Electromagnetic Metasurfaces. Christophe Caloz

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СКАЧАТЬ rel="nofollow" href="#fb3_img_img_2e46db43-0047-5d04-96f9-66e99d9878fc.png" alt="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 plus bold-script upper P right-parenthesis minus one half StartFraction partial-differential Over partial-differential t EndFraction left-bracket bold-script upper E dot left-parenthesis epsilon 0 bold-script upper E plus bold-script upper P right-parenthesis right-bracket 2nd Row 1st Column Blank 2nd Column minus one half left-parenthesis bold-script upper E dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper P minus bold-script upper P dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper E right-parenthesis comma EndLayout"/>

      which, using again , becomes

      (2.62)

      Finally, grouping the first two terms of the right-hand side of this relation yields

(2.63)

Similarly, the term in (2.57) becomes

(2.64)

Substituting now (2.63) and (2.64) into (2.57) finally yields the bianisotropic Poynting theorem:

(2.65)

      where is the energy density, is the Poynting vector, and and are the impressed source power densities, and and are the induced polarization power densities, respectively, which are defined by

      (2.66a)

      (2.66b)

      (2.66c)

(2.66d)

(2.66e)

It is generally more convenient to consider the time-average version of (2.65), which reads

(2.67)

      where denotes the time-average operation. In СКАЧАТЬ