Evolution of wave dispersion in periodic structures with increasing amplitude of corrugation

Computer simulations using the electromagnetic code HFSS show that increasing the amplitude of the periodic corrugation of slow wave structures (SWSs) leads to expanding stopbands and decreasing the maximal frequency in the first passband of a wave. Results of further increasing the amplitude decrease the cut-off frequency and result in the appearance of a backward wave in the phase interval of hd = (0 - π) (here d is the period of corrugation and h is the wavenumber). It is pertinent to note that in this case the usual interpretation of stopbands and passbands as bands of Bragg reflection or Bragg mode conversion becomes incorrect. It is also incorrect to interpret passbands and cut-off frequencies as the minimal frequencies for wave propagation. We found that backward waves appear not only in periodic systems with small period with respect to the wavelength as in metamaterial SWSs, but also in systems with large period that we demonstrate for sinusoidal and rectangular profiles of periodic corrugations. Above all, we found that cut-off frequencies for TM modes (frequencies that correspond to phases (2n+1)π, where n is the number of positive and negative spatial harmonics including n=0 on the dispersion diagram) decrease with increasing amplitude of corrugation, which is also a typical characteristic of metamaterial SWSs.