Wave propagation in a three-dimensional doubly periodic parallel plate waveguide. (English) Zbl 0605.73024
The stopband structure of a three-dimensional waveguide with doubly periodic corrugations is studied. A preliminary investigation using straightforward perturbation theory gives a formula for the resonant frequencies whereas the main part of the paper is devoted to the null- field approach. In the numerical examples the waveguide is assumed to be hard-walled with symmetric, antisymmetric or one-sided corrugations which are, moreover, doubly sinusoidal. The interaction pattern and the stopband widths are determined for the lowest modes. The resonances are found to be of stopband or crossover type depending on the relative directions of propagation of the resonating modes and it appears that geometrical symmetries of the boundaries suppress well-defined sets of resonances. There is also a considerable angular dependence which affects the positions of the resonances as well as the stopband widths. Finally, the field pattern inside the waveguide is obtained via the null-field integral representation.
MSC:
| 74J99 | Waves in solid mechanics |
Keywords:
T-matrix; stopband structure; three-dimensional waveguide; doubly periodic corrugations; straightforward perturbation theory; resonant frequencies; null-field approach; hard-walled; symmetric; antisymmetric; one-sided corrugations; doubly sinusoidal; interaction pattern; stopband widths; lowest modesReferences:
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