We consider a waveguide composed of two not necessity equal semi-infinite strips (trunks) and a rectangle (resonator) connected by narrow openings in the shared walls. As their diameter vanishes, we construct asymptotics for the scattering coefficients, justifying them by the technique of weighted spaces with detached asymptotics. We establish a criterion for the possibility of observing, at a given frequency, almost complete transmission of waves through both perforated cross-walls. This effect is revealed due to a fine-tuning of the resonator height and the criterion involves an equation relating some geometrical characteristics of the waveguide to the wave numbers in the trunks, while any mirror symmetry turns the criterion trivial.

我们考虑一个波导，它由两个不必要的相等的半无限条带（主体）和一个矩形（谐振器）组成，这些矩形由共享壁中的狭窄开口连接。当它们的直径消失时，我们为散射系数构造渐近线，并通过具有渐近渐近线的加权空间技术来证明它们的合理性。我们建立了在给定频率下观察通过两个穿孔横穿壁的波几乎完全传输的可能性的标准。这种影响是由于谐振器高度的微调而揭示的，该标准涉及一个方程，该方程将波导的某些几何特性与躯干中的波数相关联，而任何镜面对称都使该标准变得微不足道。