  The $PT$-symmetric optical grating with index profile $e^{i\beta z}$ has been
shown to have the interesting property of being essentially invisible for light
incident from one side, while possessing greatly enhanced reflection at a
particular wavelength for light incident from the other side. We extend a
previous analysis of this grating to obtain an analytic solution for the case
when the grating is embedded on a substrate, with different refractive indices
on either side. We also generalize the previous case of normal incidence to
incidence at an arbitrary angle. In that case the enhanced reflection occurs at
a particular angle of incidence for a given wavelength. Finally we discuss how
the grating may be used to give lasing.
