Klein delocalization, has been demonstrated in some previous papers.[@zhu; @bli; @zhao]

Several different concepts and approaches, which include, for example, particle-antiparticle pair production and chirality conservation, have been used to explain Klein tunneling and related Klein delocalization phenomena. In this paper, we approach these phenomena from the viewpoint of classical wave propagation theory and demonstrate that they can be interpreted readily using the concept of wave impedance.

With that purpose in mind, we rewrite the Dirac equation, Eq. (\[eq:dirac\]), as the wave equation for $\psi_A$ by eliminating $\psi_B$, which takes the form $$\begin{aligned}
\frac{d}{dx}\left(\frac{1}{\epsilon}\frac{d\psi_A}{dx}\right)+p^2\epsilon\eta^2\psi_A=0,\end{aligned}$$ where $\eta$ is defined by $$\begin{aligned}
\eta^2=\frac{1}{\cos^2\theta}\left[1-\left(\frac{\beta}{\epsilon}\right)^2-\frac{1}{k\epsilon}\frac{d}{dx}
\left(\frac{\beta}{\epsilon}\right)\right].
\label{eq:imp1}\end{aligned}$$ We notice that the wave equation of this form looks the same as that for $p$-polarized electromagnetic waves propagating normally in a medium with the effective wave impedance given by $\eta(x)$.

In the incident region where the potentials $u$ and $a$ are zero, $\epsilon$ is equal to 1 and $\beta$ is equal to $\sin\theta$, therefore $\eta$ is equal to 1 for all $\theta$. If $\eta$ is unity in all other parts of the space as well, then there will be no wave reflection and the transmittance will be 1. From the form of $\eta$, we find that 