In most generality, Maxwell's field equations are given as dH=J and dF=0, where H (field excitation) and F (field strength) are 2-forms and J (charge) is a 3-form, together with a constitutive law H=#(F) relating H and F. I will motivate these equations, following roughly the axiomatic approach of Hehl and Obukhov (among others). Setting #=* (Hodge star operator) one obtains Maxwell's equations in vacuum, but more general choices describing inhomogeneities, anisotropies, dispersion, non-linearities and non-local effects are possible (e.g., birefringent media, Born—Infeld theory, Bopp—Podolsky theory, ...). In my talk, I will consider only local, linear, non-dispersive constitutive laws; this includes in particular birefringent media. Under these assumptions, I will study solutions of the field equations by deriving propagators for the equation d#dA=J.