We analyze the polarization properties of photons which are produced i
n the unpolarized b-quark decay, b --> syg. Using the structure functi
on formalism we carry out a general analysis of the polarization chara
cteristics of y in terms of the standard Stokes parameters. The expres
sions for five independent structure functions are constructed in term
s of the weak magnetic transition form factors of the vertices b -->,
sy and b --> sg. Numerical calculations of the Stokes parameters and v
arious differential distributions for b --> syg are performed for the
two-Higgs doublet model (2HDM). We studied the dependences of all thes
e characteristics to the model parameters. These results were compared
with the Standard Model predictions for different top quark masses. S
trong sensitivity of the Stokes parameters, which defines the linear p
hoton polarization, to the model is demonstrated.