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 nontrivial wave-matter interactions of pulses with complex space-time nonseparable 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 nonseparable few-cycle pulse with links to toroidal and nonradiating (anapole) excitations in matter. Here, we propose a quantum-mechanics-inspired methodology for quantitatively characterizing space-time nonseparability in structured pulses. In analogy to the mathematics of nonseparability in quantum mechanics, we introduce the concept of space-spectrum nonseparable states to describe the space-time nonseparability of a classical electromagnetic pulse and apply the state tomography method to reconstruct the corresponding density matrix. Using the example of the FD pulse, we calculate the fidelity, concurrence, and entanglement of formation as their quantitative measures, and we demonstrate that such properties dug out from quantum mechanics can quantitatively characterize the spatiotemporal evolution of general structured pulses. Our results highlight the potential of space-time nonseparable pulses as information carriers and facilitate their deployment in information transfer and cryptography applications.
- Received 27 July 2020
- Revised 17 December 2020
- Accepted 21 January 2021
DOI:https://doi.org/10.1103/PhysRevResearch.3.013236
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society