Magnetostatic modes and wave equation

We propose a mathematical apparatus which converts magnetostatic (Walker) equations into a wave equation by introducing a specific definition of the ``magnetic refractive index.'' Its value can be manipulated by adjusting spatial distribution of the saturation magnetization or the bias magnetic field. We demonstrate that the latter can be accomplished efficiently by utilizing the bias field produced by magnetization patterns recorded onto a neighboring hard magnetic film using the current magnetic storage technology and derive a specific algorithm by which one can convert a near arbitrary two-dimensional optical device into its magnetic analogue. The wave equation formalism opens the possibility to adopt a number of optics-like analytical and numerical techniques, including those applicable to scattering, near field, diffraction and geometric (Eikonal equation) optics, as well as a generic finite difference time domain (FDTD) algorithm.