We　analyze　the　properties　and　interferograms　of　vortex　four-wave　mixing　(FWM)　beams　by　varying　the　incident　angle　of　the　probe　field.　Based　on　the　properties,　we　propose　the　model　of　a　new　type　of　nonlinear　spatial　filter　without　diffraction　using　a　Bragg　grating　in　the　nonlinear　FWM　process.　We　show　the　evolutions　of　shapes　and　interferograms　of　probe　transmission　signal　(PTS)　and　FWM　by　scanning　the　probe　detuning,　and　demonstrate　the　Kerr　nonlinearity　can　manipulate　the　shapes　and　spatial　location　of　vortex　PTS　and　FWM　images.　Further,　we　can　determine　the　center　position　of　the　new　type　of　nonlinear　filter　through　interference　patterns　and　use　the　Kerr　nonlinearity　of　related　fields　to　control　the　nonlinear　filter　precisely.　In　addition,　the　interferograms　of　the　reflected　signal　from　the　photonic　band　gap　(PBG)　structure　are　studied　both　in　experiment　and　theory.　We　demonstrate　that　the　number　of　fork-like　patterns　of　reflected　signal　changes　from　one　to　three,　revealing　that　the　superposition　of　first-order　and　third-order　beams　in　the　reflected　signal　from　PBG　structure　creates　an　inverted　fork-like　pattern.