(Abridged) We report on observations of the optical and NIR afterglow of GRB020405. Ground-based optical observations started about 1 day after the GRB and spanned a period of ~10 days; archival HST data extended the coverage up to 70 days after the GRB. We report the first detection of the afterglow in NIR bands. The detection of emission lines in the optical spectrum indicates that the GRB is located at z = 0.691. Absorptions are also detected at z = 0.691 and at z = 0.472. The latter system is likely caused by clouds in a galaxy located 2 arcsec southwest of the GRB host. Hence, for the first time, the galaxy responsible for an intervening absorption system in the spectrum of a GRB afterglow is identified. Optical and NIR photometry indicates that the decay in all bands follows a single power law of index alpha = 1.54. The late-epoch VLT and HST points lie above the extrapolation of this power law, so that a plateau is apparent in the VRIJ light curves at 10-20 days after the GRB. The light curves at epochs later than day ~20 after the GRB are consistent with a power-law decay with index alphaprime = 1.85. We suggest that this deviation can be modeled with a SN having the same temporal profile as SN2002ap, but 1.3 mag brighter at peak, and located at the GRB redshift. Alternatively, a shock re-energization may be responsible for the rebrightening. A polarimetric R-band measurement shows that the afterglow is polarized, with P = 1.5 % and theta = 172 degrees. Optical-NIR spectral flux distributions show a change of slope across the J band which we interpret as due to the presence of nu_c. The analysis of the multiwavelength spectrum within the fireball model suggests that a population of relativistic electrons produces the optical-NIR emission via synchrotron in an adiabatically expanding blastwave, and the X-rays via IC.
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