Rotation of multi-zeros optical beam during propagation and its application to distance measurement

The Laguerre-Gaussian (LG) beam has a phase term called the Gouy phase shift which is changing in proportion to the propagation distance and the order of LG beam. We consider the effect of this phase term on the multi-zeros optical beam, a beam with propagation-invariant isolated zeros generated by an common-Gaussian combination of the LG beams, and obtain a result that the zeros rotates during its propagation keeping their relative positions. In this paper, the rotation effect of the multi-zeros optical beam is formulated theoretically based on the mathematical formulae of the LG beam. We then consider an appropriate optical setup to actualize the rotation effect using the heterodyne interference of a pair of counter-rotating beams and the correlation image sensor to capture the wavefront profile. In the experiments, we examine the increasing rotation angle of the zeros arrangement according to the distance, and consider the possible application to the distance measurement.