  The opto-electronic oscillators (OEOs) hosting self-sustained oscillations by
a time delayed mechanism are of particular interest in long-haul signal
transmission and processing. On the other hand, owing to their unique
tunability and compatibility, magnons - as elementary excitations of spin waves
- are advantageous carriers for coherent signal transduction across different
platforms. In this work, we integrated an opto-electronic oscillator with a
magnonic oscillator consisting of a microwave waveguide and a yttrium iron
garnet sphere. We find that, in the presence of the magnetic sphere, the
oscillator power spectrum exhibits sidebands flanking the fundamental OEO
modes. The measured waveguide transmission reveals anti-crossing gaps, a
hallmark of the coupling between the opto-electronic oscillator modes and the
Walker modes of the sphere. Experimental results are well reproduced by a
coupled-mode theory that accounts for nonlinear magnetostrictive interactions
mediated by the magnetic sphere. Leveraging the advanced fiber-optic
technologies in opto-electronics, this work lays out a new, hybrid platform for
investigating long distance coupling and nonlinearity in coherent magnonic
phenomena.
