  This work continues the development of the raytracing method of [1] for
computing the scattered fields from metasurfaces characterized by locally
periodic reflection and transmission coefficients. In this work, instead of
describing the metasurface in terms of scattering coefficients that depend on
the incidence direction, its scattering behavior is characterized by the
surface susceptibility tensors that appear in the generalized sheet transition
conditions (GSTCs). As the latter quantities are constitutive parameters, they
do not depend on the incident field and thus enable a more compact and
physically motivated description of the surface. The locally periodic
susceptibility profile is expanded into a Fourier series, and the GSTCs are
rewritten in a form that enables them to be numerically solved for in terms of
the reflected and transmitted surface fields. The scattered field at arbitrary
detector locations is constructed by evaluating critical-point contributions of
the first and second kinds using a Forward Ray Tracing (FRT) scheme. The
accuracy of the resulting framework has been verified with an Integral Equation
based Boundary Element Method (BEM)-GSTC full-wave solver for a variety of
examples such as a periodically modulated metasurface, a metasurface diffuser
and a beam collimator.
