Prospects for multiwavelength polarization observations of GRB afterglows and the case GRB 030329

We explore the prospects for simultaneous, broad-band, multiwavelength polarimetric observations of GRB afterglows. We focus on the role of cosmic dust in GRB host galaxies on the observed percentage polarization of afterglows in the optical/near-infrared bands as a function of redshift. Our driving point is the afterglow of GRB 030329, for which we obtained polarimetric data in the R band and K band simultaneously about 1.5 days after the burst. We argue that polarimetric observations can be very sensitive to dust in a GRB host, because dust can render the polarization of an afterglow wavelength-dependent. We discuss the consequences for the interpretation of observational data and emphasize the important role of very early polarimetric follow-up observations in all bands, when afterglows are still bright, to study the physical properties of dust and magnetic fields in high-z galaxies.