This chapter presents an efficient analysis of TM-pass/TE-stop THz waveguide polarizers using a hybrid-implicit-explicit finite-difference time-domain (HIE-FDTD) method. A two-dimensional HIE-FDTD method using the trapezoidal recursive convolution (TRC) technique is newly developed to analyze waveguide polarizers. The maximum error of the guided mode power is 0.81%, and the computation time can be reduced to about 36% of that of the traditional explicit FDTD method when the ratio of the spatial sampling widths in the two directions is 1:16. The TE mode propagation is also calculated and the extinction ratio characteristics of 2-D polarizers are clarified. In addition, a thee-dimensional HIE-FDTD method is developed to analyze practical 3-D polarizers. The computation time can be reduced to about 22% of that of the traditional explicit FDTD method when the ratio of the spatial sampling widths in the three directions is 1:20:20. It is shown that an extinction ratio of more than 25 dB is obtained with a polarizer length of 126  \(\upmu \) m. The necessity of the TRC technique for analysis using the HIE-FDTD method with a large CFLN is also discussed. By comparing the 2-D and 3-D results, it is also shown that 3-D analysis is necessary for the study of practical polarizers. The final study is another polarizer with InAs sidewalls placed outside the dielectric buffer layers on either side of the core. The TE waves generate surface plasmons and become lossy, so the field is attenuated and only TM modes are guided. Also consider the case where the dielectric buffer layer is chosen to be hollow. When the buffer is hollow, it becomes a waveguide for TE and TM mode transmission, but when water is injected into the buffer, the waveguide is found to act as a TE stop/TM pass polarizer.