  We propose a multiscale spoof-insulator-spoof (SIS) waveguide by introducing
periodic geometry modulation in the wavelength scale to a SIS waveguide made of
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 GHz 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 to control the
propagation of SSPPs in such structures promise potential applications in
miniaturized microwave device.
