  A caustic is a mathematical concept describing the beam formation when the
beam envelope is reflected or refracted by a manifold. While caustics are
common in a wide range of physical systems, caustics typically exhibit a
reciprocal wave propagation and are challenging to control. Here, we utilize
the highly anisotropic dispersion and inherent non-reciprocity of a magnonic
system to shape non-reciprocal emission of caustic-like spin wave beams in an
extended 200 nm thick yttrium iron garnet (YIG) film from a nano-constricted rf
waveguide. We introduce a near-field diffraction model to study spin-wave
beamforming in homogeneous in-plane magnetized thin films, and reveal the
propagation of non-reciprocal spin-wave beams directly emitted from the
nanoconstriction by spatially resolved micro-focused Brillouin light
spectroscopy (BLS). The experimental results agree well with both micromagnetic
simulation, and the near-field diffraction model. The proposed method can be
readily implemented to study spin-wave interference at the sub-micron scale,
which is central to the development of wave-based computing applications and
magnonic devices.
