For the 2-dimensional $SU(2)$ matrices, there is a fairly general parametrization formulation:
$s_2=\begin{bmatrix} e^{i\alpha}cos(\theta) & -e^{-i\beta}sin(\theta) \\ e^{i\beta}sin(\theta) & e^{-i\alpha}cos(\theta) \end{bmatrix}$
For the 3-dimension SU(3) and the higher-dimension SU(N) matrices, what are the most general parametrization formulations? I will appreciate any references, either a book or a review paper, on this subject oriented toward the physics/engineer applications.