  We obtain a new family of exact vacuum solutions to quadratic gravity that
describe pp-waves with two-dimensional wave surfaces that can have any
prescribed constant curvature. When the wave surfaces are flat we recover the
Peres waves obtained by Madsen, a subset of which forms precisely the vacuum
pp-waves of general relativity. If, on the other hand, the wave surfaces have
non-vanishing constant curvature then all our solutions are non-Einstein (i.e.
they do not solve Einstein's equations in vacuum, with or without cosmological
constant) and we find that the curvature is linearly related to the value of
the cosmological constant. We show that the vacuum field equations reduce to a
simple linear biharmonic equation on the curved wave surfaces, and as
consequence, the general solution can be written down. We also provide some
simple explicit examples.
