  It is well known that by modifying the wavefront in a certain manner, the
light intensity can be turned into a certain shape. However, all known light
modulation techniques allow for limited light modifications only: focusing
within a restricted region in space, shaping into a certain class of parametric
curves along the optical axis or bending described by a quadratic-dependent
deflection as in the case of Airy beams. We show a general case of classical
light wavefront shaping that allows for intensity and phase redistribution into
an arbitrary profile including pre-determined switching-off of the intensity.
To create an arbitrary three-dimensional path of intensity, we represent the
path as a sequence of closely packed individual point-like absorbers and
simulate the in-line hologram of the created object set; when such a hologram
is contrast inverted, thus giving rise to a diffractor, it creates the
pre-determined three-dimensional path of intensity behind the diffractor under
illumination. The crucial parameter for a smooth optical path is the sampling
of the predetermined curves, which is given by the lateral and axial resolution
of the optical system. We provide both, simulated and experimental results to
demonstrate the power of this novel method.
