  We develop the generalized rotating-wave approximation (GRWA) approach (Phys.
Rev. Lett. 99, 173601 (2007)) to study the single-photon scattering on a
two-level system (TLS) with arbitrarily strong coupling to a local mode in a
one-dimensional (1D) coupled resonator array. We calculate the scattering
amplitudes analytically, and the independent numerical results show that our
approach works well in a broad parameter region. Especially, when the resonator
mode is faroff resonance with the TLS, we obtain more reasonable results than
the ones from the standard adiabatic approximation. Our approach is further
extended to the cases with a 1D resonator array strongly coupled to more than
one TLSs.
