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Linear polarization measurements in the optical band show polarizationdegrees of a few percent at late times. Recently, polarization at sub-percentlevel was also detected in radio by ALMA, opening the window formulti-wavelength polarimetry and stressing the importance of properly modelingpolarization in GRB afterglows across the EM spectrum. We introduce a numericaltool that can calculate the polarization from relativistically moving surfacesby discretizing them to small patches of uniform magnetic field, calculatingthe polarized emission from each cell assuming synchrotron radiation andsumming it to obtain the total degree of polarization. We apply this tool toafterglow shocks with random magnetic fields confined to the shock plane,considering electron radiative cooling. We analyze the observed polarizationcurves in several wavelengths above the cooling frequency and below the minimalsynchrotron frequency and point to the characteristic differences between them.We present a method to constrain the jet opening angle and the viewing anglewithin the context of our model. Applying it to GRB 021004 we obtain angles of10 and 8 degrees respectively and conclude that a non-negligible component ofradial magnetic field is required to explain the 1% polarization level observed3.5 days after the burst.

Modeling the Linear Polarization of GRB Afterglows Across the Electromagnetic Spectrum