  For scattering problems of time-harmonic waves, the boundary integral
equation (BIE) methods are highly competitive, since they are formulated on
lower-dimension boundaries or interfaces, and can automatically satisfy
outgoing radiation conditions. For scattering problems in a layered medium,
standard BIE methods based on the Green's function of the background medium
must evaluate the expensive Sommefeld integrals. Alternative BIE methods based
on the free-space Green's function give rise to integral equations on unbounded
interfaces which are not easy to truncate, since the wave fields on these
interfaces decay very slowly. We develop a BIE method based on the perfectly
matched layer (PML) technique. The PMLs are widely used to suppress outgoing
waves in numerical methods that directly discretize the physical space. Our
PML-based BIE method uses the Green's function of the PML-transformed free
space to define the boundary integral operators. The method is efficient, since
the Green's function of the PML-transformed free space is easy to evaluate and
the PMLs are very effective in truncating the unbounded interfaces. Numerical
examples are presented to validate our method and demonstrate its accuracy.
