  The geometry of twisted null geodesic congruences in gravitational plane wave
spacetimes is explored, with special focus on homogeneous plane waves. The role
of twist in the relation of the Rosen coordinates adapted to a null congruence
with the fundamental Brinkmann coordinates is explained and a generalised form
of the Rosen metric describing a gravitational plane wave is derived. The
Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are
described in both Brinkmann and twisted Rosen form and used to demonstrate the
coset space structure of HPWs. The van Vleck-Morette determinant for twisted
congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted
null congruences of the Ozsvath-Schucking,`anti-Mach' plane wave are
investigated in detail. These developments provide the necessary geometric
toolkit for future investigations of the role of twist in loop effects in
quantum field theory in curved spacetime, where gravitational plane waves arise
generically as Penrose limits; in string theory, where they are important as
string backgrounds; and potentially in the detection of gravitational waves in
astronomy.
