  Optical heterodyne detection is a powerful technique for characterizing a
wide range of physical excitations. Here, we use two types of optical
heterodyne detection techniques (fundamental and parametric pumping) to
microscopically characterize the high-frequency auto-oscillations of single and
multiple nano-constriction spin Hall nano-oscillators (SHNOs). To validate the
technique and demonstrate its robustness, we study SHNOs made from two
different material stacks, NiFe/Pt and W/CoFeB/MgO, and investigate the
influence of both the RF injection power and the laser power on the
measurements, comparing the optical results to conventional electrical
measurements. To demonstrate the key features of direct, non-invasive,
submicron, spatial, and phase-resolved characterization of the SHNO
magnetodynamics, we map out the auto-oscillation magnitude and phase of two
phase-binarized SHNOs used in Ising Machines. This proof-of-concept platform
establishes a strong foundation for further extensions, contributing to the
ongoing development of crucial characterization techniques for emerging
computing technologies based on spintronics devices
