  Exact models of primordial gravitational waves in the Bianchi type III
universe are constructed on the basis of the quadratic theory of gravity with a
scalar field and pure radiation in Shapovalov wave spacetimes of type II
(subtype 2). Exact solutions of field equations and scalar equation are
obtained. The characteristics of pure radiation are determined. An explicit
form of the scalar field functions included in the Lagrangian of the considered
quadratic theory of gravity is found. Trajectories of propagation of light rays
in the considered gravitational-wave models are obtained.
