Electromagnetic Metasurfaces. Christophe Caloz

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Substituting (2.46) and (2.47) into (2.45) transforms the integrand of (2.45) into

(2.48)

Expanding the bracketed terms in (2.48), using the identity , where the superscript denotes the transpose operation, and grouping the identical parameter terms, we obtain

(2.49)

The nullity of the volume integral of (2.49) (Eq. (2.45)) for any field implies then the general⁶ bianisotropic Lorentz reciprocity conditions

      (2.50a)

      (2.50b)

      In the absence of external bias, i.e. , these conditions reduce to

(2.51)

which may be expressed in terms of susceptibilities as

      (2.52)

2.5 Poynting Theorem

      This section derives the time-average bianisotropic Poynting theorem [16, 81, 140], which provides the general conditions for gain and loss in terms of susceptibility tensors.

      The time-domain Maxwell–Faraday and Maxwell–Ampère equations, assuming the presence of electric current sources, , and magnetic current sources, , are, respectively, given as

(2.53a)

(2.53b)СКАЧАТЬ