Microwave band gap and cavity mode in spoof-insulator-spoof waveguide with multiscale structured surface

We propose a multiscale spoof-insulator-spoof (SIS) waveguide by introducing periodic geometry modulation in the wavelength scale to a SIS waveguide made of a perfect electric conductor. The MSIS consists of multiple SIS subcells. The dispersion relationship of the fundamental guided mode of the spoof surface plasmon polaritons (SSPPs) is studied analytically within the small gap approximation. It is shown that the multiscale SIS possesses microwave band gap (MBG) due to the Bragg scattering. The 'gap maps' in the design parameter space are provided. We demonstrate that the geometry of the subcells can efficiently adjust the effective refraction index of the elementary SIS and therefore further control the width and the position of the MBG. The results are in good agreement with numerical calculations by the finite element method (FEM). For finite-sized MSIS of given geometry in the millimeter scale, FEM calculations show that the first-order symmetric SSPP mode has zero transmission in the MBG within frequency range from 4.29 to 5.1 GHz. A cavity mode is observed inside the gap at 4.58 GHz, which comes from a designer 'point defect' in the multiscale SIS waveguide. Furthermore, ultrathin MSIS waveguides are shown to have both symmetric and antisymmetric modes with their own MBGs, respectively. The deep-subwavelength confinement and the great degree of control of the propagation of SSPPs in such structures promise potential applications in miniaturized microwave device.