  We present a quantum field theoretical approach based on the
Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process
in a nano-architecture consisting of the coupled resonator arrays (CRA), which
are also coupled to some artificial atoms as the controlling quantum node. By
making use of this approach, we find the bound states of single photon for an
elementary unit, the T-type CRA, and explicitly obtain its multi-photon
scattering S-matrix in various situations. We also use this method to calculate
the multi-photon S-matrices for the more complex quantum network constructed
with main T-type CRA's, such as a H-type CRA waveguide.
