Counterintuitive delocalization in the strong disorder limit {#sec:sdl}
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Our formalism based on the concept of wave impedance can be used to predict and explain the counterintuitive delocalization phenomena arising in the infinite disorder limit in some cases. We first consider the case where only the scalar potential is random. Then, from the expression of the impedance, Eq. (\[eq:imp1\]), we find that in the strong disorder limit where $\delta u$ is statistically much larger than 1, the last two terms become negligibly small and the impedance approaches a constant given by $\eta\approx \vert\cos\theta\vert^{-1}$. Therefore, as the disorder parameter $g_u$ approaches infinity, the system becomes less and less random and the localization length should diverge for all $\theta$. This behavior will be verified analytically by solving our invariant imbedding equations using a strong-disorder expansion in Sec. \[sec:sdr\] and confirmed in a precise numerical calculation in Sec. \[sec:dd\].

Next, we consider the case where only the vector potential is random. Then from the alternative expression of the impedance, Eq. (\[eq:imp4\]), we find that in the strong disorder limit where $\delta a$ is statistically much larger than 1, the impedance approaches a constant given by ${\tilde\eta}^2\approx -1/\cos^2\theta$. Therefore the impedance is nonrandom, but 