  In anisotropic media, the standard perfectly matched layer (PML) technique
suffers irrevocable instability in terminating the unbounded problem domains.
It remains an open question whether a stable PML-like absorbing boundary
condition exists. For wave scattering in a layered orthotropic medium, this
question is affirmatively answered for the first time in this paper. In each
orthotropic medium, the permittivity tensor uniquely determines a change of
coordinates, that transforms the governing anisotropic Helmholtz equation into
an isotropic Helmholtz equation in the new coordinate system. This leads us to
propose a novel Sommerfeld radiation condition (SRC) to rigorously characterize
outgoing waves in the layered orthotropic medium. Naturally, the SRC motivates
a regionalized PML (RPML) to truncate the scattering problem, in the sense that
a standard PML is set up in the new coordinate system in each orthotropic
region. It is revealed that the RPML is unconditionally stable compared with
the unstable uniaxial PML. A high-accuracy boundary integral equation (BIE)
method is developed to solve the resulting boundary value problem. Numerical
experiments are carried out to validate the stability of the RPML and the
accuracy of the BIE method, showing exponentially decaying truncation errors as
the RPML parameters increase.
