Electromagnetic Metasurfaces. Christophe Caloz
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Название: Electromagnetic Metasurfaces

Автор: Christophe Caloz

Издательство: John Wiley & Sons Limited

Жанр: Физика

Серия:

isbn: 9781119525172

isbn:

СКАЧАТЬ rel="nofollow" href="#fb3_img_img_fd7b9a47-3f05-5d1d-8560-bb287824e6bf.png" alt="StartLayout 1st Row 1st Column nabla times bold-script upper H 2nd Column equals bold-script upper J plus StartFraction partial-differential bold-script upper D Over partial-differential t EndFraction comma EndLayout"/>

      with the bianisotropic constitutive relations (2.4) defined by

      (2.54b)StartLayout 1st Row 1st Column bold-script upper D 2nd Column equals epsilon 0 bold-script upper E plus bold-script upper P comma bold-script upper P equals epsilon 0 chi overbar overbar Subscript ee Baseline dot bold-script upper E plus StartFraction 1 Over c 0 EndFraction chi overbar overbar Subscript em Baseline dot bold-script upper H period EndLayout

      (2.56)bold-script upper H dot left-parenthesis nabla times bold-script upper E right-parenthesis minus bold-script upper E dot left-parenthesis nabla times bold-script upper H right-parenthesis equals nabla dot left-parenthesis bold-script upper E times bold-script upper H right-parenthesis comma

      where the cross product bold-script upper E times bold-script upper H corresponds to the Poynting vector bold-script upper S. This transforms (2.55) into

      We shall now simplify the last two terms of this relation to provide the final form of the bianisotropic Poynting theorem. We show the derivations only for negative bold-script upper E dot StartFraction partial-differential bold-script upper D Over partial-differential t EndFraction, but similar developments can be made for negative bold-script upper H dot StartFraction partial-differential bold-script upper B Over partial-differential t EndFraction. From bold-script upper D equals epsilon 0 bold-script upper E plus bold-script upper P, we have that

      (2.58)negative bold-script upper E dot StartFraction partial-differential bold-script upper D Over partial-differential t EndFraction equals negative bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction left-parenthesis epsilon 0 bold-script upper E plus bold-script upper P right-parenthesis equals minus epsilon 0 bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E minus bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper P period

      (2.59)negative bold-script upper E dot StartFraction partial-differential bold-script upper D Over partial-differential t EndFraction equals minus one half epsilon 0 bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E minus one half bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper P minus one half epsilon 0 bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E minus one half bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper P period

      Manipulating the terms in the right-hand side of this new relation, adding the extra null term one half bold-script upper P dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E minus one half bold-script upper P dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E, and using the chain rule leads to

      (2.60)StartLayout 1st Row 1st Column negative bold-script upper E dot StartFraction partial-differential bold-script upper D Over partial-differential t EndFraction 2nd Column equals minus one half bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction left-parenthesis epsilon 0 bold-script upper E right-parenthesis minus one half bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper P minus one half StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E dot left-parenthesis epsilon 0 bold-script upper E right-parenthesis minus one half StartFraction partial-differential Over partial-differential t EndFraction left-parenthesis bold-script upper E dot bold-script upper P right-parenthesis 2nd Row 1st Column Blank 2nd Column minus one half bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper P plus one half bold-script upper P dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E comma EndLayout

      Grouping the first two, middle two, and last two terms of the right-hand side reformulates this relation as

      (2.61)СКАЧАТЬ