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Gamma-ray bursts (GRBs) have been widely argued to originate from binarycompact object mergers or core collapses of massive stars. Jets from thesesystems may have two components, an inner, narrow sub-jet and an outer, widersub-jet. Such a jet subsequently interacts with its ambient gas, leading to areverse shock (RS) and a forward shock (FS). The magnetic field in the narrowsub-jet is very likely to be mixed by an ordered component and a randomcomponent during the afterglow phase. In this paper, we calculate light curvesand polarization evolution of optical afterglows with this mixed magnetic fieldin the RS region of the narrow sub-jet in a two-component jet model. Theresultant light curve has two peaks: an early peak arises from the narrowsub-jet and a late-time rebrightening is due to the wider sub-jet. We find thepolarization degree (PD) evolution under such a mixed magnetic field confinedin the shock plane is very similar to that under the purely ordered magneticfield condition. The two-dimensional `mixed' magnetic fields confined in theshock plane are essentially the ordered magnetic fields only with differentconfigurations. The position angle (PA) of the two-component jet can changegradually or abruptly by $90^\circ$. In particular, an abrupt $90^\circ$ changeof the PA occurs when the PD changes from its decline phase to rise phase.

Gamma-Ray Burst Optical Afterglows with Two-Component Jets: Polarization Evolution Revisited