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The Green dyadics for closed layered media, i.e., layered media bounded by a perfectly conducting plate at the bottom and top of the structure, can be expanded in a discrete surface wave series. For open layered media with semi-infinite layers at the top and/or bottom of the structure, the discrete series needs to be complemented by a branch-cut integral of space waves. In this paper, we present a technique to circumvent this branch-cut integral by truncating the semi-infinite layers with a perfectly matched layer (PML) that is backed by a perfect electric conductor (PEC). It is demonstrated that in this way it is possible to obtain an accurate series or closed-form representation for the Green dyadic of the open layered medium. The series allows a very efficient calculation and storage of the Green dyadic if it is needed for multiple observation and or excitation points. Very close to the source the series loses efficiency. It is shown that the determination of the surface waves in the PML truncated layered medium has the same complexity as the determination of the surface waves in a PEC truncated layered medium without a PML.