## 1 Introduction  
Electromagnetic resonant transmission through one- or two-dimensional slits has been discussed for several decades, and research on extraordinary optical transmission [1; 2; 3; 4] has led to significant physical and practical achievements. In earlier research [5; 6], perforated metallic plates are generally assumed to be perfect electric conductors (PECs), and corresponding resonant transmission characteristics through PEC slits were investigated. However, studies were limited to the microwave or millimeter-wave regimes and did not extend to the terahertz (THz) range. Therefore, it remains important to investigate resonant transmission phenomena through real metallic slits by considering actual permittivities of metals, when the frequency goes beyond the microwave range. To extend transmittance study to the THz range, the geometry of a metal-insulator-metal (MIM) waveguide was adopted, and the resulting modes formed in the MIM waveguide were examined. The resonant transmission phenomena were then systematically analyzed through a real metallic slit in the THz range [7; 8; 9]. Thanks to this fundamental research, resonant transmission phenomena have been investigated at wide THz frequencies by taking into account actual permittivities for various real metals [10; 11] and discussing transmittances through periodic metallic slits [12]. These studies found that transmittance phenomena through metallic slitsare similar to those in PEC cases at lower frequencies. However, large discrepancies are apparent at higher THz frequencies [10]. Slit transmittances in wide THz ranges can usually be solved easily via the finite-difference time-domain (FDTD) or finite element method [13; 14] and etc. [15; 16]. While transmittance results can be obtained directly under those methods, their physical meanings are not easily understood using such \"brute-force\" numerical techniques. Brute-force numerical techniques require substantial numbers of mesh grids, causing corresponding numerical dispersion errors to increase gradually at higher frequencies [14]. By contrast, the mode-matching technique (MMT) does not require grids and, consequently, has no dispersion errors. The MMT also provides physical meanings by obtaining the guide wavelengths of an MIM waveguide, making it easy to understand the resonant transmittance as a function of the metallic plate thickness. Once the eigenvalues for the geometry are obtained herein, then the transmittances as a function of the plate thickness can be resolved easily. Since electromagnetic waves do not penetrate into a PEC, no mode in the PEC region needs to be accounted for. For actual metallic plates, however, modes in the metallic region should be considered, because a tiny amount of each mode permeates into the metallic region due to their finite conductivities. To be precise, modal components in the metallic region (as well as the slit region) should be fully considered when solving transmittances. In addition, for the finite conductivity of a metal, orthogonal properties are not completely satisfied, while the orthogonality for the PEC MIM waveguide is completely fulfilled. Therefore, a validation issue of slit transmittances could be raised for real metallic slits in accordance with orthogonality. In this research, the procedure obtaining the transmittances by the MMT is as follows. First, the modes constituting each region in the free space and an MIM waveguide need to be obtained in advance. To calculate modal eigenvalues in the MIM waveguide, a dispersion equation should be applied [9]. Then, tangential incident, reflected, and transmitted electromagnetic fields are set to be continuous at each junction. The unknowns in the electromagnetic field equations can be solved though the system of equations, and the reflection and transmission coefficients can be determined. The overall reflected and transmitted electromagnetic fields of a single-slit geometry can be obtained by using multiregion problems. The entire computing procedure is listed and explained in detail in [10].