Radiation propagating over cosmological distances can probe light weakly interacting pseudoscalar (or scalar) particles. The existence of a spin-0 field changes the dynamical symmetries of electrodynamics. It predicts spontaneous generation of polarization of electromagnetic waves due to mode mixing in the presence of background magnetic field. We illustrate this by calculations of propagation in a uniform medium, as well as in a slowly varying background medium, and finally with resonant mixing. Highly complicated correlations between different Stokes parameters are predicted, depending on the parameter regimes. The polarization of propagating waves shows interesting and complex dependence on frequency, the distance of propagation, coupling constants and parameters of the background medium such as the plasma density and the magnetic field strength. For the first time we study the resonant mixing of electromagnetic waves with the scalar field, which occurs when the background plasma frequency becomes equal to the mass of the scalar field at some point along the path. Dynamical effects are found to be considerably enhanced in this case. We also formulate the condition under which the adiabatic approximation can be used consistently, and find caveats about comparing different frequency regimes.