Interferograms of Votex FWM Beam for Nonlinear Spatial Filter in Photonic Band Gap

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.