Jones Matrix Characterization of Homogeneous Optical Elements via Evolutionary Algorithms

Abstract

Jones calculus provides a robust and straightforward method to describe polarized light and polarizing optical systems using two-element vectors (Jones vectors) and 2 X 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, the polarization-dependent phase of the total delay of a light beam acquired when passing through a material. Jones matrix characterization is a technique used to characterize polarizing optical systems. By measuring the geometric phase, Jones matrix characterization can identify the sample's eigenpolarizations, which are those polarization states that exits the sample only scaled by a phase factor. Currently, there is only one existing Jones matrix characterization method available. However, said method is inefficient, since the characterization of any given element is time-consuming given that the method is based on a general sampling strategy.

Optimization techniques are used to find a solution to a problem specified by an objective function, where the variables are searched over to find the combination that results in the best objective function value while satisfying the constraints of the problem. Evolutionary Algorithms (EAs) are optimization techniques based on the theory of evolution, which explains the adaptive changes of species in nature through the survival of the fittest, heredity, and mutation. They are all random-based meta-heuristic algorithms that do not require gradient information and typically make use of several points in the search space at a time.

Therefore, using the exploration capabilities of EAs, 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 EAs. We evaluate the analytical performance of an EA with a polynomial mutation (PM) operator and a Genetic Algorithm (GA) with a simulated binary crossover operator and a PM 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.

The present analysis shows that the usage of EAs in the area of optics is a promising research area and as future research, we would like to apply EAs on the more complex case of inhomogeneous optical elements, for which no method of characterization currently exists.