Partial coherence analysis in the phase space

The processes of partial coherence in optics are analyzed by introducing the generalized coherence matrix. This matrix is extended to a 3-dimensional system that corresponds to the nature of optical fields. The structure of the resulting coherence matrix facilitates the identification of an interaction matrix, which carries the information of the mixed states of the optical field. This matrix can be associated with a nonlinear second-order differential equation, and the resulting equation is then matched to a dynamical system. This can be performed due to the elements of the coherence matrix which exhibit fluctuations, that manifest in the geometry of interference fringes allowing an analogy with nonlinear oscillatory dynamic systems and establishes a relationship between the interference fringes and their correspondence with the phase portrait. The model is validated using the Duffing equation as a prototype, and experimental results are shown.