Azimuthal beam shaping in orbital angular momentum basis

Shaping the light beam is always essential for laser technology and its applications. Among the shaping technologies, shaping the laser in its Fourier domain is a widely used and effective method, such as a pulse shaper, or a $4f$ system with a phase mask or an iris in between. Orbital angular momentum (OAM) modes spectrum, the Fourier transform of the light field in azimuth, provides a perspective for shaping the light. Here, we propose and experimentally demonstrate a shaping strategy for the azimuthal field by modulating the complex amplitude of the OAM mode spectrum. The scheme utilizes multi-plane light conversion technology and consists only of a spatial light modulator and a mirror. Multiple functions, including beam rotating, beam splitting/combining in azimuth, and OAM mode filtering, are demonstrated. Our work provides a compact and programmable solution for modulating the OAM mode spectrum and shaping beams in azimuth.