Measures of space-time non-separability of electromagnetic pulses

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 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 few-cycle pulse with links to toroidal and non radiating (anapole) excitations in matter. Here, we propose a quantum mechanics-inspired methodology for quantitatively characterizing space-time non-separability in structured pulses. In analogy to the mathematics of non-separability in quantum mechanics, we introduce the concept of space-spectrum non-separable states to describe the spacetime non-separability of a classical electromagnetic pulse and apply state tomography method to reconstruct the corresponding density matrix. Using the example of FD pulse, we calculate the fidelity, concurrence, and entanglement of formation as their quantitative measures, and we demonstrate 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 non-separable pulses as information carriers and facilitate their deployment in information transfer and cryptography applications.

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Identifiers

ORCID for Apostolos Zdagkas: orcid.org/0000-0002-1734-9722

ORCID for Nikitas Papasimakis: orcid.org/0000-0002-6347-6466

ORCID for Nikolai Zheludev: orcid.org/0000-0002-1013-6636

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