Electromagnetic Metasurfaces. Christophe Caloz

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      (2.41b)

      Using the identity reduces these equations to

(2.42a)

(2.42b)

Subtracting 2.42a from 2.42b yields

      (2.43)

      We may now integrate this equation over the volume and apply the Gauss theorem, which gives

(2.44)

The surface integral on the left-hand side of (2.44) and the second volume integral on its right-hand side both vanish when integrated over an unbounded medium [28, 81]. This results into

(2.45)

      which represents a fundamental relation for reciprocity. We next include the bianisotropic material parameters in this relation. For this purpose, we use the bianisotropic constitutive relations (2.4), which may be explicitly rewritten as

(2.46a)

      (2.46b)

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

(2.47a)

      (2.47b) Скачать книгу