Nonlocality and quantum correlations in Ince–Gauss structured light modes

Abstract

Structured light has many applications in areas such as quantum information and quantum optics. The angular momentum of structured light makes it possible to access higher dimensional systems. Ince–Gaussian beams are the solution of the paraxial wave equation in elliptical coordinates, which are characterized by a parameter called ellipticity. In this work, we obtain expressions for the Wigner function and Bell inequality for Ince–Gauss modes. This is done through the corresponding generalization of the structured light modes that the Ince–Gauss modes represent and therefore of the Wigner function. Geometric representations of structured light modes are of great use here. The Wigner function is important for the purpose of determining the nonlocal properties of Ince–Gauss modes. In this way, we demonstrate the nonlocality of the Ince–Gauss modes through the violation of the Bell inequality. We also give a detailed analysis of the behavior of the Bell function and the violation of the Bell inequality of Laguerre–Gauss modes relevant for our description of Ince–Gauss modes, therefore characterizing their nonlocality.