  We study controllable single photon scattering in a one-dimensional waveguide
coupling with an additional cavity by second order nonlinear materials in a
non-cascading configuration, where the additional cavity is embedded with
two-level atom and filled with Kerr-nonlinear materials. Considering the second
order nonlinear coupling, we analyze the transmission properties of the three
different coupling forms as follows: (i) The two-level atom is excited without
the Kerr-nonlinearity. (ii)The Kerr-nonlinearity is excited without the
two-level atom. (iii) Both of the two-level atom and Kerr-nonlinearity are
excited. The transmission and reflection amplitudes are obtained by the
discrete coordinates approach for the three cases. The results showed that the
transmission properties can be adjusted by the above three different coupling
forms, which indicate our scheme can be used as a single photon switch to
control the transmission and reflection of the single photon in the
one-dimensional coupled resonant waveguide. We compared the results with [Phys.
Rev. A 85, 053840(2012)] and find the advantages.
