Contribution of leaky modes in the modal analysis of unbounded problems with perfectly matched layers

The modal analysis of wave problems of unbounded type involves a continuous sum of radiation modes. This continuum is difficult to handle mathematically and physically. It can be approximated by a discrete set of leaky modes, corresponding to improper modes growing to infinity. Perfectly matched layers (PMLs) have been widely applied in numerical methods to efficiently simulate infinite media, most often without considering a modal approach. This letter aims to bring insight into the modal basis computed with PMLs. PMLs actually enable to reveal of the contribution of leaky modes by redefining the continua (two for elastodynamics), discretized after PML truncation.