Numerical analysis of frequency characteristics of transmitted waves by random waveguide

The frequency characteristics of the transmitted waves by the two-dimensional single-mode waveguide with a slightly rough boundary are investigated in detail. Two realizations of the waveguide with random rough boundaries are considered. Since the boundary element method based on the guided-mode extracted integral equation is employed, the boundary condition on the random rough boundary is accurately satisfied. It is found that the strong resonances with high Q-factor are created close to the cutoff frequency of the second-mode in the waveguide and they cause the small transmission (high reflection). It is shown that the Q-factors of these resonances increase with a decrease in the rms of the rough boundaries. It is shown that the rough boundary whose rms is about several thousand times smaller than the wavelength creates a strong enhanced electric field whose intensity is about several hundred times larger than that of the incident mode.