Example Abstract

We report on the study of the time-space localized solutions to Maxwell’s equations with toroidal topology that have intriguing properties and interact with interfaces and nanostructures in a peculiar fashion. The ‘Focused Doughnut’ (FD) pulse is an exact, finite-energy electromagnetic perturbation with a uniquespatio-temporal structure that is toroidal in character (Fig. 1) [1]. In contrast to conventional electromagnetic pulses, theFD pulse exists purely in a single-cycle form with 3-dimensional, polynomial energy localisation. The single-cyclenature of the pulse results in an ultra-broadband pulse spectrum. Moreover, the spatial dependence of the pulse isinseparable from its temporal dependence. In addition, the toroidal topology of the pulse gives rise to significantlongitudinal field components at the pulse centre aligned parallel to the axis of propagation, which has been shown tohave potential for particle acceleration [1]. Although the FD pulse has remained a theoretical curiosity since their firstprediction [1,2], successful experimental realisation could lead to its use in a variety of applications, such asmicroscopy, communications, directed energy transfer, spectroscopy and particle trapping and acceleration. A furtherpoint of interest is the topological similarities between the FD pulse and the near-field configuration of the toroidaldipole – a burgeoning field in electrodynamics [3]. As such, here we present the comprehensive study of the FD pulse,utilising finite-element modelling for the first time to examine the properties and propagation dynamics of these pulses(Fig. 2).The complex field topology of the FD pulse, encompassing transverse and longitudinal fields and space-timenon-separability, is expected to result in unique light-matter interactions [1]. We provide a full evaluation of thetransformations the pulse undergoes when interacting with dielectric and metallic interfaces. This has revealed theintriguing behaviour of both the TE and TM pulses under reflection, with respect to the reversal of the azimuthal andradial field components. Furthermore, the interactions of FDs with small dielectric and plasmonic particles areconsidered, where the broadband nature and complex field topology of the pulses is expected to play a significant rolein mode excitation. Possible experimental realisations of these complex electromagnetic perturbations resulting fromthe theoretical/computational treatment presented here will be discussed. References[1] R. W. Hellwarth and P. Nouchi, “Focused one-cycle electromagnetic pulses”, Phys. Rev. E. 54, 889 (1996).[2] R. W. Ziolkowski, “Localised transmission of electromagnetic energy”, Phys. Rev. A, 39, 2005 (1989).[3] T. Kaelberer et al, “Toroidal dipolar response in a metamaterial”, Science , 330, 1510 (2010).Fig. 1. Illustration of the field topology and focusingproperties of the TE FD pulse. The pulse propagatesalong the z direction.Fig. 2. TheEx (a) andHz (b) fields of the TE FD pulsefrom finite element modelling (normalised to peakvalue). The parameter q1 gives the effectivewavelength.Focal region Effective wavelengthHρ,z Eθxzy