved that the generalized HP (GHP)and generalized ET (GET) are equivalent to each other; the GHP, GET, andgeneralized FHF (GFHF) satisfy so-called topological additivity, i.e., theGHP/GET/GFHF of whole electromagnetic (EM) system equals to the superpositionof the GHP/GET/GFHF corresponding to all sub-systems. In this paper, the aboveresults obtained in our previous works, which focuses on the EM systemconstructed by material bodies, are further generalized to the metal-materialcombined EM system in inhomogeneous anisotropic lossy environment, andtraditional surface equivalence principle is generalized to line-surfaceequivalence principle.

On Huygens' Principle, Extinction Theorem, and Equivalence Principle (Metal-Material Combined System in Inhomogeneous Anisotropic Environment)