Complex periodic non-diffracting beams generated by superposition of two identical periodic wave fields

A method has been proposed to generate complex periodic discrete non-diffracting beams (PDNBs) via superposition of two identical simple PDNBs at a particular angle. As for special cases, we studied the superposition of the two identical squares (“4+4”) and two hexagonal (“6+6”) periodic wave fields at specific angles, respectively, and obtained a series of interesting complex PDNBs. New PDNBs were also obtained by modulating the initial phase difference between adjacent interfering beams. In the experiment, a 4 f Fourier filter system and a phase-only spatial light modulator imprinting synthesis phase patterns of these PDNBs were used to produce desired wave fields.