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We explore the prospects for simultaneous, broad-band, multiwavelengthpolarimetric observations of GRB afterglows. We focus on the role of cosmicdust in GRB host galaxies on the observed percentage polarization of afterglowsin the optical/near-infrared bands as a function of redshift. Our driving pointis the afterglow of GRB 030329, for which we obtained polarimetric data in theR band and K band simultaneously about 1.5 days after the burst. We argue thatpolarimetric observations can be very sensitive to dust in a GRB host, becausedust can render the polarization of an afterglow wavelength-dependent. Wediscuss the consequences for the interpretation of observational data andemphasize the important role of very early polarimetric follow-up observationsin all bands, when afterglows are still bright, to study the physicalproperties of dust and magnetic fields in high-z galaxies.Comment: accepted for publication in Astronomy & Astrophysic

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