unit magnitude $\hat{H}(x,z) = H(z)
e^{ik_xx} = e^{ik_z(L-z)+ik_xx}$ incident on the medium lying in $0\le z\le L$ from the region where $z>L$ at an angle $\theta$. The complex reflection and transmission coefficients $r =
r(L)$ and $t = t(L)$, which we consider as functions of $L$, are defined by the wave functions outside the medium by $$\hat{H}(x,z)=\cases{e^{ik_z(L-z)+ik_xx} + r(L) e^{ik_z(z-L)+ik_xx}, &if $z > L$\\
t(L) e^{-i{k_z}^\prime z+ik_xx},&if $z < 0$\\}.$$ When $\epsilon$ is equal to $\epsilon_1$ in $z>L$ and $\epsilon_2$ in $z<0$, the wave vector components $k_x$, $k_z$ and ${k_z}^\prime$ are given by $ k_x= \sqrt{\epsilon_1} k_0 \sin \theta=k_1\sin\theta$, $ k_z=
\sqrt{\epsilon_1} k_0 \cos \theta$ and ${k_z}^\prime = \sqrt{\epsilon_2}
k_0 \cos \theta^\prime$, where $\theta^\prime$ is the angle that outgoing waves make with the negative $z$ axis.

We can transform the wave equation into a set of differential equations for the reflection and transmission coefficients using the invariant imbedding method [@Kim5]: $$\begin{aligned}
{1 \over k_z} {dr(l) \over dl} & = & 2i {\epsilon(l) \over \epsilon_1}
r(l) - {i \over 2} \left[ {\epsilon(l) \over \epsilon_1} - 1 \right]
\left[ 1 - {\epsilon_1 \over \epsilon(l)}
\tan^2 \theta \right] \left[ 1 + r(l) \right]^2, \nonumber \\
%
{1 \over k_z} {dt(l) \over dl} & 