in the weak and strong disorder limits. We first consider the weak disorder regime. We write the reflection coefficient $r$ as $r=r_0+\delta r$, where $r_0$ is the reflection coefficient from an interface between free space and a half-space medium with the parameters $\epsilon_0$ and $\beta_0$. The expression for $r_0$ can be obtained from that of $r(0)$ in Eq. (\[eq:refc\]) by replacing $\epsilon_2$ and $\beta_2$ with $\epsilon_0$ and $\beta_0$ respectively.

By substituting $r=r_0+\delta r$ into the infinite number of algebraic equations obtained from Eq. (\[eq:iie2\]), we get an infinite number of coupled equations for $\langle \left(\delta r\right)^n\rangle$ for all integers $n$. We expand these averages, which are at least of the first order in $g_u$ and $g_a$, in terms of the small perturbation parameters $g_u$ and $g_a$. From analytical considerations and numerical calculations, we can demonstrate that the leading terms for $\langle \delta r\rangle$ and $\langle \left(\delta r\right)
^2 \rangle$ are of the first order, while that of $\langle \left(\delta r\right)^3 \rangle$ is of the second order, except at incident angles close to the critical angle of total reflection. From this consideration, we substitute $$\begin{aligned}
&&Z_1=r_0+\langle \delta r\rangle,~Z_2=r_0^2+2r_0\langle \delta r\rangle+\langle \left(\delta r\right)
^2 \rangle,\nonumber\\
&&Z_3\approx r_0^3+3r_0^2\langle \delta r\rangle+3r_0\langle \left(\delta r\right)^2 \rangle,\end{aligned}$$ 