Focusing of Spin Waves in YIG Thin Films

We study the focusing of bulk and surface spin waves in thin Yttrium iron garnet (YIG) films by solving the implicit dispersion relation obtained from the magnetostatic Maxwell equations. We then obtain constant frequency curves in k-space for the bulk and the surface modes. The focusing pattern is obtained from the slowness surface by finding the normal to the slowness surface and then evaluating the curvature at each point on the surface. It is found that the bulk modes are focused in four to eight distinct directions depending on the frequency and the applied magnetic field. The surface waves are not focused as strongly as the bulk waves. Furthermore, the focusing direction is tunable with the frequency and applied field