  Using Newman-Penrose formalism in tetrad and spinor notation, we perform
separation of variables in the wave equations for massless fields of various
spins s=1/2, 1, 3/2, 2 on the background of exact plane-fronted gravitational
wave metrics. Then, applying Wald's method of adjoint operators, we derive
equations for Debye potentials generating these fields and find inverse
projection operators expressing multicomponet fields in terms of scalar
potentials. For a number of shock wave backgrounds, as a special case of
non-vacuum pp-waves, the exact solutions for Debye potentials are constructed
explicitly. The possibility of generalization to the case of massive fields, in
particular, construction of exact solutions to the Dirac and Proca equations
are discussed. These results can be used in supergravity models on pp-wave
backgrounds.
