  Strong-field gravitational plane waves are often represented in either the
Rosen or Brinkmann forms. These forms are related by a coordinate
transformation, so they should describe essentially the same physics, but the
two forms treat polarization states quite differently. Both deal well with
linear polarizations, but there is a qualitative difference in the way they
deal with circular, elliptic, and more general polarization states. In this
article we will describe a general algorithm for constructing arbitrary
polarization states in the Rosen form.
