When solving an electromagnetic boundary-value problem, it is common to use the boundary conditions: Display Formula
$n^(rS)\xb7[Bout(rS,\omega )\u2212Bin(rS,\omega )]=0n^(rS)\xd7[Eout(rS,\omega )\u2212Ein(rS,\omega )]=0n^(rS)\xb7[Dout(rS,\omega )\u2212Din(rS,\omega )]=\rho s(rS,\omega )n^(rS)\xd7[Hout(rS,\omega )\u2212Hin(rS,\omega )]=Js(rS,\omega )},rS\u2208S,$(6)
with the unit normal vector $n^(rS)$ at $rS\u2208S$ pointing into $Vout$. The subscripts “in” and “out” indicate that the fields in $Vin$ and $Vout$, respectively, are being evaluated on $S$. The quantities $\rho s$ and $Js$ are the surface charge density and the surface current density, respectively. In order to accommodate model II, we set Display Formula$\rho s(rS,\omega )=\gamma (\omega )n^(rS)\xb7Bin(rS,\omega )Js(rS,\omega )=\u2212\gamma (\omega )n^(rS)\xd7Ein(rS,\omega )},rS\u2208S,$(7)
where $\gamma $ describes the surface states.