A split step approach for the 3-D Maxwellʹs equations

Split-step procedures have previously been used successfully in a number of situations, e.g. for Hamiltonian systems, such as certain nonlinear wave equations. In this study, we note that one particular way to write the 3-D Maxwellʹs equations separates these into two parts, requiring only the solution of six uncoupled 1-D wave equations. The approach allows arbitrary orders of accuracy in both time and space, and features in many cases unconditional stability.