= Single-return approximation for periodic line reflections
{title2=$R_{\rm first}=r/[1-t^2e^{2ikL}]$}
Summing only paths that reflect at one shunt, with all previous shunts crossed once in each direction, gives a <geometric series> with ratio $t^2e^{2ikL}$. This is not the full multiple-reflection solution: it excludes paths that bounce between distinct shunts. For a semi-infinite array the exact amplitude instead obeys $R=r+t^2e^{2ikL}R/(1-r e^{2ikL}R)$. Near coherent reflection peaks the omitted paths need not be small, even if each shunt is weak.
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