Modal Analysis of Point and Discretized Continuous Spectra for Metal-Insulator-Metal Waveguides in the Terahertz Region

Eigenvalue distributions for a periodic metal-insulator-metal waveguide, classified into the point spectrum and the discretized continuous spectrum (DCS), are investigated as functions of frequencies, gap widths, and periods. Muller's method is suggested for solving exact eigenvalues, and we propose the scheme for finding proper initial values in the Muller's method by considering only Re(er) in the dispersion equation. We then find that anti-crossing behavior, repulsive effect between the point spectrum and the DCS, becomes stronger when the real parts of the roots in the point spectrum have smaller values. Finally, we examine the transmittances of a single subwavelength slit for real metals using the mode matching technique. The transmittances in real metals similarly follow those of the perfect electric conductor (PEC) at low frequencies, while the patterns at higher frequencies begin to differ from the PEC.