Spatio-temporal characterization of ultrashort vector pulses

Ultrafast vectorially polarized pulses have found many applications in information and energy transfer owing mainly to the presence of strong longitudinal components and their space-polarization non-separability. Due to their broad spectrum, such pulses often exhibit space-time couplings, which significantly affect the pulse propagation dynamics leading to reduced energy density or utilized to create new effects like a rotating or sliding wavefront at focus. Here, we present a new method for the spatio-temporal characterization of ultrashort cylindrical vector pulses based on a combination of spatially resolved Fourier transform spectroscopy and Mach-Zehnder interferometry. The method provides access to spatially resolved spectral amplitudes and phases of all polarization components of the pulse. We demonstrate the capabilities of the method by completely characterizing a $10$~fs radially polarized pulse from a Ti:sapphire laser at $800$~nm

Measures of space-time non-separability of electromagnetic pulses

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

Flying Doughnuts: Space-Time non-Separable Electromagnetic Pulses.

Flying doughnuts (FD) are solutions of Maxwell’s equations that exist only in the form of short bursts of electromagnetic (EM) energy propagating in free space at the speed of light. They are distinguished from transverse waves by a toroidal configuration of EM fields and strong field components along the propagation direction. They possess a unique space-time coupling (STC) while their broadband spectrum and toroidal structure makes them ideal candidates for the study of toroidal excitations and dynamic anapoles. Their generation is expected to significantly boost the research in the field of toroidal electrodynamics while the developed technology for the control of STCs could open a new field of ultrafast optics. In this thesis I report for the first time the generation of few cycle doughnut pulses in the near-IR part of the spectrum through a spatio-temporal transformation scheme of conventional laser pulses. The transformer is a properly engineered spatially gradient metasurface that has been designed and applied for the realization of the desired space-time coupling. I have developed a new experimental technique for the complete spatio temporal characterization of cylindrical vector pulses that was not previously possible and I confirmed the generation of FDs. Furthermore, the method characterizes the aberrations of axially symmetric pulses that attract great attention for applications. I have derived closed form expressions for the Fourier and Hankel transforms of FDs that led to better understanding of their properties and provide an important tool for their further study. In particular, the pulses have been proven to be isodiffracting, a feature rendering them resistant to changes of their shape other than scaling upon propagation. Finally, I report the first topological study of complex toroidal pulses that provides the opportunity to expand the topological description of EM fields from the well-studied area of monochromatic beams to broadband pulsed fields. A first theoretical analysis of FDs towards this direction revealed the existence of a fine topological structure with the formation of time dependent vortices and areas of instantaneous energy back-propagation, indicating the presence of rich topological effects

TERMITES-MAZE python module

Code supporting Doctoral Thesis &quot;Flying Doughnuts: Space-Time non-Separable Electromagnetic Pulses&quot; Awarded University of Southampton 2021. A python implementation of the TERMITES-MAZE method for the spatio-temporal characterization of ultrashort cylindrical vector electromagnetic pulses. The first part implements the TERMITES algorithm for the characterization of linearly polarized pulses with uniform spectral properties at their center. The second part implements the analysis steps required to characterize cylindrical vector pulses. An example with simulated data is included in the example.py file.</span

Anapoles and flying doughnuts

We report on recent developments in the light-matter interactions of anapoles andsingle-cycle toroidal pulses, termed Flying Doughnuts

Space-time non-separability of complex electromagnetic fields generated by metasurfaces

We introduce a quantum mechanics inspired approach for the characterization of space-time non-separable waves, such as the Flying Doughnut pulse. We apply techniques analogous to quantum state tomography to quantify the type and degree of non-separability and provide quantitative predictions of the pulse propagation dynamic

Quantum-analogous measures for space-time non-separable light

Recent advances in structured light and topological optics have highlighted the non-trivial wave-matter interactions of pulses with complex topological and spatiotemporal structure. A characteristic example of such a pulse is the “Flying Doughnut” (FD), a few-cycle space-time non-separable (STNS) toroidal pulse with links to toroidal and anapole excitations in matter. However, little in known about the role of spacetime non-separability in the propagation dynamics and light-matter interactions of such pulse

Space-time non-separable pulses: Constructing isodiffracting donut pulses from plane waves and single-cycle pulses

Maxwell's equations can be satisfied not only by plane electromagnetic waves, but also by more exotic space-time non-separable electromagnetic pulses which cannot be represented as a product of time and space dependent functions. A family of such pulses with finite energy was identified by R. Ziolkowski in 1985. Later R. W. Hellwarth and P. Nouchi highlighted a subset of Ziolkowski's pulses, now known as Flying Donuts, a formation of polarization singularities of toroidal topology traveling at the speed of light. Spurred by recent advances in ultrafast and topological optics, space-time non-separable electromagnetic excitations are now becoming the focus of growing experimental efforts as they hold promise for topological information transfer, probing and inducing transient excitations in matter such as anapole and toroidal modes. Many practical questions are yet to be answered regarding their generation, detection and light-matter interactions. Here we demonstrate that the Flying Donut is bandwidth limited and can be constructed from an ensemble of monochromatic plane waves with continuous spatial and frequency spectrum and hence can be generated by converting broadband conventional transverse electromagnetic pulses

A topologically robust formation of broadband vortices propagating at the speed of light

We show that Flying Doughnuts, the exact propagating solutions of Maxwell equations in the form of singlecycle toroidal pulses have complex and robust fine topological structure of spectrally broadband vortices and extended areas of energy backflow