We investigate a time-harmonic wave problem in a waveguide. We work at low frequency so that only one mode can propagate. It is known that the scattering matrix exhibits a rapid variation for real frequencies in a vicinity of a complex resonance located close to the real axis. This is the so-called Fano resonance phenomenon. And when the geometry presents certain properties of symmetry, there are two different real frequencies such that we have either \(R=0\) or \(T=0\), where R and T denote the reflection and transmission coefficients. In this work, we prove that without the assumption of symmetry of the geometry, quite surprisingly, there is always one real frequency for which we have \(T=0\). In this situation, all the energy sent in the waveguide is backscattered. However in general, we do not have \(R=0\) in the process. We provide numerical results to illustrate our theorems.

我们研究波导中的时谐波问题。我们以低频工作，因此只能传播一种模式。已知散射矩阵在靠近实轴的复杂共振附近表现出对于真实频率的快速变化。这就是所谓的法诺共振现象。并且当几何图形呈现某些对称性时，存在两个不同的实际频率，使得我们具有\（R = 0 \）或\（T = 0 \），其中R和T表示反射系数和透射系数。在这项工作中，我们证明了在没有几何对称性假设的情况下，非常令人惊讶的是，总有一个真实频率具有\（T = 0 \）。在这种情况下，在波导中发送的所有能量都被反向散射。但是，通常，我们在过程中没有\（R = 0 \）。我们提供数值结果来说明我们的定理。