= Solution
For real $k^2(x)$, the <wave equation> has the conserved <Wronskian flux>
$$
\mathcal J=\frac{1}{2i}(E^*E'-EE'^*)=\operatorname{Im}(E^*E').
$$
For this <ordinary plasma wave>, the time-averaged <Poynting flux> is $\langle S_x\rangle=c^2\mathcal J/(8\pi\omega)$. With no incident <wave> from the right, evaluating the same <Wronskian flux> on both sides proves
$$
\boxed{R+T=1,\qquad R=|r|^2,\quad T=|t|^2.}
$$
The coefficients in <2/f> also satisfy this identity algebraically, before the opaque-barrier expansion.
A <plasma wave resonance> makes the ideal cold description singular and requires an appropriate causal regularization. A passive resonant layer can absorb <wave energy> into particle motion, or convert it into another branch. For the two measured outgoing channels one then has
$$
\boxed{R+T=1-A\le1,}
$$
with $A>0$ when resonant absorption or uncounted <mode conversion> occurs. A numerical value of $A$ requires the layer physics; a resonance by itself does not specify a universal loss fraction. Counting all converted and absorbed <energy> preserves <conservation of energy>.
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