Electromagnetic Metasurfaces - Christophe Caloz

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upper H dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper M minus bold-script upper M dot StartFraction partial-differential Over partial-differential t EndFraction bold-script upper H right-parenthesis period EndLayout"/>

      where left pointing angle dot right pointing angle denotes the time-average operation. In the case of time-harmonic fields, this equation can be further manipulated as follows. First, it is straightforward to show that left pointing angle StartFraction partial-differential w Over partial-differential t EndFraction right pointing angle equals 0 and langlerangleS equals one half Re left-parenthesis bold-script upper E times bold-script upper H Superscript asterisk Baseline right-parenthesis. Second, the terms langlerangleIJ and langlerangleIK may be expressed in terms of the electric and magnetic susceptibility tensors by using bold upper J equals sigma overbar overbar Subscript normal e Baseline dot bold upper E and bold upper K equals sigma overbar overbar Subscript normal m Baseline dot bold upper H, where the electric and magnetic conductivity tensors are related to the susceptibility tensors as

      (2.68a)StartLayout 1st Row 1st Column sigma overbar overbar Subscript normal e 2nd Column equals minus omega epsilon 0 Im left-parenthesis chi overbar overbar Subscript ee Baseline right-parenthesis equals StartFraction j omega epsilon 0 Over 2 EndFraction left-parenthesis chi overbar overbar Subscript ee Baseline minus chi overbar overbar Subscript ee Superscript asterisk Baseline right-parenthesis comma EndLayout

      (2.68b)StartLayout 1st Row 1st Column sigma overbar overbar Subscript normal m 2nd Column equals minus omega mu 0 Im left-parenthesis chi overbar overbar Subscript mm Baseline right-parenthesis equals StartFraction j omega mu 0 Over 2 EndFraction left-parenthesis chi overbar overbar Subscript mm Baseline minus chi overbar overbar Subscript mm Superscript asterisk Baseline right-parenthesis comma EndLayout

      which leads, after replacing the instantaneous field vectors by their phaser counterparts, to

      (2.69b)StartLayout 1st Row 1st Column langlerangleIK 2nd Column equals one half Re left-parenthesis bold upper H Superscript asterisk Baseline dot bold upper K right-parenthesis equals one half Re left-parenthesis bold upper H Superscript asterisk Baseline dot sigma overbar overbar Subscript normal m Baseline dot bold upper H right-parenthesis 2nd Row 1st Column Blank 2nd Column equals one fourth Re left-bracket j omega mu 0 bold upper H Superscript asterisk Baseline dot left-parenthesis chi overbar overbar Subscript mm Baseline minus chi overbar overbar Subscript mm Superscript asterisk Baseline right-parenthesis dot bold upper H right-bracket period EndLayout

      (2.70b)StartLayout 1st Row 1st Column langlerangleIM 2nd Column equals StartFraction mu 0 Over 4 EndFraction Re left-bracket bold upper H Superscript asterisk Baseline dot left-parenthesis j omega bold upper M right-parenthesis minus bold upper M Superscript asterisk Baseline dot left-parenthesis j omega bold upper H right-parenthesis right-bracket equals one fourth Re left-bracket j omega mu 0 left-parenthesis bold upper H Superscript asterisk Baseline dot bold upper M minus bold upper M Superscript asterisk Baseline dot bold upper H right-parenthesis right-bracket period EndLayout

      (2.71b)StartLayout 1st Row 1st Column langlerangleIM 2nd Column equals one fourth Re left-bracket j omega mu 0 left-parenthesis bold upper H Superscript <p style= Скачать книгу