Interactions between the first mode and the second Bragg gap in a cylindrical waveguide with undulated walls

Bragg resonances caused by the same transverse modes can always play a major role in periodic waveguides when the period is larger than the average radius. Because of higher-order mode cutoffs, the related Bragg gaps can be identified as interactions between different spatial harmonics of the fundamental mode, and the first Bragg gaps are more intensive than the higher ones. When we alter the parameters of the periodic waveguide, especially, decrease the period, the first transverse mode can be involved in Bragg gaps. Here, we demonstrate a direct mode-stopband interaction between the first mode and the second Bragg gap, that an extraordinary passband arises in the original second Bragg gap and splits the bandgap into two. Furthermore, the extraordinary passband is mainly composed of a pure first mode, which effectively suppresses the transmission of the fundamental one. We have also investigated the influence of wall profiles on the transmission and mode purity, and have found that the defined shape factor of wall profiles is proportionally related to the width of both pass and stop bands. The results could benefit not only the understanding of wave phenomena but also the applications in mode generators, filters, and so on.