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The finite-difference time-domain (FDTD) method incorporating an equivalent resonant cavity model is presented for the modeling and analysis of guided-wave propagation characteristics of complex periodic structures. By transforming electromagnetic field variables into a new set of periodic variables, which can also be resolved from the Maxwell's equations, one can convert a periodic guided-wave problem into an equivalent resonator problem. Thus, the FDTD method used for a resonant cavity problem can be adopted to simulate periodic guided-wave structures. In addition, the proposed FDTD algorithm can be extended to model lossy periodic propagation problems. In this study, the substrate integrated nonradiative dielectric waveguide, which is a special type of periodic guided-wave structure subject to a potential leakage loss due to its periodic gaps, is investigated as a showcase. The proposed method is first validated and is then used to analyze the guided-wave characteristics of substrate integrated nonradiative dielectric waveguides. It is shown that the substrate integrated nonradiative dielectric waveguide structure, which can easily be fabricated in planar form, has a well-behaved propagation property suitable for high-performance millimeter-wave circuit design.