Vectorial ray tracing scheme for arbitrary complex amplitude profiles through a given optical system

A comprehensive analysis of focal energy density is important in designing and improving the performance of any optical system that uses focused light beams. In this work, we propose a geometrical ray tracing-based scheme that can compute the energy densities or spot diagrams corresponding to different polarizations in the imaging plane due to any arbitrary user-defined beam. In our model, we incorporate lens-specific parameters such as radius of curvature, thickness, focal length, and refractive index, the spatial light modulator plane generating an arbitrary beam profile and 4f relay lens pairs, to trace both paraxial and skew rays up to the imaging plane through different refracting surfaces, providing a more realistic computational approach to obtain the focal spot. In particular, our model incorporates the vectorial nature of the light for each ray to facilitate computation of the vectorial spot diagrams, which are in effect a representation of the energy densities, corresponding to different orthogonal polarizations. We have implemented our model using the open-source programming language Python. The results using both low and high numerical aperture lenses indicate interesting similarities as well as distinctions in comparison with those obtained using vectorial diffraction theory.