Volumetric caustics engineering

We present a universal method for sculpting true three-dimensional (3D) light fields by engineering caustics with a digitally encoded axicon. This approach establishes a radial-to-axial coordinate mapping, allowing independent control over each axial plane within the light volume. By assigning distinct caustic-generating functions to different radial zones on a spatial light modulator, we synthesize volumetric light structures with tunable shape, scale, orientation, orbital angular momentum, and trajectory. Experiments demonstrate dynamic volumetric scenes, localized modulation, continuous transformations, and multi-object displays. This framework unifies and extends previous caustic and axially variant beam methods, enabling transversely proportional, freely reconfigurable 3D light constructs without mechanical motion. The technique opens new directions for volumetric displays, imaging and optical manipulation.