Frank Bucholtz | Searcharxiv

arXiv2026

Free-space Optical Diffraction and the Fisher Information

Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity distribution. By interpreting intensity as a probability density, we show that a) free-space diffraction will always act to flatten the intensity distribution as the beam propagates, and consequently b) diffraction will monotonically minimize the Fisher Information with respect to any parameterization of the intensity distribution model that depends on propagation distance.

physics.optics↗

arXiv2025

A General Model for Linearly Polarized Optical Vector Beams

We propose an approach for deriving a broad class of propagation models for inhomogeneously, linearly polarized ``vector'' beams. Our formulation leverages a complex scalar potential along with an appropriately constructed Lagrangian energy density. Importantly, we show that polarization inhomogeneities can be included by simple addition of a spatially dependent polarization angle to the complex potential phase. Thus, phase and polarization are seen to be equivalent from an energy perspective. As part of our development, we also show how the complex scalar potential arises naturally when considering polarization angle as a field symmetry during construction of the Lagrangian. We further show that the definition of linear momentum density in terms of the complex potential holds a distinct advantage over the conventional definition for inhomogeneously polarized beams.

physics.optics↗