The Stokes parameters xi1 and xi2 for one of the produced photons, whi
ch characterize the T-odd (and P-odd) linear polarization and P-odd ci
rcular polarization in the B(s(d)) --> gammagamma decay are calculated
. We show that these parameters are very sensitive to the t-quark mass
for the B(s) --> gammagamma decay and also to the sign and the absolu
te value of the ratio V(ub)/V(td) of the elements of Kobayashi-Maskawa
matrix for the B(d) --> 2gamma decay, in the framework of the Standar
d Model. It is further shown that in the two Higgs doublet model, ther
e is some region of parameters (namely the mass of the charged physica
l Higgs and vacuum expectation values) where the predictions for the p
olarization effects of the photons differ from the Standard Model pred
iction considerably.