Title: Shaping non-reciprocal caustic spin-wave beams

Abstract: 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.