Einstein-Maxwell fields with vanishing higher-order corrections

We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(\mathit{g},\mathit{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of Lagrangian theories including both modified gravities and (possibly non-minimally coupled) modified electrodynamics. Specifically, both $\mathit{g}$ and $\mathit{F}$ are fields with vanishing scalar invariants and further satisfy two simple tensorial conditions. They describe a family of gravitational and electromagnetic plane-fronted waves of the Kundt class and of Weyl type III (or more special). The local form of $(\mathit{g},\mathit{F})$ and a few examples are also provided.