Simulation of highly focused vector beams and their 3D Stokes vector generalization

Abstract

This work presents the development of a versatile numerical code for the simulation and polarization analysis of tightly focused vector beams in high numerical aperture optical systems. The computational framework is based on the Richards-Wolf vectorial diffraction formalism, which enables the rigorous calculation of the full three-dimensional electromagnetic field in the focal region, including non-negligible longitudinal components. The code implements a modular pipeline that defines the incident field, performs its projection onto the reference sphere, evaluates the focusing integral and characterizes the local polarization state using a three-dimensional generalization of the Stokes parameters. This approach overcomes the limitations of the conventional transverse Stokes formalism and provides a complete local description of polarization in nonparaxial fields. Numerical simulations and advanced visualization tools are used to analyze complex polarization structures, demonstrating the potential of the developed framework as a flexible platform for the study of nonparaxial optical phenomena.