Measures of space-time non-separability of electromagnetic pulses

TL;DR

This paper introduces a quantum-inspired method to characterize space-time non-separability in electromagnetic pulses, using concepts like entanglement and state tomography, exemplified on the 'Flying Doughnut' pulse.

Contribution

It develops a novel quantum-mechanics-inspired framework for analyzing classical electromagnetic pulses' space-time non-separability, including a reconstruction method for the density matrix.

Findings

Successfully applied the method to the Flying Doughnut pulse.

Quantified non-separability using fidelity, concurrence, and entanglement of formation.

Demonstrated evolution of structured pulses through quantitative measures.

Abstract

Electromagnetic pulses are typically treated as space-time (or space-frequency) separable solutions of Maxwell's equations, where spatial and temporal (spectral) dependence can be treated separately. In contrast to this traditional viewpoint, recent advances in structured light and topological optics have highlighted the non-trivial wave-matter interactions of pulses with complex topology and space-time non-separable structure, as well as their potential for energy and information transfer. A characteristic example of such a pulse is the "Flying Doughnut" (FD), a space-time non-separable toroidal few-cycle pulse with links to toroidal and non-radiating (anapole) excitations in matter. Here, we propose a quantum-mechanics-inspired methodology for the characterization of space-time non-separability in structured pulses. In analogy to the non-separability of entangled quantum systems, we introduce the concept of space-spectrum entangled states to describe the space-time non-separability of classical electromagnetic pulses and develop a method to reconstruct the corresponding density matrix by state tomography. We apply our method to the FD pulse and obtain the corresponding fidelity, concurrence, and entanglement of formation. We demonstrate that such properties dug out from quantum mechanics quantitatively characterize the evolution of the general spatiotemporal structured pulse upon propagation.