Electromagnetic Metasurfaces. Christophe Caloz

Electromagnetic Metasurfaces

Row 1st Column bold upper B 2nd Column equals ModifyingAbove Above ModifyingAbove zeta With bar With bar left-parenthesis bold upper F 0 right-parenthesis dot bold upper E plus ModifyingAbove Above ModifyingAbove mu With bar With bar left-parenthesis bold upper F 0 right-parenthesis dot bold upper H comma EndLayout"/>

where bold upper F 0 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 bold upper A dot chi overbar overbar dot bold upper B equals left-parenthesis bold upper A dot chi overbar overbar dot bold upper B right-parenthesis Superscript normal upper T Baseline equals bold upper B dot chi overbar overbar Superscript normal upper T Baseline dot bold upper A , 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. bold upper F 0 equals 0 , these conditions reduce to

(2.51) epsilon overbar overbar equals epsilon overbar overbar Superscript normal upper T Baseline comma mu overbar overbar equals mu overbar overbar Superscript normal upper T Baseline comma xi overbar overbar equals minus zeta overbar overbar Superscript normal upper T Baseline comma

which may be expressed in terms of susceptibilities as

(2.52)Скачать книгу