Arbitrary self-rotating beam array generated with the synthetic phase

In this Letter, the phase profile of the self-rotating beam is modified by introducing the radial shift factor c and the azimuthal shift factor ?0. The effect of the radial shift factor c on the corresponding intensity distribution is discussed. The results demonstrate that the focal-field intensity patterns of the modified self-rotating beams with different radial shift factors moved away from the center of the light field with the radial shift factor increased. The self-rotating beam array can be arranged arbitrarily along the azimuthal direction with a synthetic phase produced by superimposing multiple modified subphases (i.e., modified self-rotating beam phase). Furthermore, the position of each self-rotating beam in the beam array can be also adjusted arbitrarily in the transverse plane by adding the gratings into each subphase layer of the synthetic phase. The proposed beam array has potential applications in image transmission, data coding and decoding, and optical trapping.