Existence of guided waves due to a lineic perturbation of a 3D periodic medium (Q2407752)

In this paper, the authors are concerned about a three dimensional (3D) structure that allows the existence of guided waves. This structure is a perturbation of a 3D grating of equal spaced parallel pipes (with constant cross section) oriented along the three orthogonal directions, i.e., it is \(a_j\)-periodic with respect to \(x_j, j=1,2,3\). The perturbed structure is still \(a_3\)-periodic with respect to \(x_3\), but has no periodicity with respect to \(x_1\) and \(x_2\). The guided modes satisfy the homogeneous Neumann boundary conditions on the domain and propagate along the defect pipe in the \(x_3\) direction.