Surface impedance - Boundary condition

1. Apr 24, 2013

EmilyRuck

Hello!!
Let a plane wave propagate towards the -y direction. It is normally incident upon the plane $(x,z)$ (whose normal unit vector is the y-direction unit vector, $\mathbf{\hat{u}}_y$): the plane represents the interface between the free space (in $y > 0$) and a general lossy medium (in $y < 0$).
We can say that, in general, for $y < 0$

$E_z = - \eta H_x$
$E_x = \eta H_z$

where $\eta \neq \eta_0$ ($\eta_0$ is the free-space wave impedance); $\eta$ is a complex quantity which considers the losses of the medium.
This is obtained from Maxwell and Helmholtz equations. But what could happen if the plane wave is not normally incident upon the plane $(x,z)$?
Which field components will remain and propagate in the $y < 0$ region? And can we say that the interface has the boundary condition

$\mathbf{\hat{u}}_y \times \mathbf{E} = \eta \mathbf{\hat{u}}_y \times (\mathbf{\hat{u}}_y \times \mathbf{H})$

?
Why only the tangential components of the field are involved in these conditions?