In 1985, DePourcq [209] used the FDTD method to analyze various 3-D waveguide devices. A year later, Choi and Hoefer [210] applied the FDTD method to model a finline cavity and an anisotropic microstrip. Olivier and McNamara [211,212,213,214,215] have used the FDTD method to study discontinuities in homogeneous dispersive waveguides, edge slots, an H-plane T-junction, and coupling between waveguide apertures. Bi et al. [216] and Navarro et al. [217,35] have also applied the FDTD method to H-plane waveguide discontinuities. Navarro and co-workers [218,219,220] have also investigated rectangular, circular, and T-junctions in square coaxial waveguides, and narrow-wall multiple slot couplers.
In 1990, Chu and Chaudhuri [221] investigated dielectric waveguide problems while in 1991 Jarem [222] presented FDTD results for a probe-sleeve fed rectangular waveguide. Alinikula and Kunz [223] investigated waveguide aperture coupling using the FDTD method. In 1992, Van Hese and De Zutter [224] modeled coaxial waveguide structures with discontinuities, using the FDTD method in both Cartesian and cylindrical coordinates. Feng and Junmei [225] analyzed a dielectric post in a rectangular waveguide, while Dib and Katehi [226] analyzed the transition from a rectangular waveguide to a shielded dielectric image guide. In 1994, Kraut et al. [227] analyzed edge slots in waveguides. Meanwhile, ferrite loaded waveguides have been investigated by Pereda and co-workers [228,229,230,231]. Okoniewski and Okoniewska [232] have recently proposed an alternative FDTD algorithm for ferrites, and have successfully applied it to ferrite-loaded waveguides.
In the early 1990's, Navarro et al. [233,234] used the FDTD method to obtain results for cylindrical homogeneous and dielectrically loaded resonators. Shen et al. [235] and Pereda et al. [146] have extended the FDTD analysis to open cylindrical dielectric resonators. Wang et al. [236] also studied the Q-factors of resonators using the FDTD method.
There has also been active research in reducing the computations needed to analyze 3-D guided-wave devices. In 1992 Xiao et al. [237] presented a new compact FDTD method for analyzing guided-wave structures. By introducing a phase shift along the direction of propagation, the authors reduced the 3-D mesh to 2-D. Independently, Asi and Shafai [238,239] and Brankovic et al. [240] introduced similar methods to reduce 3-D guided wave problems to 2-D. In 1993, Cangellaris [241] presented a stability and dispersion analysis of Asi and Shafai's 2-D compact FDTD method. Noting that the above algorithms introduce complex numbers into an otherwise real process, Okoniewski [242] presented an alternate compact 2-D FDTD method, using a vector wave equation approach. By doing this, Okoniewski retained only real variables in the FDTD algorithm. Krupezevic et al. [243] have also developed a vector wave equation approach to investigate various waveguide structures. Xiao and Vahldieck [244] introduced a variable transformation to their original compact FDTD method so that it contained only real variables. The amount of computation needed to analyze waveguide-like structures has also been reduced by using a non-orthogonal FDTD method [74,75,76,77].
Techniques to improve the absorbing boundary conditions used in guided-wave structures was discussed in Sec. iii.