Configuration dependent reflection induced by dissipated localized modes

We study the one photon scattering problem for a super cavity (SC) coupling with two two-level atoms. With atomic decay, we find a sudden drop in reflection at $\Delta=0$ for the two atoms in the node-antinode configuration but not in the antinode-node one. The underlying mechanism is due to the scatterer has a configuration dependent localized dissipated eigen-mode at $\Delta=0$. In the node-antinode configuration, the eigen-mode localized near the input side, which can transport the photon into the SC. By exciting the atom at the node, the photon can leak into the reservoir due to atomic decay, which causes the sudden drop at $\Delta=0$ in reflection. In the antinode-node case, however, the eigen-mode is localized near the output side, no photon can be transported into the SC and leads to completely reflection at $\Delta=0$. A similar phenomenon has been observed in a recent experiment of X-ray quantum optics [Nature \textbf{482}, 199 (2012)] but with a much more complicated explanation due to electromagnetically induced transparency.