Electromagnetic Metasurfaces. Christophe Caloz

      where represents a time-odd external bias. Under phase conjugation (or time reversal), these constitutive relations become [28]

(2.47a)

      (2.47b)

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)

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