  Structured light has revolutionized optical particle manipulation and
nano-scale material processing. In particular, propagation-invariant structured
light fields, such as Bessel beams, have enabled applications that require
robust intensity distributions. Their self-healing nature facilitates imaging
with enhanced resolution e.g. in light-sheet microscopy. The prominent
high-intensity features of propagation-invariant fields such as Airy, Bessel,
and Mathieu beams can be understood in terms of caustics. While these beams
have found many applications in material processing and trapping, these
technologies would greatly benefit from structured, controllable intensities in
a variety of shapes well beyond the standard families of propagation-invariant
beams. Here we generalize propagation-invariant beams by tailoring their
caustics through two different methods. We illustrate these approaches by
implementing various tailored propagation-invariant beams experimentally, whose
patterns range from simple geometric shapes to complex configurations such as
words. This approach clarifies that the known solutions are a small subset of a
far more general set of propagation-invariant fields with intensity maxima
concentrated around any desired curve.
