  Due to their unique ability to maintain an intensity distribution upon
propagation, non-diffracting light fields are used extensively in various areas
of science, including optical tweezers, nonlinear optics and quantum optics, in
applications where complex transverse field distributions are required.
However, the number and type of rigorously non-diffracting beams is severely
limited because their symmetry is dictated by one of the coordinate system
where the Helmholtz equation governing beam propagation is separable. Here, we
demonstrate a powerful technique that allows the generation of a rich variety
of quasi-non-diffracting optical beams featuring nearly arbitrary intensity
distributions in the transverse plane. These can be readily engineered via
modifications of the angular spectrum of the beam in order to meet the
requirements of particular applications. Such beams are not rigorously
non-diffracting but they maintain their shape over large distances, which may
be tuned by varying the width of the angular spectrum. We report the generation
of unique spiral patterns and patterns involving arbitrary combinations of
truncated harmonic, Bessel, Mathieu, or parabolic beams occupying different
spatial domains. Optical trapping experiments illustrate the opto-mechanical
properties of such beams.
