Configurable optical vortex ladder in free space

Light eigenmodes with cylindrical symmetry, such as the Laguerre-Gaussian (LG) modes, are characterized by the radial and angular quantum numbers indicating radial nodes and orbital angular momentum (OAM), which are independent and invariant upon beam propagation. Here, we connect these two quantum numbers and produce a configurable optical vortex ladder. An LG vortex ladder that consists of multiple LG modes with different radial quantum numbers is proposed, whose OAM state of the mainlobe can change step by step upon propagation. By controlling radial quantum numbers within the LG vortex ladder, every step change of the OAM state can be configured arbitrarily, such as topological charge of OAM state increasing by two in every step. Manipulating the evolution of photonic OAM states is of great significance for quantum information processing and longitudinal manipulation of OAM have potential applications in communications, all-optical switch, and optical tweezers.