Parametrization of 3 x 3 unitary matrices based on polarization algebra

A new parametrization of 3 x 3 unitary matrices is presented. This mathematical approach is inspired by polarization algebra and is formulated through the identification of a set of three orthonormal three-dimensional Jones vectors representing the respective pure polarization states. This approach leads to the representation of a 3 x 3 unitary matrix as an orthogonal similarity transformation of a particular type of unitary matrix that depends on six independent parameters, while the remaining three parameters correspond to the orthogonal matrix of the said transformation. The results obtained are applied to determine the structure of the second component of the characteristic decomposition of a 3 x 3 positive semidefinite Hermitian matrix which, in its turn, allows to characterize the regularity of three-dimensional random electromagnetic waves by means of a single angular parameter.