  Metaplectic geometrical optics (MGO) is a recently developed ray-tracing
framework to accurately compute the wavefield behavior near a caustic (turning
point or focal point), where traditional ray-tracing breaks down. However, MGO
has thus far been restricted to having real-valued wavevectors. This is
disadvantageous because often upon crossing a caustic from the `illuminated'
region to the `shadow' region, two real-valued rays coalesce into one
complex-valued ray corresponding to the transition from propagating to
evanescent behavior. One can distinguish caustics as having either `illuminated
shadows' or `proper shadows' -- the former corresponds to when the shadow still
contains real-valued rays (albeit in a fewer quantity than in the illuminated
region), while the latter corresponds to when the shadow contains no
real-valued rays. Here, by means of examples, we show how MGO can be used to
model both types of shadows. First, for illuminated shadows we show that MGO
can actually be used `as is', provided a corrected quadrature-angle bias is
used compared to that proposed in the original references. This is then
implemented and demonstrated in a recently developed MGO ray-tracing code.
Second, we show that for proper shadows, the MGO formalism can still be used if
the symplectic rotation matrix that removes caustics along rays is allowed to
be complex-valued. In both cases, strong agreement is seen between the MGO and
the exact solution, demonstrating the potential of MGO for improving the
predictive capability of ray-tracing codes and laying the foundations for
modeling more complicated evanescent phenomena such as tunnelling with MGO.
