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A compact two-dimensional (2D) finite-difference time-domain (FDTD) method is proposed to analyze the propagation characteristics of arbitrary guiding structures. By transforming electromagnetic field variables into new forms of periodic variables, which also can be resolved from the Maxwell's equations, one can convert the 2D transmission line problem into an equivalent resonator problem based on the idea of translating the transmission distance-related attenuation part of complex propagation constant into a time-dependent damping factor. As a result, the FDTD method for resonator can be made use of to simulate the lossy guiding structures. Attenuation constants can be obtained by means of the quality factors of equivalent resonators. It means that some leaky wave antennas can also be analyzed by using this method. Numerical simulations show that the proposed method can quickly and accurately extract the phase constants and attenuation constants of lossy guiding structures.