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We investigate a time-harmonic wave problem in a waveguide. We work at lowfrequency so that only one mode can propagate. It is known that the scatteringmatrix exhibits a rapid variation for real frequencies in a vicinity of acomplex resonance located close to the real axis. This is the so-called Fanoresonance phenomenon. And when the geometry presents certain properties ofsymmetry, there are two different real frequencies such that we have either$R=0$ or $T=0$, where $R$ and $T$ denote the reflection and transmissioncoefficients. In this work, we prove that without the assumption of symmetry ofthe geometry, quite surprisingly, there is always one real frequency for whichwe have $T=0$. In this situation, all the energy sent in the waveguide isbackscattered. However in general, we do not have $R=0$ in the process. Weprovide numerical results to illustrate our theorems.

Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides