Microcavity effect on the electron-hole relative motion in semiconductor quantum wells

We rigorously find that for a quantum well embedded within a semiconductor microcavity near resonance with the $1s$-exciton transition, the upper (lower) polariton is associated with an electron-hole relative-motion probability-density distribution larger (smaller) than the two-dimisional exciton Bohr radius if half the normal-mode splitting exceeds the $1s$-exciton binding energy. In this case, the exciton continuum comprises an essential part of the description of the upper mode, leading to a strong asymmetry of the microcavity lines observed in transmission.