Slanted-eye featured forbidden bands in a water channel with undulated sidewalls

Abstract

Resonances induced by structure periodicity can always lead to frequency gaps, which are forbidden bands of propagating waves. Besides the traditional Bragg gaps, non-Bragg gaps have been found in periodic waveguides for years, which have been proved to be caused by the different transverse mode interference. Here, we demonstrate another observable slanted-eye feature of non-Bragg gaps by introducing the sidewall corrugations into a water channel. Based on the multiple scale expansion and group theory, we have derived the dispersion relations for water surface waves propagating in a channel with periodically corrugated sidewalls and introduced the resonance selection rule to identify the characteristics of forbidden bands. It has been experimentally found that the creation and enhancement of Bragg and non-Bragg gaps highly depend on the phase difference between the two sidewall corrugations. Furthermore, the non-Bragg nature forbidden bands are quite different from those of Bragg ones when the duty ratio of corrugations varies from 0 to 1. The non-Bragg gaps have unexpectedly formed a slanted-eye structure rather than the Bragg’s normal eye in spectra, though the both forbidden bands experience a process of producing, enhancement, decaying, and disappearing. The slanted-eye feature confirms the different nature of non-Bragg gaps over Bragg ones and could benefit applications in wave control engineering.