Fundamental characteristics of a light-guiding metal line are revealed and discussed through the eigenmode analysis using the three-dimensional (3-D) imaginary-distance beam-propagation method (ID-BPM) based on the alternating-direction implicit scheme. For the present ID-BPM, the multiplication factor of the eigenmode is derived and the paper described how the present method works in the ID procedure. An efficient absorbing boundary condition is described,which is suitable for the eigenmode analysis using the ID-BPM. After confirming the effectiveness of the present method, the characteristics of the light-guiding line composed of a metal (Au) with a finite width and thickness on a substrate (SiO2) are investigated. Numerical results for a metal thickness of 0.2 µm show that the effective index and the propagation loss decrease as the metal width is reduced. It is shown that not only the higher order modes but also the first mode has a cutoff metal width. Near the cutoff width, the propagation loss of the first mode (~ or = 10 dB/mm at a wavelength of 1.55 µm) is less than those of the higher order modes. Finally, in order to reduce the propagation loss, a dielectric core was added under the metal line.
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