Optical images rotation and reflection with engineered orbital angular momentum spectrum

According to the concept of digital spiral imaging, we reconstruct an arbitrary structured light beam with information based on orbital angular momentum (OAM) eigenstates, i.e., the Laguerre-Gaussian (LG) modes. We propose a method to realize the rotation and reflection of an image by imparting an extra phase factor to each constituent OAM mode. If each OAM mode is added by a time-varying phase, the structured light beams can be manipulated to rotate with a constant speed, similar to a reverse rotational Doppler effect. While making a conjugate transformation to each OAM mode and then adding a constant phase factor to them, the structured light beams can be flipped over along any axis. In experiment, we take two typical patterns, e.g., a smiley face and a letter “e,” to demonstrate the effectiveness of our scheme. The scheme presented in this work may find potential applications in optical micromanipulation and remote sensing.