The design of high-order, finite-difference, time-domain numerical solvers for Maxwell's equations is presented herein. Particularly, high-order spatial discrete operators are designed using Fourier techniques in κ-space; the desired accuracy order is verified both analytically and numerically. As an example of the power of the method, an eighth-order super compact operator is designed on a three-point stencil. To advance the equations the fourth-order Runge-Kutta integrator is employed. The schemes are quantified in terms of their dispersion and dissipation error characteristics and the corresponding Courant number is established using standard Fourier analysis. Case studies involving a one-dimensional cavity and the rectangular waveguide are presented. For these case studies, specific boundary operators are introduced, and the time-stability of each scheme is cataloged. Moreover, the data associated with these case studies demonstrate the key features of the numerical schemes: The low accumulation of phase and dissipation type errors.