  This paper introduces a general technique for inter-mapping the complex
spatial frequency (or propagation constant) $\gamma=\alpha+j\beta$ and the
temporal frequency $\omega = \omega_\text{r}+j\omega_\text{i}$ of an arbitrary
electromagnetic structure. This technique, based on the analytic property of
complex functions describing physical phenomena, invokes the analytic
continuity theorem to assert the unicity of the mapping function, and find this
function from known data within a restricted domain of its analycity by
curve-fitting to a generic polynomial expansion. It is not only applicable to
canonical problems admitting an analytical solution, but to \emph{any}
problems, from eigen-mode or driven-mode full-wave simulation results. The
proposed technique is demonstrated for several systems, namely an unbounded
lossy medium, a dielectric-filled rectangular waveguide, a periodically-loaded
transmission line, a one-dimensional photonic crystal and a series-fed patch
(SFP) leaky-wave antenna (LWA), and it is validated either by analytical
results or by full-wave simulated results.
