In the recent publication [Opt. Expr 28, 1249 (2020)] the single photon scattering is studied in a second-order nonlinear system. In this paper, 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 a 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 show 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, and which is compared to the results with a two level system [Phys. Rev. A 85, 053840 (2012)] and find the advantages.
