  Jones calculus provides a robust and straightforward method to characterize
polarized light and polarizing optical systems using two-element vectors (Jones
vectors) and $2 \times 2$ matrices (Jones matrices). Jones matrices are used to
determine the retardance and diattenuation introduced by an optical element or
a sequence of elements. Moreover, they are the tool of choice to study optical
geometric phases. However, the current sampling method for characterizing the
Jones matrix of an optical element is inefficient, since the search space of
the problem is in the realm of the real numbers and so applying a general
sampling method is time-consuming. In this study, we present an initial
approach for solving the problem of finding the eigenvectors that characterize
the Jones matrix of a homogeneous optical element through Evolutionary
Algorithms (EAs). We evaluate the analytical performance of an EA with a
Polynomial Mutation operator and a Genetic Algorithm (GA) with a Simulated
Binary crossover operator and a Polynomial Mutation operator, and compare the
results with those obtained through a general sampling method. The results show
that both the EA and the GA out-performed a general sampling method of 6,000
measurements, by requiring in average 103 and 188 fitness functions
measurements respectively, while having a perfect rate of convergence.
