  We present a microscopic mo del of cavity quantum electro dynamics based on a
one-dimensional coupled cavity array (1D CCA), where a sup er cavity (SC) is
comp osed by a segment of the 1D CCA with relatively smaller couplings with the
outsides. The single-photon scattering problem for the SC empty or with a
two-level atom is investigated. We obtain the exact theoretical result on the
transmission rate for our system, which predicts the transmission p eaks shall
app ear near the eigen-energies. Our numerical results further prove that the
SC is a well-defined multi-mo de cavity. When a two-level atom resonant with
the SC lo cates at the antino de of the resonant mo de, the transmission sp
ectrum shows a clear sign of vacuum Rabi splitting as exp ected. However, when
the atom lo cates at the no de of the resonant mo de, we observe a deep valley
in the transmission p eak, which can b e explained by the destructive
interference of two transmission channels, one is the resonant mo de, while the
other is arising from the atom coupling with the non-resonance mo des. The
effect of non-resonance mo des on vacuum Rabi splitting is also analyzed.
