  We give a non-perturbative construction of a distinguished state for the
quantized Dirac field in Minkowski space in the presence of a time-dependent
external field of the form of a plane electromagnetic wave. By explicit
computation of the fermionic signature operator, it is shown that the Dirac
operator has the strong mass oscillation property. We prove that the resulting
fermionic projector state is a Hadamard state.
