We consider an infinite acoustic waveguide with a local perturbation. It is well-known that they may exist non trivial solutions of the homogeneous equations which are square integrable, called trapped modes. Associated frequencies correspond to eigenvalues of the Laplacian which are embedded in the essential spectrum. They can be computed as the real part of the complex spectrum of a non-self-adjoint eigenvalue problem, defined by using the so-called Perfectly Matched Layers (which consist in a complex dilation in the infinite direction). We show here that it is possible, by modifying in particular the parameters of the Perfectly Matched Layers, to define new complex spectra which include, in addition to trapped modes, frequencies where the perturbation is, in some sense, invisible to one incident wave.