Single-return approximation for periodic line reflections ($R_{\mathrm{first}}=r/[1-t^2{e}^{2ikL}]$)

Summing only paths that reflect at one shunt, with all previous shunts crossed once in each direction, gives a geometric series with ratio $t^2{e}^{2ikL}$. 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 $R=r+t^2{e}^{2ikL}R/(1-r{e}^{2ikL}R)$. Near coherent reflection peaks the omitted paths need not be small, even if each shunt is weak.