  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.

Astrophysics